E23 | Macro Paper Warehouse

Bridging micro and macro production functions: The fiscal multiplier of infrastructure investment

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

Layer 1 — Overview

Research Question

This paper investigates the fiscal multiplier of infrastructure investment, specifically by incorporating firm-level investment decisions — a dimension absent from prior literature. The central analytical challenge is bridging the micro (firm-level) and macro (state-level) production functions for infrastructure, given that public capital is non-rivalrous: it can be used simultaneously by all firms without being depleted. The paper demonstrates that this non-rivalry generates a systematic discrepancy between firm-level and aggregate-level estimates of the elasticity of substitution between private and public capital, and it shows how this discrepancy shapes the magnitude of the fiscal multiplier.

Data and Methodology

The authors build and estimate a heterogeneous-firm general equilibrium model. Firms operate a constant-elasticity-of-substitution (CES) production function using private capital, non-rivalrous public capital (infrastructure), and labor. Firms are subject to idiosyncratic productivity shocks and make lumpy investment decisions subject to both fixed and convex capital adjustment costs, following Cooper and Haltiwanger (2006) and Winberry (2021). The economy has two regions — one with poor infrastructure and one with good infrastructure — motivated by the near-invariant cross-state distribution of infrastructure spending observed in U.S. data.

The model is estimated via an extended Simulated Method of Moments (SMM) that treats market clearing prices as additional parameters estimated simultaneously with structural parameters, reducing computational cost relative to standard GE estimation. Estimation uses a multi-block Metropolis-Hastings algorithm. Target moments include lumpy investment fraction (0.14, from Zwick and Mahon 2017), average investment-to-capital ratio (0.10), standard deviation of i/k (0.16), private-to-infrastructure capital ratio (0.75, from BEA), high-infrastructure region’s private capital share (0.83, from Census BDS), and total working hours (0.33).

The identification of the key parameter — the firm-level elasticity of substitution between private and public capital (λ) — comes from the relative size of private capital stocks across the two infrastructure groups: under greater complementarity, regions with more infrastructure should hold relatively more private capital.

External validation is provided by estimating the state-level elasticity from the model’s simulated data using a nonlinear least squares method following An et al. (2019), and comparing it to empirical state-level estimates from actual U.S. state data.

Main Findings with Quantitative Magnitudes

Firm-level vs. aggregate-level elasticity gap. The estimated firm-level elasticity of substitution is λ = 1.185, implying gross substitutability between private and public capital at the firm level. The state-level elasticity implied by the same model is 0.48 (or 0.35 in a decreasing-returns-to-scale specification), implying gross complementarity. The empirical state-level counterpart estimated from actual U.S. data is 0.445. The paper proves theoretically (Proposition 1) that, given non-rivalry and under mild conditions, firm-level gross substitutability implies aggregate-level gross complementarity. Proposition 2 further shows that this same mechanism micro-founds the increasing-returns-to-scale assumption in Baxter and King’s (1993) Cobb-Douglas aggregate production function.
Fiscal multiplier (baseline, 2-year horizon). The aggregate output multiplier over a 2-year horizon in the heterogeneous-firm general equilibrium model is 1.088 in response to a one-time unexpected infrastructure spending shock equal to 1% of steady-state GDP, financed by a lump-sum tax. The corresponding partial-equilibrium output multiplier (holding prices fixed at steady state) is 1.858; the gap reflects crowding out of private investment induced by the general equilibrium interest rate response. In the baseline, the interest rate rises by 0.39% after the shock; the investment multiplier is -0.043.
Comparison with representative-agent model. When the same implied returns-to-scale parameters are used in a representative-agent model (following Baxter and King 1993), the output multiplier is 0.991 and the investment multiplier is -0.157, both substantially lower than the heterogeneous-firm baseline. The key mechanism: under convex adjustment costs, the Jensen’s inequality effect implies that heterogeneous firms face a greater average adjustment burden than the representative firm, making their investment less responsive to the general equilibrium crowding-out pressure.
Sensitivity to elasticity of substitution. Across the heterogeneous-firm model: at λ = 3 (high substitutability), the output multiplier falls to 0.672; at λ = 0.5 (complementarity), it rises to 1.364. The multiplier is significantly more sensitive to λ in the heterogeneous-firm model than in the representative-agent model, because non-rivalry amplifies the effect of any given elasticity value through each firm’s production function.
Cross-state distribution of gains. Under the baseline spending allocation (81% to Good states, 19% to Poor states), per $1 of infrastructure spending, Good states receive $1.072 of the $1.088 total output gain, while Poor states receive only $0.016. In a counterfactual with equal spending across states, the total output multiplier falls to 0.873, Good states’ output multiplier falls to 0.810, and Poor states’ output multiplier rises to approximately 0.062 (about four times the baseline level of 0.016). This quantifies a sharp efficiency-equality trade-off in the allocation of infrastructure investment.
Employment and earnings effects. Compared to steady state, the baseline fiscal shock produces an average annual increase of 0.304% in employment and 0.389% in wages, yielding a $0.713 increase in earnings and a $0.148 increase in consumption per $1 of fiscal spending in general equilibrium. In partial equilibrium (no price changes), earnings increase by $1.294 and consumption by $0.605 per $1 spent.

Scope Conditions

Results are conditional on: (i) lump-sum tax financing of the fiscal shock; (ii) a one-time unexpected (MIT) shock with no persistence; (iii) a closed-economy framework with endogenous real interest rate; (iv) the estimated two-region structure calibrated to U.S. state-level infrastructure data; (v) firm-level investment dynamics calibrated to Compustat and BDS moments. The authors note that incorporating time-to-build assumptions (tested in an appendix) reduces the aggregate fiscal multiplier, consistent with Ramey (2020).

Layer 2 — Q&A

Q1: What is the core theoretical result connecting firm-level and aggregate-level elasticities, and what is the intuition?

A: Proposition 1 proves that, given non-rivalrous public capital and mild data conditions (at least one firm has private capital below total infrastructure, and aggregate private capital exceeds total infrastructure), if the firm-level elasticity of substitution λ ≥ 1 (gross substitutes), then the aggregate-level elasticity ξ < 1 (gross complements). The intuition is that a marginal increase in public capital raises the marginal product of private capital for every firm simultaneously due to non-rivalry; the sum of these MPK gains across all firms exceeds any single firm’s gain. To represent this amplified benefit within an aggregate production function, a stronger complementarity is required than what any single firm faces. Put differently, non-rivalry means aggregate private and public capital “look” more complementary than they truly are at the firm level.

Q2: How does non-rivalry micro-found the Baxter-King aggregate production function?

A: Proposition 2 shows that if firms use a CES production function with gross substitutability (λ ≥ 1) and non-rivalrous public capital, then fitting aggregate output with a Cobb-Douglas production function (as in Baxter and King 1993, H(K,N,L) = zK^α L^{1-α} N^ζ) yields ζ > 0, implying increasing returns to scale (IRS). This is the paper’s micro-foundation for a widely-used but previously ad hoc assumption in the macro-fiscal literature. The corollary states that both gross complementarity in the aggregate CES function and IRS in the aggregate Cobb-Douglas follow from the same non-rivalry mechanism at the firm level.

Q3: Why does the heterogeneous-firm model produce a higher output multiplier than the representative-agent model?

A: Two mechanisms drive the difference. First, due to Jensen’s inequality and the convexity of adjustment costs, heterogeneous firms face a higher average adjustment burden than the representative (average) firm; this means heterogeneous firms are less responsive to interest rate changes that crowd out investment. The investment multiplier is -0.043 in the heterogeneous-agent baseline versus -0.157 in the representative-agent model. Second, the fixed adjustment cost (present in the baseline but absent from the representative-agent model) further dampens investment sensitivity via the extensive margin. Because less private investment is crowded out, more of the direct output boost from infrastructure spending survives into the aggregate multiplier, yielding 1.088 versus 0.991.

Q4: What is the novel estimation procedure and why is it necessary?

A: Standard SMM applied to GE models requires solving for market-clearing prices for every candidate parameter vector, creating a nested optimization loop that is computationally prohibitive. The authors extend SMM by treating market-clearing prices (wage w and marginal utility of consumption p) as additional parameters and appending market-clearing conditions as additional target moments — effectively requiring those moments to equal zero. A multi-block Metropolis-Hastings algorithm jointly draws from the price block and the parameter block. This approach generates posterior draws that simultaneously satisfy market clearing and fit empirical moments, without the inner loop. The resulting market-clearing accuracy is e^{-4} at the posterior mean.

Q5: How is the firm-level elasticity of substitution (λ) identified from the data?

A: λ is identified from the cross-state difference in private capital stocks between high- and low-infrastructure regions. Under the model, if private and public capital are more complementary (lower λ), high-infrastructure regions should attract relatively more private capital. The data moment used is the Good region’s share of aggregate private capital (0.83 from Census BDS data). This identification strategy is analogous to Bartik-instrument approaches in the empirical literature, where a parameter governing cross-state sensitivity to aggregate shocks is identified from cross-sectional variation.

Q6: How is the model validated externally?

A: The authors compute the state-level elasticity from the estimated model by fixing firm-level parameters and re-estimating only the elasticity and regional productivity from the model’s simulated state-level data, using the same NLLS estimator as An et al. (2019). The model-implied state-level elasticity is 0.349 (DRS specification) or 0.482 (CRS specification). The empirical estimate from actual U.S. state-level data following the same estimator is 0.445. Both indicate gross complementarity at the state level, consistent with the theoretical prediction. This external validation is not used in the estimation itself, providing an independent check.

Q7: What are the roles of extensive vs. intensive investment margins in the crowding-out effect?

A: Table 9 decomposes the investment multiplier of -0.043 by investment margin. When only the extensive margin (the discrete decision of whether to invest) is allowed to respond, the investment multiplier is -0.032 — approximately 74% of the baseline crowding-out effect. When only the intensive margin (investment size conditional on adjusting) responds, the multiplier is -0.011 — about 25% of the total. Thus the extensive margin is the dominant channel through which higher interest rates crowd out private investment. When both margins are held fixed, the output multiplier rises to 1.139, confirming that investment crowding-out reduces the output multiplier by about 0.05.

Q8: How does the elasticity of substitution affect the fiscal multiplier quantitatively, and why does this matter more in the heterogeneous-firm model?

A: In the heterogeneous-firm GE model: λ = 3 gives an output multiplier of 0.672, λ = 1.185 (baseline) gives 1.088, and λ = 0.5 gives 1.364 — a range of 0.692. In the representative-agent model, the comparable range across the implied ζ values is much narrower (0.970 to 0.998). The amplification in the heterogeneous-firm model occurs because non-rivalry means each firm’s production function directly incorporates the public capital stock, so the elasticity parameter has first-order consequences for every firm’s investment incentive response to a fiscal shock. This heightened sensitivity underscores why accurately estimating λ at the firm level — rather than importing a state-level estimate — is critical for quantifying infrastructure multipliers.

Q9: What is the efficiency-equality trade-off in cross-state infrastructure allocation?

A: Under the baseline allocation (81% of infrastructure spending to Good states, 19% to Poor states), per $1 of infrastructure spending, the Good states receive $1.072 of output gains and Poor states receive only $0.016. In the equal-spending counterfactual, the total output multiplier falls from 1.088 to 0.873. The Poor states’ output multiplier rises from $0.016 to $0.062 (approximately fourfold), while the Good states’ falls from $1.072 to $0.810. The Poor states also see earnings multipliers more than double (from $0.017 to $0.042). This trade-off arises because Good states have both more private capital (benefiting from non-rivalry) and higher estimated TFP — so each dollar of infrastructure is more productive there. Equal allocation reduces aggregate efficiency while partially mitigating regional inequality.

Q10: How do the paper’s multiplier estimates compare to the existing literature?

A: In partial equilibrium (no GE adjustment), the authors find an output multiplier of 1.858, consistent with Chodorow-Reich’s (2019) cross-sectional multiplier of approximately 1.8. Once the general equilibrium interest rate effect is included, the multiplier falls to 1.09, which falls within the 0.6-1.2 range from Ramey (2011). Literature using representative-agent models without non-rivalry (e.g., Ramey 2020) typically reports multipliers of 0.3 to 0.8 using returns-to-scale parameters of 0.07-0.12; the paper shows these correspond to fiscal multipliers of 0.847-0.882 in the representative-agent framework. The heterogeneous-firm model, once it incorporates the non-rivalry-corrected elasticities, yields a meaningfully higher multiplier of 1.088.

Q11: What role does time-to-build play, and how does the paper handle it?

A: The baseline model assumes a time-to-build period s = 1 year (one-year lag before new infrastructure is productive). The paper notes in Appendix H that incorporating extended time-to-build reduces the aggregate fiscal multiplier, operating through two channels: a news effect (agents adjust behavior upon anticipating future infrastructure) and a general equilibrium effect endogenous to the news effect. This finding is consistent with Ramey (2020). The baseline results are therefore reported under the minimal one-year time-to-build assumption, with longer lags serving as a robustness check.

Q12: What is the role of region-specific TFP heterogeneity in the model?

A: The model includes two regions that differ both in infrastructure levels and in region-specific productivity (TFP) levels. The TFP of the Good region is estimated to be approximately double that of the Poor region (x = 2.064 for Good vs. 1 for Poor). This productivity difference is estimated to partially capture heterogeneous congestion effects (which are not separately modeled) and is estimated jointly with the infrastructure elasticity. The productivity differential is identified from the Good region’s share of aggregate output (0.849 in the data). The large TFP gap is also the reason why equal spending on Poor states generates a much smaller output gain than spending on Good states: not only is infrastructure utilization lower (fewer firms), but underlying productivity is also lower.

Key Concepts

Non-rivalry of public capital: The property by which infrastructure stock (Nj,t) enters each firm’s production function at the full regional level, not divided among firms. Formally, a single marginal unit of public capital raises every firm’s marginal product of private capital simultaneously, so the aggregate marginal product gain summed across firms exceeds any single firm’s gain. This is the central mechanism driving the micro-macro elasticity discrepancy in the paper.

Firm-level elasticity of substitution (λ): The elasticity governing the degree of substitutability between private capital (k) and public infrastructure (N) in the firm’s CES production function. At λ = 1 the production function is Cobb-Douglas; λ > 1 is gross substitutability; λ < 1 is gross complementarity. In the paper’s estimation, λ = 1.185, meaning private and public capital are gross substitutes at the firm level.

Gross substitutability vs. gross complementarity: Two inputs are gross substitutes (complements) if an increase in the quantity of one raises (lowers) the demand for the other, holding output price fixed. In the paper’s framework, private and public capital are gross substitutes at the firm level (λ = 1.185 > 1) but gross complements at the state level (ξ ≈ 0.48 < 1), with non-rivalry explaining the inversion upon aggregation.

Convex adjustment cost: A cost C(I,k) = (µ/2)(I/k)² · k that scales quadratically with the investment rate. In the heterogeneous-firm model, this cost plays a critical role: by Jensen’s inequality, heterogeneous firms’ average adjustment burden under a convex cost exceeds that of the representative (average) firm, making aggregate investment less sensitive to interest rate changes and thereby dampening crowding out.

Fixed adjustment cost (ξ): A one-time overhead cost drawn from a uniform distribution [0, ξ̄], paid only when a firm makes a large-scale investment outside the “inaction band” [−νk, νk]. This cost generates lumpy investment at the firm level, with about 14% of firms making lumpy investments in any given year. It also creates an extensive margin of investment adjustment that accounts for approximately 74% of the baseline crowding-out effect.

Fiscal multiplier (as defined in this paper): The ratio of the present value of aggregate output deviations from steady state to the present value of the fiscal spending shock, both summed over a T-year horizon. For the short run, T = 2 years; for the long run, T = 5 years. This is computed as a perfect-foresight transition path response to a one-time MIT shock equal to 1% of steady-state GDP.

MIT shock (one-time unexpected shock): An unanticipated, non-persistent one-period deviation in infrastructure spending. The term “MIT shock” refers to a deterministic transition experiment where agents have perfect foresight about all future values after the initial shock occurs. This contrasts with persistent policy rules and allows isolating the dynamic effects of a one-time fiscal impulse.

Extended SMM with market-clearing moments: The paper’s estimation innovation. Rather than solving for market-clearing prices at each parameter candidate (the standard costly inner loop), wages (w) and marginal utility of consumption (p) are treated as parameters with associated moments being the market-clearing conditions set to zero. A multi-block Metropolis-Hastings algorithm draws from the price block and the parameter block separately, generating posterior draws that jointly satisfy market clearing and empirical moment conditions.

Monopsony Makes Firms Not Only Small but Also Unproductive: Why East Germany Has Not Converged

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

Layer 1 — Summary

When employers face a trade-off between growing large and paying low wages — that is, when they have monopsony power — some productive employers will decide to acquire fewer customers, forgo sales, and remain small; these decisions have adverse consequences for aggregate labor productivity beyond the standard monopsony result that firms are too small. The paper documents that East German plants (compared to West German ones) face a steeper size-wage curve, invest less into marketing, and remain smaller, with the share of employment at plants with more than 249 employees standing at roughly 25% in East Germany versus 39% in West Germany in 2014 (and 31% versus 55% in manufacturing specifically). The steeper size-wage curve in East Germany is traceable to the historically determined underrepresentation of collective bargaining and union membership in small East German plants — a legacy of communist-era labor organization that caused union membership to collapse after reunification. The authors combine this evidence with a heterogeneous-plant model in which plants have product market power and choose how many customers to acquire subject to an upward-sloping size-wage schedule; two channels reduce aggregate productivity: a love-of-variety loss (fewer active plants means consumers bundle from a smaller variety of suppliers) and a compositional reallocation loss (labor is shifted from more productive to less productive plants, an effect exacerbated by product market power). When the model is calibrated to West Germany and the steeper East German size-wage trade-off is imposed, it predicts 10 percentage points lower aggregate labor productivity in East Germany — and for manufacturing, where East-West differences in plant size and the size-wage trade-off are particularly pronounced, the model predicts 18 percentage points lower productivity; in both cases the compression of the plant size distribution accounts for the largest share of the predicted productivity loss. The paper thus offers an explanation for why, more than thirty years after reunification, labor productivity and wages remain roughly 25% lower in the East German private sector despite uniform legal institutions across the two regions.

Layer 2 — Q&A

Q1: What is the core mechanism by which monopsony power reduces aggregate productivity, and how does it differ from the standard “firms are too small” result?

In the standard monopsony account, firms face an upward-sloping labor supply curve and choose to employ fewer workers than the competitive optimum, so individual firms are below efficient scale. The paper identifies an additional, investment-distortion channel: plants must also decide how large a customer base to acquire, and doing so requires marketing expenditure as well as the labor to service additional customers — labor whose cost rises with plant size along the size-wage schedule. A steeper size-wage curve therefore makes customer acquisition more expensive at the margin, and some productive plants optimally choose to acquire fewer customers, forgo sales, and remain small. The new aggregate productivity loss stems from this distorted investment margin: plants that could generate high value added at large scale instead operate at sub-optimal customer networks, suppressing aggregate output through both a love-of-variety effect (fewer active large plants means consumers access a smaller product variety) and a misallocation effect (the compressed size distribution shifts employment toward less productive plants).

Q2: What empirical patterns do the authors document to link the East-West productivity gap to missing large plants and steeper size-wage curves?

The authors document three nested empirical facts using the German Structure of Earnings Survey (SES) pooled across 2006, 2010, and 2014, supplemented by administrative wage panel data (AWFP) and national accounts (VGR). First, East German labor productivity in the private non-primary sector is about 25% below West Germany’s and has not converged since roughly 1995. Second, the share of employment at large plants (>249 employees) is substantially smaller in the East, and this gap is present both cross-sectionally across survey years and conditionally: East German plants enter smaller and remain smaller over their life-cycles, so plant age does not explain the difference. Third, industries where missing large plants are most pronounced in East Germany relative to West Germany are also the industries with the largest East-West productivity and wage gaps — the employment-weighted correlation between the large-plant share gap and the productivity gap is 0.53 across industries. The steeper size-wage curve itself is documented using within-industry comparisons: on average the plant size elasticity of wages is one-fifth larger in East Germany, and those industries with a steeper East-West size-wage differential are also the industries with the most missing large plants and the lowest average wages in the East.

Q3: Why is the steeper size-wage curve specific to East Germany, and why does it persist decades after reunification?

In communist East Germany, trade unions did not have the role of representing worker interests; consequently, after reunification, union membership fell dramatically. The key institutional consequence is that collective bargaining coverage in East Germany is underrepresented specifically in small plants. Workers at small plants in East Germany are more likely to have individually rather than collectively bargained wages than their West German counterparts, whereas workers at large plants in both regions are more similarly covered. Because collective bargaining flattens the size-wage curve (larger plants pay a smaller premium over small plants’ wages when both are covered by the same bargaining agreement), its absence in small East German plants produces a steeper gradient of wages with plant size in the East. This is a persistent structural feature rather than a transitional one: government policies and their enforcement are essentially uniform across regions, so the asymmetric bargaining coverage, which originates in communist-era institutional history, has not been erased by market forces or policy since 1990.

Q4: How is the model structured, and what are the three decision stages for plants?

The model is a static, long-run heterogeneous-plant framework that yields closed-form solutions. Within a period, plants face a three-stage decision problem. First, they decide whether to enter the market. Second, after entry, they choose how many customers to acquire, trading off additional sales revenue against marketing costs and the labor cost of servicing a larger customer base — a cost that rises with the number of customers because the upward-sloping size-wage curve means each additional worker hired requires a higher wage for all infra-marginal workers. Third, taking into account their product market power (each plant is a monopolistic competitor with its own customers), plants set prices to each customer and thereby determine how many workers they need. The size-wage schedule enters the second stage directly, so a steeper schedule reduces optimal customer acquisition across all plants, with the distortion being largest for the most productive plants (which would otherwise grow the largest).

Q5: Through what two channels does the steeper size-wage trade-off reduce aggregate labor productivity in the model?

The first channel is a love-of-variety effect in the product market: because more productive plants acquire fewer customers and operate at smaller scale under a steeper size-wage schedule, the average consumer bundles goods from a smaller number of distinct plants, and aggregate efficiency falls through the standard CES love-of-variety mechanism. The second channel is a misallocation effect in the labor market: the steeper size-wage schedule compresses the employment distribution across plants, reallocating labor from more productive to less productive plants relative to the benchmark with a flatter schedule. The paper shows that this second channel is exacerbated by product market power, because plants with stronger pricing power respond more aggressively to the changed labor cost trade-off. In the model’s decomposition, the compression of the plant size distribution (the misallocation channel) accounts for the largest part of the predicted 10 percentage point productivity shortfall.

Q6: What quantitative predictions does the model make, and how does it perform in untargeted moments?

The model is calibrated to two moments for West Germany: average plant size and the share of large plants (>249 employees). When the steeper East German size-wage trade-off is imposed without re-calibrating other parameters, the model predicts 10 percentage points lower aggregate labor productivity in East Germany — accounting for at least 10 of the roughly 25 percentage point observed gap. For the manufacturing sector alone, where East-West differences in plant size, the size-wage trade-off, and aggregate productivity are particularly pronounced, the calibrated model predicts 18 percentage points lower productivity. As an untargeted validation, the model also replicates the plant size distribution in East Germany, matching both the smaller average plant size and the relatively small number of large plants. These untargeted predictions provide additional support for the mechanism.

Q7: What alternative explanations for East Germany’s non-convergence does the paper rule out or place in context?

The paper addresses several confounds. In Appendix A, the authors show that East-West aggregate labor productivity differences are driven by differences in aggregate total factor productivity, not by labor quality differences, capital intensity differences, or capital quality differences — confirming within-country the finding that TFP explains a large fraction of productivity dispersion. The TFP differences are shown to be unlikely the result of greater labor market flexibility in West Germany or differences in industry composition. Appendix B shows that the East-West plant size distribution gap is not driven by differences in urbanization (West Germany has more metropolitan areas). The paper also addresses plant age: East German plants enter smaller and remain smaller at every age and across entry cohorts, ruling out the hypothesis that the size gap is purely a transitional legacy of the restructuring that destroyed many large East German plants at reunification.

Q8: How does this paper relate to the Heise and Porzio (2021) finding that plant productivity differences, not worker quality differences, drive the East-West wage gap?

Heise and Porzio (2021) use matched employer-employee data to document that plant productivity differences (as opposed to worker quality differences) account for most of the East-West wage differential, and they explain why low worker mobility does not remove these differences. The present paper complements this by providing an explanation for why plant productivity is lower in East Germany in the first place and why firm-level convergence does not occur: the steeper size-wage curve induced by the legacy of missing collective bargaining coverage in small East German plants distorts the investment and customer acquisition decisions of productive plants, keeping them small and unproductive. The two papers are thus complementary: Heise and Porzio take the plant productivity gap as given; Bachmann et al. endogenize it through the size-wage mechanism.

Key Concepts

Size-wage curve: The empirical relationship between plant size (measured by employment) and wages paid to workers, conditional on worker characteristics. A steeper size-wage curve means that the wage premium for working at a large plant relative to a small plant is larger. In this paper’s model, plants internalize that expanding their customer base and workforce requires paying higher wages to all workers (not just the marginal hire), making growth more costly when the size-wage curve is steeper.

Monopsony power (monopsonistic competition): The market structure in which an individual employer faces an upward-sloping labor supply curve — i.e., it must raise wages to attract additional workers. The paper uses “monopsonistic competition” to describe a setting with many such employers, each with some wage-setting power, in contrast to oligopsony. The paper focuses on allocative effects of this power, not on normative efficiency questions.

Customer capital / customer acquisition: Plants must incur marketing expenses to build a customer base; each customer relationship generates a stream of sales but requires labor to service. The size of the customer network is a long-run investment decision. Under monopsonistic labor markets, the cost of expanding the customer base includes not only marketing expenses but also the higher wages that a larger workforce requires, making customer acquisition a margin that is distorted by labor market power.

Love-of-variety effect: A welfare loss that arises in models with monopolistic competition and CES preferences when the number of active product varieties declines. In this paper it applies to the product market: when plants remain small and acquire fewer customers, the effective number of distinct varieties consumed falls, reducing aggregate efficiency even holding plant-level productivity fixed.

Misallocation / compressed size distribution: A situation in which factors of production are not allocated to their highest-value uses. Here, the steeper size-wage curve induces productive plants to remain small, so labor that would otherwise be employed at high-productivity large plants is instead employed at lower-productivity small plants. The resulting compression of the plant size distribution — fewer very large plants, more mass in the middle — is both the key empirical fact and the primary quantitative driver of the predicted aggregate productivity shortfall.

Collective bargaining coverage: The fraction of workers whose wages are set by collective agreements between employers (or employer associations) and trade unions, rather than by individual negotiation. The paper establishes that collective bargaining flattens the size-wage curve by compressing wages across plants of different sizes. The historically low collective bargaining coverage among small East German plants — a legacy of communist-era labor relations — is the institutional root cause of the steeper East German size-wage schedule.

Summary based on IZA Discussion Paper 15293. AI-assisted, human review pending.

The Macroeconomic Impact of Climate Change: Global Versus Local Temperature

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

The paper shows that the macroeconomic impact of climate change is an order of magnitude larger than what standard country-level panel estimates suggest. The key identification innovation is to measure the effect of global mean temperature shocks using time-series local projections, rather than using cross-country variation in local temperatures as in the conventional panel literature. A shock to global mean temperature tracks extreme weather events (droughts, heat waves, wind, precipitation anomalies) that affect all countries simultaneously; a local temperature anomaly in one country does not.

Empirical approach: The authors estimate local projections of world GDP growth on exogenous global mean temperature shocks. The shock is the innovation to global mean temperature after removing a 2-year autoregressive component and a low-frequency trend, following Hamilton (2018). Two estimation samples: BU (Barro-Ursúa macro history, 43 countries, 1860–2019) and PWT (Penn World Tables, 173 countries, 1960–2019).

Key empirical results (Section 3): A 1°C shock to global mean temperature causes world GDP to fall by 14% after 6 years in the PWT sample (95% CI: 6%–22%); significant at the 5% level in years 2–8; does not mean-revert within the 10-year sample horizon. In the BU sample, the peak GDP decline is 18% after 5 years (95% CI: 6%–30%). Converting the cumulative IRF ratio to a permanent temperature change yields a 22–34% long-run GDP decline per 1°C of permanent global warming (PWT and BU respectively). By contrast, local temperature shocks — estimated from a standard cross-country panel with country and year fixed effects — generate effects of 1–3% per °C, not statistically significant at the 5% level.

Why global > local (Section 4): Four categories of extreme climatic events (heat waves, droughts, wind, precipitation anomalies) jointly account for roughly half of the estimated global temperature effect on GDP. None of these are strongly correlated with local temperature anomalies because extreme weather reflects ocean-atmosphere dynamics (El Niño/ENSO) that elevate global mean temperature rather than any single country’s local temperature. In addition, capital and investment both decline persistently after global temperature shocks (capital response significant at 5% level), and warm/low-income countries are disproportionately affected.

Structural model (Section 5): A parsimonious neoclassical growth model embeds climate change as aggregate TFP changes. Households maximize ∫e^{−ρt}U(C_t)dt; firms use Cobb-Douglas technology Z_t K_t^α L_t^{1−α}. The damage function governing TFP is:

Z_t = Z_0 exp( ∫0^t ζ_s T̂{t−s} ds )

where T̂_t is excess global mean temperature above baseline and ζ_s = A(e^{−Bs} − e^{−Cs}) is the structural damage function. When ζ_s → 0, shocks have level but not growth effects; no statistically significant evidence of growth effects is found in Figure 3 of the paper. The model is calibrated with: risk aversion γ = 1 (log utility), capital share α = 0.33, annual capital depreciation δ = 0.08, and pure time preference ρ = 0.02. Proposition 1 (model inversion) shows that, to first order, ŷ_t = ẑ_t + α ∫K_{t,s} ẑ_s ds, where K_{t,s} is the sequence-space Jacobian of the neoclassical growth model. This delivers identification: observed output impulse responses recover the structural TFP damage function ζ_s without imposing functional form on the capital channel.

Estimation results (Section 5.3, Figure 12): The estimated damage function implies a 4% peak short-run productivity decline 2 years after a 1°C transitory global temperature shock; the effect decays slowly and remains significant for up to 10 years. The capital response (non-targeted moment) closely matches its empirical counterpart, providing an overidentification check. The local temperature damage function, estimated by targeting the local-panel output IRF, peaks at only 0.5% and is more than 8× smaller in cumulative productivity effect; it is not statistically different from zero at the 5% level.

Business-as-usual counterfactual (Section 6.1–6.2): Temperature rises from 2024, reaching 3°C above preindustrial by 2100 (asymptoting to 3.3°C), equivalent to 2°C of additional warming since 2024. Under the global temperature damage function:

World output by 2050: −28% vs. no-warming baseline
World output by 2100: −53% (accumulated TFP losses reach −40%)
Capital by 2100: −51% (investment initially rises as households anticipate lower permanent income, then decumulates rapidly)
Consumption by 2100: −53%
2024 welfare loss (consumption equivalent): 35%; welfare continues declining as temperatures rise, eventually reaching 56%
95% CI for 2100 output loss: 29%–77%
All effects statistically significant at the 5% level

Under the local temperature damage function with the same warming scenario: long-run output declines only 9%, welfare loss is 5%, and neither is statistically significant at the 5% or 10% level — consistent with conventional estimates (Nordhaus 1992, Dell et al. 2012, Burke et al. 2015).

Social Cost of Carbon (Section 6.2, Panel F): The SCC is defined as the consumption-equivalent amount households would pay at time 0 to avoid one additional ton of CO2, using the temperature-response function from Dietz et al. (2021a). Baseline result: $1,207 per ton (2024 international dollars), more than 6× larger than the $185/ton estimate in Rennert et al. (2022). 95% CI: $399–$2,015 per ton. Climate sensitivity range (half/double median): $600–$2,400 per ton. BU sample (larger damage functions): >$1,500 per ton. Using the local temperature damage function yields an SCC of only $149/ton, consistent with conventional estimates.

Sensitivity (Section 6.4): Higher time preference ρ > 0.04 lowers welfare losses below 20% and the SCC below 3× conventional high-end estimates — the only scenario where results converge toward prior estimates. Near-Stern discount rates (ρ → 0): welfare loss >40% and SCC >$2,500/ton. A 6°C-by-2100 scenario yields welfare losses >60%.

Historical growth accounting (Section 6.3): Starting the model in 1960 and imposing the realized 1960–2019 warming path, then holding temperature constant at its 2019 level, reveals:

World GDP per capita would be 25% higher today without warming since 1960
By 2040, output is 32% below potential from past warming — one-quarter of losses from historical warming are yet to materialize (due to delayed damage function and transitional capital dynamics)
Climate change reduced the annual world growth rate by as much as a third of baseline by the 21st century

Policy implication: Most decarbonization interventions cost ~$80/ton on average (Bistline et al. 2023). Under conventional SCC estimates based on local temperature ($149/ton), the US Domestic Climate Cost (DCC) falls below policy cost, making unilateral emissions reduction prohibitively expensive. Under the paper’s global temperature SCC of $1,207/ton, the DCC of the United States exceeds $80/ton even accounting for the fraction of global climate benefits that accrue domestically — unilateral decarbonization becomes cost-effective for large economies such as the US.

Scope conditions: The neoclassical model abstracts from adaptation, mitigation, trade, urbanization, and endogenous emissions. The identification assumption requires that global mean temperature innovations are uncorrelated with other global economic confounders at business-cycle and trend frequencies; the paper checks robustness against alternative detrending, exclusion of WWII and COVID-19 years, El Niño/ENSO controls, and instrumental variables for temperature based on solar/volcanic forcing. The conversion from medium-run to long-run effects relies on the constrained ζ_s = A(e^{−Bs} − e^{−Cs}) functional form ruling out growth effects — consistent with the data but not formally testable beyond the 10-year horizon. Counterfactuals involve 2–3°C temperature changes substantially beyond the sample’s moderate perturbations; the model’s extrapolation may understate damages if nonlinearities exist at extreme temperatures (the authors note their conservative constrained-form approach).

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

In depth

Q1. Why do global temperature shocks produce GDP effects an order of magnitude larger than local temperature panel estimates?

Global mean temperature shocks are strongly correlated with extreme weather events — heat waves, droughts, wind storms, and precipitation anomalies — that simultaneously affect all countries; these four event categories jointly account for roughly half of the global temperature effect on GDP. Local temperature anomalies in a given country (as measured in standard cross-country panels with year fixed effects absorbed) are not correlated with these same events, because El Niño/ENSO and related ocean-atmosphere dynamics elevate global mean temperature without proportionally elevating any one country’s local temperature. Local panel studies also implicitly allow economic activity to shift toward cooler regions within a given year — an option unavailable when global warming affects all locations simultaneously. The resulting bias in local-panel estimates is not “aggregation bias” in the sense of Jensen’s inequality, but rather an identification problem: local panels identify a different object (the effect of temperature relative to other countries in the same year) rather than the aggregate climate impact the paper measures.

Q2. What is the identification strategy and what are the main threats?

The global temperature shock is identified as the innovation to global mean temperature after removing a 2-year AR component and a Hamilton (2018) low-frequency trend, yielding a shock orthogonal to its own recent history and to long-run trends. The main threats are: (i) global business-cycle confounders (worldwide recessions that simultaneously lower activity and emissions), addressed by controlling for quadratic time trends and global aggregate demand proxies; (ii) reverse causality (economic expansion warming the atmosphere), addressed by IV estimates using solar/volcanic forcing as instruments; (iii) low-frequency correlation between climate trends and productivity growth, addressed by flexible detrending and robustness to sample period. All major specification checks generate quantitatively similar results, and the paper passes placebo tests for large global confounders (WWII, COVID-19).

Q3. How does the structural model translate medium-run shock responses into long-run warming effects?

Proposition 1 (model inversion) shows that the output impulse response decomposes into a direct TFP effect ẑ_t and a capital channel ŷ_t = ẑ_t + α ∫K_{t,s} ẑ_s ds, where K_{t,s} is the sequence-space Jacobian of the neoclassical growth model (Auclert et al. 2021); this allows recovery of the structural TFP damage function {ζ_s} from the observed 10-year output IRF by non-linear least squares, without having to observe TFP directly. The counterfactual for a gradually rising temperature path (BAU scenario with 2°C additional warming since 2024) is then solved via the full nonlinear model — not via the log-linearization used in estimation — because the 2–3°C excursion far exceeds the sample’s modest temperature perturbations. The capital response (non-targeted moment) closely tracks its empirical counterpart, providing a strong overidentification check that the model’s capital dynamics are correctly specified.

Q4. Why does capital initially rise in the BAU counterfactual before declining?

Following standard permanent-income logic, when households learn at date 0 that global temperatures will rise and future TFP will fall, they temporarily increase saving and investment to accumulate buffer capital before the productivity decline materializes; this front-loads some capital accumulation in the early transition years (2024–2030s), briefly pushing capital above baseline, before the accumulated TFP losses overwhelm the saving motive and capital begins an extended decline. The net effect is still a 51% capital shortfall by 2100 because persistently lower TFP reduces the marginal product of capital over decades, depressing investment and allowing the capital stock to drift far below its no-warming balanced growth path.

The SCC is defined as the dollar amount C such that households are indifferent between (a) a world where one additional ton of CO2 is emitted at time 0 and (b) a world in steady-state where the household has paid C at time 0 (equation 7: V^{ss}(K^{ss} − C) = V^{SCC}_0(K^{ss})). The temperature response to a 1-ton CO2 pulse is taken from Dietz et al. (2021a) — temperature peaks at 0.002°C after a 1-gigaton pulse and stabilizes. The model generates the productivity path {Z^{SCC}_t} via the structural damage function, solves for equilibrium capital and consumption paths, and computes the value function V^{SCC}_0. The resulting $1,207/ton exceeds prior estimates by 6× because the global-temperature damage function implies 4% peak TFP losses per 1°C transitory shock, compared to the ~0.5% peak implied by local temperature — and the SCC is essentially the capitalized sum of these future productivity losses, so the ratio scales proportionally.

Q6. Why are historical climate losses so large if year-to-year warming is small?

The key is cumulation: annual warming increments are individually small (tenths of a degree), but the damage function {ζ_s} is persistent (effects last 10+ years), so each year’s increment adds a flow of persistent TFP losses that stack on top of prior increments. The paper’s growth accounting shows that climate change reduced the world growth rate by up to one-third of baseline in the 21st century — a number that appears modest in any single year but, compounded over decades, translates into a 25% GDP per capita shortfall by 2019. Additionally, because the estimated damage function has a 2-year lag before peak TFP impact, a substantial share of past warming’s losses are yet to be realized — the paper estimates GDP will be 32% below its potential by 2040 even with no further warming.

Q7. What does the sensitivity analysis reveal about the robustness of the results?

The key sensitivity is the rate of time preference ρ: at ρ = 0.02 (baseline, consistent with secular interest rate decline), welfare loss is 35%; at ρ = 0.04 (above recent market rates), welfare loss is still above 20%; only at implausibly high discount rates does the welfare loss fall below 15%. The SCC is more sensitive to ρ than welfare because the SCC is a capitalized stock valuation while welfare is an annualized flow. BU sample damage functions (larger IRF) raise welfare loss to 42% and 2100 GDP loss to 61%; these represent the high end of the estimates. The climate sensitivity range ($600–$2,400/ton for the SCC) reflects uncertainty in the physics of CO2-to-temperature conversion, not in the estimated economic damage function. Across all these dimensions, the global-temperature estimates remain order-of-magnitude larger than local-temperature estimates.

Q8. What is the policy implication for large economies considering unilateral decarbonization?

The domestic decarbonization test compares the Domestic Climate Cost (DCC) — the fraction of the global SCC that accrues to the decarbonizing country — against the marginal cost of abatement (~$80/ton average, Bistline et al. 2023). Under conventional local-temperature estimates ($149/ton global SCC), the US DCC falls below $80/ton, implying unilateral action destroys domestic value. Under the paper’s $1,207/ton global SCC, the US DCC comfortably exceeds $80/ton even if the US only captures a fraction of world welfare gains — because global temperature extremes (hurricanes, heat waves, droughts) strike the US directly, the DCC/SCC ratio is much higher than under local estimates where the US appears less exposed. This fundamentally changes the cost-benefit calculus for large-economy unilateral climate policy.

Key concepts

global mean temperature shock: a time-series innovation to world average surface temperature, identified by Hamilton (2018) detrending; captures ocean-atmosphere climate variability (El Niño/ENSO) correlated with extreme weather events affecting all countries simultaneously; the paper’s key identification variable, distinct from local temperature variation used in standard cross-country panels.

global vs. local temperature effect: the paper’s central finding that the GDP effect per 1°C global mean temperature shock (14–18%) is an order of magnitude larger than the effect per 1°C local temperature shock (1–3%); the gap is explained by extreme climatic events (heat waves, droughts, wind, precipitation) that co-move with global mean temperature but not with individual countries’ local temperatures.

structural damage function (ζ_s): the kernel relating excess global mean temperature T̂_{t−s} to log TFP at time t, specified as ζ_s = A(e^{−Bs} − e^{−Cs}); estimated from the PWT output impulse response via model inversion (Proposition 1); implies a 4% peak TFP loss 2 years after a 1°C transitory shock, decaying slowly over 10 years; rules out permanent growth effects consistent with the data.

Social Cost of Carbon (SCC): the one-time dollar amount households would pay at time 0 to avoid one additional ton of CO2; equals (in the linear limit) the present discounted value of all flow consumption-equivalent welfare losses from the induced warming; paper estimates $1,207/ton (2024 international dollars), more than 6× prior estimates, because the global-temperature damage function implies much larger per-degree productivity losses than local-temperature estimates.

committed climate losses: future GDP shortfalls already locked in by past warming, arising because the estimated damage function has a delayed peak (year 2) and slow decay (10+ years) — temperature rises in recent years continue reducing productivity for the following decade; the paper estimates these committed losses alone will lower GDP 32% below potential by 2040 even with temperature held constant at 2019 levels.

BAU scenario: the business-as-usual warming path used for the main counterfactual — global mean temperature reaches 3°C above preindustrial by 2100 (asymptoting to 3.3°C), implying 2°C of additional warming since the 2024 baseline; under this scenario the model implies 53% GDP loss, 51% capital loss, 53% consumption loss, and a 35% consumption-equivalent welfare loss by 2100.

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In depth

Q1. Why do global temperature shocks produce GDP effects an order of magnitude larger than local temperature panel estimates?

Q2. What is the identification strategy and what are the main threats?

Q3. How does the structural model translate medium-run shock responses into long-run warming effects?

Q4. Why does capital initially rise in the BAU counterfactual before declining?

Q5. How is the Social Cost of Carbon defined and computed?

Q6. Why are historical climate losses so large if year-to-year warming is small?

Q7. What does the sensitivity analysis reveal about the robustness of the results?

Q8. What is the policy implication for large economies considering unilateral decarbonization?

Key concepts