Productivity | Macro Paper Warehouse

Firm idiosyncratic risk and productivity investment: Macroeconomic implications

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

This paper quantifies how idiosyncratic firm-level risk affects aggregate output, TFP, and firm life-cycle growth in an environment where firm productivity evolves endogenously through risky investment. The paper embeds endogenous productivity investment into a Lucas span-of-control model with risk-averse firm owners and endogenous entry and exit, and studies the effects of mean-preserving increases in the variance of returns to productivity investment. A mean-preserving increase in the variance of firm productivity shocks that raises the firm exit rate by 10% (from 0.10 to 0.11) is estimated to cause a 0.73% decline in output, a 0.38% decline in measured TFP, and a 3.69% decline in firm productivity investment; these elasticities remain approximately constant in the empirically relevant range. The driving force is that risk-averse firm owners reduce their risky productivity investment as variance rises; if capital financing constraints are present—as is common in developing economies—these effects are amplified and the increase in uncertainty may also slow firm life-cycle growth. Previously circulated as “Uncertainty, Firm Lifecycle Growth, and Aggregate Productivity.”

Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.

In depth

Q1. What distinguishes this paper from standard models of firm misallocation?

Unlike the bulk of firm misallocation literature (Hsieh-Klenow 2009; Gopinath et al. 2017; Sraer-Thesmar 2023), which takes firm productivity as exogenous, this paper models productivity as an endogenous outcome of risky investment, so that idiosyncratic uncertainty affects allocative efficiency not only through selection effects but also through its discouragement of productivity investment by risk-averse owners. The paper incorporates endogenous productivity investment into a standard Lucas span-of-control model, allowing the model to capture how higher uncertainty reduces the incentive to invest in productivity, on top of any selection effects from the exit option.

Q2. What are the two opposing effects of higher idiosyncratic risk?

Higher idiosyncratic firm-level risk has two opposing effects on aggregate productivity: (i) a selection effect—a mean-preserving increase in variance leads to stronger selection and raises the productivity of survivors while reallocating exiters to alternative productive uses—that tends to raise average productivity; and (ii) a productivity investment effect—risk-averse owners reduce risky productivity investment in response to higher variance—that tends to reduce aggregate productivity and firm life-cycle growth. The paper shows quantitatively that the productivity investment effect dominates in the baseline calibration, so that higher idiosyncratic risk reduces output and TFP despite positive selection effects.

Q3. What are the main quantitative findings?

A mean-preserving increase in the variance of firm productivity shocks calibrated to raise the firm exit rate by 10% (from 0.10 to 0.11) results in a 0.73% decline in output, a 0.38% decline in measured TFP, and a 3.69% decline in firm productivity investment; these elasticities remain approximately constant in the empirically relevant range. The exit-rate increase from 0.10 to 0.11 is also associated with a 7.5% increase in the job destruction rate and a 14.6% increase in the standard deviation of firm growth rates—the latter is less than one-fifth of the increases in these risk measures observed when comparing India or Mexico to the U.S.

Q4. How do capital financing constraints interact with the results?

When firms face capital financing constraints—as is common in developing economies—the negative effects of higher idiosyncratic risk are amplified and the increase in uncertainty may also slow firm life-cycle growth. The mechanism is that constrained firms must rely more heavily on internal financing, making risk-averse owners even more sensitive to increases in variance. The paper implies that the macro-financial implications of idiosyncratic risk are more severe in developing economies where both idiosyncratic risk levels and financing constraints are greater—consistent with cross-country patterns of firm growth dynamics.

Key concepts

productivity investment : endogenous spending by firms on activities that shift their productivity process; in the model, this investment exposes firm owners to idiosyncratic risk via the innovation in the productivity process; the key margin through which higher uncertainty reduces aggregate productivity and output. mean-preserving increase in variance : a statistical experiment that increases the spread of the distribution of returns to productivity investment while leaving the mean unchanged; used here to isolate the pure risk effect on firm behavior and aggregate outcomes from any change in expected returns. span-of-control model : the Lucas (1978) model of firm size distribution with decreasing returns to scale in the entrepreneurial input; used as the production environment; extended here by adding endogenous productivity investment and endogenous entry and exit.

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.

In depth

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.

Quantifying the allocative efficiency of capital: The role of capital utilization

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

Standard measures of capital allocative efficiency—based on the dispersion of the average revenue product of capital (ARPK)—are severely biased when capital utilization is endogenous. When utilization is flexible, firms can bypass physical adjustment constraints by varying intensity, so that the correct efficiency measure requires the dispersion of average revenue product of capital services (ARPKS), defined as the log difference between revenue and utilized capital, not of ARPK. Contrary to the standard view that higher ARPK dispersion signals lower allocative efficiency, the paper demonstrates that when efficiency improvements arise from greater utilization flexibility, ARPK dispersion can increase alongside efficiency gains. An application to India’s capital market liberalization reform shows that the standard approach (ignoring utilization) predicts allocative efficiency gains of 5.25% (statistically significant), while the corrected approach accounting for utilization finds gains of only 0.04% (not statistically significant).

Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.

In depth

Q1. What is wrong with ARPK dispersion as a measure of allocative efficiency?

ARPK dispersion conflates two conceptually distinct quantities—the dispersion of physical factor allocation and the dispersion of utilization intensity—so it is not a monotone proxy for allocative efficiency when utilization is endogenous. In the Hsieh-Klenow (2009) framework, higher ARPK dispersion is interpreted as higher misallocation. But ARPK is simply revenue over capital inputs, so when firms with too little (too much) capital relative to their productivity simply utilize their capital more (less) intensely, the variance of ARPK rises even as the efficiency of factor services allocation improves. The standard interpretation therefore has the causality backwards in economies with flexible utilization.

Q2. What is ARPKS and why does it correctly measure capital allocative efficiency?

ARPKS—the average revenue product of capital services, defined as the log difference between revenue and utilized capital—is the theoretically correct sufficient statistic for capital allocative efficiency when utilization is endogenous, because it measures the dispersion in the productivity of factor services rather than the dispersion of physical factor inputs. The paper embeds endogenous utilization into a neoclassical investment model and shows formally that the variance of log ARPKS is zero in the efficient equilibrium, while the variance of log ARPK is not. ARPK dispersion is a combination of ARPKS dispersion and utilization variation, and the latter is not a sign of misallocation.

Q3. Can higher ARPK dispersion accompany higher allocative efficiency?

Yes: when allocative efficiency improvements arise from greater flexibility in capital utilization, ARPK dispersion increases even though allocative efficiency improves. Greater utilization flexibility generates more variation in how intensively different firms use their capital, raising the ratio of revenue to physical capital input for high-utilization firms. A researcher using ARPK dispersion would therefore mistakenly conclude that allocative efficiency fell when it actually rose. The paper provides counterfactual simulations illustrating this phenomenon.

Q4. What is the empirical application and what do the results show?

An application to Bau and Matray (2023)’s Indian capital market liberalization reform finds that: the standard approach (ignoring utilization) predicts allocative efficiency gains of 5.25% (statistically significant); accounting for utilization, the corrected estimate is only 0.04% (not statistically significant). The analysis uses firm-level panel data for India including capacity utilization rates and capital maintenance expenses. Maintenance expenses serve as a proxy for capital utilization rates in the model, bridging the gap between observed capacity and the theoretically relevant utilization measure.

Key concepts

average revenue product of capital (ARPK) : the ratio of revenue to physical capital input; commonly used as a proxy for firm-level distortions in the Hsieh-Klenow (2009) framework, but shown to be a biased measure of allocative efficiency when capital utilization is endogenous. average revenue product of capital services (ARPKS) : the ratio of revenue to utilized capital; the theoretically correct measure of capital allocative efficiency when utilization is endogenous; its dispersion is zero in the efficient equilibrium. capital utilization : the intensity with which a firm deploys its physical capital stock; endogenous in the model, allowing firms to partially bypass adjustment constraints; the omission of utilization is the source of the bias in standard ARPK-based efficiency estimates.

The Micro and Macro Dynamics of Capital Flows

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

Using the 2001 Hungarian capital account liberalization as a quasi-natural experiment and census-level firm data covering the entire economy (1992–2008), the paper identifies two channels through which capital inflows affect resource allocation: an input-cost channel (lower cost of capital benefits capital-intensive sectors) and a consumption channel (higher household incomes benefit high-expenditure-elasticity sectors, chiefly services). The paper finds the consumption channel dominates: one standard deviation increase in expenditure elasticity is associated with 8.4% greater real value-added growth, versus 4.2% for one standard deviation in capital elasticity. Along the extensive margin, high-expenditure-elasticity sectors experience 15% higher net entry and 19% higher gross entry. A calibrated multi-sector heterogeneous-firm model with non-homothetic preferences (à la Comin–Lashkari–Mestieri 2021) replicates 12 non-targeted moments and reproduces 70% of the reallocation toward services observed in Hungary. Counterfactual exercises show that a neoclassical homothetic model underpredicts reallocation by a factor of ten and generates counterfactual real exchange rate depreciation. Despite reallocation toward less productive service firms (a negative composition effect), aggregate TFP increased 11.4% in Hungary — driven by a love-of-variety effect from entry (mass-of-firms effect of +3.5% versus composition effect of −1.9%). Non-homothetic preferences amplify this mechanism: capital-scarce economies experience 21.9% larger TFP gains than homothetic models predict.

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 is Hungary’s 2001 capital account liberalization a clean quasi-natural experiment?

Hungary deregulated only cross-border financial flows, without simultaneous trade or FDI liberalization, and the reform was predetermined by the Copenhagen Criteria of 1993 as a condition for EU accession. The content and timing of the reform were not driven by Hungarian firm-level fundamentals: by March 2001, financial liberalization was the sole remaining EU accession requirement, and neither trade nor FDI changed around the reform (Figures C.4–C.5). Exports to the EU already accounted for 80% of total exports before 2001. The nine other EU accession candidates at the time did not experience comparable patterns of capital inflows, consumption booms, or sectoral reallocation (Tables C.2–C.3), ruling out EU accession itself as the driver.

Q2. How does the paper identify the input-cost and consumption channels separately?

The identification strategy exploits three sources of variation: pre- versus post-reform timing, heterogeneous capital elasticities across four-digit industries (input-cost channel), and heterogeneous expenditure elasticities across two-digit industries (consumption channel), derived from model-implied structural relationships. Using equation (4), the DiD regression estimates γ₁ (capital elasticity × reform dummy) and γ₂ (expenditure elasticity × reform dummy). These two structural parameters are nearly orthogonal (correlation 2.1% between USDA capital and expenditure elasticities), allowing separate identification. The capital elasticities are estimated using the Petrin–Levinsohn–Wooldridge method on pre-reform data; expenditure elasticities come from USDA Seale–Regmi–Bernstein (2003) estimated for Hungary in 1996. Parallel trends hold: firms across elasticity levels shared similar pre-reform growth trajectories (Table C.9).

Q3. What do the baseline regression results show about which channel dominates?

In the preferred specification with both channels and all controls (column 4, Panel A of Table 1), capital elasticity raises value added by 4.2% per standard deviation (0.045 SD), while expenditure elasticity raises it by 8.4% per standard deviation (0.223 SD USDA); standardized beta coefficients confirm the consumption channel is larger. For capital accumulation (Panel B), only the capital elasticity coefficient is significant: a one standard deviation increase in capital elasticity is associated with 4.4% more firm-level capital, while expenditure elasticity has no significant effect — firms in high-expenditure-elasticity sectors do not accumulate more capital, they hire more workers. Employment (Panel C) shows 9.3% higher employment per standard deviation in expenditure elasticity (5.9% using Bils–Klenow–Malin elasticities). These patterns survive controls for non-tradability, financial frictions (Rajan–Zingales, Raddatz inventories-to-sales, cash conversion cycle), and firm-level debt obligations.

Q4. How does the model fit the non-targeted moments for Hungary?

Calibrated to 13 internally targeted moments (including the 3.5 percentage point decline in the domestic real interest rate and sectoral firm-size distributions), the model matches 12 non-targeted moments spanning consumption, capital accumulation, cross-sector reallocation, and within-sector selection (Table 6). Key matches: household consumption +5.8% (data), +7.2% (model); within-firm capital accumulation +22.5% vs +24.9%; value-added share of services +3.9pp vs +2.7pp (70% match); relative operational cutoff of services vs manufacturing −2.3% vs −1.7% (74% match); relative export cutoff +4.6% vs +4.5% (98% match). The model accounts for roughly 60% of the 2.9% relative price appreciation (real exchange rate). The model also reproduces the differential increase in entry rates: services +10.8pp (data) vs +18.4pp (model), manufacturing +5.7pp vs +8.6pp.

Q5. What do counterfactual exercises reveal about the role of non-homothetic preferences?

A neoclassical representative-firm model with homothetic preferences generates only 0.4 percentage points of reallocation toward services — ten times less than the 3.9pp observed in Hungary — and produces a counterfactual real exchange rate depreciation. In Table 7, four counterfactuals are compared: (1) baseline model (εS ≠ εM, αS ≠ αM): consumption ratio CS/CM +6.9pp, service value-added share +2.7pp, relative price appreciation +1.7%; (2) consumption channel only (εS ≠ εM, αS = αM): similar service reallocation but no RER appreciation; (3) input-cost channel only (εS = εM, αS ≠ αM): modest reallocation (~1.1pp) but correct RER appreciation; (4) homothetic heterogeneous-firm model (εS = εM, αS = αM): ~0.7pp reallocation, wrong RER; (5) neoclassical model: ~0.4pp, wrong RER. Non-homothetic preferences account for about two-thirds of the service reallocation; differential capital elasticities are necessary to replicate exchange rate dynamics.

Q6. How can aggregate TFP increase when resources move toward less productive services?

Financial liberalization induces firm entry — especially in high-expenditure-elasticity services — generating a love-of-variety effect that increases aggregate output more than proportionally with the number of varieties (since σ > 1), overwhelming the negative composition effect from reallocation to lower-productivity service firms. The TFP decomposition (Table 9) shows: composition effect −1.9%, mass-of-firms effect +3.5%, interaction +0.7%, sum +2.3% model (data: +11.4%). The composition effect is consistently negative across all capital-scarcity levels because service firms are less productive. But the mass-of-firms effect is consistently larger and positive. Non-homothetic preferences amplify entry in services (the high-expenditure-elasticity sector), strengthening the love-of-variety channel.

Q7. How do non-homothetic preferences affect TFP gains in capital-scarce economies, and what are the policy implications?

Capital-scarce economies experience larger consumption booms upon financial liberalization (given lower initial capital levels and higher intertemporal borrowing gains), inducing stronger entry in high-expenditure-elasticity services and larger mass-of-firms TFP effects; non-homothetic preferences amplify this gradient by 21.9% relative to homothetic preferences (Table 10). Specifically, an economy liberalizing at 25% of its open-economy steady-state capital stock gains 5.5× more TFP than one liberalizing at 70%; under homothetic preferences the ratio is 4.5×, yielding a 21.9% amplification from non-homotheticity. This helps explain the empirical puzzle documented by Bekaert–Harvey–Lundblad (2011) and Bonfiglioli (2008) that financial liberalization episodes associate with productivity gains in capital-scarce economies, which neoclassical models predict incorrectly as productivity declines. The policy implication is that the gains from financial openness are largest — and most driven by consumption-driven entry — when economies are capital-scarce, but these gains also carry macro-financial risks (as in Gyongyosi–Rariga–Verner 2023 on the 2008 Hungarian forint depreciation).

Key concepts

input-cost channel : the mechanism through which capital inflows reduce firms’ cost of capital (borrowing rate), benefiting sectors with higher capital elasticity; identified in Hungary through the differential expansion of firms in high-capital-elasticity industries after the 2001 deregulation.

consumption channel : the mechanism through which capital inflows increase household consumption, benefiting sectors with higher expenditure elasticity; found to dominate the input-cost channel in Hungary, explaining the reallocation toward services.

non-homothetic preferences : demand preferences (modeled following Comin–Lashkari–Mestieri 2021) in which sectoral expenditure shares change with income levels — goods with expenditure elasticity above one gain share as income rises; these preferences are quantitatively necessary to explain the 3.9pp reallocation toward services in Hungary (versus 0.4pp under homothetic preferences).

mass-of-firms effect : the aggregate productivity gain from an increase in the number of active firm varieties under CES demand (σ > 1), whereby output grows more than proportionally with the number of varieties; this love-of-variety mechanism explains why aggregate TFP increases in Hungary despite resource reallocation toward less productive service firms.

expenditure elasticity : the sector-level responsiveness of consumption to a proportional increase in aggregate income; used in the paper’s DiD identification to separate the consumption channel from the input-cost channel, measured using USDA (Seale–Regmi–Bernstein 2003) estimates for Hungary, with services having higher elasticity (1.18 in model calibration) than manufacturing (0.75).