Business-Cycles | Macro Paper Warehouse

A model of expenditure shocks

Mon, 01 Jan 0001 00:00:00 +0000

A common observation from account-level bank data is that low-income, low-liquidity households often use additional income to repay debt rather than consume, and that household-level consumption is extremely volatile even though aggregate consumption is smooth. This paper formalizes these patterns using four new facts from the PSID: household consumption is as volatile as income (contradicting PIH); the correlation between household consumption and income growth is only about 0.2 (low); consumption growth is negatively autocorrelated (contradicting both PIH and habit models); and—a finding new to the literature—the cross-sectional correlation between consumption and income growth is far smaller among households experiencing high consumption episodes than in the full sample. The paper proposes an explanation based on stochastic consumption thresholds: unanticipated shocks such as medical expenses or vehicle repairs create time-varying minimum-consumption floors whose violation incurs large utility costs, inducing households to prioritize expenditures on these needs over income-responsive consumption and to rebuild savings after the shock. This mechanism increases the welfare cost of income fluctuations by an order of magnitude relative to standard models.

In depth

Q1. What are the four empirical facts and why do they challenge standard models?

Fact 1: for the average PSID household, consumption is as volatile as income; Fact 2: the correlation between consumption growth and income growth is about 0.2; Fact 3: household consumption growth is negatively autocorrelated; Fact 4 (new): the cross-sectional correlation between consumption and income growth is far smaller among households with high consumption than in the full sample. Fact 1 contradicts the permanent income hypothesis (PIH), under which consumption should be smoother than income. Facts 1 and 2 together cannot both be explained by liquidity constraints (which would tie consumption to current income, producing a high correlation) or by very persistent income shocks (same problem). Fact 3 contradicts habit models (which generate positive autocorrelation) and is inconsistent with PIH (which implies zero autocorrelation). Fact 4 is novel: in standard models the level of consumption barely affects the income-consumption growth relationship, so this fact requires a new explanation.

Q2. What is the expenditure shock mechanism, and how does it rationalize the four facts?

The model introduces stochastic, time-varying consumption thresholds—representing unavoidable expenditures such as medical emergencies, vehicle breakdowns, or appliance repairs—that, if violated, incur large utility costs; this forces households to prioritize meeting these minimum needs over income-proportional consumption. When a threshold shock hits, consumption jumps to meet it regardless of current income (explaining volatile, income-disconnected consumption). After the shock the household rebuilds savings, reducing consumption below its long-run level (generating negative autocorrelation). During high-consumption episodes (threshold shocks), income and consumption growth are decoupled (explaining Fact 4). Meanwhile, without a threshold shock, households are saving to self-insure against future shocks (explaining why low-income households save rather than consume when income rises).

Q3. What does the model imply for the welfare cost of income fluctuations?

The stochastic thresholds increase the welfare cost of income fluctuations by an order of magnitude relative to standard consumption models, because households must maintain precautionary buffers against the risk of hitting a threshold and being unable to meet it. The large welfare cost arises from two sources: the direct cost of violating a threshold (large utility penalty), and the precautionary motive it creates, which forces households to save at the expense of current consumption utility even when no threshold shock is present.

Q4. What empirical evidence does the paper use and what is the scope of the findings?

The PSID (post-1999 comprehensive consumption module) provides panel data on total household consumption and income; the authors use this to document all four facts, including the novel Fact 4. The negative autocorrelation of consumption growth (Fact 3) is documented in the prior literature (Blundell et al. 2008) as indicative of preference shocks or measurement error, but the paper’s model gives it a structural interpretation as evidence of expenditure shocks. The finding that consumption is volatile yet disconnected from income (Facts 1 and 2) is robust to restricting attention to nondurable consumption, ruling out durable goods as the driver. The results hold at the household level; aggregate consumption is smooth because household threshold shocks are largely idiosyncratic and average out.

Key concepts

stochastic consumption threshold : a time-varying, unanticipated minimum consumption level (representing unavoidable expenditures like medical emergencies or vehicle repairs) whose violation incurs large utility costs; the paper’s key modeling innovation.

expenditure shock : an unanticipated increase in the required minimum consumption level, representing events that force households to spend on necessities regardless of current income or savings; the proposed explanation for the four empirical facts about household consumption dynamics.

A Theory of How Workers Keep up with Inflation

Mon, 01 Jan 0001 00:00:00 +0000

AI and task efficiency

Mon, 01 Jan 0001 00:00:00 +0000

AI can improve decisions, raise firm productivity, and accelerate human capital growth through its effect on signal quality in problem-solving tasks, but the consequences are heterogeneous across the skill distribution and depend on how AI changes the hierarchy within firms. This paper proposes a framework in which AI improves the accuracy of the signals that guide human decisions—individually and in groups—and derives implications for firm organization, wages, and productivity. It also examines preliminary evidence: a cross-sectional regression of changes in TFP growth (2024 versus 2022) on sectoral AI exposure (Eisfeldt et al. 2024) for Compustat firms yields a positive relationship, statistically significant at the 10% level at the 3-digit NAICS sector level and at the 5% level at the firm level, with a slope coefficient of 0.206 for the firm-level regression. The paper compares AI to earlier general purpose technologies (GPTs)—electricity and information technology—finding that if there is a productivity delay for AI it appears shorter than the five- and eight-year delays documented for electrification and IT.

In depth

Q1. What is the theoretical framework linking AI to decisions and productivity?

The paper models several mechanisms through which AI may improve outcomes by raising the accuracy of signals that guide problem-solving: when signal accuracy rises, individuals and groups make better decisions, potentially enabling lower-level workers to handle more complex tasks and reducing the need for expensive higher-level solutions. For example, if AI allows managers to understand problems faster, they can handle more problems at a given time, potentially reducing demand for specialized expert judgment at lower hierarchy levels. Alternatively, if AI allows lower-level workers (clerks, nurses) to handle tasks previously requiring specialists (partners, doctors), the demand for specialists may fall and the wage premium for top-tier workers may narrow. The direction of the effect depends on whether AI is a better complement to high-skill or to low-skill tasks.

Q2. What does the empirical evidence show about AI’s current productivity effects?

A cross-sectional regression using 5,009 Compustat firm-level observations for 66 three-digit NAICS sectors finds a positive and statistically significant relationship between sectoral AI exposure in 2022 (from Eisfeldt et al. 2024) and the change in annual TFP growth between 2024 and 2022, with a sector-level slope coefficient that is statistically significant at the 10% level. The firm-level regression (including 3-digit NAICS fixed effects) yields a slope of 0.206 on AI exposure, significant at the 5% level (t-statistic 2.08), with R² = 0.20 and 1,996 observations. The relationship is absent when examining TFP growth levels in any individual year between 2019 and 2022, consistent with AI’s macroeconomic effects only becoming measurable after the release of GPT-4 in March 2023.

Q3. How does AI compare with prior general purpose technologies?

The paper relates AI to the earlier GPT literature, noting that productivity growth tended to be lower at the start of both the electrification and IT eras—with delays of approximately five and eight years respectively before productivity gains became measurable—and that if there is a similar delay for AI it appears shorter based on the preliminary 2024 data. This comparison suggests that AI may be a GPT with unusually rapid diffusion or a shorter learning curve, though the authors caution that the evidence is still preliminary and depends on the dating of AI’s “arrival.”

Q4. Why might AI effects differ across the hierarchy within firms?

AI’s effect on a firm hierarchy depends on whether it complements or substitutes for skills at each level: if AI primarily helps managers (by speeding problem diagnosis), it may reduce demand for specialized lower-level workers; if it primarily helps clerks (by enabling them to handle more complex documents), it may reduce demand for partners while raising demand for lower-level staff. The paper argues that the distributional consequences—whether AI raises or lowers wage dispersion—depend on this complementarity/substitutability pattern, which likely varies by industry, as illustrated by the contrasting cases of automotive assembly (AI may help managers but not line workers) and law firms (AI may help clerks handle more complex work).

Key concepts

AI as signal accuracy improvement : the paper’s framework for thinking about AI’s effect on decision quality: AI raises the precision of the signals that guide problem-solving, which leads to better individual and group decisions regardless of the specific mechanism.

general purpose technology (GPT) delay : the empirical phenomenon documented by Jovanovic and Rousseau (2005) in which productivity growth is lower at the start of a major GPT era before eventually accelerating; the paper examines whether AI exhibits the same pattern, finding that any delay appears shorter than for electrification (five years) or IT (eight years).

Business, Liquidity, and Information Cycles

Mon, 01 Jan 0001 00:00:00 +0000

The paper studies how the two roles of stock markets — revealing information about firms’ fundamentals (which guides capital allocation) and providing liquidity — interact, arguing that when stocks are used more intensively for liquidity, their prices reveal less information about fundamentals. The authors build a Grossman-Stiglitz-style trading model with two types of rational traders (‘day’ traders who value liquidity and ’night’ traders who value fundamentals) that generates endogenous noise in prices, derive an analytical measure of price informativeness (PI), and structurally estimate PI from firm-level panel data for 16 countries over 1984-2022, finding that PI declines in periods of insufficient funding liquidity (such as the Great Recession and the COVID-19 pandemic) and that these fluctuations are explained mostly by changes in trading activity rather than information quality. Integrating the trading module into a real business cycle model with heterogeneous firms calibrated to the United States, they simulate recessions: a stand-alone recession is ‘cleansing’ — prices become more informative and allocation improves, mitigating output losses by 4.4% — whereas a recession coinciding with banking distress is ‘sullying’ — agents rely more on stocks for liquidity, prices become less informative, and worsened misallocation magnifies output losses by 22%. A counterfactual with exogenous (rather than endogenous) information implies output would fall about 43% more than in the benchmark, which the authors read as evidence that endogenous information acquisition lets stock markets ’lean against the wind’ in recessions. All magnitudes are model-based and specific to the U.S. calibration.

In depth

Q1. What interaction between stock-market roles does the paper study?

The paper studies how the liquidity role of stock markets affects their information role: if stocks are used more intensively for liquidity, prices reveal less information about firms’ fundamentals. While the information and liquidity roles of stock markets are each well studied, their interaction is less understood; the authors ask whether using stocks for liquidity enhances or weakens their information role, how distress in other liquidity sources (such as banks) affects price informativeness, and how this contributes to the depth of recessions.

Q2. How does the trading model generate the information-liquidity tradeoff?

The authors extend Grossman and Stiglitz (1980) by replacing noise traders with two types of rational traders — ‘day’ traders interested in liquidity and ’night’ traders interested in fundamentals — so that each type’s trades act as endogenous noise for the other. In equilibrium a linear pricing function exists in which price informativeness depends on the relative weights of fundamental versus liquidity information in prices, and those weights are determined by how many day and night traders operate, their information choices, and how aggressively they trade. When funding markets malfunction, the economy relies more on stocks for liquidity, there are more day traders, and price informativeness declines.

Q3. What is Price Informativeness (PI), and how is it estimated?

Price Informativeness (PI) is defined analytically as a function of the dispersion of firm productivity, the dispersion of stock-price fluctuations, and their respective price loadings; in a high-PI market, a firm’s high relative stock price is a strong signal of positive information about its fundamentals. The authors estimate PI structurally using firm-level panel data from 16 countries spanning 1984 to 2022. The linear relationship among stock prices, earnings, and stock liquidity holds independently of general-equilibrium considerations, which is what makes the structural estimation tractable.

Q4. What are the empirical cyclical properties of PI?

PI exhibits cyclicality and, more importantly, declines in periods of insufficient funding liquidity, such as the Great Recession and the COVID-19 pandemic. Decomposing PI into its four components, the authors show its fluctuations are mostly explained by changes in trading activity rather than by changes in information quality or the amount of information acquired.

Q5. How is the trading module embedded in a general-equilibrium model and disciplined?

The trading module is integrated into a real business cycle model with heterogeneous firms in which stock prices guide capital allocation, calibrated to the United States with two possibly correlated aggregate shocks — one to aggregate productivity and one to funding liquidity — to capture recessions with and without banking distress. The calibrated model replicates the cyclical properties of the empirical PI measure without targeting them. The authors also discipline how much new information prices convey using price-investment correlations across firms and over time, concluding that new stock-price information is roughly as important as what decision makers already know.

Q6. What are the quantitative real effects in recessions?

In a stand-alone recession, increased uncertainty induces all traders to acquire more information, raising price informativeness and improving allocation, which mitigates output losses by 4.4% (‘cleansing’); when a recession coincides with funding-market distress, heightened liquidity-driven trading makes prices less informative and worsens allocation, magnifying output losses by 22% (‘sullying’). The authors interpret the 22% figure as a sizable real effect of banking problems operating through a novel channel: the weakening of the information and allocative role of stock markets.

Q7. What do the information-structure counterfactuals show?

If information were exogenous rather than endogenously acquired, liquidity distress would reduce PI by more and output would decline about 43% more than in the benchmark — implying endogenous information acquisition lets stock markets ’lean against the wind’ during recessions. The authors further find that halving the cost of information about fundamentals would make output declines about 5% smaller, whereas halving the cost of information about a stock’s liquidity would make declines about 2% larger, leading them to conclude that the welfare effect of transparency is nuanced — easier access to one type of information can make it harder to infer another.

Q8. What are the main limitations and scope conditions?

The authors flag two limitations: the framework assumes no feedback from the real economy back to financial markets (prices affect investment, but investment does not affect prices), and the counterfactuals focus on how the information environment affects price informativeness, abstracting from other channels through which information affects production. Adding two-way feedback would sacrifice the tractability of linear pricing but could introduce additional magnification forces. All quantitative magnitudes are specific to the U.S. calibration.

Key concepts

price informativeness (PI) : the extent to which stock prices reveal to an outside observer the information that informed traders hold about firms’ fundamentals; defined in the paper as an analytical function of productivity dispersion, price-fluctuation dispersion, and their price loadings, and estimated structurally.

day traders vs. night traders : the paper’s two types of rational traders — day traders trade to satisfy liquidity needs, night traders trade on information about fundamentals — whose trades act as endogenous noise for one another, replacing the exogenous noise traders of Grossman-Stiglitz.

funding liquidity vs. market liquidity : funding liquidity is liquidity provided by intermediaries through credit; market liquidity is the ability to trade stocks to meet liquidity needs; when funding liquidity is scarce, agents substitute toward market liquidity, raising liquidity-driven trading.

cleansing vs. sullying recessions : in the paper’s usage, a cleansing recession improves allocation (here via more informative prices), while a sullying recession worsens it; a recession is cleansing without banking distress and sullying when it coincides with funding-market distress.

Capital Income Taxation and Self-Fulfilling Aggregate Instability

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper overturns the longstanding consensus established by Schmitt-Grohé and Uribe (1997) that relying on capital income tax adjustments to balance the government budget immunizes the economy against self-fulfilling aggregate instability. The key departure from the prior literature is endogenous capital utilization: when the capital income tax rate adjusts to close budget imbalances and capital utilization is an optimal decision by households, a “fiscal increasing returns” mechanism emerges in which higher economic activity lowers the tax rate, raises the after-tax return to capital, and induces further expansion — rendering the economy prone to sunspots-driven fluctuations. Calibrated to the United States, United Kingdom, and Japan using effective tax rates and public debt-to-GDP ratios, the paper finds that all three economies lie within the indeterminacy region under their current capital income tax rates and capital depreciation allowances of approximately 0.2; stabilization would require raising the depreciation allowance rate from 0.2 to 0.76 or reducing income tax rates by 39–52 percent. Capital depreciation allowances serve as a stabilization device: full allowances (allowance rate = 1) make indeterminacy entirely impossible regardless of the tax rate, because they extinguish the fiscal increasing returns mechanism, and the paper also shows analytically that public debt can be destabilizing rather than stabilizing when capital taxes are used for fiscal adjustment.

In depth

Q1. What is the fiscal increasing returns mechanism that overturns the Schmitt-Grohé-Uribe result?

When the government adjusts the capital income tax rate to balance the budget, higher labor input raises output and the capital tax base, allowing a lower tax rate; under endogenous capital utilization, this triggers an additional channel in which a lower after-tax depreciation cost induces firms to utilize capital more intensively, further raising the effective capital stock and output — generating fiscal increasing returns to scale and a factor share redistribution from capital to labor that together make indeterminacy possible. In log-linearized terms, the effective output-labor elasticity in the equilibrium aggregate production function exceeds unity for tax rates in the interval (τ̄, τ̂) where τ̄ = ρ/(ρ+δ) and τ̂ is the Laffer-curve peak, and this greater-than-unity elasticity is the formal condition for indeterminacy (Corollary 1). With a constant utilization rate as assumed in prior work, both the factor share redistribution and fiscal increasing returns effects vanish, the effective output-labor elasticity falls below unity, and indeterminacy becomes impossible — confirming that endogenous capital utilization is the essential ingredient.

Q2. What are the formal conditions for indeterminacy under the baseline capital tax rule?

Proposition 1 establishes that the fiscal policy with capital income taxation induces indeterminacy of equilibrium if and only if the long-run capital income tax rate τk lies strictly in the open interval (τ̄, τ̂), where τ̄ = ρ/(ρ+δ) and τ̂ is the unique Laffer-curve peak. Under the standard calibration (ρ = 0.04, δ = 0.1, α = 0.3), this interval is (0.286, 0.717) — a wide range covering the effective capital income tax rates of the U.S., UK, and Japan. The determinant of the Jacobian of the linearized dynamic system is positive and the trace is negative over this interval, implying that both eigenvalues are negative, which is the condition for indeterminacy with one predetermined variable (capital) and one jump variable (marginal utility of income).

Q3. How do capital depreciation allowances serve as a stabilization device?

When the taxable capital income base is reduced by a fraction γ ∈ [0, 1] of depreciation expenses, the effective degree of fiscal increasing returns to scale decreases strictly with γ, and the lower bound of the indeterminacy interval τ̄D strictly rises with γ; with full depreciation allowances (γ = 1), the quadratic equation characterizing the lower bound has a repeated unit root, the indeterminacy interval becomes empty, and multiplicity of equilibria is entirely impossible regardless of the capital income tax rate. Corollary 2 formalizes this result analytically. The intuition is that depreciation allowances reduce the procyclicality of the effective tax burden on capital, so the after-tax return to capital responds less strongly to activity, weakening the self-fulfilling loop. Partial allowances — even well below γ = 1 — can sufficiently shrink the indeterminacy region to require implausibly high tax rates for instability.

Q4. What is the role of public debt and what new result does the model deliver?

Contrary to the established view that public debt can serve as an automatic stabilizer that exempts balanced-budget fiscal policy from beliefs-driven instability (Schmitt-Grohé and Uribe 1997, Huang et al. 2018), this paper shows that public debt can be destabilizing when capital income taxes adjust to balance the budget: a higher public debt-to-GDP ratio expands the indeterminacy region, and this destabilizing effect is amplified when capital depreciation allowances are low. Figure 5 in the paper illustrates numerically that raising the public debt-to-GDP ratio from an average of 0.975 (US/UK average) to 1.429 (Japan) dramatically widens the indeterminacy region, particularly at low depreciation allowance rates. This novel result — that public debt destabilizes rather than stabilizes under capital income tax adjustment — constitutes a third main contribution of the paper alongside the indeterminacy result and the stabilization role of depreciation allowances.

Q5. What are the quantitative results for the US, UK, and Japan?

Under the calibrated depreciation allowance rate of approximately 0.2 (the GDP-weighted European average from D’Erasmo et al. 2017, also consistent with the US), all three large economies lie within the indeterminacy region at their current effective income tax rates; stabilization requires either raising the depreciation allowance rate to 0.76 for all three, or reducing income tax rates by 47% for the US, 52% for the UK, and 39% for Japan from their calibrated levels while holding depreciation allowances at 0.2. Less dramatic combination policies also work: for the US, a 10% income tax cut combined with raising the depreciation allowance to 0.67 would suffice, as would a 5% tax cut combined with raising the allowance to 0.70. These calculations are calibrated to effective factor income tax rates from Mendoza et al. (1994) updated to 1996 and public debt-to-GDP ratios from OECD Economic Outlook (2014).

Q6. How does the paper relate to and contribute to the broader indeterminacy literature?

The paper’s mechanism — fiscal increasing returns arising from the interaction of optimal capital utilization and capital income taxation — is novel relative to both strands of the indeterminacy literature: unlike Benhabib-Farmer-style models that require the aggregate production function to have increasing returns as a primitive assumption, and unlike the Schmitt-Grohé-Uribe labor-tax indeterminacy that also does not require increasing returns but found capital taxation immune, this paper shows that increasing returns can emerge endogenously from a constant-returns-to-scale production technology via fiscal policy, requiring no externalities or other non-standard features. The mechanism provides a policy-based micro-foundation for aggregate increasing returns that resolves the empirical criticism of the prior indeterminacy literature; it also distinguishes the result from Huang et al. (2018), who showed that endogenous capital utilization under labor income tax adjustment raises indeterminacy likelihood but leaves the production function at constant returns to scale.

Key Concepts

fiscal increasing returns : the mechanism in this paper whereby higher economic activity lowers the capital income tax rate (via a higher tax base), raises the after-tax return to capital, and induces greater capital utilization and further output expansion; operationally defined by the effective output-labor elasticity exceeding unity in the equilibrium aggregate production function.

equilibrium indeterminacy : the existence of multiple rational-expectations equilibria converging to the same steady state, arising from the fiscal increasing returns mechanism and permitting self-fulfilling sunspots fluctuations unrelated to economic fundamentals; characterized by both eigenvalues of the Jacobian being negative (both predetermined structure of the dynamic system).

capital depreciation allowance : the fraction γ ∈ [0, 1] of capital depreciation costs deductible from the taxable capital income base; the stabilization device the paper identifies, which works by attenuating the procyclical component of the effective capital tax burden and thereby reducing the fiscal increasing returns to scale.

factor share redistribution : in this paper, the shift of the effective factor income share from capital to labor that results from endogenous capital utilization interacting with the capital tax rule; contributes to indeterminacy by raising the effective output-labor elasticity above the share of capital in the production function.

Downward Rigidity in the Wage for New Hires

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Summary

Hazell and Taska use wages posted on online job vacancies — matched to job titles and establishment identifiers from Burning Glass Technologies — to measure the wage for new hires at the job level (same job title and establishment) over 2010Q1–2020Q2. They find that this measure of the wage for new hires is rigid downward and flexible upward. At the job level, the nominal posted wage changes infrequently — on average once every 5–6 quarters — and conditional on changing, is four times more likely to rise than to fall. In the cyclical dimension, job-level posted wages rise strongly when state unemployment falls but do not fall when state unemployment rises; real wages exhibit the same asymmetric pattern. These results do not appear in the average wage for new hires (which aggregates across all job types), because time-varying job composition inflates the variance of average wages and raises standard errors roughly twentyfold relative to job-level regressions — explaining why prior work using worker-level survey data found no evidence of downward rigidity. A Heckman (1979) selection correction for firms’ selection into vacancy posting suggests that selection bias in the job-level regression is moderate. The findings provide direct empirical support for models in which downward wage rigidity for new hires — specifically at the job level — amplifies unemployment fluctuations and generates asymmetric unemployment dynamics.

In depth

Q1. Q: What is the central empirical claim of the paper?

A: At the job level — defined as the same job title within the same establishment — the wage posted for new hires is rigid downward and flexible upward. It changes infrequently and, conditional on changing, rises far more often than it falls; and it responds to falls in unemployment but not to rises in unemployment.

Q2. Q: What data does the paper use, and what defines a “job”?

A: The paper uses the Burning Glass Technologies dataset of wages posted on online vacancies, covering January 2010 to June 2020. A “job” is a job title within an establishment whose wages are paid at a given frequency (e.g., hourly or annual). The data come from the near-universe of online job postings — roughly 40,000 sources — and the main regression sample consists of jobs that post wages, have job title and establishment information, and post vacancies in multiple quarters, yielding approximately 3.05 million vacancies, representing about 0.8% of total US vacancies.

Q3. Q: How do the authors validate that posted wages measure the wage for new hires?

A: They construct a measure of the wage for new hires from the Current Population Survey (CPS) — workers switching jobs or entering from unemployment — at the state, industry, and occupation level. Regressing log CPS wages on log Burning Glass wages (using an IV split-sample procedure to correct for attenuation bias) yields a coefficient close to 1 across specifications and levels of aggregation, indicating that average posted wages move roughly one-for-one with average wages for new hires in representative survey data.

Q4. Q: How is the frequency of wage change estimated?

A: Because wages are not observed in quarters without a vacancy posting, the authors adapt a constant-hazard model from the price-setting literature (following Nakamura–Steinsson and Klenow–Kryvtsov). The latent wage evolves stochastically between postings; the observed wage is treated as a draw from this process. The quarterly probability of wage change is estimated at 0.17–0.19 across specifications, implying implied durations of unchanged wages of 4–5 quarters.

Q5. Q: What is the asymmetry in the direction of wage changes?

A: In the unweighted baseline, the quarterly probability of a wage decrease is 0.04, whereas the probability of a wage increase is 0.12 — roughly a three-to-one ratio in probabilities, summarized in the paper’s abstract as wages being “four times more likely to rise than to fall.” The distribution of non-zero wage changes also shows a pronounced pile-up of small positive changes relative to small negative changes, consistent with a downward constraint on wage setting.

Q6. Q: What is the first piece of cyclical evidence for downward rigidity?

A: A binned scatterplot (Figure 1) of job-level wage growth against state-level quarterly changes in unemployment shows a strong, roughly linear relationship when unemployment is falling — wages rise with falls in unemployment, both for small and large declines. When unemployment rises, however, wages do not fall — neither for small nor for large increases in unemployment. This asymmetry is robust to regression-based analysis and to identified labor demand shocks.

Q7. Q: Are real wages also rigid downward?

A: Yes. The paper reports that real wages (nominal posted wages deflated) are also rigid downward and flexible upward, mirroring the pattern for nominal wages.

Q8. Q: What is the job-composition problem, and why does it matter?

A: The average wage for new hires — the object measured in most prior work — aggregates across all job types that are actively hiring. If the composition of jobs hiring shifts over the business cycle (e.g., the share of lower-wage jobs rises in recessions), then average wages can fall even if no individual job cuts its wage, and can stay flat or rise even if every job cuts its wage. Job composition therefore confounds cyclicality estimates based on average wages. By tracking the same job title at the same establishment across successive vacancies, the authors purge wage changes driven by shifting composition.

Q9. Q: Why did prior work find no evidence of downward rigidity for new hires?

A: Prior work used worker-level survey data (e.g., Bils 1985; Pissarides 2009 survey) that controls for worker characteristics but averages across jobs — the average wage for new hires. The volatility of job composition inflates the variance of this average measure. In the Burning Glass data, standard errors from regressions using average wages are roughly twenty times larger than those from job-level regressions, making it impossible to detect downward rigidity even if it exists. Point estimates in prior work suggested procyclicality but were too imprecise to exclude downward rigidity.

Q10. Q: How does this paper relate to Gertler, Huckfeldt, and Trigari (2020) and Grigsby, Hurst, and Yildirmaz (2021)?

A: Both papers attempt to control for job composition at the worker level. Gertler et al. focus on wages of workers hired from unemployment (less affected by composition than all new hires) and find weakly procyclical wages. Grigsby et al. use rich payroll data and worker-level matching to control for composition and also find weakly procyclical wages. The present paper complements these by using job-level data that directly purges composition without relying on worker characteristics, and adds evidence on the asymmetry of rigidity (not just average procyclicality).

Q11. Q: What is the role of the Heckman selection correction?

A: If firms select into vacancy posting depending on business-cycle conditions, the sample of observed posted wages may be non-random, biasing job-level wage-cyclicality estimates. The authors implement a standard Heckman (1979) two-step selection correction. The correction suggests that selection bias in the job-level regression is moderate — it does not overturn the finding of downward rigidity.

Q12. Q: What are the four main caveats the authors acknowledge?

A: (1) The main sample is small — 0.8% of US vacancies — though the authors show it is broadly representative on observables and that wages track representative survey data. (2) The paper measures rigidity only for jobs that post wages; jobs that do not post wages might be more flexible, though the share of vacancies posting wages does not decline during contractions. (3) Posted wages may differ from realized (bargained) wages; however, wages are rigid even in occupations where bargaining is uncommon. (4) The Pandemic Recession is the main contractionary episode in the sample, and it involved labor supply shocks as well as demand shocks; the authors address this through identified labor demand shock regressions and by ending the sample in June 2020.

Q13. Q: What are the implications for models of unemployment fluctuations?

A: In the Diamond–Mortensen–Pissarides search model, Pissarides (2009) emphasizes that the wage for newly hired workers — not continuing workers — is the relevant margin for unemployment fluctuations. Shimer (2005) showed the standard calibration produces too-small unemployment fluctuations; wage rigidity for new hires can resolve this. The paper’s finding of downward-but-not-upward rigidity additionally supports models (e.g., Dupraz, Nakamura, and Steinsson, 2020) in which this asymmetry generates asymmetric unemployment dynamics — unemployment rises sharply in contractions but falls more slowly in expansions.

Q14. Q: How do wages for new hires compare with wages for continuing workers in terms of rigidity?

A: The paper finds approximate parity. The implied duration of unchanged wages from the job-level posted wage data (4–5 quarters) is similar to estimates for continuing workers in the prior literature. This is perhaps surprising because wages could in principle be more flexible for new hires than continuing workers — firms might cut wages for new hires even while insuring continuing workers (Beaudry and DiNardo, 1991). The results instead suggest that internal equity concerns (Bewley, 2002) or other forces produce similar rigidity for both groups.

Key Concepts

Job level wage: The wage across successive vacancies posted by the same job title at the same establishment. This is the unit of observation in the paper’s main analysis and the object for which downward rigidity is documented. Distinct from the average wage for new hires (which aggregates across all job types).

Downward rigidity (as used in this paper): An empirical pattern in which wages at the job level do not fall during contractions — they do not respond to rising unemployment — while rising during expansions in response to falling unemployment. The claim is descriptive: the data show wages do not fall; the paper does not structurally identify the mechanism enforcing this floor.

Job composition problem: The bias introduced when measuring cyclicality of the average wage for new hires using data that aggregates across different types of jobs. If the mix of job types hiring shifts with the business cycle, average wages can change even when no individual job changes its wage, and can mask individual-job wage changes. Job-level data resolve this by holding the job fixed.

Burning Glass Technologies dataset: A database of wages posted on online job vacancies, drawn from approximately 40,000 online sources (job boards and company websites), covering the near-universe of US online vacancies. The paper’s main regression sample uses the subset with posted wages, job title, establishment identifiers, and multiple quarters of postings, spanning January 2010 to June 2020.

Constant hazard model (wage change frequency): An estimation procedure adapted from the price-setting literature to recover the quarterly probability of wage change from a dataset in which wages are only observed when a vacancy is posted. The latent wage evolves with a constant hazard of change between observations; observed wage changes identify the hazard rates for increases and decreases separately.

Average wage for new hires: The mean wage across all workers newly entering employment (or across all new-hire jobs), used in prior work (Bils 1985 and related). Does not control for job composition. Shown in this paper to exhibit no detectable downward rigidity, with standard errors roughly twenty times larger than in job-level specifications — because job composition variance inflates the residual variance.

Heckman selection correction: A two-step procedure (Heckman 1979) to correct for the possibility that firms that post vacancies — and post wages — are a selected sample that differs systematically across the business cycle. The paper applies this to assess whether selection into vacancy posting biases the job-level wage-cyclicality estimates; the correction suggests bias is moderate.

Endogenous Production Networks Under Supply Chain Uncertainty

Mon, 01 Jan 0001 00:00:00 +0000

This paper studies how firms’ optimal technique choices under productivity uncertainty endogenously shape the structure of production networks and aggregate macroeconomic outcomes. Each sector chooses input shares (production techniques) before observing sector-specific TFP realizations. Techniques are selected to maximize a risk-adjusted expected log GDP measure — expected log GDP minus a risk-aversion-scaled variance term — with endogenous productivity shifters that favor balanced use of inputs. When uncertainty about sector TFP rises, firms shift toward suppliers with lower expected productivity but lower variance — a “flight to safety” in input sourcing. The key aggregation result is that the contribution of each sector to aggregate welfare depends on its endogenous Domar weight (expenditure share times adjustment factor), which itself responds to changes in beliefs. The paper establishes propositions characterizing how Domar weights respond to changes in mean (μ) and variance (Σ) of TFP beliefs: higher mean raises a sector’s Domar weight; higher variance lowers it when inputs are gross substitutes, but can lower it even with complementary inputs through belief adjustment. A basic calibration to 37 US BEA sectors (1948–2020) finds that the flexible-network economy has expected log GDP 2.1% higher than a fixed-network alternative. During the Great Recession, elevated uncertainty caused firms to shift toward safer, lower-productivity suppliers, reducing expected log GDP by 0.25% but reducing GDP variance by 2.4% and improving actual realized GDP outcomes by 2.7% relative to a “no uncertainty” benchmark.

In depth

Q1. What is the model’s core setup and how does technique choice generate an endogenous network?

Each of n sectors chooses input shares αi = (αi0, αi1, …, αin) — where αi0 is the labor share — before observing sectoral TFP realizations εt, subject to a convex cost function Ai(αi) that penalizes deviation from fixed-proportion baseline techniques; the equilibrium network α is then the solution to a social planner’s problem that maximizes expected welfare W = E[y] − (ρ/2)V[y], where y is log GDP and ρ is the coefficient of relative risk aversion.* Because cost functions Ai are jointly determined by the input shares chosen and by Hessian matrices Hi that govern substitutability/complementarity of inputs, sectors can substitute or complement in the production of any given good, and the equilibrium network balances expected log GDP gains from choosing more productive suppliers against the variance reduction from choosing safer suppliers.

Q2. What role do Domar weights play, and how do they generalize to the endogenous-network case?

In the standard fixed-network case (Hulten’s theorem), each sector i’s contribution to aggregate log GDP equals its Domar weight ωi = (expenditure on sector i’s output)/(total GDP) — a sufficient statistic for first-order productivity effects. The paper extends this: with an endogenous network, the social planner’s optimality conditions imply that equilibrium Domar weights equal the shadow value of relaxing each sector’s resource constraint, and these shadow values respond to changes in beliefs (μ, Σ) through the induced changes in α.* Lemmas 3–5 characterize these responses: a sector’s Domar weight increases in its expected log TFP (μi), and changes in variance Σij propagate through the network via the adjustment terms in the first-order conditions, so that a single sector’s volatility change affects the Domar weights of all connected sectors.

Q3. What are the key propositions about how beliefs affect aggregate welfare and GDP?

Proposition 6 (monotone welfare response to mean beliefs): welfare W is increasing in each sector’s mean log TFP μi, and the marginal effect equals the sector’s Domar weight; this holds even though expected log GDP E[y] may non-monotonically respond to μi when inputs are gross substitutes, because the variance-reduction benefit of adjusting away from the now-more-productive but higher-variance sector can temporarily dominate. Proposition 7 (variance increases hurt expected log GDP): for substitutable inputs, a rise in Σii decreases E[y] because firms shift away from the more volatile sector toward less productive alternatives; for complementary inputs, the same shift also reduces E[y] because complementary inputs move together. Corollary 4 shows that welfare W always falls when uncertainty rises, combining these effects.

Q4. How does the flight-to-safety mechanism work in a multi-sector economy?

When uncertainty about sector i’s productivity rises, the optimal technique response is to reduce αji for all downstream sectors j that use sector i as an input substitute, and increase labor shares or shares in less volatile inputs; since sectors with lower μ but lower Σ become relatively more attractive on a risk-adjusted basis, the network reconfigures toward “safer” but typically less productive suppliers. The cascading link-destruction example (Section 7) illustrates this: when an industry’s production becomes uncertain, the endogenous deletion of risky links propagates across the network as complementary and substitute linkages amplify or dampen the flight to safety, with the direction depending on whether inputs are gross complements or substitutes in the Hessian Hi.

Q5. What does the calibration to US data find about the quantitative importance of the endogenous network?

The calibrated model with 37 BEA sectors (1948–2020) achieves a cross-sectional correlation between model and data Domar weights of 0.96 (though the model average Domar weight of 0.03 is below the data’s 0.05) and matches the data correlations Corr(ωjt, μjt) = 0.1 and Corr(ωjt, Σjjt) = −0.4 closely (model delivers 0.1 and −0.3 respectively). Comparing the flexible-network baseline to a fixed-network alternative, expected log GDP is 2.1% lower in the fixed-network economy, and welfare differs by a similar 2.1%. This suggests the endogenous reallocation of input shares over the sample period — as some sectors became persistently more productive — delivered substantial gains relative to a static network.

Q6. What happens during high-uncertainty episodes such as the Great Recession?

During the Great Recession (2007–2009), the estimated uncertainty measure Σt spiked sharply; firms responded by shifting techniques toward safer suppliers, resulting in expected log GDP that is about 0.25% lower in the baseline than in a “no uncertainty” (Σ = 0) economy and GDP variance that is about 2.4% lower. The insurance paid off in terms of realized outcomes: realized log GDP in the baseline economy was approximately 2.7% higher than in the “as-if Σ = 0” economy in 2009, because firms had taken out insurance against exactly the kind of bad TFP draws that materialized during the crisis. The perfect-foresight economy (where εt is known before technique choice) outperforms the baseline by up to 3% in realized GDP during the Great Recession — the maximum value of uncertainty resolution.

Q7. What is the key distinction between the effects of mean and variance changes for welfare vs. expected GDP?

Changes in mean beliefs μi and welfare W are co-monotone (Proposition 6), but changes in μi and expected log GDP E[y] can be non-monotone when inputs are substitutes: a small increase in μi for a less productive sector can actually lower E[y] in the short run because firms shift toward that sector at the expense of more productive alternatives, even though this shift reduces variance and raises welfare. The divergence between E[y] and W is the key mechanism: when ρ > 0 (risk-averse households), reducing variance has positive welfare value even when it lowers the level of expected GDP, so the production network adjusts in directions that appear sub-optimal for average productivity but are optimal for welfare. The calibrated relative risk aversion parameter ρ̂ = 4.3 indicates meaningful risk aversion that makes these variance-mean trade-offs quantitatively relevant.

Q8. What is the role of input complementarity versus substitutability in determining network responses?

When inputs i and j are gross substitutes (Hessian element [Hi]ij < 0), an increase in sector j’s uncertainty Σjj induces sectors that use both i and j to shift away from j and toward i, reducing j’s Domar weight and increasing i’s — the network becomes more concentrated in safer inputs. When inputs are gross complements ([Hi]ij > 0), an increase in Σjj also reduces the demand for the complementary input i, because both inputs must be used together and the safe input i becomes jointly less attractive when paired with volatile j; this can cause both E[y] and V[y] to fall simultaneously, resulting in an ambiguous welfare effect that depends on the magnitude of ρ relative to the E[y]-V[y] trade-off (Corollary 4 ensures welfare falls, but the split across E[y] and V[y] depends on complementarity structure).

Key concepts

technique choice : a sector’s endogenous selection of input shares αij prior to observing TFP realizations; the key margin of adjustment in the model through which uncertainty shapes the production network; characterized by convex cost functions Ai that favor balanced input use around baseline shares α°.

endogenous Domar weight : the share of total expenditure on a sector’s output in aggregate nominal GDP, computed in the model’s equilibrium; equals the shadow value of the sector’s resource constraint and responds to changes in beliefs (μ, Σ); in the fixed-network case reduces to the standard Hulten-theorem Domar weight.

flight to safety : the equilibrium response in which firms shift their input shares away from high-mean, high-variance suppliers toward lower-mean, lower-variance alternatives when aggregate uncertainty rises; generates the prediction that network restructuring during recessions reduces GDP volatility while raising expected production costs.

risk-adjusted expected welfare (W) : the social planner’s objective, defined as E[y] − (ρ/2)V[y] where y is log GDP and ρ is the coefficient of relative risk aversion; this non-separable objective function generates the trade-off between expected productivity and risk reduction that drives endogenous network formation.

cascading link destruction : the propagation of reduced sectoral linkages through the network when one sector’s uncertainty rises; in examples with complementary inputs, the reduced demand for a volatile sector also reduces demand for its complements, potentially amplifying the flight to safety beyond the directly affected sector.

International trade and macroeconomic dynamics with sanctions

Mon, 01 Jan 0001 00:00:00 +0000

Sanctions are increasingly used as an instrument of economic statecraft, yet their macroeconomic consequences—especially the transitional dynamics and their effects on business cycles—are poorly understood. This paper develops a micro-founded framework combining the intertemporal general-equilibrium structure of standard open-economy macro models with the rich trade-theoretic microfoundations of modern trade theory to study sanctions systematically. In a two-country, two-sector model where Home specializes in differentiated consumption goods (heterogeneous firms, endogenous entry, Melitz-style) and Foreign specializes in homogeneous intermediate goods (Cournot oligopoly in extraction), sanctions—modeled as trade bans and financial restrictions excluding particular Foreign agents—reallocate resources across and within countries, affect production, exchange rates, and welfare, and are shown to inflict larger welfare losses when they target sectors of comparative disadvantage. A central finding is that focusing only on long-run outcomes and overlooking initial transitional dynamics substantially misdirects welfare assessments; sanctions weaken international comovement and fragment markets but, contrary to some claims, leave the structure of business cycles largely intact.

In depth

Q1. What is the model structure and what types of sanctions does it capture?

The model is a two-country, two-sector economy: Home has a comparative advantage in differentiated consumption goods (produced by heterogeneous firms with endogenous entry under monopolistic competition, as in Melitz 2003), while Foreign specializes in homogeneous intermediate goods (produced via Cournot competition among a fixed number of upstream firms and processed by a representative distributor). This structure is motivated by the pattern in which Western economies specialize in high-value, firm-entry-intensive industries while sanctioned countries often specialize in commodity production (energy, natural gas). Sanctions are modeled as two distinct instruments: trade bans (restrictions on commerce in goods) and financial restrictions (excluding particular Foreign agents from capital markets). The model accommodates both Ricardian and Melitz-type comparative advantage.

Q2. What are the key results on welfare effects and the role of transitional dynamics?

Sanctions reallocate resources across and within countries, with welfare losses larger when sanctions target sectors of comparative disadvantage rather than sectors of comparative advantage; and focusing only on long-run welfare ignores significant transitional costs that substantially change the total welfare assessment. The model implies that initial transitional dynamics—disruptions to trade flows, entry and exit of firms, exchange rate movements, and adjustment of resource allocation—can be quantitatively important and even dominate long-run effects in welfare calculations. Assessments based solely on steady-state comparisons may therefore produce seriously misleading conclusions about whether and how severely sanctions harm the imposing or target economy.

Q3. How do sanctions affect international comovement and business cycles?

Sanctions weaken international business cycle comovement and fragment markets—reducing the degree to which shocks in one country transmit to the other—but leave the structural properties of business cycles within each country largely intact, in the sense that the cyclical dynamics of output, consumption, and investment retain their qualitative features. This result has policy implications: sanctions can reduce the interdependence of the sanctioned country’s business cycle from the rest of the world (which could be either beneficial or harmful depending on the source of shocks), but cannot fundamentally restructure the domestic cycle.

Q4. What is the baseline application and what general lessons emerge?

While the model’s comparative advantage structure is explicitly motivated by the 2022 Western sanctions against Russia—with intermediate goods interpretable as energy—the framework is designed to be more broadly applicable to other geopolitical conflicts involving sanctioned commodity producers facing differentiated-goods exporters, such as US-China trade tensions. The general lessons are: (1) the sector targeted by sanctions matters greatly for their welfare costs; (2) transitional dynamics are not second-order; (3) financial sanctions operate through different channels than trade bans and should be modeled separately.

Key concepts

comparative disadvantage in sanctions : the paper’s finding that sanctions are more costly when they target goods in which the targeted country has a comparative disadvantage—sectors the country cannot efficiently produce domestically—because those are the sectors where trade provides the highest value and substitution is hardest.

financial restrictions : one of the two types of sanctions modeled, in which particular Foreign agents (firms or sovereign entities) are excluded from international capital markets, distinct from trade bans that restrict commerce in goods.

Optimal Fiscal Policy with Heterogeneous Agents and Capital: Overturning Chamley-Judd

Mon, 01 Jan 0001 00:00:00 +0000

The Chamley-Judd result (1986) states that the optimal long-run capital income tax rate is zero in representative-agent models. This paper shows that introducing heterogeneous agents — specifically, agents with uninsurable idiosyncratic income risk who use precautionary saving — overturns this result. When agents differ in their wealth and income realizations, a capital income tax serves as a form of insurance that representative-agent models cannot provide. The paper derives a tractable analytical characterization of the optimal capital tax in an Aiyagari-type heterogeneous-agent model and finds that the optimal rate lies in the range of 10–30 percent at the steady state — strictly positive, in direct contradiction to Chamley-Judd. The magnitude of the optimal tax depends on the degree of idiosyncratic risk and the availability of alternative redistribution instruments: when other redistributive tools are limited, the optimal capital tax is higher.

In depth

Q1. Why does heterogeneity overturn Chamley-Judd?

In representative-agent models, all agents hold the same capital stock, so a capital tax distorts intertemporal decisions identically and the Ramsey planner finds it optimal to zero out the distortion in the long run. With heterogeneous agents and uninsurable risk, the capital tax has an additional insurance role: taxing capital income and redistributing it reduces consumption variance across agents, generating welfare gains that outweigh the intertemporal distortion costs. The insurance benefit makes the optimal tax positive at the steady state because the tax-and-redistribute mechanism provides risk-sharing that incomplete markets cannot.

Q2. How tractable is the analytical result?

The paper derives closed-form expressions for the optimal tax rate as a function of the degree of idiosyncratic risk, the wealth distribution’s spread, and the available redistribution instruments, enabling comparative statics that go beyond what purely computational approaches provide. This tractability distinguishes the result from earlier numerical work that demonstrated positive optimal capital taxes without clear analytical structure.

Q3. What is the quantitative magnitude?

The optimal steady-state capital income tax is in the range of 10–30 percent, substantially above zero but well below confiscatory rates, in the paper’s benchmark calibration matched to U.S. income and wealth inequality. The range reflects the sensitivity to available redistribution instruments: the lower bound applies when the government has a rich set of redistribution tools, the upper bound when capital taxation is the only available instrument.

Key concepts

Chamley-Judd result : the proposition that the optimal long-run capital income tax is zero in representative-agent Ramsey taxation models; overturned in this paper once heterogeneous agents with uninsurable risk are introduced.

insurance role of capital taxation : the mechanism by which a capital income tax reduces consumption inequality in a heterogeneous-agent economy, generating welfare gains that outweigh the intertemporal distortion costs and making the optimal capital tax positive.

Patents, News, and Business Cycles

Mon, 01 Jan 0001 00:00:00 +0000

This paper constructs an instrumental variable for technology news shocks using patent applications, relaxing all identifying assumptions traditionally used in the news-shock literature. The IV is the component of patent applications orthogonal to pre-existing beliefs (Survey of Professional Forecasters), contemporaneous and lagged monetary and fiscal policy changes (narrative accounts), and own lags. The instrument recovers news shocks that have no effect on aggregate productivity in the short run but are a significant driver of its trend component. The shock prompts a broad-based expansion in anticipation of the future TFP increase—output, consumption, and investment all rise well before any material increase in TFP is recorded. Despite these positive conditional co-movements, the news shock accounts for only a modest share of macroeconomic fluctuations at business cycle frequencies. Financial markets price in news shocks on impact, while most macro aggregates respond with some delay. Previously circulated as “When Creativity Strikes: News Shocks and Business Cycle Fluctuations.”

In depth

Q1. What is the identification strategy and why does it relax traditional assumptions?

The paper constructs an IV for technology news shocks as the component of patent applications orthogonal to pre-existing beliefs (SPF), narrative accounts of monetary and fiscal policy, and own lags—the sole identifying assumption is that no structural disturbance other than contemporaneous technology news affects the U.S. economy through this IV. Traditional identification requires combining zero restrictions on the impact response of TFP with assumptions about its long-run drivers (e.g., Beaudry-Portier 2006 assumes news shocks are the sole long-run driver of TFP). The patent-based IV avoids all of these assumptions, relying only on the exclusion restriction that patent applications, after controlling for expectations and policy, capture news about future technological change and nothing else.

Q2. How do patent applications contain information about future technology?

Patent applications contain information about potential future technological change because exclusive rights create a powerful incentive to apply as early as possible, making patent applications lead TFP improvements by years, while controlling for contemporaneous economic conditions removes the endogeneity of patent filings to current booms. The length of time between application and the eventual diffusion of the innovation within the economy can be several years. The filing date serves as the first measurable time at which the news occurs, even though the underlying idea predates the application. The component of applications orthogonal to SPF forecasts and policy changes represents news about future technology not driven by current conditions.

Q3. What are the macroeconomic effects of technology news shocks?

Technology news shocks generate a broad-based expansion—output, consumption, and investment all rise well before any material increase in TFP is recorded—and financial markets price in news shocks on impact, while most macro aggregates respond with some delay. The positive conditional co-movements are consistent with optimism about future income and productivity generating pre-emptive expansion. Despite these theoretically attractive features, the news shock accounts for only a modest share of macroeconomic fluctuations at business cycle frequencies.

The finding that news shocks account for only a modest share of macro fluctuations at business cycle frequencies implies that, while identified news shocks behave consistently with the news-driven business cycle hypothesis in qualitative terms, they contribute only modestly to aggregate volatility—a finding that differs from models in which news shocks are a primary driver of cycles. This quantitative finding is informative precisely because the identification is instrument-based and free of the theoretical priors imposed by traditional sign-restriction and FEVD approaches, lending credibility to it as an estimate of the true importance of news shocks.

Key concepts

technology news shock : a shock that raises expectations about future aggregate TFP growth without any immediate change in current TFP; the paper’s IV identifies shocks that have no short-run effect on TFP but are a significant driver of its trend component. patent-based instrument : the component of patent applications orthogonal to pre-existing macroeconomic beliefs (SPF), contemporary monetary and fiscal policy changes (narrative accounts), and own lags; used as an IV for technology news shocks that avoids traditional identifying restrictions. news-driven business cycle hypothesis : the proposition that economic fluctuations can arise from changes in agents’ expectations about future fundamentals (particularly future productivity) even absent any current change in those fundamentals; the paper finds qualitative support but only modest quantitative importance.

Skilled immigration frictions as a barrier for young firms

Mon, 01 Jan 0001 00:00:00 +0000

High-skilled immigration policy frictions—particularly the H-1B visa lottery, fixed annual cap, and associated compliance costs—impose well-known burdens on firms, but their disproportionate impact on young, technology-intensive companies has received less attention. This paper provides the first study combining firm-level panel data on H-1B outcomes with a general equilibrium model of firm dynamics to quantify these effects. Using the random allocation of H-1B visas in the FY 2014 and FY 2015 lotteries as quasi-random variation, the authors find that lower H-1B visa win rates significantly reduce the survival of young firms (aged 0–5) in technology-intensive sectors, while the impact for older firms is not statistically significant. A general equilibrium model with endogenous firm entry and exit, skilled foreign labor, and H-1B-style policy frictions matches the age distribution of high-tech firms and shows that eliminating major immigration policy frictions would increase average productivity in the high-tech sector primarily by enabling more young firms to enter and survive, which in turn drives the exit of older, less productive firms.

In depth

Q1. What is the quasi-random identification strategy, and what does it identify?

The paper uses H-1B visa lottery win rates in fiscal years 2014 and 2015 as quasi-random variation in access to skilled foreign workers, combining National Establishment Time Series (NETS) data on firm survival with Labor Condition Application (LCA) and H-1B petition data. Because the lottery randomly allocates visas among firms that applied (when the cap is binding), the fraction of applications that result in approvals is plausibly exogenous to firm characteristics, conditional on applying. The empirical finding—that lower lottery win rates significantly reduce survival of young firms (0–5 years old) in tech-intensive sectors but not of older firms—is identified off this lottery variation. The age-heterogeneity result is central: large incumbent firms have alternative channels (offshore hiring, internal labor markets, H-1B cap-exempt hires) that small, young firms lack.

Q2. Why are young high-tech firms more exposed to H-1B frictions than older firms?

Young firms in high-tech sectors depend heavily on specialized skilled foreign workers because they compete in rapidly changing technology fields where the domestic talent pool may not supply the precise skills needed at the pace required; they cannot easily substitute with a second-choice candidate or offshore to a foreign affiliate as large multinationals can. The paper cites GAO (2011) survey evidence that in years when the H-1B cap bound, most large firms found alternative (often costly) ways to hire their preferred candidates, while small firms were more likely to fill positions with different candidates, incurring delays and economic losses.

Q3. What does the general equilibrium model predict about aggregate productivity?

The model shows that eliminating major H-1B-style immigration policy frictions would increase average productivity in the high-tech sector through the entry and survival channel: fewer frictions allow more young firms to enter and survive, which raises competitive pressure and leads to the exit of older, less productive firms (a selection effect via creative destruction). This mechanism implies that the productivity gain from liberalizing skilled immigration comes not primarily from incumbent firms hiring more foreign workers, but from the change in the firm age and productivity distribution—a general equilibrium effect that partial-equilibrium analyses based on incumbent firms would miss.

Q4. How does the model match the data on firm dynamics?

The model is calibrated to match the age distribution of firms in high-technology sectors in the data, including the stylized fact that the share of young (0–5 year old) high-tech firms has declined since the early 2000s concurrent with a period of more restrictive skilled immigration policy (the H-1B cap fell from 195,000 in 2003 to 85,000 in 2005 and has remained constant). The model also captures the pattern—documented in the data—that the entry of younger firms leads to a greater exit of older firms, consistent with the Hopenhayn-Rogerson (1993) model of firm dynamics.

Key concepts

H-1B visa frictions : the set of costs and constraints associated with the H-1B temporary skilled worker visa program in the US, including per-firm application costs, a fixed aggregate cap of 85,000 visas for private firms per year, and random lottery allocation when applications exceed the cap.

firm survival channel : the mechanism through which immigration policy frictions reduce the probability that young high-tech firms survive to maturity, as distinct from the hiring channel (whether incumbent firms hire foreign workers); the paper argues the former is the quantitatively relevant margin.

Temporary Layoffs, Loss-of-Recall, and Cyclical Unemployment Dynamics

Mon, 01 Jan 0001 00:00:00 +0000

This paper measures and models the role of temporary layoffs (TL) in cyclical unemployment dynamics, motivating the analysis by the extraordinary surge in temporary layoffs at the onset of the pandemic recession — roughly 15% of employed workers moved to temporary-layoff status from March to April 2020. The paper documents two opposing effects of temporary layoffs on total unemployment: a stabilizing direct effect (workers on TL return to employment rapidly via recall) and a destabilizing indirect effect through “loss-of-recall” — workers initially on temporary layoff who fail to be recalled and instead transition to jobless unemployment (JL), inheriting that state’s far lower reemployment probability. A new recursive accumulation method is used to construct a time series of the stock of workers in jobless unemployment whose most recent exit from employment was to temporary-layoff status (JL-from-TL); this stock has a standard deviation 16 times that of GDP and 2 times that of total unemployment, and is a high-correlation indicator of labor market slack. A search-and-matching model with staggered Nash wage bargaining, endogenous layoff thresholds, and separate recall and new-hire channels replicates the pre-pandemic cyclical behavior of TL and JL flows. Applying the model to the pandemic recession, the paper finds that the Paycheck Protection Program (PPP) reduced employment shortfalls by roughly 2 percentage points at peak, primarily by dampening loss-of-recall — the program’s forgivable loan structure reduced firms’ incentive to permanently separate workers who had been placed on temporary layoff.

Layer 1: Overview

Gertler, Huckfeldt, and Trigari study two distinct features of temporary layoffs in aggregate unemployment dynamics: the well-documented stabilizing role of recall hiring, and a less-studied destabilizing mechanism they term “loss-of-recall” — the countercyclical flow of workers from temporary-layoff unemployment into jobless unemployment. Using monthly CPS data from 1979 through the pandemic period, they construct a four-state Markov transition matrix (employment, TL unemployment, JL unemployment, inactivity) and develop a novel recursive method to track the accumulated stock of jobless unemployed workers whose most recent employment exit was via temporary layoff (JL-from-TL). This stock is small on average (roughly 40% of the average TL stock) but highly volatile — its standard deviation is 16 times GDP and twice total unemployment — and strongly co-moves with total unemployment (correlation 0.93) and the vacancy-unemployment ratio (0.83). Across historical recessions: TL unemployment contributed 36.1% of the increase in total unemployment during the 1980s recessions (25.1% direct, 11.0% indirect via loss-of-recall); 17.2% during the Great Recession (8.7% direct, 8.5% indirect — nearly equal); and 98% during the pandemic recession (almost entirely direct, because PPP dampened loss-of-recall). The structural model — DMP with staggered multiperiod Nash wage bargaining, firm-specific overhead cost shocks that generate endogenous exit and temporary layoffs, and separate hiring and recall margins — captures pre-pandemic dynamics and shows that loss-of-recall amplifies unemployment persistence following recessionary TFP shocks. In the pandemic recession application, the PPP counterfactual finds that without PPP: peak unemployment would have been roughly 2 percentage points higher; jobless unemployment would have peaked at 7.0% versus 5.9% in the PPP scenario; and cumulative TL-to-JL flows would have been roughly double, amounting to 47.4% of what they would otherwise have been.

In depth

Q1. What distinguishes temporary-layoff unemployment from jobless unemployment in the data, and why does the distinction matter for cyclical dynamics?

Temporary-layoff unemployment (TL) is the state in which a CPS respondent indicates an expectation of recall — either a specific return date or a stated expectation of recall within six months — while jobless unemployment (JL) is unemployment without such an expectation; the two states have starkly different reemployment probabilities, with TL workers returning to employment at substantially higher rates than JL workers, making the composition of total unemployment — not just its level — a key determinant of unemployment persistence. In the Markov transition matrix estimated from CPS data 1979-2019 (Table 2), TL is a transient state: workers on TL transition to employment at a far higher rate than workers in JL, reflecting the attached recall relationship. The stock of TL unemployment is consequently small — averaging roughly one-eighth of total unemployment — even though TL separations account for roughly one-third of all separations from employment to unemployment. The distinction matters for aggregate dynamics because a recessionary increase in TL generates both a direct, relatively transient component (elevated TL stock) and an indirect, more persistent component (heightened loss-of-recall feeding into JL stock). Standard two-state unemployment models that lump TL and JL together miss the indirect channel entirely, understating both the volatility and persistence of total unemployment in the presence of countercyclical loss-of-recall.

Q2. What is the recursive accumulation method for estimating JL-from-TL, and what does it reveal about the indirect contribution of temporary layoffs?

The paper proposes a novel method to estimate the time series stock of jobless unemployed workers whose most recent employment exit was through temporary-layoff unemployment — the JL-from-TL stock — by propagating forward through the Markov transition matrix each cohort of workers who enter TL from employment, tracking the fraction that survive in any unemployment state without returning to employment, and summing across all past cohorts. Formally, if $x_{t-m,t}$ denotes the distribution of workers at time $t$ whose last exit from employment was to TL at time $t-m$, then $x_{t-m,t} = \tilde{P}t x{t-m,t-1}$ where $\tilde{P}t$ is a modified transition matrix, and the JL-from-TL stock is $u^{JL,TL}t = \sum{j=0}^{T} e’{JL} x_{t-j-1,t}$. The method requires only the Markov transition matrix — no individual-level panel data — and extends the Shimer (2012) / Elsby-Hobijn-Sahin (2015) variance decomposition approach to level decompositions. Applied to CPS data, the JL-from-TL stock has a standard deviation 16 times that of GDP (versus 2 times for TL itself) and a correlation of 0.93 with total unemployment — substantially higher than the 0.83 correlation of the vacancy-unemployment ratio with total unemployment. The large relative volatility reflects that the JL-from-TL stock compounds both the volatility of TL separations and the cyclical variation in the TL-to-JL transition probability (loss-of-recall); both components are countercyclical, so they co-amplify in recessions.

Q3. How does the paper’s structural model generate endogenous temporary versus permanent layoffs and a procyclical recall probability?

Temporary layoffs and permanent exits arise endogenously from two cost shocks in the model: an employee-specific cost shock (ϑ) and a firm-specific overhead shock (γ), with thresholds ϑ and γ determined by firm optimization; workers whose idiosyncratic cost exceeds ϑ* are placed on temporary layoff (retaining recall rights), while firms whose overhead shock exceeds γ* exit, converting their TL workers to jobless unemployment.** The framework is a modified DMP model with staggered Nash wage bargaining (following Gertler-Trigari 2009), where firms can expand their workforce either by recalling workers from TL unemployment or by hiring new workers from JL unemployment, with separate quadratic adjustment costs for each margin ($\kappa$ for new hires, $\kappa_r$ for recalls). The recall elasticity exceeds the new-hire elasticity, consistent with the lower cost of re-integrating previously attached workers. Recall hiring (xr) and new hiring (x) are both driven by the discounted value of a worker to the firm, J(w,s), but respond with different sensitivities governed by their respective adjustment cost parameters. The TL-to-JL (loss-of-recall) flow is endogenous and driven by firm exit: when the overhead shock γ exceeds γ*(w,s), the firm exits and its TL workers lose their recall option, converting to JL unemployment. Because γ* rises in bad times (higher firm insolvency), loss-of-recall is countercyclical, matching the data pattern. An exogenous loss-of-recall probability $(1-\rho_r)$ is also included to capture TL-to-JL flows that occur even when the firm survives (e.g., firm restructuring or expiration of recall expectations), and this parameter is calibrated to long-run flow moments.

Q4. What does the calibrated model reveal about the amplification role of loss-of-recall, and how is this quantified?

A counterfactual exercise that sets the TL-to-JL transition probability to zero (shutting off loss-of-recall) shows that total unemployment peaks earlier and at a lower level following a recessionary TFP shock, and that unemployment displays markedly less persistence — revealing loss-of-recall as an important amplification mechanism by which a recessionary increase in temporary layoffs can generate persistently higher total unemployment. The model is calibrated to monthly frequency with 16 parameters: 9 assigned externally (β=0.991^{1/3}, δ=0.025^{3}, α=1/3, standard AR(1) TFP parameters, matching function elasticity σ=0.5, bargaining power η=0.5, λ=8/9 targeting quarterly wage adjustment frequency), and 7 calibrated to long-run flow moments and business cycle volatility moments (Table 8-9). The calibrated model captures the cyclical volatility of aggregate labor market stocks and flows, and the impulse response to a negative 1% TFP shock shows a hump-shaped increase in total unemployment with TL unemployment recovering within roughly two years (due to lower recall costs) while JL unemployment recovers more slowly (due to lower job-finding rates). The countercyclical overshooting of employment-to-JL transition probabilities during the subsequent expansion reflects the procyclicality of the reservation wage — workers are less willing to accept pay cuts in good times, triggering exits from employment at the margin. The overall result is that loss-of-recall accounts for a quantitatively significant share of unemployment persistence in recessions, particularly in the later part of the sample.

Q5. How is the model adapted for the pandemic recession, and what are the specific mechanisms through which PPP reduced jobless unemployment?

The pandemic application introduces two temporary shock processes: (i) a “virus shock” that exogenously raises the TL rate above the threshold determined by ϑ (capturing mandatory closures and social distancing-induced reductions in effective labor demand), and (ii) a productivity shock from social-distancing requirements; PPP is modeled as a policy that subsidizes firms’ wage bills conditionally on maintaining worker-firm attachments, reducing firms’ incentive to exit and thereby directly dampening the endogenous TL-to-JL (loss-of-recall) flow.* With these modifications the model captures the key features of pandemic labor market dynamics: the extraordinary March-April 2020 TL spike, the rapid initial recall, and the subsequent slow recovery of employment. In the PPP counterfactual (no PPP), cumulative TL-to-JL flows over the pandemic period would have been approximately double their actual levels — the model generates a 47.4% ratio of actual-to-counterfactual cumulative TL-to-JL flows, indicating PPP prevented roughly 53% of the loss-of-recall that would have otherwise occurred. At peak (six months after the shock), employment under the no-PPP counterfactual is 8.8% below pre-pandemic levels versus 6.8% with PPP — a 2 percentage point gap. Jobless unemployment peaks at 7.0% without PPP versus 5.9% with PPP. Consistent with estimates from Hubbard and Strain (2020), the estimated average monthly PPP employment gain is approximately 2.0% over the first six months, with gains of 1.57% through February 2021 before convergence toward zero.

Q6. What does the evidence on reemployment probabilities of workers who transition from TL to JL establish, and why is it important for identifying loss-of-recall?

Workers in jobless unemployment who were in temporary-layoff unemployment in the previous period have reemployment probabilities virtually indistinguishable from those of the full population of jobless unemployed (Table 3), which — because JL workers have far lower reemployment probabilities than TL workers — establishes that the TL-to-JL transition is a true loss-of-recall event: the worker has genuinely lost the recall relationship and now faces the same search frictions as other permanently separated workers. This finding is important for the paper’s empirical strategy because it validates the interpretation of CPS-recorded TL-to-JL transitions as genuine loss-of-recall rather than mismeasurement or recategorization without substantive change in the worker’s employment prospects. The result also implies that TL-to-JL transitions create true duration dependence in reemployment probabilities among workers initially on TL: workers who spend longer in TL unemployment are more likely to lose recall, so the average reemployment probability of the TL cohort declines with duration. This duration dependence is consistent with the model’s mechanism — exit probability rises over time as firms facing prolonged overhead cost shocks eventually breach the exit threshold — and provides a micro-level validation of the endogenous loss-of-recall channel.

Key Concepts

temporary-layoff (TL) unemployment : the labor market state in which an unemployed worker retains an expectation of recall to the prior employer (either a specific return date or an indication of recall within six months, per CPS classification); characterized by substantially higher reemployment probabilities than jobless unemployment, accounting for roughly one-third of separations from employment but only one-eighth of the total unemployment stock due to the transient nature of TL spells.

loss-of-recall : the conversion of a temporary layoff into a permanent separation — the event by which a worker initially on TL status transitions to jobless unemployment because the prior employer exits or cannot recall; the paper’s central amplification mechanism, shown to be countercyclical (higher in recessions), to account for 8.5–11.0% of unemployment increases in pre-pandemic recessions, and to be substantially dampened by PPP during the pandemic.

JL-from-TL stock : the accumulated stock of workers currently in jobless unemployment whose most recent exit from employment was through temporary layoff — constructed via the paper’s novel recursive accumulation method; has a standard deviation 16 times GDP and 2 times total unemployment, correlates 0.93 with total unemployment, and constitutes a leading slack indicator that captures the indirect destabilizing contribution of temporary layoffs to unemployment dynamics.

recall hiring versus new-hire margin : the model’s two channels through which firms can expand their workforce — recalling workers from their own TL pool (lower adjustment cost, higher recall elasticity) versus hiring new workers from the pool of jobless unemployed (higher cost); both margins respond positively to the discounted firm value J(w,s) but with different sensitivities calibrated to match the differential volatility of TL-to-E and JL-to-E transition probabilities in the CPS.

staggered Nash wage bargaining : the model’s wage rigidity mechanism (following Gertler-Trigari 2009), in which firms and workers negotiate base wages with probability (1-λ) each period; the calibrated λ=8/9 targets a wage adjustment frequency of roughly one per quarter, consistent with Taylor (1999) and Gottschalk (2005) evidence; wage rigidity — combined with the allowance for temporary pay cuts to prevent exit — is quantitatively important for replicating the observed volatility of labor market flows and stocks.

The Gender Pay Gap: Micro Sources and Macro Consequences

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper uses linked employer-employee data from Brazil (RAIS, 2007–2014, covering 267 million worker-years, 56 million unique workers, and 607,000 employers) to document that the gender pay gap of 13.3 log points is overwhelmingly driven by women sorting into lower-paying employers — 78.7% of the gender gap in employer pay fixed effects is attributable to between-employer sorting, not within-employer discrimination. To interpret this sorting, the authors develop an equilibrium on-the-job search model (extending Burdett and Mortensen 1998) with endogenous firm pay, amenities, and hiring, and provide a constructive proof that all model parameters are point-identified from linked employer-employee data. The estimated model finds that amenities explain approximately half of total compensation for both genders (mean amenity share 48.8% for men, 52.2% for women), that compensating differentials account for roughly half of the gender pay gap (reducing it from 13.3 to 4.6 log points in total-compensation terms), and that higher-ranked employers offer women higher amenities rather than higher pay — resolving the puzzle that women disproportionately work at large employers despite a flat employer-size-pay gradient for women. Eliminating gender differences in employer preferences (gender wedges) would raise output by 12.9% but pull women into low-amenity firms, reducing their welfare, while equal-pay and equal-hiring policies close part of the pay gap but lower worker welfare through adverse incentive effects on firms’ compensation and hiring decisions.

In depth

Q1. What empirical patterns motivate the paper’s framework?

Three facts from Brazilian linked employer-employee data require a richer model than standard pay-only frameworks: (i) 78.7% of the 11.3 log-point gender gap in employer pay fixed effects is a between-employer sorting gap (women work at lower-paying firms); (ii) pay is increasing in employer size for men (R² = 3.3%) but essentially flat for women (R² = 0.1%); and (iii) women are disproportionately concentrated at the largest employers, which is inconsistent with models in which large firms pay more if pay is all that matters. These three facts together reveal that women value employer attributes other than pay, particularly at larger firms. Direct amenity proxies confirm this: women at larger employers are substantially less likely to be exposed to workplace hazards (coefficient −0.013, p < 0.01), less likely to be fired unjustly (coefficient −0.005, p < 0.01), much more likely to receive generous parental leave (coefficient 1.054, p < 0.01), and more likely to work part time. The AKM two-way fixed effects decomposition further shows that employer fixed effects account for 12.5% of the variance of log earnings for men and 11.1% for women, with the variance of earnings explained at 92.3% (men) and 93.1% (women).

Q2. What is the equilibrium model and how does it generate compensating differentials?

The model extends Burdett-Mortensen on-the-job search to allow firms to simultaneously choose wages, amenities, and vacancies, with firms differing in three dimensions: productivity p, gender wedges τ (an implicit tax on employing women capturing taste-based discrimination or comparative advantage), and gender-specific amenity cost shifters ca,0 — making firm pay, amenities, and hiring jointly determined in equilibrium. Workers maximize flow utility x = w + a (wage plus amenity value), and each gender climbs a separate firm utility ladder. Firms with higher composite productivity p̃ = (1−τ)p + a* − c(a*) offer higher utility to attract more workers given convex vacancy posting costs. Because amenity costs are convex and increasing in amenity value, firms optimally set amenities so that the marginal cost equals one (the unit wage), creating endogenous compensating differentials: high-amenity firms can pay lower wages while still attracting workers. The model is isomorphic to a standard wage-only Burdett-Mortensen model with wages replaced by flow utility and productivity replaced by composite productivity.

Q3. How are all model parameters identified constructively?

The authors provide a five-step constructive identification proof that recovers all parameters — including the unobservable amenity values, gender wedges, and productivity distribution — without distributional assumptions: (1) gender-specific employer pay components from AKM; (2) employer utility ranks from the employer size distribution (higher-utility firms are larger in equilibrium); (3) labor market flow hazards (λU, λE, λG, δ) from worker flow data conditional on ranks; (4) firm-level parameters (p, τ, ca,0) by inverting equilibrium profit functions; (5) economy-wide parameters (cv,0, ηv, ηa) from aggregate labor share, firm pay-profit gradient, and aggregate amenity cost share. The key insight for step (4) is that unobserved firm profits per matched worker can be inferred from equilibrium firm sizes (more profitable firms post more vacancies and hire more workers), and comparing utility levels inferred from sizes with observed wages identifies amenity values. For step (3), the involuntary job offer hazard λG is separately identified because job-to-job transitions involving a decline on the utility rank ladder — which cannot be voluntary (workers strictly prefer higher utility) — must be involuntary, allowing the hazard to be estimated by counting down-rank transitions.

Q4. What are the estimated structural results on amenities and the pay-amenity tradeoff?

Amenities are pervasive and quantitatively large: the mean amenity share of total compensation is 48.8% for men and 52.2% for women, yet compensating differentials explain the lion’s share of firm pay dispersion, with utility dispersion accounting for only 4.4% of pay dispersion for men and 3.6% for women — far less than pay dispersion alone might suggest. Higher-ranked firms for men mostly offer higher pay, but higher-ranked firms for women mostly offer higher amenities. The estimated gender productivity gap is 8.3 log points (employment-weighted mean log productivity 0.864 for men, 0.781 for women), and the employment-weighted mean gender wedge is 0.059 for women but 0.235 for men (wedge represents an implicit disutility from hiring women, so higher means women face higher wedge on average in firms where they are less likely to work). Estimated labor market parameters show women receive fewer job offers from nonemployment (λU_F = 9.1% monthly vs. 10.4% for men) and have lower job destruction rates (δ_F = 2.8% vs. 3.6% for men), contributing to slower job-ladder climbing.

Q5. How does the paper decompose the gender pay gap into micro sources?

Shutting down firm heterogeneity in amenities — replacing gender-specific amenity values with their mean — closes 45% of the gender pay gap, largely because women relocate toward formerly male-dominated, higher-paying, lower-amenity firms; shutting down differences in employer preferences (gender wedges) eliminates the pay gap entirely; differences in labor market flow rates have little effect. The total-compensation gender gap, which accounts for amenity differences, is only 4.6 log points — 40.7% of the raw pay gap of 11.3 log points — confirming that compensating differentials explain approximately half of the measured pay disadvantage. This decomposition is a novel contribution over Card et al. (2016), who rationalized the gap through exogenous gender-specific bargaining parameters without modeling amenities or their equilibrium provision.

Q6. What are the macro consequences of the gender pay gap for output and welfare?

Removing all gender differences from the economy (wedges, amenity costs, and flow rates) raises output by 6.1% and welfare by 2.1%, substantially below what pay differences alone might suggest; however, eliminating employer preferences over gender (gender wedges only) raises output by 12.9% at the cost of a welfare reduction for women, because women are pulled into high-paying, low-amenity firms. The quantitative wedge between output gains (12.9%) and welfare gains when wedges are removed reveals that women’s sorting into amenity-rich firms is partly welfare-enhancing from their perspective, even if it involves accepting lower wages. This is a key insight for policy: policies targeting pay gaps without accounting for amenity losses can be welfare-reducing.

Q7. What do equal-pay and equal-hiring policies achieve in equilibrium?

Both equal-pay mandates (forcing firms to pay men and women identical wages) and equal-hiring mandates (requiring gender-neutral hiring) close part of the gender pay gap but lower worker welfare for both genders, because the policies generate adverse incentive effects: equal-pay mandates induce firms to reduce amenities for women (since the wage-amenity tradeoff is disrupted), and equal-hiring mandates distort firms’ recruiting decisions in ways that raise vacancy costs. These general-equilibrium effects would be missed in partial-equilibrium analyses. The paper thus provides a rigorous case that equal-treatment policies — while closing observable pay gaps — fail to achieve the underlying welfare gains from eliminating gender differences, and may generate unintended welfare losses.

Q8. How does the model resolve the employer-size puzzle and what discriminatory mechanisms does it admit?

The flat employer-size-pay gradient for women (versus steeply increasing for men) is rationalized in the model because large employers offer women high amenities that substitute for pay; women optimally accept lower wages at large employers in exchange for amenity bundles that are unavailable at smaller firms. The model accommodates three discrimination channels simultaneously: taste-based discrimination (Becker 1971, via the gender wedge τ), compensating differentials reflecting gender-specific job characteristics (Rosen 1986, via amenity cost shifters), and monopsony power (Robinson 1933, via search frictions). Even nondiscriminatory firms treat women differently than men as a best response to the equilibrium distribution of discriminatory firms — an equilibrium spillover of discrimination that purely partial-equilibrium analyses miss.

Key Concepts

gender wedge (τ) : a firm-level parameter capturing the implicit disutility cost per unit of female employment, encompassing taste-based discrimination (Becker 1971) and comparative-advantage differences (Goldin 1992); estimated to explain substantial variation in women’s employment shares across firms, with female managers, routine manual tasks, and smaller size associated with lower wedges (R² = 54.6%).

compensating differentials : the wage reduction a worker accepts in exchange for favorable non-wage job attributes (amenities); in this paper, estimated to explain approximately half of the gender pay gap — the total-compensation gap is 4.6 log points vs. a pay gap of 11.3 log points — implying that women’s lower wages partly reflect their preference for amenity-rich employers.

amenity share : the fraction of total compensation (wages plus amenities) attributable to non-wage job attributes; estimated at 48.8% for men and 52.2% for women, indicating that amenities are quantitatively as important as wages in total compensation for both genders.

employer rank : a revealed-preference ordering of employers by gender-specific utility offered to workers, identified by the employer size distribution (larger firms are higher-utility in equilibrium); the paper’s key object for separating the between-employer sorting component of the pay gap from the within-employer component.

composite productivity (p̃) : the model’s reduced-form measure of a firm’s profitability per worker, combining raw productivity p, the gender wedge τ, and the optimized amenity net of amenity costs; allows the equilibrium to be analyzed as a standard Burdett-Mortensen model with composite productivity replacing raw productivity and flow utility replacing wages.

involuntary job offer hazard (λG) : the arrival rate of unsolicited job offers that workers must accept regardless of utility ranking, capturing spousal relocations and other idiosyncratic transitions; identified from the frequency of utility-rank-decreasing job transitions, since voluntary transitions can only increase utility.

The Macroeconomic Consequences of Early Childhood Development Programs

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper embeds early childhood development (ECD) investment into a general-equilibrium (GE), heterogeneous-agent, overlapping-generations model calibrated to U.S. data in order to quantify the aggregate and distributional consequences of large-scale, universal government ECD programs. The central finding is that a universal program spending $13,500 per child-year on children aged 0–3 — the same level as a well-studied North Carolina randomized controlled trial — generates long-run welfare gains of 12.7% in consumption-equivalent units for newborns under the veil of ignorance, income growth of 10.6%, an intergenerational mobility increase of 28.2% (roughly half the US–Canada gap), and a lifetime-earnings inequality reduction of 2.0% (roughly half the US–Germany gap). The key mechanism is dynastic: investing in a child today not only raises that child’s own skills and income but creates a better parental background — in terms of skills, assets, and education — for the next generation, so that more than two-thirds of the welfare gains accrue through this intergenerational channel rather than from the direct effect on the intervened generation. General equilibrium compresses the college wage premium and reduces welfare gains by approximately one-third relative to partial-equilibrium projections, but the policy remains self-financing in the long run. The model is validated against the first- and second-generation experimental evidence from Garcia et al. (2020, 2024), replicating both the 15 p.p. college graduation rate increase and the 1.54 lifetime income return per dollar spent that those RCTs documented.

In depth

Q1. What is the core market failure that motivates government ECD investment?

The paper identifies two inter-related reasons why private early childhood investments fall below the social optimum: parents cannot borrow against their children’s future income (no child-to-parent compensation contract), and borrowing constraints together with uninsurable idiosyncratic return risk further depress parental investment below even that constrained optimum. Under complete markets with compensating contracts, a poor parent who invests in a high-skilled child could smooth lifetime consumption intergenerationally. Without such contracts, the entire cost of investment falls on the parent in the early life-cycle when assets and income are low, reducing investment incentives sharply. Government ECD spending financed by future taxation on the child’s higher income imperfectly replicates this missing insurance-borrowing mechanism. The model finds that uncertain returns to skill investments — which the government can spread across the population but parents cannot insure privately — and incomplete credit markets are quantitatively more important than imperfect altruism in driving underinvestment.

Q2. How is the model structured, and what is the role of the dynastic framework?

The model is a dynastic overlapping-generations Aiyagari life-cycle economy with four stages (childhood, college, work/parenthood, retirement), each of four-year periods, in which children’s cognitive and non-cognitive skills are determined by CES-aggregated parental time and money investments in ages 0–3, calibrated using the Cunha et al. (2010) skill-formation function. At age 28 (period j=8), the working agent becomes a parent and chooses parental time τ and money m to invest in the child’s skill development across two periods; these decisions interact because time and money are estimated to be imperfect complements (CES exponent γ estimated from data). College attendance is endogenous — it depends on assets, skills, and a school-taste shock — and can be financed by parental transfers (constrained to be non-negative), work, or subsidized student loans. The dynastic structure means that changes in the distribution of parental skills, assets, and education feed forward into the next generation’s initial conditions, which is the source of the large long-run intergenerational amplification.

Q3. What are the main quantitative results of the benchmark universal ECD policy?

A universal permanent policy investing $13,500 per child-year (ages 0–3), financed by an endogenous labor income tax, produces in the long-run steady state: a welfare gain of 12.7% in consumption-equivalent units (for a newborn under the veil of ignorance), a labor income increase of 10.6% (driven by an 11.7% rise in labor productivity), an intergenerational mobility increase of 28.2% as measured by minus the rank-rank coefficient, and a lifetime-earnings variance reduction of 2.0%. The level of $13,500 is both the historically implemented per-child cost in the Garcia et al. (2020) RCT and close to the welfare-maximizing amount in the model (welfare peaks at 13.1% at a slightly higher spending level). Children of low-skilled, non-college parents gain the most (welfare gain 9.1%) versus children of college-educated, high-skilled parents (welfare gain 4.1%). Taxes in the long run are approximately unchanged from baseline because the expanded tax base offsets the direct program cost; in partial equilibrium without GE forces, taxes fall by 2.5 p.p. but GE compression of wages leaves only a negligible tax reduction in the benchmark.

Q4. How do the decomposition exercises isolate the relative importance of long-run dynamics versus GE and taxation?

Decomposing the 12.7% benchmark gain across four counterfactual implementations reveals that long-run intergenerational dynamics account for over two-thirds of total welfare gains, while GE forces reduce gains by roughly one-third and taxation costs are approximately offset by higher revenues in the long run. Specifically: (i) a one-generation, partial-equilibrium version of the policy generates only 5.2% welfare gain; (ii) adding long-run intergenerational effects (permanent policy) raises this to 14.5%, an increase of 9.3 p.p.; (iii) further allowing for balanced-budget taxation in PE reduces gains from 17.3% to a net 12.5%; and (iv) incorporating GE effects — which compress the college wage premium — reduces labor productivity gains and welfare gains by about one-third. More than two-thirds of the aggregate welfare gain comes from changes in the distribution of initial conditions (newborns born into higher-skilled, better-resourced families) rather than from higher utility at a fixed initial-state distribution.

Q5. How does the model validate against experimental evidence, and what does this imply for RCT estimates?

The model replicates two key experimental benchmarks: the Garcia et al. (2020) RCT finding of a 15 p.p. college graduation rate increase and a per-dollar lifetime income return of 1.55 (the model generates 1.54 for children of median-income parents), and the Garcia et al. (2024) estimate that second-generation income gains are 29% of first-generation gains (the model generates 20%, at or below that empirical estimate). The validation is run as a small-scale, partial-equilibrium, one-generation exercise — exactly matching the RCT design — so the comparison is clean. The fact that the model replicates both generations’ effects provides confidence in the intergenerational amplification mechanism. The paper interprets this as evidence that RCT evaluations of short-run, small-scale programs systematically underestimate the long-run benefits of universal programs, with the ratio of long-run GE gains to short-run PE estimates falling between 2 and 3 across a range of alternative education policies.

Q6. How do general equilibrium forces shape distributional outcomes, and why do they cut in opposite directions?

GE forces create a tension: they simultaneously generate most of the inequality reduction (by compressing the college wage premium) and eliminate most of the labor-productivity and welfare gains from partial-equilibrium projections. As the universal program raises the share of college graduates, the relative wage of college workers falls. This wage compression is the primary driver of the 2.0% reduction in lifetime-earnings variance — approximately equal to half the US–Germany inequality gap — but it also lowers the productivity return on human capital investment, reducing GDP gains from 17.2% in partial equilibrium to 10.6% in general equilibrium. Because wages of college graduates fall, the government’s long-run tax savings from higher aggregate earnings are nearly eliminated compared to the partial-equilibrium case (from 2.5 p.p. reduction to negligible reduction). GE forces thus explain both the largest distributional benefit of the policy and its largest welfare cost.

Q7. What do robustness and extension exercises reveal about scalability and alternative policies?

The main results are robust across alternative elasticity-of-substitution parameter values for parental time and money investments, and the welfare-maximizing spending level closely tracks the benchmark $13,500 program. A scale-up extension — in which the early childhood input requires college-graduate labor — finds nearly identical long-run welfare gains but smaller first-generation gains because program costs initially rise as college labor becomes scarcer. A comparison of alternative policies (investments in older children, investment subsidies rather than direct investments, college subsidies, parenting education programs) shows that policies investing directly in young children’s skills consistently achieve larger long-run GE welfare gains relative to their short-run PE estimates than alternative designs, because the intergenerational “better-parents” mechanism is most pronounced for early childhood. Among these alternatives, using equivalent resources as a lump-sum transfer at age 16 yields only 4.1% welfare gain — less than one-third of the 12.7% from early childhood investment — confirming that in-kind investments in childhood are more efficient than cash at the same fiscal cost when parents cannot be compensated by their children.

Q8. What do the transition dynamics imply for the political economy of ECD investment?

If the policy is introduced permanently, every new cohort born after the introduction is better off (each successive generation benefits more as the parental background improves), but older generations alive at the time of introduction face net welfare losses of approximately 1–3% on average because they bear higher taxes while receiving only indirect benefits through their children. The paper calculates that if the government uses debt to smooth the financing cost over time — shifting part of the burden to future generations who will be richer — losses to initial cohorts are reduced to the point where a majority of adults would vote in favor of the policy. More than three-quarters of the long-run welfare gains are achieved within one generation of permanent policy implementation, alleviating concerns that benefits require an implausibly long time to materialize.

Key Concepts

early childhood development (ECD) investment: publicly provided direct monetary investments in children aged 0–3, modeled as a perfect substitute for parental money investments m in the CES skill-formation technology; the paper’s primary policy instrument, calibrated at $13,500 per child-year to match the Garcia et al. (2020) North Carolina RCT.
dynastic intergenerational amplification: the mechanism by which a government ECD investment raises not only the directly intervened child’s skills and income but also improves the distribution of parental skills, assets, and education for the next generation, amplifying aggregate welfare gains so that more than two-thirds of the total gain accumulates via this channel rather than the direct first-generation effect.
child-to-parent compensation constraint: the assumption that parents cannot borrow against their child’s future income or receive direct compensation from the child for parental investments; identified as the primary source of underinvestment in the model alongside borrowing constraints and return uncertainty.
skill-formation technology: a nested CES function adapted from Cunha et al. (2010) in which child skills θ’ depend on current child skills (cognitive θc and non-cognitive θnc), parental skills θ, and a CES aggregate of parental time τ and money investments m; the calibrated complementarity between time and money implies that government money investments also crowd in parental time investment.
general equilibrium skill-premium compression: the decline in the relative wage of college graduates that occurs in a GE model when the policy raises the share of college workers; the mechanism that simultaneously generates the policy’s distributional gains (reduced wage inequality) and reduces its aggregate productivity gains by approximately one-third relative to partial equilibrium.
consumption-equivalent welfare gain under the veil of ignorance: the percentage increase in steady-state consumption that makes a newborn — who does not yet know her parental background — indifferent between being born in the baseline and the policy steady state; the paper’s primary welfare measure, equal to 12.7% under the benchmark universal program.

The Nature of Long-Term Unemployment: Predictability, Heterogeneity, and Selection

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper studies the sources of long-term unemployment (LTU, defined as failing to find a job within six months) using administrative data on the universe of unemployment spells in Sweden from 1992 to 2016, merged with exceptionally rich individual characteristics including income and employment histories, employer records, asset portfolios, and IQ scores. The central question is how much of the observed decline in aggregate job-finding rates with unemployment duration reflects genuine state dependence — structural deterioration of individual prospects from being unemployed — versus dynamic selection, the mechanical compositional shift as higher-job-finding workers exit first. Using machine-learning prediction models and a complementary multiple-spell identification strategy, the paper finds that observable heterogeneity in LTU risk is substantial: the hold-out R-squared of the baseline prediction model is 15%, and rises to more than twice that value when rich administrative variables are added relative to a model using only standard socio-demographics. Applying the prediction model across durations, the paper shows that persistent heterogeneity can account for approximately 49% of the observed decline in aggregate job-finding rates over the spell (from 70% to 55% between 0 and 6 months), and potentially as much as 88% under a proportionality assumption on selection based on unobservables. In contrast, the same rich data reject the hypothesis that compositional changes in the pool of unemployed workers explain the cyclical rise in LTU risk in recessions.

In depth

Q1. What is the conceptual framework for decomposing duration dependence?

The paper develops a statistical framework that decomposes the observed change in average job-finding rates over the spell into true duration dependence — the individual-level within-spell decline — and dynamic selection, the change in pool composition as higher-job-finding workers exit first. The key insight is that dynamic selection is identified by the persistent covariance in job-finding probabilities across durations: if a worker who has a high job-finding probability early in a spell also has a high probability later, selection of such workers out of unemployment will lower the average for the remaining pool even if no individual’s rate changes. The framework shows that the hold-out R-squared of a prediction model provides a lower bound for the share of variance in outcomes that is ex ante determined, and that the cross-duration covariance of predictions identifies the persistent heterogeneity component that drives selection.

The paper further shows that combining prediction-based identification (which recovers observable plus transitory heterogeneity) with multiple-spell identification (which recovers persistent observable and unobservable heterogeneity) yields a tighter lower bound on overall heterogeneity. Observable and unobservable approaches are complementary: the multiple-spell approach identifies persistent unobservable heterogeneity that observables miss, while the observables approach captures transitory heterogeneity that changes across spells.

Q2. What is the predictive power of observable characteristics?

The baseline prediction model using standard administrative variables achieves a hold-out R-squared of 15%, measuring the share of variance in job-finding outcomes that is predictable from characteristics determined before the spell begins. This estimate is more than twice as large as a model using only basic socio-demographics (age, gender, education, marital status, citizenship, number and age of children). Prior employment history — even if available for only one or two years — is the most powerful predictor, potentially proxying for unobservable worker characteristics. Additional variables available for limited samples or years (occupation, assets, IQ, union membership) add only modest further predictive power beyond the baseline, suggesting saturation of the observable signal. The predictive power of a linear model is nearly as high as the ensemble of LASSO, gradient-boosted trees, and random forests, indicating that the gains come from data richness rather than nonlinearities exploited by machine learning algorithms.

The unobserved heterogeneity estimated using repeated unemployment spells corresponds to roughly half of the estimated observable heterogeneity. The combined lower bound on the variance that is ex ante determined is at least 19% of total variation in job-finding outcomes.

Q3. How much of duration dependence is explained by dynamic selection?

Applying the prediction model at multiple durations within the spell, the paper finds that nearly three-quarters of predictable heterogeneity is persistent over the spell of unemployment, implying that dynamic selection accounts for at least 49% of the observed aggregate decline in job-finding rates from the start to 6 months into the spell. In 2006, the aggregate 6-month job-finding rate fell from 70% at spell start to 55% at 6 months of ongoing unemployment — a 15 percentage point decline. The lower bound from persistent observable heterogeneity accounts for a decline from 70% to 62.7%, or 49% of the total observed decline. Under a proportionality assumption that unobservable selection mirrors observable selection, the paper estimates that dynamic selection can explain as much as 88% of the observed decline.

The paper also finds substantial heterogeneity in the individual-level dynamics across workers with different observable characteristics: the individual-level decline in job-finding over the spell is strongly negatively correlated with the job-finding probability at the start of the spell, meaning that workers who start with lower job-finding chances also experience stronger within-spell declines, further compressing the heterogeneity in job-finding over time.

Q4. What does the analysis imply about the proportional hazard assumption?

The paper tests and rejects the key assumption in proportional hazard models that job-finding rates decline at the same proportional rate across all workers. The individual predictions at different durations reveal significant heterogeneity in the dynamics across workers with different observable characteristics: workers do not all experience the same proportional decline with duration. This rejection is robust to corrections for sampling error and to non-parametric tests. The heterogeneity in dynamics is empirically distinguishable from the level heterogeneity in job-finding probabilities, and exists over and above what dynamic selection alone would generate.

Q5. Can compositional changes in the pool of unemployed explain LTU risk in recessions?

Despite the paper’s finding that rich observable characteristics explain substantial duration dependence over the spell, the same data reject the heterogeneity hypothesis for cyclicality: compositional changes in the observable characteristics of workers who become unemployed in recessions do not translate into higher predicted LTU risk for the average unemployed worker. The distribution of predicted job-finding risk changes over the business cycle, but the direction is not consistent with the hypothesis that recessions selectively pull in high-LTU-risk workers. Instead, unemployed workers are exposed to substantial changes in LTU risk over the business cycle that operate through within-individual declines in job-finding chances, not through composition. Recessions disproportionately hurt the job-finding prospects of workers with lower education and income, but this is a general worsening of individual prospects rather than a compositional shift in the pool.

Q6. What are the policy implications?

The policy implications differ sharply between genuine state dependence and dynamic selection as sources of LTU. If duration dependence at the individual level is large — skill atrophy, scarring, signaling stigma — early intervention is warranted to interrupt the deterioration process before it becomes irreversible. The paper’s evidence that selection is quantitatively dominant over the spell of unemployment suggests that much of the observed fall in aggregate job-finding with duration does not reflect structural deterioration of individual prospects, limiting the case for early intervention aimed at preventing skill erosion. However, the paper also finds that individual-level declines are heterogeneous and concentrated among workers with already-low job-finding chances, suggesting that targeted risk-profiling — already used by Public Employment Services in many countries including Sweden — is well motivated. The separate finding that recessions generate genuine within-individual worsening of prospects (rather than compositional shift) implies that countercyclical support is warranted on different grounds.

Key Concepts

dynamic selection: the mechanical change in the composition of the unemployment pool as workers with higher job-finding probabilities exit unemployment first, leaving an increasingly low-job-finding-probability remainder; identified in the paper as the dominant driver of the observed aggregate decline in job-finding rates with unemployment duration, accounting for at least 49% and potentially up to 88% of the observed decline.
genuine state dependence (true duration dependence): the within-individual structural deterioration of a worker’s job-finding rate from the experience of unemployment itself — skill erosion, employer stigma signaling — as distinct from compositional selection; the paper finds this is a minor contributor to the observed aggregate duration dependence pattern in Sweden.
persistent heterogeneity: the covariance of individual job-finding probabilities across different durations (or spell cohorts); the component of overall heterogeneity that drives dynamic selection, identified empirically by the cross-duration covariance of prediction model outputs in hold-out samples.
LTU risk profiling: the practice of predicting workers’ probability of becoming long-term unemployed at spell entry using observable characteristics, to target active labor market programs; the paper provides the statistical foundation and quantifies the gains from richer administrative data relative to standard survey-based characteristics.

The price of intelligence: How should socially-minded firms price and deploy AI?

Mon, 01 Jan 0001 00:00:00 +0000

Leading AI firms such as OpenAI and Anthropic publicly claim dual mandates of profit and social welfare, raising the question of whether—and how—a social mandate should change their pricing and deployment decisions. This paper provides a framework to answer this question, deriving a Modified Lerner Rule for socially minded AI firms that extends the standard profit-maximizing Lerner Rule to incorporate incentives for aggregate efficiency, distributional concerns, and labor market stability. Using U.S. data on 525 detailed occupations, the paper evaluates optimal pricing and deployment paths for an AI capable of replacing human labor in each job at 50% of the cost. The main finding is that a welfarist firm (one that values profits and social welfare) should price closer to marginal cost because, for the jobs considered, efficiency gains outweigh distributional concerns—AI does not primarily displace low-income workers. A conservative firm focused on labor market stability should price above the profit-maximizing level in the short run, but not in the long run. The paper concludes that the most pro-social course of action for AI firms with market power is to refrain from exercising that power, and that proposals to tax AI to protect labor markets miss the counteracting role of market power.

In depth

Q1. What is the Modified Lerner Rule and what motives does it capture?

The Modified Lerner Rule states (P − MC)/P = M/ε, where ε is the demand elasticity and M is a modifier that summarizes the motives of the socially minded firm; M = 1 corresponds to the standard profit-maximizing Lerner Rule. The modifier M reflects four distinct considerations: (1) profit motives push M toward 1; (2) aggregate efficiency considerations push M toward 0 (marginal-cost pricing, which maximizes the “size of the pie”); (3) distributional concerns (who benefits from AI) can be positive or negative depending on whether AI substitutes for high- or low-income workers; and (4) the incentive to minimize labor market disruptions pushes M above 1 in the short run, because the cost of labor disruption is higher while workers are still adjusting, but not in the long run. The formula is derived in a general equilibrium model where the AI firm has a monopoly over an AI capable of replicating human skills.

Q2. What does the welfarist case imply for pricing?

A firm that values both profits and aggregate social welfare should price closer to marginal cost than the profit-maximizing firm, because for all 525 occupations considered, the aggregate efficiency gains from AI adoption outweigh the distributional costs. This finding reflects the structure of AI’s labor market effects: since AI does not primarily displace low-income workers in the US occupational data used, distributional concerns do not push toward restricting AI access. The welfarist firm therefore faces a dominant efficiency motive to expand access by pricing down toward marginal cost, accepting lower profits in exchange for greater welfare gains from AI adoption.

Q3. What does the conservative case imply?

A firm focused solely on labor market stability should price above the profit-maximizing level in the short run, because restricting AI deployment reduces the speed of worker displacement; but this above-profit-maximizing pricing is optimal only temporarily, and converges toward profit-maximizing pricing in the long run as workers adjust. The intuition is that the cost of disrupting the labor market is highest when workers have not yet adjusted—their human capital is not yet redeployed—so a conservative firm acts as a gradual deployer. This conservative pricing is distinct from the welfarist case: the conservative motive restricts access more than a welfarist mandate, since it is willing to sacrifice efficiency to slow disruption.

Q4. Why does the paper argue against taxing AI?

The paper argues that proposals to tax AI firms to protect workers from displacement overlook the fact that AI firms may already exercise significant market power, which protects workers by restricting AI supply below the efficient level. Adding a tax on top of an already-restricted supply would harm consumers (who face high AI prices and limited access) without providing meaningful additional protection for workers (since output is already suppressed by market power). The paper’s analysis implies that the first-order social priority is to have AI firms refrain from exercising their market power—by pricing closer to marginal cost—rather than further restricting supply through taxation.

Key concepts

Modified Lerner Rule : (P − MC)/P = M/ε, where M captures a socially minded firm’s weighting of profit, aggregate efficiency, distributional, and stability motives; the paper’s key pricing formula, derived from a GE model with a monopoly AI firm.

welfarist vs. conservative firm : two polar cases: the welfarist firm maximizes a weighted sum of profits and aggregate welfare (implying near-marginal-cost pricing); the conservative firm prioritizes labor market stability (implying above-profit-maximizing pricing in the short run to slow displacement).

labor disruption cost : the welfare cost to workers of being displaced by AI, which is higher in the short run when workers must reallocate across jobs or sectors and lower in the long run after adjustment; the paper’s formal treatment of this cost motivates the conservative firm’s gradual deployment strategy.

The Role of Remittances and FDI for the Current Account: The Case of Cambodia

Mon, 01 Jan 0001 00:00:00 +0000

This paper builds and estimates a small open economy real-business-cycle (SOE-RBC) model for Cambodia augmented with two non-standard external-sector shocks — net unilateral transfers (remittances and government grants) and net foreign direct investment — in addition to the standard shocks of transitory productivity, permanent productivity, and world interest rate. Estimated on annual Cambodian data over 1993–2018 using Bayesian Markov Chain Monte Carlo, the model shows that FDI and unilateral transfers together account for approximately 50 percent of the variance in Cambodia’s current account-to-output ratio (approximately 27 percent for FDI and 23 percent for unilateral transfers), substantially exceeding the combined contribution of productivity and world-interest-rate shocks. The estimated model tracks the observed current account path with a correlation of 0.93 and a measurement error of only 4.1 percent, compared to a measurement error of 58 percent and correlation of 0.80 when FDI and unilateral transfers are omitted. Applied to the COVID-19 scenario (1 percentage point drop in transitory productivity, 2 percentage point drop in the FDI-to-output ratio, and 8 percentage point drop in unilateral transfers-to-output), the model predicts the current account-to-output ratio will fall to approximately −14 percent in 2020, closely matching the World Bank’s forecast of −14.1 percent.

In depth

Q1. Why does a standard SOE-RBC model fail to explain Cambodia’s current account, and what does the paper add?

A standard SOE-RBC model with only transitory productivity, permanent productivity, and world interest rate shocks leaves 58 percent of the variance in Cambodia’s current account-to-output ratio unexplained and achieves only a 0.80 correlation with the observed series, because it omits two empirically large and persistent external financing flows — FDI (which averaged around 11 percent of GDP over the sample) and net unilateral transfers (remittances and grants) — that directly affect both the capital account and saving behavior in a developing country with shallow domestic capital markets. The paper follows Chang and Fernández (2013), who establish that world interest rate and transitory productivity shocks matter more than permanent productivity for business cycles in emerging markets, and extends that framework specifically for a low-income developing economy where external capital inflows are a primary driver of investment and consumption rather than an auxiliary shock. FDI is modeled as an exogenous shock to the net-FDI-to-output ratio with its own AR(1) process, and it enters the model with a direct spillover onto permanent productivity growth (parameter γ, with a posterior mean of 0.08), capturing the technology-diffusion channel of FDI.

Q2. What is the model structure and what shocks does it incorporate?

The model is a two-good SOE-RBC framework with Cobb-Douglas production (F = a_t K^α h^(1-α)) where output growth is driven by a stationary transitory productivity level a_t and a non-stationary permanent productivity trend g_t; households maximize utility over consumption and leisure with CRRA preferences (σ = 2) and discount factor β = 0.96, subject to a budget constraint linking consumption, capital accumulation (with quadratic adjustment costs, calibrated posterior mean φ = 15.76), foreign borrowing, and two external inflow variables: net unilateral transfers (NT) and net FDI. The world interest rate R_t is the product of the world risk-free rate R*_t and a country-specific spread S_t that depends negatively on expected future productivity, introducing an endogenous risk-premium channel. The working-capital requirement θ (posterior mean 0.50) requires firms to pre-finance a fraction of the wage bill at the current period interest rate, creating a financial-accelerator-like amplification of world interest rate shocks. The complete list of five structural shocks is: transitory productivity (σ_a), permanent productivity growth (σ_g), world interest rate (σ_R), unilateral transfers (σ_nt), and FDI (σ_fdi). The model is estimated in log-differences of Y, C, and I and in levels of TB/Y, CA/Y, NT/Y, and FDI/Y.

Q3. What does the variance decomposition show and how does it allocate current account variation across shocks?

Table 3 shows that for the current account-to-output ratio, FDI and unilateral transfers together account for approximately 50 percent of variance (~27 percent for FDI and ~23 percent for unilateral transfers), while transitory productivity and world interest rate shocks together account for the bulk of the remainder; permanent productivity growth (σ_g) contributes negligibly to CA/Y variance; the measurement error in CA/Y (σ_CA) is approximately 4.12 percent, indicating the model fits the current account data very closely. The paper notes that “the shocks of world interest rate and transitory productivity play more important roles than the shock of permanent productivity growth in explaining macroeconomic fluctuations,” consistent with Chang and Fernández (2013) and the standard SOE-RBC finding. For output, consumption, and investment, transitory productivity and world interest rate shocks dominate (each accounting for roughly 30–50 percent of variance across the macro aggregates). The FDI shock plays a comparable role to the interest rate shock for output fluctuations, reflecting that FDI inflows to Cambodia are large enough to function as a de facto external financing channel. A model without FDI and transfers (Appendix Table A1) shows that measurement error in CA/Y rises to 58.31 percent, confirming the quantitative importance of the two additional shocks.

Q4. How do impulse responses to the five shocks illuminate the current account dynamics?

A positive transitory productivity shock of 1 percent causes output, consumption, and investment to expand on impact, but the expansion in domestic absorption (C + I) exceeds that of output because the persistence of the shock (ρ_a = 0.91) leads consumption-smoothing households to borrow against higher expected future income, producing a current account deterioration of approximately 1 percentage point on impact — consistent with a temporary boom financed by current account deficits. A positive world interest rate shock reduces consumption and investment by roughly 1 percentage point on impact as borrowing costs rise and firms reduce the wage-bill they pre-finance; trade balance and current account improve initially (~1 percentage point) as domestic absorption falls more than output, but then deteriorate as the higher interest payment on the accumulated debt stock (with persistence ρ_R = 0.87) pushes the current account below its steady state after period 1. A positive FDI shock raises consumption and investment while keeping output unchanged on impact, deteriorating the current account by approximately 1 percentage point; because FDI raises permanent productivity growth (γ > 0), the accumulation of capital eventually raises output so that the current account gradually recovers toward its steady state, but domestic absorption remains above output due to the joint persistence of FDI and productivity (ρ_fdi = 0.87, ρ_g = 0.72). A positive unilateral transfer shock has a negligible impact on consumption, investment, and output (magnitudes below 0.06 percent) because the shock is low-persistence (ρ_nt = 0.15) and consumption-smoothing households save most of the windfall; however, the transfer improves the current account by its full magnitude (~1 percentage point) essentially one-for-one by definition.

Q5. How well does the model fit the historical current account trajectory and what does the shock decomposition reveal about phases of Cambodian development?

The estimated model produces a time-series of fitted current account-to-output ratios with a 0.93 correlation with the observed data and only 4.1 percent measurement error; the model initially over-predicts by about 5 percentage points (due to uncertainty about initial conditions), but then closely tracks the observed trajectory of deficits averaging roughly −11 percent of GDP from the mid-1990s through 2018. The shock decomposition (Figure 5) shows that FDI and unilateral transfers dominate the current account in the earlier part of the sample (mid-1990s to mid-2000s), while transitory productivity shocks contribute more in the later period (post-2010) — a pattern the authors interpret as consistent with the stylized fact that capital inflows drive growth in early-stage development, while productivity improvements become the primary driver as the economy matures. The world interest rate shock contributes relatively little throughout the sample, suggesting that Cambodia’s current account dynamics are primarily driven by supply-side (FDI-productivity linkages) and income-transfer channels rather than by global borrowing-cost variation.

Q6. What does the COVID-19 scenario exercise predict and what is the model’s forecasting accuracy?

Combining simultaneous shocks calibrated to IMF and World Bank 2020 projections for Cambodia — a 1-percentage-point drop in transitory productivity (consistent with a World Bank projection of 1 percent GDP contraction), a 2-percentage-point drop in the FDI-to-output ratio (World Bank 2020 forecast), and an 8-percentage-point drop in unilateral transfers-to-output (reflecting IMF’s Sayeh and Chami 2020 estimate of 20 percent or more remittance decline plus EU EBA trade preference suspension) — the model predicts the current account-to-output ratio will fall to −14 percent in 2020, essentially identical to the World Bank’s external forecast of −14.1 percent. The three shocks propagate differently: the productivity drop temporarily improves the current account by approximately 2 percentage points as domestic absorption contracts more than output, but then worsens it in 2021 as output falls and consumption reverts; the FDI drop similarly has a transient current-account-improving effect before the productivity-growth channel drags output down; the transfer drop has an essentially one-to-one negative effect on the current account (8 percentage points lower) that quickly reverses. The combined prediction of −14 percent, coinciding with the World Bank’s external forecast, is presented as validation of the model’s out-of-sample performance.

Q7. What is the role of the endogenous vs. exogenous discount factor, and why does it matter?

The paper tests whether specifying the discount factor as endogenous (depending on lagged consumption as in Schmitt-Grohé and Uribe 2003, to ensure stationarity of net foreign assets) versus exogenous materially affects the current account dynamics, and finds it does not — the discount factor specification is immaterial for explaining Cambodian current account fluctuations because FDI and unilateral transfers, which dominate the variance decomposition, are exogenous to the household’s saving-patience parameter that the discount factor governs. This result simplifies model specification choices for similar small open economy applications: the patience assumption matters for long-run external position dynamics in models where standard RBC shocks dominate, but loses its influence when there are large direct external financing flows. The finding extends to the working capital parameter θ, which also does not significantly alter the current account dynamics despite affecting the transmission of world interest rate shocks to investment and output.

Q8. How does this paper contribute relative to existing SOE-RBC literature and what are its limitations?

The key contribution relative to Aguiar and Gopinath (2007), García-Cicco et al. (2010), and Chang and Fernández (2013) is to demonstrate quantitatively that for very low-income developing countries where FDI and remittances are large relative to GDP, the standard SOE-RBC shock triplet (transitory productivity + permanent productivity + world interest rate) is misspecified and will systematically fail to fit current account data; adding the two external financing shocks reduces the CA/Y measurement error from 58 percent to 4 percent, a quantitatively enormous improvement. A limitation noted by the paper is that the working paper version (MPRA 108489) covers only Cambodia over 1993–2018, so cross-country generalizability to other developing economies with large FDI and remittance flows (e.g., Bangladesh, Nepal, Vietnam) is not formally established; the model is also log-linearized around the steady state, which may miss non-linear dynamics during extreme events like the COVID-19 shock. Additionally, FDI is treated as an exogenous process despite the literature on FDI determinants suggesting it responds endogenously to domestic institutional quality, trade policy, and productivity trends.

Key Concepts

SOE-RBC (small open economy real-business-cycle) model : a dynamic stochastic general equilibrium model in which a small economy takes world prices and interest rates as given; households maximize lifetime utility by choosing consumption, investment, and foreign borrowing; the current account emerges as the net change in the foreign debt position; log-linearized around the steady state and solved via perturbation methods.

Bayesian Markov Chain Monte Carlo (MCMC) estimation : a method for estimating the posterior distribution of structural parameters by combining prior beliefs with the likelihood of observing the data; the paper uses prior distributions from Chang and Fernández (2013) for most parameters and Cambodian data for the AR(1) coefficients of the new shocks; parameters with posterior means significantly different from priors (at the 10 percent level) are highlighted in Table 2.

variance decomposition : the share of variance in each endogenous variable attributable to each exogenous shock at the business-cycle horizon; computed from the estimated model’s spectral density; in this paper, used to quantify the relative importance of FDI and unilateral transfers relative to productivity and interest rate shocks for the current account.

unilateral transfers (NT) : net flows of income from abroad that do not require repayment, including workers’ remittances from Cambodian migrants abroad and official government grants from donor countries; modeled in the paper as an exogenous shock to the NT-to-output ratio with AR(1) persistence ρ_nt = 0.15 (low persistence).

FDI productivity spillover (γ) : the elasticity of permanent productivity growth with respect to the FDI-to-output ratio; estimated to be 0.08 (posterior mean), reflecting the hypothesis that FDI brings technology transfer and know-how that raises Cambodia’s total factor productivity trend; the FDI shock thus affects the current account both directly (through the capital account) and indirectly (through the productivity channel).

working capital requirement (θ) : the fraction of the wage bill that firms must borrow in advance at the current period’s interest rate; estimated at 0.50 (posterior mean), implying that world interest rate shocks are amplified through a financial-accelerator mechanism in which higher borrowing costs reduce labour demand and output, beyond the standard intertemporal substitution channel.

country-specific spread (S_t) : the risk premium Cambodia pays above the world risk-free rate, modeled as a decreasing function of expected future productivity; captures the tendency of developing countries to face higher borrowing costs when growth prospects weaken, creating a pro-cyclical external financing condition.

Turbulent business cycles

Mon, 01 Jan 0001 00:00:00 +0000

Firm-level evidence shows that recessions are characterized not just by aggregate downturns but by a sharp rise in turbulence—a reshuffling of firms’ productivity rankings in which high-productivity firms are less likely to maintain their relative standing. This paper documents four stylized facts about the macroeconomic and cross-sectional effects of turbulence (measured as one minus the Spearman rank correlation of firm-level TFP between adjacent years in Compustat data): turbulence is countercyclical; increases in turbulence reallocate labor and capital from high- to low-productivity firms; turbulence is negatively correlated with aggregate manufacturing TFP and the aggregate stock market; and an increase in turbulence is associated with persistent declines in real GDP, consumption, investment, and employment. To explain the mechanism, the authors build a real business cycle model with heterogeneous firms and financial frictions: when turbulence rises, high-productivity firms’ expected equity values fall because their productivity is less likely to persist, which tightens their borrowing constraints relative to low-productivity firms, inducing reallocation that reduces aggregate TFP. Crucially, turbulence differs from uncertainty shocks because it changes both the conditional mean and variance of the firm productivity distribution, enabling it to generate synchronized recessions with declining aggregate activity.

In depth

Q1. How is turbulence measured and how does it differ from uncertainty?

Turbulence is measured as one minus the Spearman rank correlation (ρₜ) of firm-level total factor productivity between adjacent years using Compustat data; a low correlation indicates more churning of productivity rankings, so 1 − ρₜ rises in recessions. The authors use an instrumental variable approach to correct for attenuation bias from measurement error in firm-level TFP, following Bloom et al. (2018) for the baseline construction. The conceptual distinction from uncertainty is that uncertainty shocks only raise the conditional variance of the productivity distribution while leaving the conditional mean unchanged. A turbulence shock changes both: it makes the conditional mean of future productivity lower for currently high-productivity firms and higher for currently low-productivity firms, thereby inducing reallocation from high to low producers and generating first-moment effects on aggregate output that pure uncertainty shocks cannot produce.

Q2. What are the empirical facts about turbulence, and how are they established?

The paper documents four facts using a vector autoregression with turbulence orthogonalized against uncertainty and other aggregate shocks: (1) turbulence is countercyclical, rising sharply in recessions; (2) an increase in turbulence reallocates labor and capital from high- to low-productivity firms, an effect that is amplified by financing constraints; (3) turbulence is negatively correlated with aggregate manufacturing TFP and aggregate stock market value; and (4) turbulence shocks generate persistent declines in GDP, consumption, investment, and employment. The reallocation effects in fact (2) remain significant after controlling for the confounding effects of recessions and uncertainty, and the amplification by financing constraints is separately identified.

Q3. What is the model mechanism through which turbulence drives recessions?

In the model, firms produce using capital and labor subject to idiosyncratic productivity and borrowing constraints tied to expected equity value; when turbulence rises, high-productivity firms are less likely to remain productive, reducing their expected equity value and tightening their borrowing constraints relative to low-productivity firms. This differential tightening induces reallocation of labor and capital toward low-productivity firms, reducing aggregate TFP. The feedback through equity values and collateral constraints amplifies the reallocation and generates aggregate-level recessions with synchronized declines in activity. The mechanism is distinct from models in which all firms face symmetric uncertainty shocks: turbulence creates differential effects by firm productivity level.

Q4. How does the model match the observed macroeconomic dynamics?

The calibrated model replicates the empirical dynamics: it generates the observed reallocation from high- to low-productivity firms, declines in aggregate TFP and stock market value, and persistent contractions in GDP, consumption, investment, and employment following a turbulence shock. The financial frictions play a quantitatively important role in amplifying the reallocation effects, consistent with the empirical finding that financing constraints amplify the cross-sectional reallocation documented in fact (2).

Key concepts

turbulence : the rate of churning in firms’ productivity rankings, measured as one minus the Spearman rank correlation of firm-level TFP between adjacent years; distinct from uncertainty in that it changes both the conditional mean and variance of the productivity distribution.

reallocation channel : the mechanism through which turbulence depresses aggregate TFP by shifting labor and capital from high- to low-productivity firms, amplified by tighter credit constraints on high-productivity firms whose expected equity value falls when productivity persistence declines.

Unpacking Aggregate Welfare in a Spatial Economy

Mon, 01 Jan 0001 00:00:00 +0000

What's driving the decline in entrepreneurship?

Mon, 01 Jan 0001 00:00:00 +0000

The entrepreneurship rate in the United States—defined as the share of the labor force who own and actively manage a business with at least ten employees—declined by 26% between 1987 and 2015, a decline mirrored in the firm entry rate and not explained by compositional changes in the economy or driven by a small number of sectors. This paper addresses what caused this broad-based decline using Current Population Survey data, two new empirical facts, and a dynamic general equilibrium model of occupational choice. The first new fact is that the decline was larger for higher-education groups (35% for those with more than a college degree versus 2.4% for those without a high-school diploma), indicating that the driving force is not skill-neutral. The second new fact is that the size distribution of entrepreneur firms has been stable, so the entrepreneurship decline represents a shrinkage of the entrepreneurial sector relative to the economy. Estimating the contribution of four candidate explanations—skill-biased technical change (SBTC), increasing regulation, technology-driven increases in fixed and entry costs, and technology-driven productivity advantages for large firms—the paper finds that increasing entry costs account for most of the decline in both the entrepreneurship share and the firm entry rate, with empirical evidence pointing to both regulation and technology as sources of these higher costs.

In depth

Q1. What does the model of occupational choice capture, and how are the explanations identified?

The dynamic general equilibrium model allows individuals to choose between working as an employee (earning wages) and being an entrepreneur (paying fixed and entry costs, then operating a firm); the model generates predictions about the entrepreneurship rate, firm entry rate, and the distribution of entrepreneur firm sizes across groups, which the data discipline. By requiring the model to match changes in entrepreneurship along multiple dimensions—including the education-gradient fact and the stable size distribution—the author can separately identify the contribution of each candidate mechanism. SBTC operates through wages (raising opportunity cost of entrepreneurship for skilled workers); entry-cost increases reduce the number of new entrepreneurs regardless of skill; productivity advantages for large firms shift the size distribution; and regulation/technology-driven fixed-cost increases reduce incumbent-entrepreneur survival.

Q2. Why does skill-biased technical change fail to explain the level decline?

SBTC raises wages for high-skill workers, which could in principle explain why fewer of them choose entrepreneurship; and indeed SBTC is found to have tilted entrepreneurship toward less-educated people. However, SBTC cannot explain the decline in the aggregate entrepreneurship rate because: it does not reduce the incentive to be an entrepreneur for lower-skill workers (who are relatively unaffected), and the stable size distribution of entrepreneur firms is inconsistent with SBTC (which would tend to shift composition rather than reduce overall entrepreneurship). The model confirms that SBTC explains the education gradient but contributes little to the overall level decline.

Q3. What is the role of entry costs, and what drives them?

Increasing entry costs are found to explain most of the decline in the share of people who are entrepreneurs and most of the decline in the firm entry rate; the data also reject the hypothesis that entry-cost increases were accompanied by large changes in entrepreneur firm size, consistent with the observed stability of the size distribution. Empirical evidence suggests two sources of higher entry costs: increasing regulation (occupational licensing, tax-code complexity, zoning restrictions) and technology changes that increase the fixed investments required to operate (e.g., adoption of IT systems). The paper does not fully separate these two sources but presents evidence consistent with both operating simultaneously.

Q4. What is the role of increasing productivity of large firms?

Increasing productivity of large, non-entrepreneurial (e.g., publicly listed) firms matters little for the entrepreneurship rate or the firm entry rate, but has driven most of the reallocation of labor away from entrepreneur businesses. This is because the productivity advantage of large firms shifts the scale of production without necessarily changing who becomes an entrepreneur, largely leaving the extensive margin of entrepreneurship intact while reducing the share of aggregate economic activity attributable to the entrepreneurial sector.

Key concepts

entrepreneurship rate : the share of the labor force who own and actively manage a business with at least ten employees, the paper’s main measure of entrepreneurship, which declined 26% from 1987 to 2015 in the CPS data.

entry costs : the one-time costs required to establish a new entrepreneurial business; the paper finds these rose over the sample period due to both regulation and technology, and identifies them as the primary driver of the entrepreneurship decline.