Frictional Wage Dispersion and its Causes

where we again apply our approximated wage schedule from equation (2.1). All our statistics regarding frictional wages in the model are based on this expression.

Table 2.4 compares the frictional wage dispersion in our model to the amount of residual wage dispersion present in the data. Our model successfully reproduces the amount of residual inequality. In the baseline specification, the mean residual wage paid is 2.57 times the smallest observation. This is comparable, though slightly larger, to the Mm-ratio of 2.18 when taking the first percentile in the data to be the minimum wage. When looking at higher percentiles, model and data line up closely as well. Also the other statistics look favorable: the Gini coefficient matches up almost exactly and our model explains 84 percent of the variance of residual log wages in the data. When comparing different model specifications in our subsequent analysis, we only report changes in the Mm-ratio. This increases clarity of presentation and facilitates comparison with other studies, foremost HKV themselves, that report this summary statistic. When using percentiles as minimum wage, is also has the advantage of being robust to classical measurement error.

Table 2.4: Frictional Wage Dispersion

Mean-Min Ratio Gini V ar(log( ˜wit))

Model Data Model Data Model Data

Pctl.

M in 2.57

0.0894 0.091 0.026 0.031 1^st 1.45 2.18

5^th 1.38 1.48 10^th 1.31 1.31

Notes: The table compares frictional wage dispersion generated by the baseline specification to resid-ual wage dispersion in the 1993 SIPP. We report the Mm-ratio using the 1st, 5th, and 10th percentile as possible minimum wages. For comparability, we report the corresponding statistic in the data as well.

Sources of Frictional Inequality

We now analyze how the details of our model specification interact with the range of job offers acceptable to the worker given the distribution of firm productivities in our baseline. Therefore, we resolve a number of restricted versions, each time

2.5 Results excluding one of the main channels and recalibrating to the flow rates and the residual wage profile. In each calibration, the unemployed sample at most one job offer per month, which imposes an upper bound on the flow value of unemployment for one of the experiments. Table 2.5 reports the resulting frictional wage dispersion and replacement rates.

It turns out that the main driver behind our results is the interaction of our process for general human capital with the possibility to search on the job. Specifications A to C turn off each of those channels one after another. When setting expected experience gains during employment to zero, the Mm-ratio falls to only 1.43. As potential experience gains are equal in all firms, being employed at all becomes much more important than in which firm specifically. The same argument applies to the effects of skill depreciation, specification B, even though its effects are less pronounced. When settingδto zero, the Mm-ratio drops to 1.98, which is still sizable, but a substantial decrease from 2.57. When denying workers the possibility to search on the job, the Mm-ratio plummets to 1.19 and no positive replacement rates are able to match observed flow rates. Finally, as demonstrated in specification D, the limited payout duration of unemployment benefits is only of second order importance to the empirical success of our model.

Table 2.5: Contributions to Frictional Wage Dispersion

Specification Mm-Ratio rr_b+rr_z

Baseline 2.57 0.4

A No learning on the job

(ν(φ) = 0) 1.43 0.4

B No skill depreciation

(δ = 0) 1.98 0.4

C No search on the job

λ = 0 1.19 0

D Infinite UI

(λ_l = 0) 2.35 0.4

Notes: The table displays the mean-min ratio and the replacement rate for four different model specifications that differ from our baseline model by some param-eter restriction.

We have stressed previously the importance of accounting for job to job transitions resulting in wage losses when inferring search efficiencies from job to job flow rates.

In the absence of forced movements, we could generate any value for the Mm-ratio as workers would accept even negative wages. There are two reasons for this: First, when a job offer is a forced one, moving is almost always preferred to quitting into unemployment. Second, forced job movements decrease the rate at which agents climb up the productivity ladder of firms, making future job offers more likely to be better than today’s offer. In consequence, search on the job is more efficient in a model not featuring forced job movements. The value of employment increases relative to the value of unemployment, which increases frictional wage dispersion.

A competing explanation

Our previous analysis identifies on the job search as an important channel in understanding frictional wage dispersion. Indeed, one might ask how far a more

“standard” on the job search specification would go on its own in explaining the data when calibrating it to observed flow rates only and ignoring forced movements. We discuss such an experiment in this section. The combination of a job-ladder model with heterogeneous initial worker productivities and general human capital uncertainty, but no trend growth on and off the job, calibrated to our targets by itself yields an Mm-ratio of 2.83 with solidly positive replacement rates³³. Given our previous estimates, this appears to be an empirically successful alternative explanation.

As discussed in Section 2.2.3; however, these model types largely overstate the efficiency of on the job search by ignoring the frequent occurrence of job to job transitions resulting in wage losses. We therefore take the ability to realistically account for wage dynamics upon job to job movement as a means of discriminating between these rival model specifications. Table 2.6 highlights the differences.

In the data, job to job movements result in wage gains of two percent on average.

Conditional on suffering a wage loss upon movement, workers lose 22 percent of

33Hornstein et al. (2011) also consider a job-ladder model and obtain Mm-ratios between 1.16 and 1.27 for a replacement rate of 0.4. However, the presence of individual productivity heterogeneity in our model implies heterogeneous reservation wages. In consequence, the homogeneous job offer arrival rate and the unemployment to employment flow rate are no longer identical. Moreover, the stochastic productivity process implies a higher option value of employment because workers can quit at any time into unemployment. These differences account in our case for the much larger frictional wage dispersion.

2.5 Results

Table 2.6: Wage Changes from Job to Job Movements

Specification Avg. gain Avg. loss

Data 0.0203 -0.22

Baseline 0.069 -0.21

Job-Ladder model

ν(1) =ν(2) = 0 = δ λ_l = 0 0.26 -0.07

Notes: The table compares the model baseline specification with a pure on the job search specification on their implications for job to job transitions. Statis-tics are the resulting average wage gain upon job movement and the average wage loss conditional on observing a loss. Datarefers to computation from the 1993 SIPP for nominal wages.

their previous wages. Our baseline specification fares quite well in reproducing these statistics. Wage gains are too high, but the order of magnitude is comparable. The model does well in reproducing the large conditional wage losses. In the job-ladder model, average wage gains of 26 percent are much too large compared to the data.

Since workers in this model only transit to more productive jobs, the wage losses are only observed as result of a negative productivity shock or of measurement error. A conditional seven percent average wage loss clearly fails in this respect. We come back to this specification in Section 2.5.2 when discussing structural inference.