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Specific capital, firm insurance, and the dynamics of the postgraduate wage premium IFS Working Paper W26/19 Ran Gu Specific Capital, Firm Insurance, and the Dynamics of the Postgraduate Wage Premium Ran Gu∗ 2nd September 2019 Abstract Postgraduate degree holders experience lower cyclical wage vari- ation than those with undergraduate degrees. Moreover, postgradu- ates have more specific human capital than undergraduates. Using an equilibrium search model with long-term contracts and imperfect monitoring of worker effort, this paper attributes the cyclicality of the postgraduate-undergraduate wage gap to the differences in specific cap- ital. Imperfect monitoring creates a moral hazard problem that requires firms to pay efficiency wages.

More specific capital leads to lower mo- bility, thereby alleviating the moral hazard and improving risk-sharing. Estimates reveal that specific capital explains the differences both in labour turnover and in wage cyclicality across education groups. ∗ Department of Economics, University of Essex, CO4 3SQ, UK, email: ran.uk and Institute for Fiscal Studies. I am grateful for the generous sup- port of Richard Blundell, Jeremy Lise, and Fabien Postel-Vinay.

I am also thankful for the invaluable advice of Arun Advani, Ben Etheridge, Carlos Carrillo-Tudela, Alex Clymo, Melvyn Coles, Søren Leth-Petersen, Attila Lindner, Costas Meghir, Andreas Müller, Imran Rasul, Jean-Marc Robin, Uta Schönberg, Eric Smith and seminar participants at Bristol, Essex, EIEF, Royal Holloway, IFS, and UCL for helpful comments and suggestions. 1 1 Introduction Firms can provide employment contracts to insure workers from aggregate shocks (Azariadis, 1975; Beaudry and DiNardo, 1991). Significant research efforts have been devoted to characterizing optimal contracts in frictional labour markets (Burdett and Coles, 2003; Rudanko, 2009; Menzio and Shi, 2011). While it has been recognized that workers with more specific human capital face lower cyclical variation in employment than unskilled workers (Cairó and Cajner, 2016), little evidence is available on the relative variation of their wages.

In this paper, I build an equilibrium search model to study the impact of specific human capital on wage variation over the business cycle. Then, I apply this model to explain novel stylised facts about the cyclicality of the postgraduate wage premium. Beginning with the data, can education provide shelter against wage shocks over the business cycle? As the employment share held by post- graduates has doubled since 1980, I compare postgraduates to those with only undergraduate degrees and document a new result: In the US, the postgraduate-undergraduate wage premium is counter-cyclical.1 To illus- trate, Figure 1 plots the detrended real GDP and the postgraduate wage premium.2 The postgraduate wage premium increases substantially during all recent recessions, and its correlation with real GDP is -0. Table 1 reports that when real GDP goes up by 1%, the median postgraduate wage increases by 0.34%, and the median undergraduate wage increases by 0.58%, indicating that postgraduate wages respond less to business cycle shocks than undergraduate wages.3 Table 1 also shows that both the college-noncollege 1 Postgraduate degrees include masters, Ph., and professional degrees.

Lindley and Machin (2016) document that in 2012 nearly 15% of the adult workforce, or 40% of all college graduates, have a postgraduate degree. As I discuss further in my review of the literature, the existing literature analyzes the cyclicality of the college-noncollege wage premium, and finds it to be acyclical. 2 See Appendix A for a description of the data. 3 In terms of means, when real GDP goes up by 1%, the average postgraduate wage increases by 0.25%, and the average undergraduate wage increases by 0.

2 wage premium and the undergraduate-noncollege wage premium are largely acyclical.4 Therefore, education can provide insurance against cyclical wage shocks only if a postgraduate degree is obtained. Figure 1: Detrended Real GDP and Postgraduate Wage Premium Current Population Survey March Supplement (March CPS) 1976–2016, males, aged 26–64. NBER dated recessions are shaded. Series are logged and detrended using a Hodrick–Prescott (HP) filter with parameter 100.

Furthermore, I find that the difference in wage cyclicality between post- graduates and undergraduates is significant for workers with a long tenure in a given job, but not for new hires.5 As workers’ job tenure is the gener- ally used proxy for specific human capital (Altonji and Shakotko, 1987), I argue that this phenomenon occurs because experienced postgraduates accu- mulate more specific capital in their jobs than their undergraduate degree- 4 The undergraduate-noncollege wage premium is weakly pro-cyclical in the mean, while it is acyclical in the median and the top 25%. As is argued by Lindquist (2004), the median wage premium is a more suitable measure of the correlation between output and the wage premium than the mean wage premium, because composition bias and top-coding have a smaller impact on the median wage premium. 5 I show that the counter-cyclical postgraduate wage premium is due neither to cyclical changes in the composition of the workforce, nor to postgraduates and undergraduates sorting into different industries and occupations. 3 Table 1: Elasticity with respect to GDP Wage Wage Premium Postgrad Undergrad College Postgrad Undergrad Noncollege Undergrad Noncollege Noncollege Median .13) Wages are deflated to constant 2000 dollars.

College = undergraduates + post- graduates. holding counterparts, and thus, they are offered contracts with smoother wages. Since new hires have not yet built any specific capital, the difference in wage cyclicality between postgraduates and undergraduates is small. I provide empirical evidence showing postgraduates have more specific capital in two dimensions: the size of specific capital that new hires have to build and the time needed for this process.

First, with regard to the time dimension, I construct a new measurement using the data on the adaptation period in a new job: newly hired postgraduates need 58.5 weeks to become fully com- petent, twice as long as the time needed by undergraduates. Second, with regard to the size dimension, Dustmann and Meghir (2005) argue that more specific capital leads to larger wage losses from exogenous job displacement. I show that displaced postgraduates suffer an average wage loss of 17.8%, twice as much of a loss as undergraduates. To understand how specific capital affects labour turnover and wage cycli- cality, I develop a directed search model of wage contracting and firm com- mitment, based on the work of Tsuyuhara (2016) and Lamadon (2016).

I depart by adding specific human capital and aggregate shocks to matches. I assume new hires have zero endowment of any specific capital, which they obtain through a period of job adaptation. In the model, risk-neutral firms provide long-term contracts, and risk-averse workers choose their effort level 4 to avoid job separation. If effort were observable, because of the difference in risk aversion, firms would bear all the risk, offer constant wages, and pre- scribe constant effort.

I assume worker effort is unobserved by firms (Azari- adis, 1975). With this assumption, workers might shirk. Firms pay efficiency wages to induce them to provide the optimal level of effort. The optimal contract is such that wage changes track aggregate produc- tivity shocks: When aggregate productivity increases, firms increase wages of workers to incentivize them to make a greater effort.

I show that the effort level of skilled workers increases with specific human capital: After gaining specific capital, skilled workers have strong incentives to keep their jobs longer. As these incentives increase with the level of specific capital, skilled workers with more specific capital make a greater effort to avoid job separation. I further show that wage smoothing of skilled workers increases with specific capital. On the one hand, as skilled workers with more specific capital are less likely to leave their current jobs, they will value more about firms’ promises of future wage changes.

As wage changes becomes more effective in motivating workers, firms do not need to give workers a lot of incentives. Intuitively, firms do not have to increase wages to keep them in booms. On the other hand, as the level of effort increases with the level of specific capital, the response of effort to increased incentives decreases. Then, it becomes increasingly costly for firms to provide incentives for worker effort.

Firms face the trade-off between insurance and incentives. As more specific capital increases both the effectiveness and the marginal cost of providing incentives, it becomes optimal for firms to provide more insurance to workers with more specific capital, i. smaller wage changes caused by changes in aggregate productivity. Although the model is parsimonious, it can endogenously generate the differences in both labour turnover and wage cyclicality across education groups, given the observed empirical differences in specific human capital.

5 Additionally, my paper implies that lower educated workers, and even un- dergraduates, are unlikely to receive much insurance from firms, thereby, increasing the demand for social insurance among this group. I conduct a counterfactual policy experiment to raise the unemployment insurance (UI) replacement rate by 20%. I find that this policy increases wage cyclicality, indicating UI crowds out the implicit insurance provided by firms. However, the effect is less pronounced for lower educated workers than for postgradu- ates.

Lower educated workers have a higher welfare gain than postgraduates from such a policy, which supports the argument for a lower UI replacement rate for postgraduates. Related Literature A large literature has studied the extent to which workers can insure them- selves against uncertain labour income (see e. Krueger and Perri, 2005, 2006; Heathcote, Storesletten and Violante, 2005; Blundell, Pistaferri and Preston, 2008). This paper explores where income shocks arises from in the first place, and argues that postgraduates get more firm insurance than other education groups because they have more specific capital.

The theoretical literature on how specific capital affects wage cyclicality is inconclusive. Azariadis (1976) studies long-term contracts with commitment and implies that firms are more willing to offer constant wages to workers with more specific capital. On the other hand, Hashimoto (1975) and Raisian (1979) study implicit contracts with lack of commitment and imply that workers with more specific capital accept higher cyclical fluctuations in wages in return for higher employment security. My work extends this literature by showing that, in an economy with search frictions and firm commitment, workers with more specific capital are offered contracts with smoother wages.

In the search literature, Hudomiet (2015) and Cairó and Cajner (2016) evaluate the effect of specific capital on employment and labour turnover. To my knowledge, the current paper is the first to quantify the effect of specific 6 capital on both labour turnover and wage cyclicality. This paper contributes to the literature that studies the cyclicality of education wage premium. Keane and Prasad (1993) and Lindquist (2004) compare wage cyclicality between noncollege workers and college graduates, a group which includes both undergraduates and postgraduates.

They find that both types of workers experience the same degree of cyclical wage shocks, i. that the college wage premium is acyclical. I confirm their result, but show that the cyclicality emerges once undergraduates and postgraduates are considered separately. Outline Section 2 and 3 provide empirical evidence on wage cyclicality and specific capital.

Section 4 presents the equilibrium search model. In Section 5, I outline the estimation strategy, discuss the identification, and report the estimation results. In Section 6, I analyze the estimated model and report the counterfactual simulations. Section 7 evaluates the counterfactual policy.

2 Empirical Evidence on Wage Cyclicality In this section, I use individual-level data to compare the wage cyclicality between postgraduates and undergraduates, controlling for observed char- acteristics. Then, I study the relationship between the cyclicality of the postgraduat wage premium and job tenure.1 Regression of Wage on Degree Interaction To estimate the effects of postgraduate degree on the wage cyclicality, I follow Keane and Prasad (1993) and run the regression of log real hourly wage 7 ln Wit = θP Git + αUt + γP Git × Ut + Xit β + εit (1) where P Git is a postgraduate degree dummy, which equals 1 if the worker has a postgraduate degree and 0 if he only has an undergraduate degree. I use the aggregate unemployment rate in the economy, Ut , as an indica- tor of the business cycle.