Financial Frictions and Fluctuations in Volatility

During the recent U.S. financial crisis, the large decline in economic activity and credit was accompanied by a large increase in the dispersion of growth rates across firms. However, even though aggregate labor and output fell sharply during this period, labor productivity did not. These features motivate us to build a model in which increased volatility at the firm level generates a downturn but has little effect on labor productivity. In the model, hiring inputs is risky because financial frictions limit firms’ ability to insure against shocks that occur between the time of production and the receipt of revenues. Hence, an increase in idiosyncratic volatility induces firms to reduce their inputs to reduce such risk. We find that our model can generate about 67% of the decline in output of the Great Recession of 2007—2009. Keywords: Uncertainty shocks, Great Recession, Labor wedge, Firm heterogeneity, Credit constraints, Credit crunch JEL classification: D52, D53, E23, E24, E32, E44 ∗The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. The recent U.S. …nancial crisis has been accompanied by severe contractions in economic activity and credit. At the micro level, the crisis has been accompanied by large increases in the cross-section dispersion of …rm growth rates (Bloom et al. 2011). At the macro level, it has been accompanied by a large decline in labor, even though labor productivity has barely fallen. Motivated by these observations, we build a quantitative general equilibrium model with heterogeneous …rms and …nancial frictions in which increases in volatility at the …rm level lead to increases in the cross-section dispersion of …rm growth rates and decreases in aggregate labor and output in the face of ‡at labor productivity. The key idea in the model is that hiring inputs to produce output is a risky endeavor. Firms must hire inputs to produce and take on the …nancial obligations to pay for them before they receive the revenues from their sales. Because of the separation between the time of production and the receipt of revenues, any idiosyncratic shocks, such as demand shocks, that occur between these times make hiring inputs risky. When …nancial markets are incomplete, …rms have only limited means to insure against such shocks, and hence, they must bear this risk. This risk has real consequences if, when …rms cannot meet their …nancial obligations, they must experience a costly default. In such an environment, an increase in uncertainty arising from an increase in the volatility of idiosyncratic shocks leads …rms to pull back on their hiring of inputs. We quantify our model and ask, can an increase in the volatility of …rm-level idiosyncratic shocks that generates the observed increase in the cross-section dispersion in the recent recession lead to a sizeable contraction in aggregate economic activity? We …nd that the answer is yes. Our model can generate about 67% of the decline in output and 73% of the decline in employment seen in the Great Recession of 2007–2009. More generally, we …nd that the model generates labor ‡uctuations that are large relative to those in output, similar to the relationship in the data. Generating such a pattern has been a major goal of the business cycle literature. Our model has a continuum of heterogeneous …rms that produce di¤erentiated products. The demand for these products is subject to idiosyncratic shocks. The volatility of demand shocks is stochastically time varying, and these volatility shocks are the only aggregate shocks in the economy. A continuum of identical households supply labor to …rms and lend to …rms using uncontingent debt through …nancial intermediaries. The model has three key ingredients. First, …rms hire their inputs— here, labor— and produce before they know their demand. Second, …nancial markets are incomplete in that …rms have access only to state-uncontingent debt and …rms default if they cannot pay for their debt. Third, since …rms must pay a …xed cost to enter a market, in equilibrium they make positive expected pro…ts in each period that they do not default. The cost of default is the loss of future expected pro…ts. Given these ingredients, when …rms choose their inputs, they face a trade-o¤ between expected return and risk. As …rms increase their employment, they increase the expected return conditional on not defaulting, but they also increase the probability of default. For a given variance of idiosyncratic demand shocks, they choose their optimal employment to balance o¤ the increase in expected return against the losses from default. The potential losses from default are an extra cost of increasing labor and thus distort the …rm’s …rst-order condition for labor. When the variance of the idiosyncratic shocks increases, at a given level of employment, the probability of default increases, and thus, so does this distortion. In equilibrium, in the face of such an increase in variance, …rms become more cautious and decrease employment. At the aggregate level, these …rm-level responses imply that when the dispersion of idiosyncratic shocks increases, aggregate output and employment both fall. The result that …rms decrease employment when the variance of demand shocks increases depends critically on our assumption of incomplete …nancial markets. If …rms had access to complete …nancial markets, there would be no trade-o¤ between expected return and default risk. Thus, an increase in the variance of these shocks would lead to no change in their employment; …rms would simply restructure the pattern of payments across states so that they would never default. In our model, …rms optimally time the purchases and sales of uncontingent debt to help meet their …nancial obligations in the presence of the stochastic revenue stream generated by the demand shocks. In this sense, …rms have a precautionary motive to use debt to self-insure. Since …rms have only limited means to repay their debt, they face upward-sloping interest rate schedules and a credit limit, a maximum amount they can borrow. Firms typically maintain a bu¤er stock of unused credit. By running this bu¤er stock up and down, …rms can partially