The Aggregate Costs of Uninsurable Business Risk

Layer 1: Overview

Research question and motivation. A large literature argues that credit constraints are the dominant financial friction holding private businesses below their optimal scale, so that easing credit access would yield large aggregate efficiency gains. This paper challenges that view. Private businesses are also poorly diversified — their owners bear undiversifiable business-income risk — and the authors argue the macroeconomic costs of this lack of diversification are far larger than those of credit constraints. The crux is that entrepreneurs can limit risk exposure by operating at a smaller scale, so productive-but-poor entrepreneurs choose an inefficiently low scale and are unwilling to borrow to expand. Firm size is thus limited by risk, not by credit availability.

Data and setup. The empirical analysis uses the historical Orbis dataset (Moody’s Bureau van Dijk), 1995–2019, focusing on Spain (best coverage; results extend to Italy, France, Norway, Portugal, Slovakia in the appendix). Output is value added; the sample is partnerships and private limited companies, excluding FIRE, public administration, defense, education. The final sample is 622,883 firms (6,298,358 firm-year observations), observed on average 10 years; the mean (median) firm has 12 (5) workers and 486 (151) thousand EUR value added. The Spanish Survey of Household Finances (EFF, 2008–2020) provides entrepreneur wealth/prevalence and consumption data. The model is a small-open-economy model of entrepreneurial dynamics (à la Quadrini 2000; Cagetti–De Nardi 2006) with two frictions: each firm is owned by a single (undiversified) entrepreneur, and a collateral constraint k’ ≤ a’/(1−ξ). Key modeling choices: capital AND labor are chosen before productivity is observed (time-to-build), and productivity has persistent and transitory shocks drawn from fat-tailed mixtures of normals. Parameters are estimated by simulated method of moments (9 parameters, 16 moments; objective 0.013, ~1.3% average deviation).

Main quantitative findings. Profit shares fluctuate sharply: 5% of firms have losses exceeding 20% of output, against an average profit share of 0.13; the 5th percentile of profit-share deviations is −0.33 and the 95th is +0.47. Output growth is fat-tailed (s.d. 0.48, IQR/s.d. ratio 0.65 vs 1.35 Gaussian; excess kurtosis 10.7). Inputs do not track output: regressing wage-bill growth on output growth gives 0.40 (capital 0.16); restricting to |Δlog y|<0.5 gives 0.58 and 0.31. A change in profit share on output growth has slope 1.56 (0.46 in the restricted sample). The headline result: eliminating both frictions would raise output by 15.8%; eliminating the risk wedge alone raises output by 15.4%, while eliminating the credit wedge alone raises output by only 0.4%. Misallocation losses are 10.8% (11.0% due to risk, 0.2% due to credit). Aggregate wedges are equivalent to a 12.8% tax on labor and 14.9% on capital. Wage losses are 27.8% (26.4% risk, 0.4% credit).

Mechanisms and implications. Two wedges distort choices: a risk wedge (from the covariance of consumption and productivity) that distorts both labor and capital, and a credit wedge (from the binding collateral constraint) that distorts only capital. The credit wedge falls quickly with wealth (vanishing once unconstrained), but the risk wedge declines only gradually and persists even for wealthy entrepreneurs. Aggregate losses are governed by the distribution of wedges weighted by efficient firm size (Hopenhayn 2014): risk wedges are large precisely for high-ability entrepreneurs who would be large under efficiency, whereas credit-constrained firms are mostly unproductive with small efficient size. Policy implication: improving credit access has limited impact unless it also improves risk sharing. The findings also imply firm profits largely reflect compensation for risk (75% of the aggregate profit share), and dispersion in returns to business wealth largely reflects risk compensation.

Layer 2: Deep Dive

What is the identification strategy for the model, and how are parameters pinned down?

Parameters ϑ=(β,α,η,ρ,σu,σε,s,p,ϕ) are estimated by simulated method of moments, minimizing a weighted distance between 16 empirical and model moments scaled by 1+empirical moment (objective = 0.013, ~1.3% average deviation). Intuitively: β is pinned by the entrepreneur wealth-to-income ratio (12.5 in data and model); α and η by the capital-output ratio (1.22 vs 1.21), labor share (0.72 vs 0.71) and profit share (0.13 vs 0.14); ρ, σu, σε by output autocorrelations at horizons 1–3, the cross-sectional s.d. of output, and the s.d. of output growth at horizons 1–3; the tail parameters s and p by the IQR of output growth relative to its s.d.; and ϕ by the entrepreneurship rate. Three assigned parameters: δ=0.10, r=0.02, θ=2, with ξ=0.408 set to match the aggregate debt-to-capital ratio of 0.408. Standard errors (bootstrapped) are small because the firm sample is very large.

What is the main mechanism, and how are the risk wedge and credit wedge distinguished?

Because labor and capital are chosen before productivity is realized and risk is undiversified, the entrepreneur weights future states by their own stochastic discount factor. The risk wedge τ (>1) arises from the negative covariance between marginal utility of consumption and productivity and distorts both labor and capital equally. The credit wedge ω (>1 when the collateral constraint binds) distorts only capital. As wealth rises, the credit wedge falls rapidly and vanishes once the firm is unconstrained, but the risk wedge declines only gradually and never disappears. The two are isolated quantitatively by setting ω=1 (to get the role of risk) or τ=1 (to get the role of credit) in the productivity-loss mapping (eq. 13).

Why does risk dominate credit in the aggregate even though most firms are credit-constrained?

Aggregate outcomes depend on the distribution of wedges weighted by efficient firm size n_it (Hopenhayn 2014). Weighted by efficient size, the risk wedge ranges from 1.27 (10th pct) to 1.61 (90th pct), while the credit wedge is essentially 1 except at the very top (1.02 at the 90th pct). Unweighted, the risk wedge is only 1.12 at the 90th pct and the credit wedge is positive for more than half of firms — but those constrained firms are unproductive with small efficient size. Risk wedges are large precisely for high-ability entrepreneurs who would be large under the efficient allocation, so they drive the aggregate.

Why is the result robust to the form of the collateral constraint?

The authors consider two extremes: no borrowing at all (ξ=0) and unlimited borrowing (ξ=1, no credit limit). With no borrowing, misallocation losses rise only from 10.8% to 11.7%, still mostly risk-driven (8.3% risk vs 1.4% credit). With no credit limit, risk wedges remain nearly as large as baseline and removing credit frictions has negligible effects. Intuitively, risk leads entrepreneurs to operate small and accumulate precautionary wealth, so they self-finance most desired capital and credit wedges stay small even without credit.

Which three ingredients are essential to the risk-dominates result, and what happens without each?

(1) Fat-tailed productivity shocks, (2) transitory productivity shocks, and (3) labor chosen before productivity is realized. Removing each in isolation (with re-estimation) reverses the conclusion so that credit becomes the primary driver: without fat tails, misallocation losses fall to 2.1% (credit 1.5%, risk 0.3%); without transitory shocks, losses are 12.1% (credit 10.9%, risk 0.4%); with flexible labor, losses fall to 3.3% (credit 2.4%, risk 0.1%). The flexible-labor case matters because risk then distorts only capital, whose share is smaller than labor’s, reducing income volatility and pushing firms to expand and hit the credit constraint. In all three counterfactuals, the 1st percentile of profit-share deviations ranges −0.21 to −0.43, far smaller in magnitude than the data (−1.66) or baseline model (−1.92).

Is the result driven by high risk aversion?

No. The baseline uses relative risk aversion θ=2. Re-estimating with θ=0.5 (low end of usual values) still yields sizable, risk-dominated losses: productivity losses 6.4%, output losses 9.2%, wage losses 16.7% — roughly three-fifths of the baseline — and again primarily driven by risk rather than credit.

What untargeted moments does the model match (model validation)?

The model reproduces the distribution of profit-share deviations (10th pct −0.17 data vs −0.16 model; 1st pct −1.66 data vs −1.92 model), the full distribution of output growth rates, the low wage-bill/output comovement (0.58 data vs 0.55 model in the restricted sample), the profit-share/output comovement (0.46 vs 0.42; falling to 0.10 vs 0.06 when holding the labor share constant), and the persistence/volatility of capital and labor (e.g., wage-bill growth s.d. 0.36 vs 0.32). Critically, it matches the low comovement of entrepreneur consumption with profits: regressing Δc on Δπ gives a slope of 0.02 in both data and model (data based on 799 EFF observations, three-year changes).

What heterogeneity and external validity does the paper document?

The motivating facts hold for Italy, France, Norway, Portugal and Slovakia, and for Spanish public firms; for young (age≤5) and old firms; for small and large firms (top decile of value added vs rest); and across the five largest sectors (manufacturing, construction, wholesale/retail, accommodation/food, professional activities). Output-growth kurtosis ranges roughly 11–18 across countries. On diversification: 12% of households are entrepreneurs; 93% of entrepreneurs own exactly one business; multi-business owners hold 71% of their business wealth in their main business; the average ownership share is 83%, and 71% own 100% of their main business.

What are the extensive-margin and unconstrained-firm results?

Extensive margin: when the planner can also choose who becomes an entrepreneur, it cuts the entrepreneurship rate from 13.2% to 1.2%, but because marginal entrepreneurs are low-ability the gains are small — productivity, output and wage losses relative to the unconstrained planner are 10.8%, 16% and 27.8%, very close to the intensive-margin numbers. Unconstrained firms: adding a frictionless sector calibrated to match the 58.7% output share of public firms in Orbis leaves misallocation losses at 10.5% (vs 10.8% baseline), still mostly risk-driven (risk 10.1%, credit 0.1%); wage losses fall to about three-fifths of baseline because the unconstrained sector reduces the aggregate labor wedge.

What are the implications for profits and returns to wealth?

Decomposing the profit share into span-of-control, risk and credit components: risk accounts for 75% of the aggregate profit share (0.11/0.146), with the rest from span of control; credit contributes little. Risk also drives most of the profit-share dispersion (s.d. 5.5%, essentially all from risk; credit contributes only 1%). For excess returns to wealth, the mean of 2.2% is almost entirely accounted for by risk, and risk drives most of the dispersion (s.d. 5.5%). This implies dispersion in returns to private business wealth — a driver of wealth inequality — largely reflects compensation for risk rather than credit constraints.

What is the working-capital robustness check?

Adding a working-capital constraint where a fraction ϑ=0.25 of the wage bill is paid in advance (à la Mendoza 2010), evaluated at baseline parameters, gives misallocation losses of 11.1% (vs 10.8% baseline), with risk still accounting for the bulk (9.4%) and credit less important (1.3%); risk accounts for 13.4% of the 16.3% total output losses. So even when credit frictions can also distort labor, risk remains dominant.

What are the policy implications and their scope conditions?

The central implication is that policies expanding firms’ access to credit will have limited aggregate impact unless they also improve risk sharing. This holds within the scope of the model — undiversified private businesses with single owners, where risk exposure is endogenously chosen via scale and can be partly self-insured through wealth, labor income, and occupational switching. The authors note their framework assumes (rather than micro-founds) the lack of diversification, and suggest future work should model the moral-hazard or informational frictions preventing diversification, and broaden redistributive tax analysis to incorporate uninsurable-risk distortions (as in Di Tella et al. 2024).

How does this paper relate to and differ from closely related prior work?

It contributes to the misallocation literature (Hsieh-Klenow 2009; Buera et al. 2011; Moll 2014; Midrigan-Xu 2014; Gopinath et al. 2017). Prior work on risk and investment (Tan 2018; Robinson 2021; David et al. 2022a) studies how risk distorts investment; this paper instead emphasizes how risk distorts LABOR choices, relating it to Arellano et al. (2019) and David et al. (2022b). It differs from the credit-constraint-centric tradition by showing credit matters little once undiversified risk and the three key ingredients are present. Di Tella et al. (2024), partly motivated by these findings, study optimal policy under uninsurable risk and show it is the opposite of optimal policy when misallocation stems from markups.

Key Concepts

Risk wedge (τ): In the paper’s sense, the gap between the expected marginal product of an input and its price arising from undiversifiable business risk. It equals [1 + COV(c^{-θ}, zε)/(E c^{-θ} · E zε)]^{-1}, generally >1 because of the negative covariance between the entrepreneur’s marginal utility of consumption and productivity. It distorts both labor and capital, declines only gradually with wealth, and persists even for wealthy entrepreneurs.

Credit wedge (ω): The distortion from a binding collateral constraint, ω=1+(1−ξ)μ/R, where μ is the multiplier on the constraint k’≤a’/(1−ξ). It exceeds one only when the constraint binds, distorts only capital, falls rapidly with wealth, and vanishes once the entrepreneur is unconstrained.

Profit share: In this paper, the ratio of profits to output (value added), π_it/y_it, where profit is output net of the wage bill and the user cost of capital. Its average is 0.13; the paper studies its large transitory firm-level fluctuations as the empirical signature of uninsurable risk.

Time-to-build (inputs chosen before productivity): The assumption that both capital and labor are chosen before the firm observes its productivity shock. This parsimoniously generates the imperfect high-frequency comovement between inputs and output and makes wealth affect employment as well as investment.

Efficient-size-weighted wedge distribution: The paper’s organizing device (following Hopenhayn 2014): aggregate productivity losses depend on the distribution of risk and credit wedges weighted by each firm’s efficient size n_it. Because high-ability firms have large efficient size and large risk wedges, risk dominates the aggregate even though most firms are credit-constrained.

Self-financing: The mechanism by which entrepreneurs, operating at small scale and saving for precautionary reasons because of risk, accumulate enough wealth to finance most of their desired capital — so credit wedges stay small even in an economy with no credit, rendering the borrowing limit nearly irrelevant for aggregates.