Who bears the cost of the business cycle? Labor-market institutions and volatility of the youth unemployment rate

The way age-specific unemployment rates fluctuate over the business cycle differs significantly across countries. This paper examines the effect of labor-market institutions on the fluctuations of age-specific unemployment rates based on panel data of 18 OECD countries between 1971 and 2008. Empirical results suggest that the cost of the business cycle disproportionately falls on youths in countries with stricter employment protection. This implies that a higher adjustment cost of an existing workforce induces the employment adjustment of new entrants into the labor market. JEL codes: E24, J80


Introduction
Although the unemployment rate fluctuates in line with the business cycle, the fluctuation of age-specific unemployment rates differs significantly across Organisation for Economic Co-operation and Development (OECD) countries. Figure 1 is a time-series plot for the age-specific male unemployment rate in the US, France, and Japan for the 1960-2008 period. The way age-specific unemployment rates fluctuate over the business cycle significantly differs across these three countries. First, and adults' (45-54) unemployment rates move in parallel in the US. Business-cycle fluctuations seem to be absorbed equally across generations. Second, youths' unemployment rate fluctuates more sharply adults' unemployment rate in France. This implies that employment adjustments occur more often for youths than for adults in France. The Japanese trend lies somewhere between those of the US and France. Shocks to the economy are equally absorbed by generations in the US, while they are intensively absorbed by younger generations in France. To see the heterogeneity of the age distribution of unemployment-rate volatility adjusting for the difference in the levels of unemployment rates by age groups, Table 1 reports the coefficient of variation of the unemployment rates for these three countries. Again, we find that the youths' unemployment-rate volatility relative to adults' employment-rate volatility is higher in France than in the US or Japan.
What factors cause this international difference in the responses of age-specific unemployment rates over the business cycle?
Many theoretical and empirical investigations also account for higher unemployment rates for youth than for adults. Literature has shown that stricter employment protection or a higher unionization rate raises the unemployment rate of youths relative to adults (Canziani and Petrongoro (2001), Jimeno and Rodriguez-Palenzuela (2003), Bertola, Blau, and Kahn (2007), Kahn (2007), Modesto (2008)). These papers study how employment protection or wage-setting institutions affects the levels of unemployment rates of youths and adults. In other words, these studies examine the long-run effect of employment protection or wage-setting institutions on the unemployment rate of youths relative to that of adults.
To the best of our knowledge, none of the existing studies explain why the fluctuations of age-specific unemployment rates differ across countries. It is important to study which age groups of workers absorb the short-run macroeconomic shocks from the point of view of inter-generational risk-sharing. Economies where macroeconomic shocks are disproportionately absorbed by younger generations place more burdens of the business cycle on youths, who presumably have a lower capacity for absorbing risks because of a lower level of asset accumulation. Neumark (2000), von Wachter and Benders (2006), and Genda, Kondo and Ohta (2010) report that the employment status 3 of youths has prolonged effects on the employment status of adults because of the hysteresis of employment status over a life cycle. Thus, short-run macroeconomic shocks experienced when workers are young may well have a considerable long-run effect on their welfare, and workers belonging to different birth-year cohorts may have significantly different levels of welfare in an economy where short-run macroeconomic shocks are absorbed disproportionately by young workers.
This paper explores the extent to which labor-market institutions, such as the degree of employment protection, affect the heterogeneous responses of age-specific unemployment rates to macroeconomic shocks. We introduce a theoretical model that analyzes firms' employment policies in a dynamic setting when the adjustment of labor input is costly. Numerical results indicate that existing workers' higher adjustment costs make firms adjust labor input by reducing new hires from the labor market. Our empirical analysis is based on panel data of the male unemployment rate of 18 developed countries spanning the period between 1970 and 2000. By regressing changes of age-specific unemployment rates on overall unemployment rate, the heterogeneity of the responses of age-specific unemployment rates to a macroeconomic shock is estimated. We further examine how this heterogeneity depends on various labor-market-institution indexes, published by Blanchard and Wolfers (2000) and others.
Our results indicate that stricter employment protection amplifies the effect of the cyclical unemployment rate on youths' unemployment rate. This implies the cost of the business cycle disproportionately falls on youths in the countries with stricter employment protection and high union-coverage rates. Other institutions, such as the unemployment insurance system and the wage-setting institution, do not have significant impacts on the cyclical sensitivity of age-specific unemployment rates.
The rest of this paper is organized as follows. Section 2 provides a simple model of a firm's decision to hire youth and adult workers and shows that the firing cost disproportionately insulates adult workers' employment. Section 3 discusses the empirical strategy. Section 4 describes our data.
Section 5 reports the empirical results. Section 6 provides conclusions.

Theoretical background.
In this section, we introduce a theoretical model that analyzes the firms' employment policy in a dynamic setting when the adjustment of labor input is costly.
We consider a firm that operates infinitely, discounting future profit with a constant interest rate.
The firm produces output using L Y young workers, and L O adult workers as inputs. Young and adult workers are combined by the CES production technology with the elasticity of substitution where A is the total factor productivity, which takes either a high or low value and follows a first-order Markov process. We denote transition probabilities as P H|H , P L|H , P H|L , P L|L where P | stands for the probability of transition from state i to j. Hence, the firm has an incentive to adjust employment, responding to productivity realization in each period. We assume that the number of young workers in the previous period becomes the number of adult workers at the beginning of a period. The firm bears the labor adjustment cost when it decides to change the number of adult employmees from this initial value, as well as hiring costs for the young workers.
Given the wage rate of young workers W Y , and adult workers W O ,, its profit in period t is represented as follows; where f . is a hiring cost function for young workers and g . is an adjustment cost function for adult workers. In the above setting, the firm's employment policy must be consistent with the following Bellman equations, with the current state variables A , L Y .
where L Y, is the number of youths employed in the previous period (initial old), β is a discount factor, and A′ is productivity realization in the next period.
We solve the model numerically with parameters in Table 2 and simulate the economies for 10,000,000 periods. Specifically, we conduct them with three different sets of σ, P | , each of which is calculated with three different values of α. We calculate the mean, standard deviation, and coefficient of variation (CV) of the simulated path of age-specific unemployment. Then, we calculate the relative CV between youth and adult workers.
Results are presented in Table 3. In the table, all three cases (a)-(c) show that with higher α, the relative CVs of the young workers also mark a higher value. That is, the higher adjustment cost of existing workers makes firms adjust labor input by reducing new hires from the labor market. This inclination is more evident in the case of the higher substitutability of youth and adult workers (higher σ) or lower uncertainty (higher P | ).
More volatile labor demand for youths leads to higher volatility of youths' unemployment rate with some degree of rigidity in the wage setting (Shimer (2005a) and Hall (2005a)). In the following empirical sections, we test whether the higher adjustment costs of adult workers as compared with young workers results in a higher volatility of youths' employment relative to that of adults.

Empirical Strategy
Theoretical analysis in the previous section emphasizes the role of adjustment cost on labor-demand fluctuation by age groups. The degree to which this demand fluctuation is transmitted to unemployment rate fluctuation crucially depends on wage rigidities. Thus, other labor-market institutions, such as unemployment-insurance systems, unions, and wage-setting institutions, which differ across countries, may well affect unemployment rates by age groups. Hence, we control for those labor-market institutions as well.
The literature adopts labor productivity as a measurement of productivity shock to the labor market (Shimer (2005b), Hall (2005b), Fujita and Ramey (2009) and Fujita (2011)). Labor-productivity shocks, however, affect the unemployment rate through inflow to and outflow from unemployment with a complex lag structure. Accordingly, there is no consensus on a time-series relation between a positive shock to labor productivity and the unemployment rate. Given this state of the literature, we avoid directly estimating the relation between the labor-productivity change and the change of unemployment rates by age groups. Instead, the shock to the labor market is approximated by the unemployment rate defined over all age groups, and the relation between the overall unemployment rate and the age-specific unemployment rate is examined. Particularly, we specify a model as follows.
where In equation (1), the coefficient on the overall unemployment rate of all ages identifies the impact of the overall change of the unemployment rate on the change of the age-specific unemployment rate.
The coefficients on lagged labor-market institutions identify the long-run effect of labor-market institutions, such as firing restrictions, on the age-specific unemployment rate change. The coefficients on the interaction terms between the labor-market institution index and the overall unemployment rate change identify how the effects of overall labor-market shock on the age-specific 6 unemployment rates depend on labor-market institutions, such as firing restrictions, unemployment insurance, and wage-setting institutions.
Since the overall unemployment rate is the weighted average of age-specific unemployment rates, the overall unemployment rate is an obvious endogenous variable. This endogeneity is circumvented by instrumenting the overall unemployment rate by the weighted average of unemployment rates, excluding the unemployment rate of the target age group. We estimate the above equation with a random-effect IV model, assuming unobservable heterogeneity c age i is not correlated with regressors. In addition, we run regressions with the difference of the unemployment rate change by age group as dependent variables to quantify the difference of the coefficients across age-groups.

Data
We build the cross-country time-series dataset from two sources. First, we draw age-group-specific and overall unemployment rates and population for male workers from the OECD Stat Extracts. 2 Age groups of our concern are 15-24, 25-34, and 45-54. Second, we draw labor-market-institution indices from the "CEP-OECD Institution Dataset," which is compiled by Center for Economic Performance (London School of Economics). This dataset is constructed on the basis of an earlier work by Nickell and Nunziata (2001), which is in turn based on the OECD Employment Outlook and other related research. 1. The EPL Index takes a higher value if employment protection legislation is more stringent. This index is essentially based on Blanchard and Wolfers (1994), which in turn is based on OECD (1994) and Lazear (1990). Blanchard and Wolfers (2000) extend an EPL measure of OECD (1994) by connecting with Lazear (1990). In particular, Blanchard and Wolfers (2000) (2007)  4= Predominantly industrial bargaining, but also recurrent central-level associations.
5= Central-level agreements of overriding importance.
In these decades, there is no country in which bargaining processes became more centralized, while several countries, such as New Zealand, Switzerland, and Denmark, became more decentralized.
The In general, centralization may not necessarily mean coordination or vice versa (OECD, 1997). First, if there is a significant discrepancy between individual firm-level negotiated wage and globally negotiated wage, which is called wage drift, the extent of coordination may be weaker despite the centralized wage setting. Second, institutions such as pattern-setting may promote coordination, while it is also substitutable to institutions that are intended to promote centralization. 7 There are several different claims regarding the effect of centralization and coordination on unemployment rates. Nickell (1997) refers to the notion of OECD (1994, Table 5.16) that coordinative arrangements lower wages while centralized arrangements do not, and summarizes that the negative effects of unionization on employment are mitigated by coordination. In contrast, Calmfors and Driffill (1988) claim that the relation between centralization and employment is U-shaped.
Time-series, cross-section values of these indexes are summarized in Table 4. The indexes do not vary much over time within a country; thus the estimation mainly relies on the cross-country variation of labor-market institutions. The descriptive statistics of the analysis sample are summarized in Table 5. Since the values of the index of labor markets do not carry information in themselves, we normalize all the indexes for the purpose of comparing the relative importance of institutions in determining the change of unemployment rates. The coefficients of the overall unemployment rate are positive in each of the age groups. The estimated coefficients are larger for younger workers than adult workers, indicating that youths' unemployment rate is more procyclical than adults' unemployment rate.

Estimation Results
Estimation results suggest that labor-market institution indexes, such as firing restrictions, unemployment system, and wage-setting institutions, are broadly irrelevant to unemployment fluctuation.
The coefficients of the interaction terms between institution indexes and the overall unemployment rate identify the heterogeneous impact of the macroeconomic shock on the change of age-specific unemployment rates by institutional setting. We first examine the results for employment protection. Table 3 shows that stricter employment protection amplifies the effect of overall shock on the unemployment change of young workers, while it has no effect on that of adult workers. This implies that firing restrictions mitigate the cyclical unemployment rate fluctuation for adults, while it does not for youths. These results are consistent with the theoretical result of the previous section.
This also well explains why unemployment rates of all age groups move simultaneously in the US where firing restrictions are less stringent, while youths' unemployment rate fluctuates more than that of adults in France, where firing restrictions are more stringent.
Notable results other than that of firing restrictions (EPL) are coefficients of the interaction terms between the overall unemployment rate and union coverage. The estimated coefficient is positive and statistically significant for youths' unemployment rate change, but it is not statistically significant for adults' unemployment change. Put differently, the higher union coverage amplifies the difference between youths' and adults' unemployment rate change in response to macro shocks, and this implies that macroeconomic shocks are more likely to be absorbed by young workers in economies with higher union coverage.
Given that younger workers are less likely to be employed and so are less likely to be covered by union contracts, the above empirical results are consistent with the result of Blanchard and Summers's (1986) insider-outsider theory, where unions care about the employment of their members in the labor-bargaining process, resulting in fewer employment opportunities for outsiders.
These results imply that in economies with stringent firing restrictions or high union coverage, macro shocks are disproportionately absorbed by younger workers. This finding is also consistent with a robust findings that the role of seniority in determining the order of layoffs is greater in union sector than non-union sector (Abraham and Medoff (1984)).
The relative youth cohort size and relative young-adult cohort size are negatively correlated with unemployment rate of the young and both of them are statistically significant. These signs are consistent of Shimer's (2001) finding that an increase in the share of youth significantly reduces youths' unemployment rate in US state-level data.

Conclusion
In this paper, we empirically explore the effect of labor-market institutions on cyclical variations of age-specific unemployment rates. A theoretical model with a numerical simulation suggests that a firing restriction has the heterogeneous impacts of a macroeconomic shock on the fluctuation of age-specific labor demand. In particular, a high adjustment cost of adult workers amplifies the cyclical variation of labor demand for young workers, while it mitigates the fluctuation of such demand for adult workers.
Our empirical analysis from 18 OECD countries shows that the firing restriction amplifies the cyclical fluctuation of unemployment rate for youths, but not for adults. This implies that macroeconomic shocks are disproportionately absorbed by younger workers than older workers in economies with the stricter firing restrictions. The other notable result is that macroeconomic shocks are more likely to be absorbed by young workers in economies with higher union density.
Previous literature has shown that youths' unemployment rate is more cyclically sensitive than that of adults. Another strand of literature has shown that employment protection and wage-setting institutions tend to increase the long-run unemployment rate of young workers. On top of that existing knowledge, this paper adds a new finding that a stricter firing restriction and a higher  Age-specific unemployment rate, Japan    Year 1960196519701975198019851990199520002003年 Year 19601965197019751980198519901995

Union Density Union Coverage Ratio
Year 1960196519701975198019851990199520002003年 Year 19601965197019751980198519901995   Note: Each institution index is calculated as a deviation from the mean over the standard deviation for normalization. 20 Notes: Standard errors are in parentheses. Each institution index is computed as the deviation from the mean over standard error. All specifications include year dummy variables.