Firm exit during recessions

Ayres, Joao; Raveendranathan, Gajendran Working Paper Firm exit during recessions IDB Working Paper Series, No. IDB-WP-1117 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Ayres, Joao; Raveendranathan, Gajendran (2020) : Firm exit during recessions, IDB Working Paper Series, No. IDB-WP-1117, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0002289 This Version is available at: https://hdl.handle.net/10419/234698 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/igo/legalcode Firm Exit during Recessions João Ayres Gajendran Raveendranathan IDB WORKING PAPER SERIES Nº IDB-WP-1117 A pril 2020 Department of Research and Chief Economist Inter-American Development Bank A pril 2020 Firm Exit during Recessions João Ayres* Gajendran Raveendranathan** * Inter-American Development Bank ** McMaster University Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library A yres, João (João Luiz). Firm exit during recessions / João Ayres, Gajendran Raveendranathan. p. cm. — (IDB Working Paper Series ; 1117) Includes bibliographic references. 1. Recessions-United States-Econometric models. 2. Credit-United StatesEconometric models. 3. Labor productivity-United States-Econometric models. 4. Business cycles-United States-Econometric models. I. Raveendranathan, Gajendran. II. Inter-American Development Bank. Department of Research and Chief Economist. III. Title. IV. Series. IDB-WP-1117 Copyright © Inter-American Development Bank. This work is licensed under a Creative Commons IGO 3.0 AttributionNonCommercial-NoDerivatives (CC-IGO BY-NC-ND 3.0 IGO) license (http://creativecommons.org/licenses/by-nc-nd/3.0/igo/ legalcode) and may be reproduced with attribution to the IDB and for any non-commercial purpose, as provided below. No derivative work is allowed. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the UNCITRAL rules. 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The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. http://www.iadb.org 2020 Abstract* We analyze a general equilibrium model of firm dynamics to study the effects of shocks to productivity, labor wedge, and collateral constraint (credit shock) on firm exit. We find that only the credit shock increases firm exit. This result is robust to the magnitude of shocks and different model specifications. Calibrating the model to match the behavior of output, employment, and firm debt during the Great Recession (2007-2009) in the United States, we find that the credit shock accounts for the observed rise in firm exit and its concentration among young firms. Furthermore, it accounts for 20 percent of the drop in output and employment. JEL classifications: D21, D22, E24, E32 Keywords: Credit, Firm dynamics, General equilibrium model, Output, Employment * We are indebted to Manuel Amador and Timothy J. Kehoe for invaluable advice and guidance. We thank Pau Pujolas, Kei-Mu Yi, Horacio Sapriza, and participants at the International Trade Workshop at the University of Minnesota, AWESOME 2018, CEA 2018, Midwest Macro 2018, MEA 2015, and LACEA-LAMES 2019 for useful comments and discussions. The views expressed herein are those of the authors and not necessarily those of the Inter-American Development Bank. Author emails: Ayres ([email protected]), Raveendranathan ([email protected]). 1 Introduction In this paper, we ask the following question: how do aggregate shocks affect firm exit? To answer this question, we build a general equilibrium model of firm dynamics with financial frictions and analyze the implications of shocks to productivity, collateral constraint (credit shock), and the labor wedge.1We show that in general equilibrium, only the credit shock increases firm exit, and that this result is robust to the magnitude of the shocks as well as to different model specifications. Next, we calibrate the model to match the observed behavior of output, employment, and firm debt during the Great Recession (2007–2009) in the United States. We show that the credit shock not only accounts for the overall rise in firm exit, but also accounts for the heterogeneous behavior of firm exit across age groups, with young firms accounting for most of the rise. In this exercise, the credit shock accounts for 20 percent of the decline in output and employment during the Great Recession. Our model economy builds on Khan and Thomas (2008,2013) and Clementi and Palazzo (2016). We enrich Clementi and Palazzo (2016)’s model of firm entry and exit by incorporating financial frictions and solving the model in general equilibrium, as in Khan and Thomas (2008,2013). More specifically, we add debt decisions with collateral and non-negative dividend payments constraints to the firm’s problem, and savings and labor choices to the representative consumer’s problem. The inclusion of debt accumulation by firms, together with collateral and non-negative dividend payments constraints, allows us to study the implications of credit shocks. The savings and labor choices close the economy, allowing us to solve for interest and wage rates in general equilibrium. Our results are derived from two exercises. In the first exercise, we separately analyze the transition dynamics following negative shocks to productivity, labor wedge, and collateral constraint, with a focus on the dynamics of firm exit. The temporary shock is unexpected in period one and, after that, agents have perfect foresight on the evolution of the economy. The magnitude and persistence of the shocks are chosen to match the average drop in U.S. GDP in the last four recessions (1982, 1990, 2001, and 2007) as well as the average time it took for U.S. GDP to complete half of the recovery since the beginning of the recession. Our results show that, among these three shocks, only the credit shock increases firm exit. The effects of productivity and labor wedge shocks on firm exit are quantitatively negligible. The intuition for these results are as follows. Everything else constant, a negative productivity shock reduces firms’ revenues. That lowers the value of operating for any given firm while keeping the value of exit constant. Hence, it should lead to an increase in firm exit. However, in general equilibrium, the negative productivity shock leads to 1The labor wedge refers to a shock from the business cycle accounting literature that generates a larger fall in labor relative to output. 1 lower wage and interest rates, which offset the impact of the negative productivity shock on the value of operating, and consequently, the rate of firm exit remains approximately unchanged. In turn, the labor wedge shock is modeled as in Chari, Kehoe, and McGrattan (2007), where the shock directly impacts the household’s labor supply decision. The shock does not affect the firm’s fundamentals directly, so it could only impact firm’s exit decision through general equilibrium effects. Since the labor wedge shock reduces labor supply, it puts upward pressure on the wage rate. However, in our model, most of the adjustment for a labor wedge shock comes through lower firm entry, which dampens the upward pressure on the wage rate, leaving the rate of firm exit approximately the same. In contrast, a shock to the collateral constraint increases firm exit for two reasons. First, it constrains the ability of firms to borrow and accumulate capital, specially among the young ones. This reduces their value of operation and they choose to exit. Second, firms that come into the period with debt that matures in the current period might not be able to issue enough new debt to pay non-negative dividends. Those firms are forced to exit. In our second exercise, where we calibrate the model to the Great Recession in the U.S., around 80 percent of the increase in firm exit results from firms choosing to exit even though they could pay non-negative dividends. That means that the first reason dominates. Therefore, while general equilibrium offsets the effect of the productivity and labor wedge shocks on firm exit, it only partially dampens the effect of the shock to the collateral constraint. This result is robust to the magnitude of the shock and to different model specifications (e.g., fixed operating costs in units of the final good as opposed to units of labor, GHH preferences as opposed to standard log preferences, and GHH preferences with habit formation).2 In our second exercise, we jointly calibrate productivity, labor wedge, and collateral constraint shocks to match the behavior of output, employment, and firm debt in the U.S. during the Great Recession (2007–2009), and compare the model with all three shocks (including the credit shock) to a counterfactual one with only the productivity and labor wedge shocks (excluding the credit shock). We find that only the model with the credit shock increases firm exit. The model without the credit shock actually decreases firm exit, which is at odds with the data. Furthermore, the model with the credit shock accounts for the increased firm exit concentrated among young firms. We view this result as additional evidence that a credit shock played a significant role during the Great Recession. Finally, comparing the models with and without the credit shock, we find that the drop in both output and employment in 2009 would have been 20 percent lower if there were no credit shock. Related literature Our paper contributes to several strands of the literature: the 2Osotimehin and Pappad`a (2017) find that negative productivity and financial shocks increase establishment exit in a partial equilibrium model of firm dynamics. While this result is also true in our model, only the credit shock increases firm exit in general equilibrium. 2 literature on firm entry and exit, the literature on firm dynamics and credit shocks, the literature on business cycle accounting, and the empirical literature on firm dynamics statistics. The paper that is most closely related to ours is Clementi and Palazzo (2016). They extend Hopenhayn (1992) to analyze how a shock to aggregate productivity propagates to changes in output in models with and without firm entry and exit. They find that incorporating firm entry and exit leads to higher persistence and volatility of output. The main difference between their analysis and ours is that we focus on implications of shocks for firm exit rather than how firm entry and exit affect aggregate fluctuations. Furthermore, our modeling choices differ from Clementi and Palazzo (2016) in other aspects, as we assume a general equilibrium model with endogenous interest rates, financial frictions, and firm entry with an unbounded mass of ex-ante identical entrants. The unbounded mass of ex-ante identical entrants implies that, in our model, the zero profit condition for entry holds with equality for all entrants. In Clementi and Palazzo (2016), potential entrants are bounded and ex-ante heterogeneous. Hence, in their model, the zero profit condition for entry does not hold with equality for all entrants. This feature of our model generates entry that is more cyclical than exit, a feature of the data documented by Lee and Mukoyama (2015). Our paper contributes to the literature that uses firm dynamics models to study aggregate fluctuations. Khan and Thomas (2013) study productivity and credit shocks in a firm dynamics model with collateral constraints and partial irreversibility of investment. Khan, Senga, and Thomas (2016) study productivity and credit shocks in a firm dynamics model with endogenous default. Both papers argue that credit shocks are important to account for the behavior of aggregates and employment among small and large firms during the Great Recession. Clementi, Khan, Palazzo, and Thomas (2015), Sedl´aˇcek (2019), and Siemer (2016) study how the decrease in firm entry during the Great Recession affected the slow recovery, which they term the “missing generation effect”. Buera, Fattal-Jaef, and Shin (2015) analyze productivity shocks and credit shocks in a model with frictions in both the labor and the financial markets. A credit shock decreases employment among both young firms or small firms and increases employment among old and large firms. Mehrotra and Sergeyev (2019) target changes in job flows across firm age categories to calibrate their model of firm dynamics with financial frictions. The identification for the credit shock comes from lower job creation. They find that the credit shock accounts for 15 percent of the drop in total employment during the Great Recession. These papers have primarily emphasized the effect of credit shocks on firm entry and on young and small firms. We contribute to this literature by emphasizing the importance of a credit shock to account for firm exit during the Great Recession. We also contribute to the literature on business cycle accounting. This literature estimates productivity, investment, labor, and government wedges to exactly match aggregates such as output, investment, consumption, and labor (Chari, Kehoe, and McGrattan, 3 2007). The idea is that upon estimation, the researcher could use these wedges to identify potential shocks. Brinca, Chari, Kehoe, and McGrattan (2016) estimate wedges in the standard real business cycle model and find that the labor wedge shock played a large role during the Great Recession. Furthermore, they emphasize that a credit shock might show up as a productivity or labor wedge or investment wedge shock in the standard real business cycle model depending on the underlying economic environment. This finding is further emphasized in Buera and Moll (2015), who find that a shock to the collateral constraint could show up as a shock to productivity or the labor wedge or the investment wedge depending on the underlying form of firm heterogeneity. In our model, even after controlling for the credit shock, we find that the labor wedge played a large role during the recession. Our calibrated value for the increase in the labor wedge is more than 3 percentage points. While this complements the finding in Brinca, Chari, Kehoe, and McGrattan (2016), it also suggests that the large labor wedge that they estimated was not driven primarily by a credit shock. These results also complement Kehoe et al. (2019a) and Kehoe et al. (2019b), who emphasize the role of tightening household credit rather than firm credit during the Great Recession. Finally, we contribute to the empirical literature on firm dynamics. In particular, Siemer (2019) compares the performance of firms with high and low external financial dependence during the Great Recession using confidential data on the universe of firms in the U.S., and finds that financial constraints affected firm employment growth of young firms primarily through firm entry and exit. Fort, Haltiwanger, Jarmin, and Miranda (2013) and Decker, Haltiwanger, Jarmin, and Miranda (2014b) emphasize the importance of firm age in addition to firm size in their analyses. Our finding that a credit shock accounts for the increased firm exit across different age groups complements these empirical studies and emphasizes the importance of firm age in addition to firm size. This is because in the presence of financial frictions and firm entry and exit, age is one of the determinants of a firm’s idiosyncratic state (productivity, capital, and debt in our model).3 This paper is organized as follows. Section 2presents empirical evidence on firm exit during recessions in the United States. Section 3describes the model economy, and Section 4presents its calibration. Section 5discusses the properties of the model in the stationary equilibrium, and Section 6shows the results. Section 7presents our final remarks. 3Other papers related to our study are Ottonello and Winberry (2018), Winberry (2020), and Xiao (2018), Sedl´aˇcek and Sterk (2017), Bloom et al. (2018), Arellano et al. (2018), Gilchrist et al. (2014), Dyrda (2016), Jermann and Quadrini (2012), Moscarini and Postel-Vinay (2012), Gomes and Schmid (2010), Gavazza et al. (2016), Crouzet and Mehrotra (2018), Lee and Mukoyama (2018), Schott (2015), and Adrian et al. (2012). 4 to one, and the labor wedge τhis set to zero. Table 1: Parameters determined outside of the stationary equilibrium Parameter Value Discount rate (β) 0.960 Labor elasticity (φ) 0.500 Borrowing spread (τb) 0.013 Span of control (ν) 0.836 Depreciation rate of physical capital (δk) 0.060 Persistence of idiosyncratic productivity (ρ) 0.859 Fixed entry cost (fe) 1 Aggregate labor productivity (Z) 1 Labor wedge (τh) 0 The idiosyncratic productivity is assumed to follow a log AR(1) process given by log 0=ρlog +η0, in which the innovation η0is iid and follows a Normal distribution with zero mean and variance σ2 η. The persistence parameter ρis set to 0.859, following Khan and Thomas (2008). We discuss the calibration of the variance parameter σ2 ηbelow. The productivity process is discretized to a Markov chain with 30 grid points following the method described in Tauchen (1986). Entrants draw their initial productivities from the stationary distribution of the discretized Markov chain. Table 2 presents the eight remaining parameters, which are jointly calibrated so that the model matches eight targeted moments in the stationary equilibrium. The choice of the targeted moments is based on the specific set of parameters we want to calibrate. The collateral constraint θis related to the amount of debt firms have. We use as a target the average non-finance business debt-to-GDP ratio in 1948–2015 using data from the US Financial Accounts from the Board of Governors of the Federal Reserve System, which is 50 percent. The leisure share ψis related to the fraction of total employment to working age population in the data, approximately 60 percent.9The capital share αis related to the labor share, and we use its average from 1970–2015 of 65 percent as a target. Our specification of the capital adjustment cost function allows our model to match moments of the distribution of the investment rates (investment/capital) of individual firms reported in Cooper and Haltiwanger (2006). The investment irreversibility parameter γis related to the fraction of firms with investment rates below 1 percent in absolute value, the inaction region, while the quadratic adjustment cost λis related to the fraction of firms with investment rate above 80 percent, and the variance of innovations to idiosyncratic productivity σ2 ηto the standard deviation of investment rates.10 Finally, 9Working age population is defined as the number of individuals between 16 and 64 years old. 10Cooper and Haltiwanger (2006) compute investment statistics using a balanced panel of large manufacturing plants that are continually in operation between 1972 and 1988. We account for that by simulating the initial stationary distribution for 30 years and computing the investment statistics based 11 Table 2: Parameters determined jointly in equilibrium and targeted moments Parameter Value Collateral constraint (θ) 0.73 Leisure share (ψ) 1.75 Capital share (α) 0.37 Entry capital (ke) 2.45 Fixed operating cost (fo) 0.78 Variance of innovations to idiosyncratic productivity (σ2 η) 0.08 Investment irreversibility (γ) 0.02 Quadratic adjustment cost (λ) 1.08 Target Data Model Ratio of non-finance business debt to GDP 0.50 0.48 Total labor 0.60 0.60 Labor share 0.65 0.63 Entrants’ 5-years survival rate 0.46 0.46 Entry rate 0.11 0.09 Standard deviation of investment rate 0.34 0.33 Fraction of firms with absolute investment rate below 1% 0.08 0.08 Fraction of firms with investment rate above 80% 0.02 0.03 the entry capital keand fixed operating cost foare related to the entry rate and the survival rate of young firms. Regarding the latter, we chose to target the entrants’s 5-years survival rate. The targeted moments in the data and their respective values in the model are listed in Table 2.11 5 Properties of the initial stationary equilibrium In this section, we analyze the lifecycle properties of firms in the stationary equilibrium under the benchmark calibration and validate the model against non-targeted moments in the data. Figures 2a and 2b plot the average employment and average capital stock of firms in each cohort, respectively. Firms start with the initial capital stock keat age 0 and begin to accumulate capital up to an age in which it stabilizes, around 15 years old on average. Employment follows a similar pattern. In fact, the employment decision is a static one, in which operating firms equalize the marginal product of labor to its marginal cost, lt(k, b, ) = (1 −α)ν(Zt)1−αν kαν wt!1 1−(1−α)ν . on the restricted sample of firms that survive for the entire period. 11Even though we described a relation between each parameter and a specific moment, it is important to emphasize that they are all estimated jointly because they affect the other targeted moments as well. 12 This implies that employment is increasing in firms’ capital, idiosyncratic productivity, and aggregate productivity, decreasing in the wage rate, and does not depend on the level of debt. There are several features in the model that explain the growth pattern of young firms. The capital adjustment cost makes it costly for firms to adjust their capital stock by large amounts, so they smooth investment over time. The collateral and non-negative dividend payment constraints pose additional difficulties to capital accumulation. Firms rely on retained earnings and debt issuance to finance investment. However, the lower initial capital stock makes it difficult for firms to raise enough operating revenues and issue enough debt to achieve their desired stock of capital. Figures 2c and 2d show that firms leverage themselves with debt to finance investment in the early years. Average debt increases up to age 8 and decreases thereafter, reaching negative values for firms older than 13 years, which means that they begin to save to avoid hitting the non-negative dividend constraint in the future. Accordingly, firms choose to not pay dividends in their early ages until they have accumulated enough capital and savings. Figure 2e plots the average dividend payments by age of incumbent firms that choose to operate. Dividends are zero up to around age 7 and begin to increase thereafter, which means that all the revenues from sales and debt issuance are used for capital investment in the initial years. Finally, firms also grow due to a selection effect. In our model, the only reason firms exit is because of low idiosyncratic productivity shocks. Some firms might be forced to exit because they cannot satisfy the non-negative dividend constraint, or they may choose to exit if the net present value of operation becomes lower than the value of exit. Consequently, the firms that are more likely to exit are the ones with lower capital and higher debt. In our model, these represent the young firms, which are trying to accumulate capital and have less space (low capital and high debt) to accommodate these negative shocks. Hence, the productivity threshold that triggers exit is higher for these firms. This adds to the higher exit rates at younger ages in Figure 2f. Therefore, the most productive firms survive in the initial years, implying that the average productivity increases, as Figure 2g shows. Interestingly, the life cycle profile of average productivity is not monotone. It starts to decrease after age 6. This is because by then firms have accumulated capital and start reducing their debt. Hence, they are more capable of accommodating low productivity shocks and the productivity threshold that triggers exit decreases. Figure 3compares the properties of the stationary equilibrium to the data, and shows that the model accounts for several non-targeted moments. Figure 3a plots the distribution of firms across age groups and Figure 3b plots the average employment size of firms by age group. The model statistics closely match the data even though none of these moments were targeted except one. In Figure 3a, we implicitly targeted the ratio of the mass of firms that are 5 and 0 years old, because we calibrated the model to match the 13 Figure 2: Life cycle properties (a) Employment, l(b) Capital, k (c) Debt, b(d) Debt-to-capital ratio, b/k (e) Dividend, D(f) Exit rate (g) Productivity,  14 Figure 3: Firm age distribution, firm employment size, and job flows by age group (a) Firm age distribution (b) Firm employment size by age group (c) Job creation (d) Job destruction 15 entrant’s 5-years survival rate. The stationary equilibrium also matches the rates of job creation and destruction by age groups, presented in Figures 3c and 3d. The rates are computed as the fraction of jobs created/destructed over the total number of employees in the respective age group. This implies that age 0 firms have rates of job creation and destruction of 100 and 0 percent, respectively, both in the model and in the data. 6 Results In this section, we perform two exercises. In the first exercise, in Section 6.1, we analyze the implications of negative shocks to aggregate productivity, labor wedge, and collateral constraint (also referred to as a credit shock) for firm exit. We show that only the credit shock increases firm exit in general equilibrium and that this result is robust to alternative model specifications. In the second exercise, in Section 6.2, we jointly calibrate the shocks to target the behavior of output, employment, and firm debt during the Great Recession (2007–2009) in the United States. We show that the credit shock not only accounts for the observed increase in firm exit, but it also accounts for the different behavior of exit rates across age groups. We also quantify its impact on aggregate output and employment. 6.1 Aggregate shocks and firm exit Starting from the stationary equilibrium under the benchmark calibration, we analyze the impulse response functions from temporary shocks to aggregate productivity, labor wedge, and collateral constraint. These shocks are unexpected one-time events, but once they occur agents have perfect foresight of how these variables will evolve over time.12 In this exercise, we analyze each shock separately. The size and persistence of the shocks are jointly calibrated such that they generate the same drop and recovery in GDP. We match the average drop in US real GDP normalized by the working age population from peak to trough in the last four recessions, 5.2 percent, and the average time that it takes for GDP to complete half of the recovery since the beginning of the recession, 4 years. Figure 4shows the calibrated values of the shocks and the impulse response functions of main macroeconomic aggregates resulting from each shock. Given our calibration strategy discussed above, GDP is the same for all shocks in periods 1 and 4 as indicated by the gray markers in Figure 4d. In addition, Figure 4e shows that all shocks lead to reductions in employment, which also characterize recessions in the data. Figure 4f, which plots firm debt-to-GDP ratio, shows that firm debt-to-GDP decreases with the credit shock, but increases with the productivity and labor wedge shocks. The productivity and labor wedge shocks increase firm debt-to-GDP because they lead to a larger drop in 12We study transition dynamics as in Samaniego (2008). 16 Figure 4: Transition dynamics of main aggregates (a) Productivity, Zt(b) Labor wedge, τh t (c) Collateral constraint, θt(d) GDP (e) Employment, Ht(f) Debt-to-GDP ratio 17 GDP compared to the drop in firm debt. Given that these responses are qualitatively and quantitatively different across shocks, we will use these responses to jointly calibrate shocks during the Great Recession in our second exercise in Section 6.2. In this first exercise, we focus on firm exit. As Figure 5shows, the implications for exit rates are very different across shocks. In particular, only the credit shock leads to a spike in the exit rate.13 Figure 5: Firm exit rate: 3 years old and older To better understand the exit dynamics following each shock, Figure 6breaks down the effects of each type of shock into partial and general equilibrium effects. It plots the exit rate together with the changes in the wage and interest rates. Let’s start with the productivity shock. The red dashed line in Figure 6a shows what the exit rates would be if wages wt, interest rates rt, and entry rates mtremained fixed at their initial levels (this relaxes labor market clearing, assets market clearing, and the zero profit condition). In this case, the only change an incumbent firm would observe is the lower aggregate productivity. This does not change the value of exit. However, it implies lower revenues and therefore a lower value of operating. That explains the rise in exit rates in period 1 for the dashed red line. However, once wages and interest rates are allowed to change, they offset most of the negative impact of the lower aggregate productivity for incumbent firms such that the overall changes in exit rates become negligible. This happens regardless of whether we keep entry rates fixed (relaxes the zero profit condition) and allow the wage and interest rates to change (black dotted line) or allow the entry, wage, and interest 13In the Appendix, Figure 11 shows that the entry rate decreases in all cases. Hence, in our model, lower firm entry is a response to all three shocks. 18 rates to change (benchmark general equilibrium—blue solid line). Figure 6d analyzes the exit rate following the labor wedge shock. Note that the labor wedge does not enter the firm’s problem. Hence, it could affect exit only through general equilibrium effects. That explains why the red dashed line (fixed wage, interest, and entry rates) does not respond. Once we allow wage and interest rates to change while keeping the mass of entrants fixed, the black dotted line, we observe an increase in exit rates. The reason is the following. The higher labor wedge leads to a lower supply of labor. Keeping entry rates fixed, but allowing the interest rate and wage rate to adjust leads to an adjustment in employment through incumbent firms. That leads to a large increase in wage rates, the black dotted line in Figure 6e. This makes firms demand less labor and pushes some of them to exit, which explains the rise in exit rates for the black dotted line. However, the higher wages make entry less attractive. Hence, at those wages, the firms that are entering would prefer not to. When we allow the entry rate to vary (zero profit condition holds), the lower mass of entrants lead to lower demand for labor. Consequently, the increase in the wage rate becomes much smaller in general equilibrium (blue solid line in Figure 6e) than when entry was fixed. This leads to almost no change in exit rates. Finally, Figure 6g analyzes the case of a credit shock. As in the productivity shock case, the lower collateral constraint directly impacts firms. In fact, it mostly impacts young productive firms that are borrowing to accumulate capital as shown in Figure 2d. These are the firms that are financially constrained, and once the shock hits, there is a spike in exit rates. There are two main reasons for that. First, borrowing firms decided the amount of debt they brought into the period assuming that they would be able to borrow again. Once the issuance of debt unexpectedly becomes more difficult, and given that firms still have a low stock of capital, some of them are forced to exit because they are unable to generate non-negative dividends. Second, some exiting firms would be able to cut investment to generate positive dividends, but that would imply a much slower process of capital accumulation, which is further amplified due to the interaction with the lower collateral constraint. This leads some firms to choose to exit because it would take much longer for them to generate positive dividend payments. These two effects hold even when we allow for wages and interest rates to change, as well as the mass of entrants. General equilibrium only partially dampens the rise in firm exit. In the exercise in the next section in which we study the Great Recession, we further decompose changes in firm exit due to a credit shock. The different behavior of exit rates following a credit shock is robust to the magnitude of the shock and to different specifications of the model. We show the behavior of firm exit in Figure 7for a small shock and different model specifications. For the small shock, we consider the case where the shock is half of the calibrated value in Figure 4. Even then, the credit shock increases firm exit. For the different model specifications, we consider 19 Figure 6: Partial and general equilibrium effects (a) Productivity: exit rate (b) Productivity: wage rate (c) Productivity: interest rate (d) Labor wedge: exit rate (e) Labor wedge: wage rate (f) Labor wedge: interest rate (g) Credit: exit rate (h) Credit: wage rate (i) Credit: interest rate 20 Jermann, U. and V. Quadrini (2012). Macroeconomic effects of financial shocks. American Economic Review 102(1), 238–271. Kehoe, P. J., V. Midrigan, and E. Pastorino (2019a). Debt constraints and employment. 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Lumpy investment, business cycles, and stimulus policy. American Economic Review, Accepted. Xiao, J. (2018). Capital allocation and investment dynamics in credit crises. Working paper. 28 A Appendix A.1 Firm entry Figure 11 illustrates the behavior of firm entry for the three shocks analyzed in Section 6.1. It shows that all three shocks (shocks to productivity, labor wedge, and collateral constraint) lead to a drop in firm entry. Figure 11: Firm entry rate A.2 Algorithm to compute transitions •Guess sequence of rt •Back out sequence of Ctgiven that Ct=Ct+1/(β(1 + rt+1)) •Guess wtand solve for incumbent firm’s value and policy functions; solve for sequence of wtthrough backward induction such that Ventry t= 0 •Back out sequence of Htfrom household intra-temporal condition •Solve for sequence of mtsuch that labor market clears •Back out sequence for Πt,At+1, and Ct •Update rtuntil convergence 29