Financial Shocks and Labor: Facts and Theories

Abstract

The global financial recession of 2008–9 as well as historical precedents with financial crises suggest that financial shocks do translate into the labor markets. This paper first documents that financial recessions are different from other recessions in terms of their labor market impact, as they involve a larger employment/unemployment response conditioning on output. Second, it surveys the various mechanisms linking financial shocks to employment adjustment, developing a new theory of the effects of leverage on job creation and destruction. Third, it presents evidence coherent with one of such mechanisms, notably with the prediction that more leveraged firms experience larger job destruction during financial recessions, controlling for the scale of output falls.

A.I. Appendix

Okun’s Law and the Great Recession

Figures A1 and A2 report actual and predicted unemployment and employment responses to output change during the Great Recession for the remaining 68 countries.

Figure A1

Okun’s Law and the Great Recession ISource: Estimates of Okun’s law equation (see the text for details) drawing on data from OECD and IMF.Note: Actual (data points) and predicted (regression line) unemployment and employment responses to output change during the Great Recession.

Figure A2

Okun’s Law and the Great Recession IISource: Estimates of Okun’s law equation (see the text for details) drawing on data from OECD and IMF.Note: Actual (data points) and predicted (regression line) unemployment and employment responses to output change during the Great Recession.

Estimates with Firm-Specific Output Variation

Table A1 displays the estimates of Equation (4) when allowing for firm-specific output variation.

Table A1 All Firms

A Simple Model of Finance and Job Matching

Production requires an entrepreneur, a worker and, potentially, finance or credit. In other words, finance or credit (used interchangeably) is akin to an input in production. All agents are risk neutral and discount the future at rate r. Entrepreneurs must choose ex-ante the finance intensity of their production. We call the finance intensity the leverage of the firm and we indicate it with l. Finance is pulled back at rate λ _o , in which case the firm is in financial distress. Financial distress is an absorbing state.

Formally, the production level y can be written as

where the superscript d refers to the financial distress function. More leverage increases production in normal times, but it reduces production during financial distress.

The labor market is imperfect and is characterized by a standard equilibrium search unemployment model (Blanchard and Diamond, 1992; Mortensen and Pissarides, 1999). Entrepreneurs post vacancies and search for workers. Search is random and the meeting between entrepreneurs and workers is described by a traditional matching function x(u, v), where u is the unemployment rate and v is the stock of vacancies also normalized by the labor force. We let θ=v/u denote market tightness, q(θ) is the firm arrival rate while α(θ)=θq(θ) is the worker meeting rate of vacancies.

Wages are the outcome of Nash Bargaining between workers and firms, subject to a participation constraint. We assume that workers obtain a fraction β of the total surplus. Entrepreneurs post vacancies at a marginal cost c and there is free entry of firms. Jobs are exogenously destroyed at rate s.

Value Functions, Stocks, and Equilibrium Definition

Conditional on leverage l, the value of a vacancy V(l) reads

where J(l) is the value of production when finance is available. The value of production in normal times is

where Δ+l^α−ρl−w(l) are simply net operational profits while the max operator conditional on a finance shock is the key decision of the entrepreneurs, involving the trade-off between operating in distress at value J^d or destroying the job and getting the value of a vacancy V(l). The value of the firm in financial distress reads

The corresponding value functions for the workers are readily obtained. Unemployment workers receive income b, so that rU=b+θq(θ)[W(l)−U].

Wages are set by Nash bargaining and workers obtain a fraction β of the total surplus from the job, so that

where Wⁱ is the value function of workers and Sⁱ is total surplus. Job destruction takes place when the surplus from the job is zero. Free entry of the entrepreneur in the financial market implies that V(l)=0 so that, for the chosen degree of leverage, the value of a vacancy is zero. Since J(l)=(1−β)S(l) from the Nash bargaining condition, the zero profit condition writes

The optimal leverage l* is chosen by the entrepreneur before entering the market and is set so as to maximize the value of a vacancy. In other words, l*=arg max _l V(l) so that

In steady state, unemployment inflows are equal to unemployment outflows, and the same for distressed firms. As before let u denote the stock of unemployed workers, and N^d the stock of workers employed by firms in distress. Employment in ordinary firms (not in distress) is then N¹=1−N^d−u. Job creation is given by θq(θ)u while job destruction is exogenously given by the separation rate plus the financial shock λ _o conditional on the optimal job destruction. This suggests that the balance flow condition is

where Φ is an indicator function that takes the value 1 when J^d(l)<0. From the second equation, it follows that N^d=N¹(1−Φ)λ₀/s. For Φ∈{0, 1} the equilibrium unemployment rate reads

Hence, for a given θ, the equilibrium unemployment rate is higher if firms in distress destroy their job.

Proposition 1

• The equilibrium is a set of asset values [J, J^d, V, W, W^d, U], a market tightness θ, leverage l and aggregate quantities u satisfying (i) Optimal Job Destruction, (ii) Job Creation, (iii) Wage determination, (iv) Optimal Leverage, (v) Equilibrium unemployment.

Solving the Model

The central issue is the firms’ choice of l. One can show that although S(e) is continuous, it is not smooth everywhere, as S′(l) is undefined at the point were S^d(l)=0. We refer to the corresponding value of l as . For , the firm operates in financial distress. Hence dS^d/dl<0, and this shifts down the marginal value of credit. For , the firm is closed down when hit by financial distress and the surplus is zero. Hence the cost of increasing l in terms of lower output when facing distress is irrelevant. In what follows, we say that we are in a low-credit equilibrium whenever (firms don’t fire after a negative shock) and in a high-credit equilibrium whenever (firms do fire after a negative shock).

In the high-credit equilibrium, firms destroy jobs in financial distress. The value of the surplus in normal condition determines immediately the optimal leverage l* equating the marginal benefits of an additional unit of leverage to its marginal cost so that ρ=αl^α−1 and

In the low-credit equilibrium firms operate in financial distress, and the net difference between the two surplus is proportional to leverage so that

Making use of the previous expression, the optimal leverage in the low-credit equilibrium is

where

Proposition 2

• There exists a unique ρ*>0 so that the equilibrium is a low-credit equilibrium whenever ρ>ρ*, and high credit whenever ρ<ρ*.

For a proof we refer to the working paper version of the paper.

Financial Shocks in High- and Low-Credit Economy

We compare two economies, a high-credit economy and a low-credit economy. To get a straight comparison we assume that ρ¹, the cost of finance in the high-credit equilibrium, is just below ρ*, while ρ², the cost of finance in the low-credit equilibrium, is just above ρ*. It follows that ρ¹≈ρ². Owing to the continuity of the value functions S in ρ, it follows that S¹≈S², and hence that θ*¹≈θ*²=θ* (where again superscripts 1 and 2 indicate high- and low-credit equilibrium values, respectively). However, owing to the discontinuity of l, it follows that l¹l² and that S^d0 (not approximately equal).

We define total output in the economy as Y=N¹y(l)+N^dy^d(l).

Proposition 3

• In the high-credit equilibrium, total output is higher.

We do not provide an algebraic proof for the proposition, but will give a heuristic argument. Since S*¹≈S*² and θ*¹≈θ*², it follows that U*¹≈U*². Since firms obtain zero profits, U is equal to the net present value of the output flow of the worker (net of credit costs) less the search cost incurred by the firm in order to employ him. In the high-credit equilibrium, a worker experiences more frequent unemployment spells; hence, the NPV of future search costs is higher than in the low-credit equilibrium. Accordingly, the NPV of future output is also higher in the high-credit equilibrium than in the low-credit equilibrium. As this is true for all workers, and the economy is in steady state, the result follows.

Although the model is static in nature, we can use an increase in the shock arrival rate as a way to study aggregate dynamics. An increase in λ _o is akin to an aggregate financial shock. The idea is that in the aftermath of an increase in λ _o , the high-credit market equilibrium features a larger response in unemployment.

Note that, generically we can write (by using that rU=βθq(θ)S)

Inserted into Equation (A.2) this gives that

Consider now the effect of an increase in λ _o on the two equilibria (assuming that the change is sufficently small so that the equilibrium constellation does not change).

Proposition 4

• The adverse effect of an increased arrival rate of financial shocks on the labor market tightness is greater in the high-credit equilibrium than in the low-credit equilibrium.

By definition, we have that

Hence it follows from Equation (A.8) that

The result immediately follows.

Finally, the total effects on the unemployment rate can be found by taking the derivative of Equation (A.4) and get that (for i=1, 2)

Proposition 5

• In the high-credit market equilibrium, unemployment responds more to an adverse financial shock. This is caused both through the job creation margin and the job destruction margin.

where Φ¹=1 and Φ²=0. The first term, increase in job destruction, is strictly positive in the high-credit equilibrium, and zero in the no-credit equilibrium. In the second term, the first factor is strictly higher in the high-credit equilibrium than in the low-credit equilibrium (because of equation (A.9)), the adverse effect on the labor market tightness of an increase in λ is higher in the high-credit equilibrium. The second factor in the second term is a level effect of the unemployment rate, and is also higher in the high-credit equilibrium under the reasonable assumption that θ*q(θ*)>s (the arrival rate of jobs is higher than the arrival rate of firm-specific negative shocks.

The Model with Heterogeneous ρ

To take the model closer to the data, let us consider a simple extension of the model, and allow firms to have different costs of credit. Firms are characterized by a value of ρ _i ∈[ρ_min, … ρ_max]. The value of ρ is learned by the firm (and the worker) only after meeting the worker and before having access to credit.

As above, define the match surplus as of a new match as

We assume that S(ρ _i )0 for all i. Note that the workers’ outside option is independent of the employer’s draw of ρ. It follows that the expected value of S(ρ), denoted ES, can be written as

where g(ρ _i ) is the probability that ρ=ρ _i .

The lower the ρ, the more valuable is a high l. We assume that the parameter values of the model are such that the firms with ρ=ρ_min strictly prefer to go for the high-credit solution and fire workers after a negative credit shock, while firms with ρ=ρ_max prefer the low-credit solution and not firing the worker after a negative financial shock. It is then straightforward to show that there exists a threshold value ρ* so that the firm chooses a high l and fires the worker after a negative financial shock if and only if ρ<ρ*. The two following equations close the model

Given θ, the equilibrium unemployment rate can be derived as follows: First

where e^hc and e^lc are respectively employment in high- and low-credit firms (that is, with ρ _i below and above ρ*, respectively. The additional flows conditions are

where G(ρ*) is the fraction of firms that draw a value of ρ below ρ*. The equilibrium unemployment level is then obtained by solving the last three equations and reads