Heterogeneous-Agent-Macro | Macro Paper Warehouse

A Heterogeneous Agent Model of Energy Consumption and Energy Conservation

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

This paper embeds energy in both the consumption and production sides of a tractable New Keynesian model with heterogeneous agents, unemployment risk, and nominal asset holdings, adding an energy conservation capital margin as a response to rising energy prices. Energy price shocks sharpen the inflation-output trade-off facing the central bank, because containing inflation requires raising rates while the supply-driven nature of the shock already reduces welfare. The paper finds that a weaker-than-standard interest rate response is welfare-improving for agents despite generating higher inflation, as the reduction in employment and output losses outweighs the cost of elevated prices. The Ramsey-optimal policy features a sharp initial rate increase followed by a subsequent decline, reflecting standard front-loaded tightening logic modulated by heterogeneous welfare implications of unemployment risk.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is energy conservation capital and why does it matter?

Energy conservation capital is a durable investment that reduces future household energy demand; it adds a savings margin absent from standard energy macro models and interacts with nominal asset returns in the HANK environment. When energy prices rise, households can respond not only by substituting toward non-energy consumption but also by investing in conservation capital to lower future energy costs. Through the HANK asset-holding channel, this margin interacts with monetary policy: rate increases that reduce asset returns also affect the return to conservation investment, creating a novel interaction between energy and monetary policy.

Q2. Why does a weaker policy response improve welfare?

Because the energy price shock is supply-side, the inflation it generates cannot be eliminated without destroying output and employment, and in the heterogeneous-agent setting the employment destruction from aggressive rate increases falls disproportionately on lower-wealth households — making the welfare cost of tightening exceed the welfare cost of allowing higher inflation. The paper’s finding that a weaker policy response is welfare-superior reflects a standard HANK result: unemployment risk is asymmetrically costly for agents with limited asset buffers, so policies that prioritize employment preservation over inflation stabilization can be socially optimal even when they generate above-target inflation.

Key concepts

energy conservation capital : durable investment that reduces future household energy demand; the margin through which households and firms in this model respond to energy price increases beyond immediate consumption substitution.

supply-side monetary policy trade-off : the intensified tension between inflation stabilization and output stabilization when inflation originates from a cost-push supply shock; a weaker policy response may dominate in welfare terms when unemployment costs fall disproportionately on lower-wealth agents.

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.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

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.

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.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

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.

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.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

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.

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.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

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.