Keenan Viney
“Do matching frictions explain unemployment? Not in Bad Times?” by Pascal Michaillat adds to the standard search theoretic model in order to better match the empirical facts of unemployment during recessions.
Previous search models of unemployment were able to show that the costs associated with matching hiring firms to unemployed workers were significant enough to cause some level of unemployment. Furthermore, these models allowed economists to think about the tightness in labour market.
For example, when unemployment is very high an additional unemployed worker will not decrease the arrival rate of jobs for other unemployed agents by a large amount. The converse is true when adding a hiring firm, if there were few firms to start with, matching will be increased by a large margin with the addition of a firm. The problem with these models, that Michaillat identifies, is their counterfactual prediction that in a recession matching frictions will decrease and full employment will return. Said another way, in a recession there is a large number of unemployed, firms therefore find recruiting costs low and easily match with workers, the wage is bid down to a new equilibrium level and full employment is restored. This does not match empirical observations of persistent unemployment during recession.
Since matching frictions do a poor job of explaining unemployment during recessions, Michaillat claims that there is another effect operating during recessions: job rationing. Since matching frictions asymptotically go to zero during a recession there are plenty of unemployed workers to be matched with firm vacancies but if the wage cannot fall enough, full employment will not be restored. The key to this job rationing mechanism are sticky wages which do not move with the same magnitude as the total factor productivity (TFP) shocks hitting the economy. Under perfect competition when a negative TFP shock happens, the marginal product of labour falls which implies that wages fall by the same amount. In Michaillat’s modelling environment, the wage is not going to fall as much as the marginal product of labour. The result is that the least productive workers would have to be paid more than they can produce and no rational firm would be willing to hire them. Since there is a surplus of workers and the price of labour cannot fall, this model predicts persistent unemployment in recessions.
The methodology of this paper uses a search theoretic model of unemployment and nests a wage structure within it which delivers sticky wages. Unlike other bargaining wage search models such as Pissarides (2000), Michaillat’s model does not assume that wages are completely flexible or that there are constant returns to labour. Either of these assumptions are sufficient to return full employment when matching frictions fall to zero in recessions. With the inclusion of rationing into the model unemployment can be generated by frictions or rationing, in a recession these effects are moving in the opposite directions. In deep recessions, frictional unemployment is going to zero while rationing unemployment is large. This means that the model can deliver persistently high levels of unemployment and furthermore can facilitate a decomposition of unemployment into its frictional and rationing component. One problem with this type of decomposition is the assumption of a homogenous labour market. To the extent that recessions are caused by structural changes in the economy, unemployment may persist due to a mismatch of skills and job requirements which can only be remedied with time consuming retraining. Without accounting for these structural frictions in the model, any decomposition of unemployment will have the rationing unemployment part pick up any structural unemployment as a residual.
The model was calibrated using United States data and attempts to match the unemployment rate, vacancy rate, and thereby labour market tightness, which is the ratio of the two, and finally the wage. This is accomplished by feeding in a total factor productivity (TFP) shock which is amplified by the structure of the model and estimated moments. One very sensitive variable is degree of wage rigidity, however even micro data estimates of wage rigidity are sufficient to cause the requisite level of shock amplification. In general the model closely matches the variable targeted, including wages which only change 0.7% due to a 1% TFP shock, explaining wage variation is often a major stumbling block of standard RBC models. The Beveridge curve which maps unemployment to vacancies has its slope empirically estimated at -0.89 which exactly matches the models prediction about the correlation between vacancy and unemployment. Despite affirmative results in moment matching this model has problems with the correlation between the targeted variables and the TFP shock. The correlation of unemployment, vacancy, tightness, and wages with TRP is close to one in each case when empirically these correlations should fall between -0.5 and -0.65. Michaillat suggests that with only TFP shocks we should not dismiss the power of this model and that demand and financial shocks could correct the correlation with targeted variable to TFP. The author fails to propose the specific mechanisms which would correct this problem, particularly disquieting since these correlations are not only off by an order of magnitude but are in the wrong directions. Furthermore, the RBC literature continues to use TFP shocks as the baseline innovation because other proposed shocks do not explain nearly as great a proportions of business cycle fluctuations.
With the model calibrated it is possible to feed in TFP shocks and produce a decomposed time series of unemployment. Figure 5 shows unemployment from 1964-2009; it has been decomposed into rationing and frictional unemployment. This graph clearly shows that while in recessions, unemployment due to matching frictions falls but total unemployment rises as a result of the presence of rationing, driven by sticky wages. This gives rise to a set of policy recommendations quite different from the ones that come out of the standard search models. Generally, pure frictional unemployment can be dealt with by increasing matching efficiency, higher search effort of the unemployed, and by decreasing competition from government hiring. However, reducing recruiting costs will not decrease unemployment in recessions when matching frictions are small. This suggests that there is a role for government hiring as well as policies which can reduce wage rigidities in recessions since the driver of unemployment is rationing.
The mechanism that sets this paper apart from other search models is the embedding of wage rigidities; the results gleaned from this approach comes at a cost. The general wage schedule has several mechanisms operating: “generalized Nash bargaining, intra-firm bargaining, and various reduced form rigidities” (2012). The first two types of bargaining are optimizing behaviour and would not induce a wage rigidity, so the wage stickiness is coming from these reduced from rigidities. The problem is that these rigidities do not come from optimizing behaviour, being ad hoc in nature makes this modelling technique vulnerable to the Lucas critique. These nominal rigidities reflect the wage stickiness observed in the current policy environment but there is no guarantee that these relationships would stay fixed under different policy regimes. This is a similar problem that is encountered when trying to exploit the trade-off implied by the Phillips curve – the relation is not fixed across policy regimes. The outcome of this ad hoc method is a model that is only externally consistent for marginal changes in policy.
Pascal Michaillat’s model delivers results that seem to match what we see empirically in terms of unemployment in recessions. This is accomplished by nesting nominal wage rigidities in an otherwise standard job search model. The mechanism of high unemployment during recessions is induced by wages which cannot be bid down and hence unemployment occurs due to rationing. Higher unemployment during recessions contrasts with other search models which bring the economy back to full employment when search frictions are diminished. By raising another channel for unemployment during recessions, this model allows us to consider a different set of policy options and understand their effects more clearly.
References
Michaillat, P. (2012). Do Matching Frictions Explain
Unemployment? Not in Bad Times. American Economic
Review, 102(4), 1721-1750.
Pissarides, C. A. (2000). Equilibrium Unemployment Theory.
2nd ed. Cambridge, MA: MIT Press.
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