Abstract
This paper studies the correlates of subjective assessments of how easy it would be for a worker to find another job as good as the present one and how easy it would be for an employer to replace a worker. First, I study the correlates of these two subjective assessments. Second, I study whether respondents who report better chances of reemployment receive higher wages and whether respondents who think they are easy to replace receive lower wages. The results are consistent with the standard job-matching model, which predicts that wages increase with better outside opportunity of the worker and fall with better outside opportunity of the employer.
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Notes
Note that in the matching literature, the term p is interpreted as the productivity of a match. For the purposes of this paper I treat it as a human capital variable.
It is usually assumed that entry is costless for the firm, V = 0. A more general case allows firms to pay an entry cost to enter the market. If the firms exhaust the gains from opening a vacancy, then V equals the cost of entry.
Also other models of involuntary unemployment predict that outside options matter for wages. For example, in the basic sequential job search model, the strategy of the worker is to compare wage offers and pick the best option. The implication of the optimal strategy is that wages increase with better employment prospects. Also, nonsearch models of unemployment may postulate a wage-setting mode dependent on outside options of the worker or the firm or both. For example, the shirking model of the efficiency wage theory (Shapiro and Stiglitz 1984) predicts the efficiency wage to be increasing with the rate at which workers find new jobs. Note that in the standard version of the shirking model of the efficiency wage theory, the firm should not have difficulty in replacing a fired worker. In some versions of efficiency wage models, however, firms may be keen to pay a higher wage because of concerns about worker retention and costs of recruitment; see Lang (1991) and Montgomery (1991). The prediction is that workers who are difficult to replace will be paid higher wages. I focus on the matching literature because one can derive an intuitive and linear relationship between wages and the outside options and because it is a well-known framework for analyzing the labor market.
The equilibrium wage expression in Hall and Milgrom (2008) includes an outside option term scaled by the probability of a wage bargain breakdown. The authors argue that when this breakdown parameter equals 1, their model is reduced to the standard job-matching model with a Nash bargain, whereas when this breakdown parameter equals 0, the wage bargaining process is completely separate from the outside option. For their numerical simulations, the authors set the value equal to 0.0055, making the impact of the outside option in practice negligible for wages.
Note that I assume that the job-arrival rate and the vacancy-filling rate vary between workers and their employers, while the remaining factors do not. Instead, in the standard job-matching model the transition probabilities are the same for all workers and firms, workers and firms are ex-ante identical, and the model predicts a single wage. Albrecht and Vroman (2002) study a standard job-matching model that generates worker and firm heterogeneity in wages and outside options by allowing for differences in skills among the workers and differences in job requirements demanded by the firms.
The 2000 wave of LNU includes 5,142 individuals, of who 2,973 report a positive wage. I keep “prime-aged” workers, aged 25–54, and I drop self-employed workers and those employed in farming. The analysis sample consists of 1787 observations.
Pearson’s \(\chi ^2\) test statistic for the hypothesis that the columns and rows in Table 1 are independent has a p value of 0, suggesting that they are not independent. Cohen’s kappa coefficient of agreement between these ordinal variables equals 0.0217, suggesting only slight “agreement” between the two measures.
Ideally, one would have instrumental variables (IVs) to correct for the endogeneity in the two subjective measures. To be valid, such IVs would have to affect wages only through the effect they have on the respondents’ subjective assessments. In order to construct such instruments, I calculated average region-by-industry responses to each of the two subjective questions, using the rationale that the conditions in the labor market may affect an individual’s wage through the effect they have on the respondent outside options. Unfortunately, the first-stage in the two-stage least squares regressions was relatively weak (F-statistic on the excluded instruments \(<\)10). These results are available from the author.
The more standard ordered logit imposes the “parallel-regression assumption,” which, in effect, constraints the coefficients on the covariates to be constant across the ordered categorical outcomes. The test of this assumption showed that in particular for the outcome variable “Ease of finding as good a job,” the human capital variables (in particular, years of education, employer-provided training, and tenure) reported p values that were close to or less than 0.05; for the other ordered outcome, “Ease of being replaced,” the test generated fewer low p values; I conducted the test using the “brant” command in Stata. This suggests that, at least for the human capital covariates, the data might be better described by a generalized ordered logit. I include estimates from a standard ordered logit in the appendix, see Table 7.
As a robustness check, I also estimated two linear models. In the first model, I rescaled the dependent categorical variable so that a marginal change in a regressor can be interpreted as a standard deviation change in the subjective assessment; Praag and Ferrer-i-Carbonell (2006) call this the “probit-adapted OLS” (POLS) model. Second, I use the 0–1 variables “Easy the find as good a job” and “Easy to be replaced” and estimate linear probability models (LPM). The take-away from the POLS models (in Table 8) and the LPMs (in Table 9) is very similar to that from the standard ordered logit from Table 7, but not surprisingly, the LPM explains less variation than the POLS model.
Table 10 presents results where log wages have been regressed on the full set of categorical subjective assessments. Similarly to Table 5, the coefficients on “Ease of finding as good a job” are mostly positive and the coefficients on “Ease of being replaced” are negative, but there is often not enough power to precisely estimate individual coefficients on the categorical variables.
In Table 11, in the appendix, I present log-wage regressions where each binary indicator instead equals one if the respondent has answered “fairly easy,” “very easy” or “not particularly difficult” and zero if the respondent has answered “very difficult” or “fairly difficult.” Defining the variables this way makes the \(\upbeta _{1}\)-coefficient and \(\upbeta _{2}\)-coefficient lose precision for men when I control for respondent characteristics. For women, the \(\upbeta _{1}\)-coefficient remains significant and positive but the \(\upbeta _{2}\)-coefficient also loses precision.
Also when I pool men and women and estimate ordered logits for the two subjective measures, the coefficients on the indicator for a female indicate that, conditional on other observables, women are more likely to report worse chances of reemployment and higher chances of becoming replaced.
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I would like to thank Henry Farber, Lars Lefgren, Alan Krueger, and the participants at Princeton University graduate labor seminar and the Midwest Economics Association meetings for suggestions on an earlier version of this paper. I thank Bernd Fitzenberger and three anonymous referees for their helpful comments. I am grateful for comments from Ronny Freier, Matthew Lindquist, Andreas Mueller, Zhuan Pei, Kevin Rinz, Åsa Rosén, Anders Stenberg, Michael Tåhlin, Eskil Wadensjö, and Stephen Woodbury.
Appendices
Appendix 1: Outside options
In this section, I derive the expressions for the outside options in the standard job-matching model. Consider the asset value of employing a worker, where J is the value of the firm with a worker, V is the value of holding a vacancy, p denotes productivity, w is the wage paid, and \(\upsigma \) is the probability of job separation:
The next equation describes the asset value for the firm of having a vacancy, where c is the cost the firm pays to post a vacancy and \(q (\theta )\) is the probability that the firm fills a vacancy, which depends on \(\theta \), the labor market tightness:
Analogously, for the workers we have that:
where W is the value of employment and U is the value of being unemployed. \(\theta q(\theta )\) is the probability of finding a job, and b is the level of unemployment insurance benefits (or the value of leisure). The wage is an outcome of an asymmetric Nash bargain subject to the equations above:
Taking the first-order conditions, we obtain Eq. (1): \(w = \beta p + (1 - \beta )rU - \beta rV\).
Solving for rU and rV gives that:
Appendix 2: Description of variables
Wage Gross hourly wage. Constructed from questions on gross fixed monthly and weekly pay, bonus pay, and remuneration for inconvenient working hours, divided by hours usually worked. (1 SEK = 7 USD.) (Survey question)
Ease of finding as good a job Answer to question, “How easy do you think it would be for you to get a job as good as your current one if you for some reason had to leave your employer?” 1 = very difficult, 2 = fairly difficult, 3 = not particularly difficult, 4 = fairly easy, 5 = very easy. (Survey question)
Easy to as good a job Equals one if answer to question, “How easy do you think it would be for you to get a job as good as your current one if you for some reason had to leave your employer?” is equal to “fairly easy” or “very easy” and zero otherwise. (Survey question)
Ease of being replaced “How easy do you think it would be for your employer to replace you if you left?” 1 = very difficult, 2 = fairly difficult, 3 = not particularly difficult, 4 = fairly easy, 5 = very easy. (Survey question)
Easy to be replaced Equals one if answer to question, “How easy do you think it would be for your employer to replace you if you left?” is equal to “fairly easy” or “very easy” and zero otherwise. (Survey question)
Education How many years of full-time education do you have? (Survey question)
Experience How many years altogether have you spent in gainful employment? Years of labor market experience. (Survey question)
Tenure Years of job tenure. Calculated from the year of employment at present work. (Survey question)
Employer-provided training Have you in the past 12 months received training during paid work time? (Survey question)
Private Equals one if employed in the private sector. (Survey question)
Union member Equals one if a member of a trade union. (Survey question)
Woman Equals one if a woman. (Survey question)
Married Equals one if married. (Registry information)
Unemployed in 1999? Equals one if unemployed at any time during 1999. (Survey question)
Socioeconomic status (SES) categories Categories: unskilled blue-collar; skilled blue-collar; skilled blue-collar, a supervisor; white-collar; “higher-level” white-collar. (Survey question)
No. of industry switches How many times a respondent switched 1-digit industry of employment in the past eight years. (Registry information)
Index of physical capabilities based on questions regarding mobility (whether the respondent can walk 100 meters without difficulties, run 100 meters without difficulties, and walk up and down the stairs without difficulties). 1 = if yes to all questions, 4 = if no to all questions, 3 = if no to walk and run, but yes to walk up/down the stairs, and 2 = if yes to walk and walk up/down the stairs, but no to run.
Region The region of residence: Stockholm; Gothenburg; Malmö; medium-sized city; southern urban area; northern urban area; northern rural area. (Survey question)
Appendix 3: Additional results
See Tables 7, 8, 9, 10 and 11.
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Lachowska, M. Outside options and wages: What can we learn from subjective assessments?. Empir Econ 52, 79–121 (2017). https://doi.org/10.1007/s00181-016-1077-5
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DOI: https://doi.org/10.1007/s00181-016-1077-5