Collateral Constraints, Wage Rigidity, and Jobless Recoveries

3.1 The Labor Market

The number of matches on the labor market is determined by m t = ν u t γ v t 1 − γ , where ν is the efficiency of the matching technology, u _t is unemployment, and v _t vacancies. The parameter γ governs the elasticity of the matching function with respect to unemployment and vacancies. The job-filling rate, the probability with which a firm fills a vacancy, is given by m t / v t ≡ q ( θ t ) = ν θ t − γ . The job-finding rate, the probability with which an unemployed worker finds a job, is given by m t / u t ≡ f ( θ t ) = ν θ t 1 − γ . Labor market tightness θ is defined as θ _t ≡ v _t /u _t . When labor market tightness is low, many unemployed workers compete for few vacant jobs. The job-filling rate is high and the job-finding rate is low.

At the beginning of each period, a fraction x of all existing worker-firm matches is exogenously separated. Newly separated workers immediately begin searching for a new job and have the same job-finding rate as all other unemployed workers. Employment evolves according to

and at the end of each period

workers remain unemployed. Since search is costless from the household perspective, all non-employed workers search for a job.

Posting a vacancy entails costs of c ( v t ) = κ 2 v t 2 per period, where κ 2 ∈ ( 0 , + ∞ ) represents the resources a firm must spend because of matching frictions.^[4] Furthermore, I assume that there is no risk on the firm side. Firms can hire h _t workers with certainty by posting m _t /q(θ _t ) vacancies.

3.2 Households

The setup allows for the existence of a representative household, consisting of a continuum of workers of measure one. The household aims at maximizing lifetime utility by allocating consumption optimally across all members:

where c _t is consumption, β _h is the discount factor of the household, φ is the disutility from work, and n _t is the share of workers that is employed at time t.^[5] The household’s flow of funds constraint is given by

Employed workers earn wages w _t and unemployed workers receive benefits s. The benefits are financed through a lump-sum tax T _t = (1 − n _t )s. The one-period riskless bond a _t pays an interest rate of R _t and is used for consumption smoothing.^[6]

The representative household chooses consumption and the number of bonds in order to maximize the expected discounted lifetime utility over consumption and leisure. Since it takes the job-finding rate as given, employment evolution from the household perspective can be described by

The complete household maximization problem is given in Appendix A. Combining the first order conditions with respect to consumption and bonds results in the standard Euler equation

Intuitively, the household invests into bonds until the marginal utility of today’s consumption is equal to the discounted marginal utility of consuming tomorrow, weighted by the rental rate R _t .

3.3 Financial Markets

Due to a cash-flow mismatch firms need to raise funds via intra-period loans l _t in order to finance their working capital requirements.^[7] Wage payments, dividend payouts, investment, current debt, and vacancy posting costs all accrue before the realization of revenues. Since contract enforcement is costly, firms are subject to a collateral requirement. Following a default, financial intermediaries cannot seize production. Only the installed capital stock can be recovered and sold at η _t q _k,t k _t , where q _k,t is the marginal Tobin’s Q and η _t captures uncertainty regarding the tightness of the credit market. As is standard in the literature, financial intermediaries are assumed to have no bargaining power in the debt renegotiation and they do not value the stock of workers in the firm (cf. Garín 2015; Perri and Quadrini 2018). η _t is interpreted as an exogenous collateral shock following the stochastic process

with ϵ η , t ∼ N ( 0 , σ η ) , where η ̄ is the mean of the stochastic process.

The derivation of the enforcement constraint follows the derivation in Garín (2015). Referring to the respective optimization problem, the value of a firm can be written as

where the vector ω t c = { k t , n t − 1 , b t } contains the individual states of a firm and the vector Ω _t = {k _t , n _t−1, z _t−1, η _t−1} contains the aggregate states.

With the possibility of default before the loan is due and after production is realized, the value of not defaulting is

In the case of default, firms and lenders renegotiate. If an agreement is reached, firms pay lenders a fraction ν _t of the continuation value. Therefore, the value of a successful renegotiation is

where firms continue to produce, get another loan l _t , but have to pay a part of the continuation value to the lenders. As production cannot be seized by lenders in the case of default, the value of an unsuccessful renegotiation for the firm is simply ν ^f,u = l _t . Consequently, the net value of an agreement is given by

From the perspective of a lender, the value of a successful renegotiation is

In the case that no agreement is reached, lenders cannot seize production. As they do not value the stock of workers in the firm, the value of an unsuccessful renegotiation is

from the lender’s point of view. This results in the net value of an agreement for the lender of

The joint surplus of renegotiating is the sum of the net values of the firm and the lender. Since financial intermediaries have no bargaining power in the renegotiation of debt, the firm gets the value

in case of a default. This value is equal to its liquidity plus the joint surplus of renegotiating the debt. In order to rule out defaults, the value of not defaulting for the firm has to be at least as large as the value of defaulting. Using this inequality and rearranging terms results in the enforcement constraint

which constrains a firm’s ability to borrow below the value of the fraction of the physical capital stock that lenders can recuperate after default.

3.4 Firms

Capitalists are risk-averse and derive utility from the consumption of dividend payouts. They can only access the financial market through the firm and are assumed to be more impatient than households, i.e. β _h > β _c , where β _c is the discount factor of the firm.^[8] Thus, capitalists’ expected lifetime utility is a function of dividends,

As firms are owned by capitalists, the objective of a firm is to maximize the expected future stream of discounted dividends. Firms own the capital stock k _t and use it together with labor n _t to produce a homogenous good with y t = z t n t α k t 1 − α , where 0 < α < 1 and technology z _t follows the stochastic process ln z _t = ρ _z  ln z _t−1 + ϵ _z,t with ϵ z , t ∼ N ( 0 , σ z ) . Firms can borrow using one-period riskless bonds b _t+1 at the gross interest rate R _t . Since the model does not feature any idiosyncratic shocks, I focus on a symmetric equilibrium and a representative firm. Under these assumptions, the optimization problem of the firm can be summarized by

subject to the budget constraint

the law of motion for the capital stock

the law of motion for employment,

and the borrowing constraint

where the loan l _t is replaced by the working capital requirements. Denoting the multipliers on the budget constraint, the law of motion for the capital stock, the law of motion for employment, and the borrowing constraint with μ _c,t , μ _k,t , μ _e,t , and μ _b,t , respectively, and taking derivatives results in the following first order conditions:

where q _k is the ratio of the Lagrange multipliers μ _k,t and μ _c,t . As is standard in the literature, q _k,t represents the value of the installed capital relative to its replacement costs.

The marginal value of an additional worker for the firm J n , t is obtained by taking the first derivative of the firm’s value function J t with respect to employment

where Λ t | t + j c = β j d t d t + 1 σ is the stochastic discount factor of capitalists and μ _b,t is the Lagrange multiplier on the borrowing constraint. The term in square brackets is equal to the net return of an additional worker, while the second term is the present discounted value of the hired worker. Note that without financial frictions μ _b,t is equal to zero. Consider an increase in collateral requirements. The firm is more constrained, which increases the value of relaxing the borrowing constraint, i.e. μ _b,t . This reduces the net return of an additional worker and therefore the marginal benefit of hiring. Intuitively, the firm has to finance an additional worker’s wage via intra-period loans. When the borrowing constraint is already binding, this can only be done by reducing investment or dividend payouts. This reduces the marginal value of an additional worker.

This implies that the marginal benefit of hiring an additional worker reacts more strongly to changes in the wage rate compared to standard search and matching models. Consequently, even a small amount of wage rigidity has large effects on labor market variables in my model.

3.5 Wage Bargaining and Wage Rigidity

As is standard in most of the search and matching literature, wages are determined as the solution of a generalized Nash bargaining problem. The production function exhibits constant returns to scale, which greatly simplifies the bargaining problem, as models with diminishing returns are subject to the critique by Stole and Zwiebel (1996). Moreover, I assume that firms first hire workers, subsequently bargain about wages, and only then choose the capital stock, which further simplifies the bargaining problem (cf. Cahuc and Wasmer 2001). The wage equation is thus given by^[9]

Since the model economy is subject to two kinds of shocks, wage rigidity in the style of Blanchard and Galí (2010) or Michaillat (2012) is not feasible. Instead, as in Hall (2005) and Krause and Lubik (2007), wage rigidity is introduced through a backward-looking wage norm that limits the adjustment capability of wages

where w t * is the solution to the generalized Nash bargaining problem given by Eq. (14) and τ determines the extent of wage rigidity. With this wage schedule, the steady state real wage rate remains the same regardless of the amount of wage rigidity in the model.

This proposition implies that no worker-firm match generating a positive bilateral surplus is separated because of wage rigidity as long as the actual wage remains within the postulated bounds. Thus, the wage schedule in Eq. (15) is not subject to the Barro (1977) critique that bargaining workers and firms should be able to exploit all possible bilateral gains in long-term worker-firm relationships with reoccuring wage renegotiations. Due to constant returns in production, the model is also not affected by the critique of Brügemann (2017) concerning wage rigidity in search and matching models with diminishing returns.

3.6 Equilibrium

With the model completely described, I define the equilibrium.

4.1 Calibration

Table 1 lists the exact parameter values as well as the source that encourages the specific choice. The discount factors are set to β _h = 0.996 and β _c = 0.983. The assumption β _h > β _c implies that the annual interest rate will be lower than the annual return on equity. The specific choices match an annual interest rate of 1.6% and an annual return on equity of 7%.

Next, I calibrate the labor market variables. For the separation rate, I choose a conventional value of 0.1 (cf. Shimer 2005). Regarding vacancy posting costs, there is a relatively wide range of admissable values in the literature. Silva and Toledo (2009) estimate recruitment costs equal to 3.6% of a worker’s monthly wage. Using microdata by Barron, Berger, and Black (1997), Michaillat (2012) estimates the costs of posting a vacancy at 9.8% of a worker’s steady state wage. Vacancy costs calibrated to match the latter value imply steady state vacancy posting costs of 0.28% of the total wage bill and 0.17% of GDP in Michaillat (2012). I calibrate κ/2 to 0.18, which is slightly more than 9% of a worker’s steady state wage. Given this value, steady state vacancy posting costs account for 0.31% of the total wage bill and 0.2 % of GDP.

The efficiency of the matching function is chosen to match a quarterly job-finding rate of 0.8 and the elasticity of the matching function with respect to unemployment to match empirical evidence from Petrongolo and Pissarides (2001). Unemployment benefits are set to 0.4. This value implies a steady state replacement rate of about 0.2, which is at the lower end of the values found in the literature and implies a ratio of unemployment benefits to consumption of 0.23. The parameter φ, governing the disutility of labor, is set to match a steady state unemployment rate of 11%.^[11]

Next, I calibrate the parameter governing wage rigidity based on the interpretation of the wage schedule arising from a staggered Nash bargaining setting as in Gertler and Trigari (2009). Equation (15) is the equivalent of the wage equation in Gertler and Trigari (2009) under financial frictions if neither firms nor workers take into account that they might not be able to renegotiate wages in the subsequent periods. With this calibration strategy, τ can be interpreted as representing an upper bound on wage rigidity. Taylor (1999) argues that medium sized and large firms typically readjust wages anually. Additional evidence is provided by Gottschalk (2005), who finds that wage adjustments are most common one year after the last change. Thus, I set τ to 0.25, implying an average renegotiation frequency of once per year.

Since investment adjustment costs can potentially generate asymmetric unemployment dynamics, they are cautiously set to ξ = 0.05, a value at the very low end of the values found in the literature.^[12]

Using the dataset constructed by Jermann and Quadrini (2012), the parameters for the persistence and standard deviation of the technology shocks are calculated using an approach similar to the one used to calculate Solow residuals. The parameters for the mean, persistence, and standard deviation of the credit shocks are calibrated to capture important aspects of the data. The mean of the credit shock process, η ̄ , is set to match the empirical ratio of outstanding debt in the private non-financial sector from all other sectors to GDP between 1964 and 2004 of 1.59 calculated from the Bank for International Settlements (BIS) total credit statistics. For the persistence of the credit shock series I choose the midpoint between the persistence of the credit shock series calculated by Jermann and Quadrini (2012) and the persistence of the series on the Net Percentage of Domestic Respondents Tightening Standards for Commercial and Industrial Loans for Medium and Large Firms obtained from the Senior Loan Officer Opinion Survey on Bank Lending Practices from Federal Reserve Economic Data (FRED). Finally, the standard deviation of the credit shock series is chosen to match the empirical volatility of the ratio of outstanding debt in the private non-financial sector from all other sectors to GDP between 1964 and 2004 of 0.1042.

4.2 Simulated Moments

I compare the simulated moments of the model to business cycle statistics for U.S. data. For the vacancy series I take data from Michaillat (2012), who merged the Job Openings and Labor Turnover Survey (JOLTS) for 2001–2004 with the Conference board help-wanted advertising index for 1964–2001. Unemployment data is taken from the Bureau of Labor Statistics (BLS) and labor market tightness is calculated as the ratio of vacancies to unemployment. For each of these series I take the quarterly average. The real wage estimates are average hourly earnings in the nonfarm business sector constructed by the BLS Current Employment Statistics. Output is quarterly real output from the BLS Major Sector Productivity and Costs program. In order to isolate business cylce fluctuations, I use a Hodrick-Prescott filter with smoothing parameter 100.000 as recommended in Shimer (2005).^[13]

I simulate 264 quarters of data corresponding to the empirical sample size of 1964:I to 2004:IV.^[14] The data is detrended using the same HP filter. The simulation is repeated 500 times and each repetition provides an estimate of the means of the simulated data. While the technology and credit shock processes are calibrated to match the empirical data, all other simulated moments are outcomes of the mechanics of the model. All simulations are performed using a second-order perturbation method. Since I am interested in asymmetric unemployment dynamics, a first order approximation is obviously not feasible. As the results remain virtually unchanged when using third- or fourth-order approximations, a second-order approximation seems to capture most of the relevant dynamics.

Table 2 displays the second order moments for key labor market variables both for U.S. data and for the simulated model. The model performs well along most dimensions that a model without financial frictions and without wage rigidity fails to capture.^[15] While the standard deviation of unemployment is still too low compared to U.S. data, it is about four times the standard deviation of output. In addition, the model accounts for roughly 65% of the volatility of labor market tightness, 80% of the volatility in vacancies, and over 90% of the fluctuations in the job-finding rate. Robustness exercises in the form of business cycle statistics for a model with financial frictions but without wage rigidity and for a model with wage rigidity but without financial frictions are provided in Appendix F. These simulations confirm that the interaction between wage rigidity and financial frictions, and not only the sum of the separate effects, plays an important role in matching business cycle statistics and in explaining unemployment dynamics.

Shocks are amplified considerably in the model: a 1% decrease in productivity increases unemployment by 3.6%, decreases vacancies by 5.7%, and decreases labor market tightness by 9.1%.^[16] In the data, a 1% decrease in productivity increases unemployment by 4.2%, decreases vacancies by 4.5%, and decreases labor market tightness by 8.6%. The response of vacancies and labor market tightness is a bit higher in the model than in the data, which might be due to a lower elasticity of wages with respect to changes in technology. Haefke et al. (2013) find an elasticity of about 0.7, while the presented business cycle statistics for the U.S. suggest a value of 0.65. The simulated elasticity is a bit lower with a value of 0.6.

Comparing the elasticity of unemployment to technology in this model with the elasticity in a model with perfect credit markets, I find that the effect of wage rigidity is six times larger when firms are constrained in their ability to borrow. Additionally, the effect of financial frictions on the elasticity of unemployment to technology is more than twice as large under wage rigidity compared to a model with flexible wages. As they reinforce each other, the combined effect of wage rigidity and financial frictions is two times larger than the sum of the two separate effects.

Next, I turn to the asymmetric behavior of the cyclical component of the unemployment rate documented and analyzed in, for example, McKay and Reis (2008), Barnichon (2010), and Atolia, Gibson, and Marquis (2018). Following Sichel (1993), I measure asymmetry in unemployment dynamics with the skewness coefficient.^[17] For U.S. data in the time period between 1964 and 2004, the skewness of the unemployment rate is 0.72 in levels and 1.30 in changes.^[18] These values suggest that the unemployment rate is characterized by short periods of sharp increases and long periods of flat decreases.

Figure 2 illustrates the asymmetry of the unemployment rate in the model based on the impulse response functions. The absolute value of the deviation of the unemployment rate from its steady state following a positive one standard deviation shock to technology is subtracted from the deviation of the unemployment rate from its steady state following a negative shock to technology of the same size. A value larger than zero implies that the deviation of the unemployment rate is larger after a negative shock. The asymmetry is most pronounced for the model with financial frictions and wage rigidity. In contrast, the impulse response functions for output are almost completely symmetric.

Figure 2:

Asymmetric impulse response functions: unemployment.

This figure plots the difference between the deviation of the unemployment rate from its steady state following a negative one standard deviation shock to technology and the absolute value of the deviation of the unemployment rate from its steady state following a positive one standard deviation shock to technology.

Table 3 displays the skewness of the simulated unemployment rate in levels and in changes for different amounts of wage rigidity.^[19] A standard search and matching model with symmetric shocks is unable to match these observations despite the inherent asymmetry resulting from costly vacancy posting, which is frequently emphasized in the literature (cf. Petrosky-Nadeau, Zhang, and Kuehn 2018; Hairault, Langot, and Osotimehin 2010). The simulated unemployment series in a benchmark model without financial frictions and without wage rigidity displays a skewness of 0.12 in levels and 0.02 in changes, explaining only about 17 and 2% of the respective skewness in the data.^[20] In the model with financial frictions and wage rigidity, the skewness of the simulated unemployment series is 0.49 in levels and 0.27 in changes. About 75% of the skewness in levels and nearly 25% of the skewness in changes in the data can be explained by combining both frictions in a search and matching framework.^[21]

As with the elasticity of unemployment to technology shocks, financial frictions and wage rigidity reinforce their respective effects. The combined effect of wage rigidity and financial frictions on the skewness in levels is 48% larger than the sum of the two separate effects. For the skewness in changes the combined effect is 9% larger.^[22]

5.1 Simulated Recoveries

In a first step, I demonstrate that a DSGE model with frictional labor and financial markets is able to generate jobless recoveries. Technology and credit shock series are calibrated to match the behavior of output during the Great Recession. The resulting series for output and unemployment are depicted in Figure 3. Negative shocks to credit tightness and to technology cause a recession in which output decreases by 4% during the first four quarters. Technology recovers but credit conditions continue to deteriorate. Firms invest into capital and output fully recovers after six to seven quarters. At the point of output recovery the unemployment rate has only recovered by around 31% relative to its peak (compared to a recovery by 15% after the Great Recession) and is two percentage points above its pre-crisis level (compared to four percentage points after the Great Recession).

Figure 3:

Simulated Great Recession.

The jobless recovery is generated using series of technology and credit shocks in the simulated model with financial frictions and wage rigidity. The shock series are calibrated to match the behavior of output during the Great Recession. The pre-recession levels of unemployment and output are normalized to 100.

The model does not rely on wage rigidity to generate jobless recoveries. This stands in sharp contrast to the results obtained by Calvo, Coricelli, and Ottonello (2014) using a competitive labor market model. Nonetheless, the joblessness of the recovery period is more pronounced under wage rigidity. Without wage rigidity, the unemployment rate would have recovered by about 45% at the point of output recovery.

Next, I consider the ability of the model to account for jobless recoveries given technology and credit shocks estimated from the data. To that end I use the dataset provided by Jermann and Quadrini (2012) to estimate credit and technology shock series for the time period between 1964 and 2010.^[23] The estimated shock series are depicted in Figure 4.

Figure 4:

Estimated technology and credit shock series, 1964–2010.

The technology shock and credit shock series are estimated from the dataset to Jermann and Quadrini (2012). Periods classified as recessions by the National Bureau of Economic Research (NBER) are highlighted in gray.

Figure 5 plots the simulated series for unemployment and output. In line with U.S. data, the model only predicts jobless recoveries following the recessions after 1990. At the point of output recovery after the recessions in 1990–1991, 2001, and 2007–2009, the simulated unemployment rate has only recovered by 62, 38, and 68%, respectively, compared to its peak.^[24] In all simulated recoveries following recessions prior to 1990, the unemployment rate has fully recovered at the point of output recovery. Overall, the simulated model is able to account for 64% of the variation in the unemployment rate over the considered time period.

Figure 5:

Simulated unemployment and output, 1964–2010.

Output and unemployment are simulated using technology shock and credit shock series estimated from the dataset to Jermann and Quadrini (2012). Periods classified as recessions by the NBER are highlighted in gray.

Turning to the initial capital deepening commonly observed in the U.S. during recessionary periods, the model predicts an increase of 1.6% in the capital-labor-ratio during the recession in 1990–1991, 2.6% during the recession in 2001, and 2.6% during the recession in 2007–2009, explaining between 66 and 90% of the increase observed in the data.^[25] Moreover, both in the model and in the data, the capital-labor-ratio peaks slightly after the end of the recessions.

Table 4 displays the development of output and employment in the model and in the data for the three U.S. recessions after 1990. In line with the data, the model predicts employment to be below its peak value two years after the peak for all three recessions. Comparing the recent recessions with recessions prior to 1990, lower employment after two years is a unique feature of jobless recoveries.^[26]

5.2 Impulse Response Functions

In this section, I present the impulse response functions of several variables to a negative one standard deviation shock to total factor productivity and a negative one standard deviation shock to credit tightness. The scale represents log deviations from steady state.

The impulse response functions for a negative shock to technology depicted in Figure 6 comply with the literature. Following a negative shock, firms decrease hiring with vacancies dropping by nearly 9% on impact. The unemployment rate increases, leading to an even larger decrease in labor market tightness. The marginal value and the collateral value of the capital stock drop, which triggers the decrease in investment. As the initial decrease in hiring is larger compared to the initial increase in investment, the capital-labor-ratio increases on impact and only drops below its steady state value after several periods. The hump-shaped response of both the unemployment rate and investment is generated by the respective adjustment costs.^[27]

Figure 6:

Impulse response functions: negative technology shock.

The scale represents percentage deviations from the steady state. The size of the technology shock is one standard deviation.

Figure 7 depicts the response of the model to a negative one standard deviation shock to credit market tightness. Firms are immediately able to borrow less against their collateral and respond by sharply cutting hiring and investment on impact. This lowers the future capital stock and further tightens the credit constraint. The drop in vacancies, however, is not persistent. Lower expenditures reduce working capital requirements and the capital-labor-ratio increases, which relaxes the borrowing constraint and allows firms to increase investment and vacancies again in the following periods. Still, the initial drop in vacancies is large enough to generate a persistent increase in the unemployment rate. After dropping on impact, hiring increases above its steady state value long before output has recovered.^[28]

Figure 7:

Impulse response functions: negative credit shock.

The scale represents percentage deviations from the steady state. The size of the credit shock is one standard deviation.

Note that neither technology nor credit shocks are able to generate dynamics in the unemployment rate that are more persistent than output dynamics. Therefore, and in contrast to the results obtained by Calvo, Coricelli, and Ottonello (2014) in a competitive model of the labor market, neither a simple shock to credit tightness nor a simple shock to total factor productivity is able to induce a jobless recovery in a DSGE model with labor market frictions, rigid wages, and an endogenous borrowing constraint.

5.3 Mechanism

In my model, regardless of whether the recession is caused by a technology or by a credit shock, output and unemployment behave very similarly as long as only one shock drives the economy. Jobless recoveries emerge when credit conditions continue to erode while total factor productivity recovers. They are jobless because worsening credit conditions are an important driver of unemployment dynamics and keep unemployment high, but play only a minor role for fluctuations in output. In the variance decomposition exercise in Table 5, over 30% of the fluctuations in unemployment are caused by credit shocks, while virtually all of the fluctuations in output are due to productivity shocks.^[29]

Figure 8, which depicts the effect of a positive one standard deviation shock to technology on the ratio of investment to hiring, illustrates this mechanism. With financial frictions, a positive technology shock tightens the credit constraint as it increases working capital requirements. Rather than to increase hiring, firms invest into the asset used as collateral, as this puts less strain on the borrowing constraint. The increase in employment is delayed and the decrease in unemployment is flatter compared to standard search and matching models. Relative to the increase in hiring, the increase in investment is most pronounced in the model with financial frictions and wage rigidity, reflecting the preference of firms to invest into the asset used as collateral after a positive technology shock.

Figure 8:

Impulse response functions: investment/hiring.

This figure plots the impulse response function of the ratio of investment to hiring (i/m) following a one standard deviation positive technology shock.

The mechanism is also evident in the first order conditions of the firm. Credit conditions directly affect the marginal value of an additional worker. A tightening of future credit conditions increases μ _b,t+1, the Lagrange multiplier on the borrowing constraint, and thus the marginal value of relaxing this constraint. The increase in credit tightness reduces the marginal value of an additional worker by

Now consider the effect of the same increase in credit tightness on the marginal value of an additional unit of capital

As for the marginal value of an additional worker, the increase in credit tightness reduces the marginal value of the capital stock in the production process. However, capital can also be used as collateral, the value of which increases with credit tightness. Thus, the effect of credit shocks on unemployment is larger than the effect of credit shocks on capital and output.^[30] When total factor productivity recovers after a recession, firms increase their capital stock which in turn increases production. If this recovery is accompanied by tightening credit conditions, the marginal value of an additional worker stays low and at the point of output recovery the unemployment rate will be above its pre-crisis level.

5.4 Empirical Evidence

Evidence for deteriorating credit conditions during jobless recoveries can be found in the dataset provided by Jermann and Quadrini (2012) as well as in the Senior Loan Officer Opinion Survey on Bank Lending Practices from FRED.

Table 6, which displays the average size of credit shocks following the end of a recession estimated from the dataset provided by Jermann and Quadrini (2012), is used to gauge the development of credit conditions following recessionary periods in the U.S. A negative value implies a tightening of credit conditions. Prior to the two jobless recoveries in 1990–1991 and in 2001, credit conditions remained virtually constant immediately after the end of a recession.^[31] Following the end of the recessions in 1990–1991 and in 2001, credit conditions continued to worsen with the credit shocks amounting to −1.4 and −0.82 times a standard deviation of the estimated credit shock series on average.

A tightening of credit conditions during the recent recoveries, including the recovery after the Great Recession, is also reported in the Senior Loan Officer Opinion Survey on Bank Lending Practices from FRED depicted in Figure 9.^[32] Credit market tightness is calculated as the fraction of surveyed banks reporting to tighten credit standards minus the fraction of banks reporting to lower their standards. A positive value therefore implies a tightening of credit conditions.

Figure 9:

Unemployment rate, output, and credit market tightness, 1990–2021.

The unemployment rate is the quarterly average of the seasonally adjusted monthly unemployment series constructed by the BLS from the CPS. Credit market tightness is measured as the Net Percentage of Domestic Respondents Tightening Standards for Commercial and Industrial Loans for Medium and Large Firms obtained from the Senior Loan Officer Opinion Survey on Bank Lending Practices from FRED. Output is the quarterly, detrended real gross domestic product in billions of chained 2012 dollars from FRED. Periods classified as recessions by the NBER are highlighted in gray.

Two observations are striking. First, following the end of all three recessions, credit conditions continued to deteriorate – for several months after the recessions in 1990–1991 and in 2007–2009, and for nearly two years after the recession in 2001. Second, following the end of the recessions, the unemployment rate only began to decrease after credit conditions had stabilized.

Further evidence for the mechanism is provided in Figure 10, which depicts gross real investment and the unemployment rate. After the recessions in 1990–1991 and 2001, investment had recovered by 26.7 and 47.7%, respectively, before unemployment even began to recover. Two years after the Great Recession, at the point of output recovery, investment had recovered by over 78% while unemployment had only recovered by 15%.

Figure 10:

Unemployment rate and real gross investment, 1990–2021.

The unemployment rate is the quarterly average of the seasonally adjusted monthly unemployment series constructed by the BLS from the CPS. Real gross investment is measured as the seasonally adjusted FRED Real Gross Private Domestic Investment series measured in billions of chained 2012 dollars. Periods classified as recessions by the NBER are highlighted in gray.

Finally, Figure 11 displays the unemployment rate for different industries between 2000 and 2021. In line with the model predictions, industries that exhibit large working capital requirements and rely heavily on collateralized borrowing, like the construction and manufacturing industries, have experienced a lot steeper increases in the unemployment rates during the Great Recession compared to, for example, the telecommunications industry or other service industries.^[33] Moreover, Jaimovich and Siu (2020) point out that the manufacturing and construction industries have been exceptionally affected by the recessions in 1990–1991, 2001, and 2007–2009 and that subsequent recoveries have been jobless in both industries, whereas in prior recovery periods manufacturing and construction employment displayed strong cyclical rebounds. This suggests a high relevance of the proposed mechanism for those industries that heavily rely on collateralized borrowing at the very least.^[34]

Figure 11:

Unemployment rate by industries, 2000–2021.

The unemployment rates by industries are taken from the Labor Force Statistics from the CPS provided by the BLS. The data series is available from 2000 onward. The other services sector consists of the repair and maintenance industry, the personal and laundry services industry, service industries labeled as religious, grantmaking, civic, professional, and similar organizations, as well as private household services. Periods classified as recessions by the NBER are highlighted in gray.