L26 | 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.

What's driving the decline in entrepreneurship?

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

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

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

In depth

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

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

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

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

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

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

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

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

Key concepts

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

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