Youth unemployment in the OECD: demographic shifts, labour market institutions, and macroeconomic shocks¹

Juan F. Jimeno² and Diego Rodriguez-Palenzuela³

9 April 2002

3rd

¹We are very grateful to Mario Izquierdo for excellent research assistance, and to Olivier Blanchard for comments on a earlier version of this paper.Comments from participants at the 3^rd ECB Labour Markets Workshop, in particular from Julian Messina, are gratefully acknowledged. The authors are responsible for any remaining error.

²FEDEA, Universidad de Alcal· and CEPR. Email: jimeno@fedea.es.

³European Central Bank. Email: diego.rodriguez@ecb.int. The views and opinions expressed in this paper are those of the authors do not necessarily reflect views and opinions of the European Central Bank.

Abstract

We use a panel of OECD countries to gauge the relevance of the relative size of the youth population, labour market institutions and macroeconomic shocks at explaining observed relative youth unemployment rates. We find that the fluctuations of the youth population size caused by the baby boom of the 1950s and 1960s and the subsequent decline of fertility in many European countries are positively associated with fluctuations in relative youth unemployment rates. We also find that some labour market institutions contribute to increase youth unemployment, and that the adjustment to macroeconomic shocks has afected relatively more to young workers than to adult workers. To motivate the efects of institution on the relative unemployment rate of young workers, we lay out a simple theoretical model that builds on the imperfect substitutability of workers of diferent ages, and on the non-allocative role of (age specific) wages.

JEL Code: J64.

Keywords: youth unemployment, labour supply, labour market institutions.

Non-technical summary

The performance of the European economies in terms of unemployment rates has been in general dismal since the 1970s. Some significant improvements have only been seen in the recent years. Even within the EU there are some crosscountry diferences in the incidence of unemployment, which are more noticeable when unemployment rates are observed for particular demographic groups. While the unemployment rate of the prime age male workers has in most countries fluctuated around generally moderate average rates, those of the youth have fluctuated quite widely around considerably higher average rates. Therefore, a thorough understanding of the dismal performance of European labour markets should comprise an analysis of youth unemployment. Meanwhile, other motivations to study youth labour markets should not be discounted. First, the disaggregate analysis of unemployment across demographic groups might shed light on the precise workings of labour market institutions. Second, the analysis of youth unemployment could pave the way for the design of policies aimed at improving overall labour market performance. The beneficial efects of such reforms can hardly be exaggerated, as it has been well established by now that high youth unemployment rates have significant detrimental efects in factors that afect welfare in the longer term, like human capital accumulation and fertility rates.

This paper reviews the main factors explaining the unemployment rates of the youth. For this, we develop an analytical framework which suggests that to obtain a labour market equilibrium with broadly similar unemployment rates for prime age and young workers, a certain degree of wage flexibility must exist. In particular, two institutional characteristics would seem to be associated with high relative youth unemployment rates. First, those that have a positive impact on the overall cost of the standard labour contract (e.g. employment protection, a higher tax wedge, etc.) are likely to make young workers less attractive for firms, since given the average lower job experience of young workers their average productivity tends to be lower. Second, an instititutional setting that does not make provision for some contractual flexibility for the particular characteristics of the young workers (e.g. age-specific minimum wages, age-specific fiscal treatment) would leave the youth in disadvantage relative to more experienced prime age workers, if the general labour market setting is predominantly rigid.

The empirical results in the paper broadly confirm the insights in the theoretical part. Our main results follow the approach successfully implemented by Blanchard and Wolfers (2000) to study aggregate unemployment rates in OECD countries. This approach focuses primarily in the interaction of macroeconomic shocks and labour market institutions to account for countries unemployment performance. We implement this approach in a panel of OECD countries, to measure the joint efect of macroeconomic shocks, labour market institutions and demographic developments to explain the (gender specific) youth relative unemployment rates (i.e. the diference between the youth unemployment rates -of men and women, respectively- and that of prime age male workers). The leading results indicate that -once the main relevant factors have been taken into accountdemographic developments have a significant, albeit limited, impact on relative youth unemployment rates. In addition, it would appear that youth workers tend to play a role of a ìbuferî to absorb macroeconomic shocks, through wider fluctuations in their unemployment rates. This is reflected in the very significant impact of cyclically-related variables in the relative youth unemployment rates (i.e. weaker activity along the economic cycle would have a strong impact on relative youth unemployment). Furthermore, this is reflected in the fact that cyclical variables seem to have a markedly stronger efects at higher (annual) frequencies than at lower (five year) frequencies. In addition, and in line with our model, we find that institutional settings that increase the overall rigidity of the labour market tend to increase the youth unemployment rate, and that specific institutional features that particularly reduce the restrictions afecting the youth labour markets (e.g. youth specific -lower- minimum wages, or lower strictness in temporary contractual forms) tend to somewhat reduce the relative youth unemployment rate.

1 Introduction

One of the main socioeconomic developments which has significantly challenged macroeconomists and labour economists in the last quarter of the 20th century is the rise in unemployment and its persistence at historically very high levels. Economists have been puzzled not only by the strikingly contrasting evolution of unemployment rates in the US, the EU and Japan, but also by significant diferences across EU countries. The European unemployment experiences during the last quarter of the 20th Century are indeed markedly diverse. They range from the ìsuccessî stories of the Netherlands and the UK, which were able to revert the increase of unemployment after the mid-1980s (see Nickell and van Ours, 2000), to the partial success of Scandinavian countries, which with exception of the early 1990s were able to maintain relatively low unemployment rates, and finally to ìfailureî stories like, for instance, Spain, which sustained unemployment rates close to 20% during the 1980s and first half of the 1990s, although it has witnessed substantial progress in the fight against unemployment in the second half of the 1990s.

Many papers and much empirical efort have been devoted at explaining the causes of unemployment and its variability across countries and regions. The first vintage of papers in this branch of the literature used cross-sectional or pooled cross-sectional data on indicators of labour market performance and labour market institutions to account for unemployment diferentials across countries (see Scarpetta, 1996, Nickell and Layard, 1999, Belot and van Ours, 2000). Recently, this literature has evolved into a new vintage of papers which try to explain unemployment diferentials across countries by the interactions of macroeconomic shocks and labour market institutions (see Blanchard and Wolfers, 2000, and Bertola, Blau, and Kahn, 2002).¹

There is another dimension of European unemployment which has received less attention in the macroeconomic literature, namely, the diferent incidence of unemployment and non-employment across gender and age population groups.² For instance, when comparing the EU and the US, it is the lower employment rates (higher unemployment rates) of youth, unskilled adult women, and workers aged 55-64 what explains the main bulk of the diferences in aggregate employment and unemployment rates (see Dolado, Felgueroso, and Jimeno, 2001). Even within the EU, there is a clear division between the Nordic countries, where the gaps between female and youth unemployment rates and the aggregate ones are relatively small, and the Southern countries, where female and youth unemployment rates have been persistently at much higher levels than those of prime aged men. While it seems plausible that the lower employment rate of workers above 55 years of age is primarily the result of early retirement provisions rather than of any other labour market institutions (see Gruber and Wise, 1998), the unemployment rates of young, unskilled workers are most afected by labour market institutions which impose some kind of wage floors (like minimum wages, collective bargaining, employment protection legislation, unemployment benefits, and so on). As stressed by Bertola, Blau, and Kahn (2002) many labour market institutions have stronger and more clear cut implications for the distribution of wages than for the level of the average wage, and, hence, for the composition of employment and the incidence of unemployment across population groups with diferent levels of productivity.

¹There are also papers showing that, even within EU countries, labour market institutions seem to have diferent efects across regions creating persistent regional unemployment diferentials (see Jimeno and Bentolila 1998, and Brunello et al., 2001).

²Nonetheless, there have been many reports and conferences on the causes of youth and female unemployment, which are not very much cited in the literature about the macroeconomics of unemployment. See, for instance, the conferences and subsequent publications sponsored by the NBER, such as The Youth Labor Market Problem, 1982; The Black Youth Employment Crisis, 1986; Training and the Private Sector, 1994; Youth Employment and Joblessness in Advanced Countries, 2000, and by the OECD, such as Youth Unemployment, 1978; The OECD Jobs Study, 1994; Employment Outlook, 1986, 1996, 1998, 1999, and From Initial Education to Working Life. Making Transition Works, 2000.

The incidence of youth unemployment has been related to the efectiveness of the educational system at easing the transition from school to work (see, for instance, OECD, 2000), to some labour market institutions (such as unemployment benefits for the young, minimum wages, etc.), to the role of the family at providing income support (Bentolila and Ichino, 2000), and to the evolution of the relative size of the youth population (Korenman and Neumark, 2000).

As for demographic shifts, there have been indeed quite intense changes in the age composition of the labour force over the last three decades in OECD countries. The Figures in Appendix C (at the end of the paper) illustrate these changes by plotting the evolution of the youth population size (defined as proportion of the prime-aged population, that is, population aged 25-54, in the left scale)³ together with the youth male and female unemployment rates and the unemployment rate of prime aged men (25-54 years of age, in the right-scale). All the countries in our sample experienced, first, an increase of the relative size of the youth population up to the early 1970s and then a decline (with the exceptions of Australia, Belgium, Germany, Italy, Spain, and the UK where this variable reached its peak in the early 1980s). Table 1 gives some descriptive statistics of the ratio of population aged 15-24 to the population aged 25-54. The range of variation over the sample of this variable is 11 percentage points. In Canada, The Netherlands and the US, the range of variation is above 20 percentage points.

³This is also the definition of relative size in Korenman and Neumark (2000). We choose for comparability with their results. But there is an additional justification. The participation rate of the population above 55 years age has been declining since the early 1980s in many countries, mainly due to early retirement and Social Security provisions.

Table 1. Relative size of youth population. Descriptive statistics

As for youth unemployment, there are noticeable cross-country diferences in prime age male unemployment rates, with the gap varying by gender, across countries, and across time. In most countries there is an increasing trend in youth unemployment rates (the exceptions being the US and, since the mid-1980s, Denmark, Ireland, The Netherlands and the UK). Youth unemployment rates have been particularly high in Belgium, Finland, France, Italy, and Spain, with a significant positive gap between men and women in the case of the last two countries, and to a lesser extent, in France. Table 2 reports some descriptive statistics of unemployment rates of the three population groups considered (men 15-24, women 15-24 and men 25-54)

Table 2. Unemployment rates. Some descriptive statistics

The relevance of demographic changes at explaining youth unemployment is somewhat controversial. Korenman and Neumark (2000), using pooled crosscountry data for some OECD countries, estimate the elasticity of the youth unemployment rate with respect to the youth cohort size to be around 0.5. Shimer (2001) challenges this result showing that across US states a higher share of the youth population decreases unemployment. Ahn, Izquierdo, and Jimeno (2000) find that, across Spanish regions, there seems to be a close positive relationship between the relative size of the youth population and youth unemployment. Bertola, Blau, and Kahn (2002) show that demographic shocks (i.e., changes in the youth population share) interacted with labour market institutions contribute to explaining the diference in the aggregate unemployment rate and in the relative employment rates of young and female workers between the US and some EU countries.

In this paper we jointly estimate the relevance of demographic and institutional variables at explaining cross-country diferences in youth unemployment rates. For this estimation, we construct a data set with gender and age specific unemployment rates, the relative size of youth population, and labour market institutions with information on 19 countries (the EU countries -excluding Luxembourg and Greece-, Norway, US, Canada, Australia, New Zealand, and Japan) over the 1968-1996 period.⁴

Before turning to the empirical analysis we present a theoretical framework to rationalise the relationship between the age composition of the labour force and labour market institutions, on the one hand, and the incidence of unemployment across diferent population age groups, on the other. The main assumption is that workers of diferent ages are not perfectly substitutes, so that, if some labour market institutions preclude the complete adjustment of relative wages, changes in the relative labour supply of workers of diferent ages will show up in diferent age specific unemployment rates. Thus, while in flexible labour markets (say, for instance, in the US) changes in the composition of the labour force would lead to changes in wage inequality, in countries in which labour market ìrigiditiesî (e.g. minimum wages and other regulations with diferentiated impacts on workers of diferent ages) keep wages above the clearing levels, we should expect a positive relationship between the relative size of youth population and youth unemployment. This conjecture is supported by the results in Bertola, Blau and Kahn (2002). Comparing the US and European experiences they identify some labour market institutions and the demographic evolutions that contribute to explaining both the low unemployment rate and the high wage inequality of the US relative to other OECD countries. However, it is plausible that both in ìflexibleî and ìrigidî labour markets, relative wages adjust over the long-run, so that we should expect to observe a higher efect of demographics variables on unemployment diferential on high frequency data than on low frequency data.

The rest of the paper is structured as follows. Section 2 presents a simple theoretical framework illustrating the relationship between the relative size of a given population group, relative wages and unemployment. Section 3 reports the relationship between youth unemployment and the relative size of youth population in our data set. Section 4 contains the main bulk of our empirical exercise, namely, the estimation of the relative importance of demographic shifts, institutional factors, and macroeconomic shocks at explaining the evolution of youth unemployment. For the estimation we use both annual data and five-year period averages to assess how long is the long run over which relative wages are supposed to adjust to demographic variables. Section 5 concludes.

⁴See Appendix A for the coverage of the sample and the definition of variables.

2 Theoretical framework

2.1 Labour input, production and labour demand

In order to obtain a certain relationship between the age composition of the labour force and youth unemployment, the possibility of imperfect substitution between workers of diferent ages is introduced. Thus, let us assume that there are two ìtypesî of workers, ìyoung workersî (denoted by the subscript 1) and ìadult workersî (denoted by the subscript 2), whose relative productivity is given by δ. Total labour input is a function of the two ìtypesî of labour with a constant elasticity of substitution, i.e.,

\[N = [ N _ {1} ^ {\rho} + \delta N _ {2} ^ {\rho} ] ^ {1 / \rho} \qquad 1 \geq \rho \geq 0\]

while the production function is given by

\[Y = [ N _ {1} ^ {\rho} + \delta N _ {2} ^ {\rho} ] ^ {\alpha / \rho} \qquad 1 \geq \alpha > 0\]

being α the degree of returns to labour. Firms produce to meet a constant elasticity demand curve, . The first-order condition of the cost minimization problem gives:

\[M R S = \delta \left(\frac {N _ {1}}{N _ {2}}\right) ^ {\frac {1}{\sigma}} \Rightarrow \frac {N _ {1}}{N _ {2}} = \left(\frac {w _ {2}}{\delta w _ {1}}\right) ^ {\sigma}\tag{1}\]

being the elasticity of substitution. Hence, the relative demand of young workers with respect to adult workers is decreasing in their relative unit labour costs, and the corresponding elasticity is given by the elasticity of substitution. This condition can be easily converted in labour demand curves for each worker type, which are given by:

\[N _ {1} = (\alpha k) ^ {\frac {1}{1 - \alpha k}} w ^ {\lambda} w _ {1} ^ {- \sigma}\tag{2}\]

\[N _ {2} = (\alpha k) ^ {\frac {1}{1 - \alpha k}} w ^ {\lambda} \left(\frac {w _ {2}}{\delta}\right) ^ {- \sigma}\tag{3}\]

being , a measure of the degree of competition in the product market, the aggregate wage index, and

Condition (1) yields a relationship between relative unemployment, relative labour supply and relative wages. Let and be the labour supply of ìyoungî and ìadultî workers, respectively, so that and are the unemployment rates of ìyoungî and ìadultî workers, respectively. Taking logarithms in equation (1) and using the approximation ln gives

\[\begin{array}{r c l} u _ {1} - u _ {2} & = & \ln L _ {1} - \ln L _ {2} - (\ln N _ {1} - \ln N _ {2}) = \\ & = & \sigma \ln \delta + \sigma (\ln w _ {1} - \ln w _ {2}) + \ln L _ {1} - \ln L _ {2} \end{array}\tag{4}\]

Hence, the relative unemployment rate is determined by three factors: i) the relative eficiency of adult workers with respect to young workers, ii) relative wages, and iii) relative labour supply. Relative labor supply is determined by demographic evolutions. Relative eficiency is related to diferences in eficiency across cohorts and, therefore, may depend upon technology requirements and the characteristics of educational systems. Finally, relative wages are afected by labor market institutions, such as minimum wages, employment protection legislation, unemployment benefits, etc. We now specify how relative wages are determined.

2.2 Wage determination

Under perfect competition relative wages adjust to clear the market. Under this institutional framework the reading of equation (4) is that there are exogenously given ìfull employmentî unemployment rates for each group of the population (not necessarily equal across cohorts), and, hence, given the relative eficiency of adult workers and the elasticity of substitution, equation (4) yields a relationship between relative wages and relative labour supply. We consider an alternative institutional scenario in which wages are determined by collective bargaining between employers and workers. ìYoungî and ìadultî workers have diferent reservation wages and respectively) and diferent bargaining power and , respectively). Let Π be the firmís profit function. Wages are determined by the following Nash maximization problem:

\[\begin{array}{l} \max _ {w _ {1}, w _ {2}} \left[ (w _ {1} - \overline {{w}} _ {1}) N _ {1} \right] ^ {\beta_ {1}} \left[ (w _ {2} - \overline {{w}} _ {2}) N _ {2} \right] ^ {\beta_ {2}} \Pi \\ \text { subject to: } \quad N _ {1} = (\alpha k) ^ {\frac {1}{1 - \alpha k}} w ^ {\lambda} w _ {1} ^ {- \sigma}, N _ {2} = (\alpha k) ^ {\frac {1}{1 - \alpha k}} w ^ {\lambda} \left(\frac {w _ {2}}{\delta}\right) ^ {- \sigma} \end{array}\]

The first-order conditions can be expressed as:

\[\frac {\beta_ {1}}{w _ {1} - \overline {{w}} _ {1}} - \frac {\beta_ {1} \sigma}{w _ {1}} = \left(\frac {\alpha k}{1 - \alpha k} - \frac {\lambda (\beta_ {1} + \beta_ {2})}{w}\right) \left(\frac {w _ {1}}{\overline {{w}}}\right) ^ {- \sigma}\]

and

\[\frac {\beta_ {2}}{w _ {2} - \overline {{w}} _ {2}} - \frac {\beta_ {2} \sigma}{w _ {2}} = \left(\frac {\alpha k}{1 - \alpha k} - \frac {\lambda (\beta_ {1} + \beta_ {2})}{w}\right) \left(\frac {w _ {2}}{\delta \overline {{w}}}\right) ^ {- \sigma}\]

where is the aggregate workersí reservation wage (defined as the aggregate wage index corresponding to the reservation wages of each workerís type, being. the weight which depends upon relative supplies, . These two conditions yield

\[\frac {w _ {1}}{w _ {1} - \overline {{w}} _ {1}} - \sigma = \gamma \delta^ {- \sigma} \left(\frac {w _ {2}}{w _ {2} - \overline {{w}} _ {2}} - \sigma\right) \left(\frac {w _ {1}}{w _ {2}}\right) ^ {1 - \sigma}\tag{5}\]

where is the bargaining power of adult workers relative to the bargaining power of workers.

The following particular case may be illustrative. Under a unit elasticity of substitution (Cobb-Douglas labour input function), the relative mark-up of wages over reservation wages of adult workers respect to younger ones is given just by the ratio of the relative bargaining power and the relative eficiency of adult workers:

\[\frac {w _ {1}}{w _ {1} - \overline {{w}} _ {1}} - 1 = \frac {\gamma}{\delta} \left(\frac {w _ {2}}{w _ {2} - \overline {{w}} _ {2}} - 1\right) \Longrightarrow \frac {w _ {2} - \overline {{w}} _ {2}}{w _ {1} - \overline {{w}} _ {1}} = \frac {\gamma}{\delta} \frac {\overline {{w}} _ {2}}{\overline {{w}} _ {1}}\]

More generally, a number of results can be drawn from the model:

Proposition 1 Let be the function implicitly defined by is the contract curve of older and young workers. Under and 2 it follows that:

1. is increasing and concave. Moreover,

2. An increase in relative bargaining power of older workers, γ, increases the relative wage of older workers

3. An increase in the relative eficiency of younger workers, decreases the relative wage of older workers,

4. An increase in the aggregate wage w decreases the relative wage of older workers,

Proof. See Appendix B.

Claims 1 and 2 are illustrated in Figure 1. The pairs of wages that satisfy (5) (and which are always above the diagonal) is the increasing but concave function in Figures 1 and 2. Increases in older workers relative bargaining power γ shifts this function upwards, particularly so for low values of . Note in particular that a rise in not only increases the relative wage, but also decreases the youth wage

Claim 4 is similarly illustrated in Figure 2, which shows the efects of an increase in aggregate wages (resulting for example from an increase in aggregate labor demand or the aggregate reservation wage). An increase in the aggregate wage increases of course wages of both types of workers. But it also has an efect on wage inequality between young and older workers, which is reduced upon an increase in labor demand (as at the new equilibrium the contract curve is closer to the diagonal).

The combination of the results for relative wages in the Proposition and the relative unemployment rates equation (4) capture the links that go from labor market institutions (indexed by and aggregate shocks (that afect labor demand), to the relative unemployment rate . Specifically, these variables are mainly related by the relative age-specific rent: . In particular, since job tenure and longer work histories (which correlate with age) afect the bargaining power in a number of institutional contexts,⁵ it seems natural to regard age as a variable correlated with bargaining power at wage setting.

⁵A number of labor market institution tend to favour the situation of older workers relatively to that of a recent entrant in the labour market. For example, in some countries unemployment benefits are only available to those losing an existing job, so that unemployed without a previous employment spells are not eligible. Also, firing costs typically increase with tenure.

As shown in Figure 1, the model implies in particular that institutional factors that increase adult workersí relative bargaining power, γ, increase the relative wage and therefore the relative labour market rent The efect of an increase in the relative wage of adult workers, in turn, makes young workers more attractive as hires, and the unemployment rate of the young decreases relative to that of the insiders, as equation (4) indicates.

Regarding the efects of aggregate shocks, as shown in Figure 2, shocks that increase aggregate labor demand (like increases in TFP or decreases in real rates), tend to decrease the relative wages of the older workers, therefore increasing the relative unemployment rate of the young. This result suggests that if a given institution (or shock) tends to increase the unemployment rate of the prime age workers but decreases the relative unemployment rate of the young, this institution could be generating, according to the model, relative rents to adult workers. We examine some of these hypothesis in the empirical section.

3 Empirical analysis I: Demographic shifts and relative youth unemployment

We start the empirical investigation of equation (4) above by estimating regressions where the dependent variable is the unemployment rate diferential (the diference between the unemployment rate of the population aged 15-24 and the unemployment rate of male workers aged 25-54) and the independent variable is the relative size of youth population (defined as the size of population aged

15-24 over the population aged 25-54 in logarithms). Thus, the regression to be estimated is:

\[u 1 5 2 4 _ {i t} - u m 2 5 5 4 _ {i t} = \mu_ {i} + \mu_ {t} + \beta \left[ \ln (s 1 5 2 4) _ {i t} - \ln (s 2 5 5 4) _ {i t} \right] + \varepsilon_ {i t}\tag{6}\]

where u1524 is the unemployment rate of men (women) aged 15-24, um2554 is the unemployment rate of men aged 25-54, s1524 is the relative size of population aged 15-24, and s2554 is the relative size of population aged 25-54. We include country and time specific fixed efects but also report results when either time efects, or fixed efects or both are excluded from the regression. We run diferent regressions for men and women.

Results are reported in Table 3. The efect of the relative size of youth population on the youth unemployment diferential is (almost always) positive and statistically significant. Overall, this efect seems to be higher for women than for men. Since it may seem too restrictive to impose a unit elasticity between the youth unemployment and that of men aged 25-54 over the business cycle, we also report the results from regressions where the (ln) unemployment rate of men aged 25-54 is included as an additional independent variable, which it turns out to be statistically significant in all specifications. In these regressions the coefficients on the relative size of the youth population remain positive, statistically significant, and within a same order of magnitude as in the regressions where youth unemployment rates are restricted to move with the unemployment rate of prime aged men one to one.

Overall the results are consistent with those obtained by Korenman and Neumark (2000) from a sample of 15 OECD countries over the period 1970-1994.⁶ Moreover, the efect of demographic shifts on youth unemployment is not negligible. Being the coeficient of the demographic variable around 0.15 (roughly the average between the estimated coeficients for men and women in the regressions with country and time fixed efects) and since the mean unemployment rate of the population aged 15-24 in our sample is around 14%, the elasticity of the youth unemployment rate with respect to the relative size of the young population would be 1.07 and the observed variation of the latter would explain around 13% of youth unemployment and in the average country in our sample. A similar calculation yields that the elasticity of the youth unemployment diferential with respect to the relative size of the youth population is around 1.7 and that the latter explains roughly 20% of the youth unemployment diferentials observed in our sample.

⁶Notice, however, that Korenman and Neumark (2000) use a log-log specfication. Also, since there may be an endogeneity problem due to workers moving to low unemployment-high wage regions, some authors (Shimer, 2002, Korenman and Neumark, 2000, Bertola et al. 2002) use past birth rates as instruments in this type of regressions. However, their OLS results and IV results are not qualitatively diferent. The information in our sample for most countries span the period starting at the early 1970s, when international labour mobility became almost negligible. Hence, we find it non-necessary to perform IV estimation, which, given data availability, would require to exclude some countries from the sample and, hence, to reduce degrees of freedom, needed for other estimations to be performed.

Table 3. Youth unemployment rate diferentials and demographic shifts.

Notes: Unsigned t-statistics in parentheses. u1524: unemployment rate of the population aged 15-24. um2554: unemployment rate of men aged 25-54 (A) Coeficient on the (ln) relative youth population size. (B) Coeficient on the (ln) relative youth population size when the unemployment rate of men aged 25-54 is included as an additional regressor.

4 Empirical analysis II: Demographic shifts, institutions, and interactions with shocks

We now turn to the analysis of the joint efects of a larger set of factors afecting age-specific unemployment rates. Our goals are twofold: i) to estimate the diferential efects of demographic shifts, labour market institutions and macroeconomic shocks on the unemployment rates of three diferent population groups: men aged 15-24, women aged 15-24 and men aged 25-54, and ii) to assess the extent to which the efect of demographic shifts on youth unemployment rates vanishes over the medium run.

To achieve these goals we add to our data set the indicators of labour market institutions often used and some measures of macroeconomic shocks, namely, labour demand shifts, real interest rates and total factor productivity growth⁷. The information of labour market institutions is as in Blanchard and Wolfers (2000). It covers the unemployment benefits system (replacement rate and duration of benefits), the extent of active labour market policies (an instrumented measure of spending), wage determination (union density, union contract coverage, and the degree of coordination), the tax wedge, and the pervasiveness of employment protection legislation (from a ranking of OECD countries).⁸ To this set of institutional variables we add a measure of relative minimum wages (computed on information from the OECD) and an indicator of the strictness of the legislation regarding the use of temporary contracts, two institutions which we expect to strongly influence youth unemployment through its efects on relative wages and hiring rates. As for macroeconomic shocks, we use Blanchard and Wolfersí (2000) measures of labour demand shifts, real interest rates, and total factor productivity growth.

Before commenting on the results there are some caveats to be made. First, when looking at the efects of labour market institutions on aggregate unemployment, it is reasonable to use medium-term averages to smooth out cyclical fluctuations in unemployment, even at the cost of reducing degrees of freedom (which are already quite limited in the typically available panel data set of this type). Given this restriction, when looking at the interactions of shocks and institutions, Blanchard and Wolfers (2000) and other papers using their data set (for instance, Bertola, Blau, and Kahn, 2002) impose some specific form of the interaction terms. Since we are interested not only in the medium-run evolution of the relative youth unemployment rate but also in its cyclical behaviour and its short-run response to the relative population size, we run our regressions with both annual data and five-year period averages as in Blanchard and Wolfers (2000).

Secondly, the use of time invariant labour market institutions may be controversial. This implies that regressions including labour market institutions would be equivalent to regressions with country fixed efects. In other words, by choosing time invariant labour market institutions we renounce to controlling country fixed efects when estimating the impact of institutions on unemployment. Alternatively, we could have exploited changes in labour market institutions over the last decades, as done, for instance, in Nunziata (2001). In order to facilitate the comparability of our results with those of Blanchard-Wolfers (2000) for aggregate unemployment rates, we have chosen to stick to the time-invariant measures of institutional characteristics, leaving the analysis under time-varying institutional measures for further work.

⁷ Ideally, the analysis of the efect of institutional variables on age and gender specific unemployment rates should include the role of age and gender specific labour market wages and rents, precisely as pointed out by the theoretical model above. Such data is available for some countries for some years, mainly from countriesí labour force surveys (implying in particular that the information cannot be expected to be fully comparable across countries). Importantly, the availability of such evidence on age and gender specific wages clearly cannot match the coverage of our panel in terms of time period and number of countries (which is reflected in Table 1 above). Therefore, imposing ourselves the inclusion of demographically disaggregated wage data would imply a very considerable reduction on the final size of our data panel. Finally, the exclusion of wage data has the non-negligible advantage of facilitating the comparison of our results with the benchmark in Blanchard-Wolfers (2000). For all these reasons, we have cho sen to analyse econometrically the reduced-form link between institutions and macroeconomic shocks to demographic unemployment performance.

⁸For a more detailed description of the variables, see Blanchard and Wolfers (2000).

The third caveat refers to the functional form of the unemployment equation to be estimated. Since our model is a labour demand model in which the equilibrium is defined in terms of relative employment rates, equation (4) links the unemployment diferential between young and adult workers and the rest of demographic and institutional variables⁹.

Finally, it is becoming increasingly popular to use non-employment rates rather than unemployment rates when assessing the causes of diferent labour market performance across countries. This is quite sensible since very often the definition of unemployment has some country-specific component (like the verification of job search which is required for a non-working individual to be classified as unemployed) and the line between unemployed and non-participants in the labour markets is dificult to draw. However, for our interest in this paper, the use of youth employment rates would require to control for large changes occurring in demand and supply of education which afected participation of young workers in the labour market.

Given these qualifications, we start by performing the estimation following Blanchard and Wolfersí (2000) strategy of imposing a specific form of interaction between institutions and shocks. Tables 4 and 5 present the results regarding the efects of labour market institutions interacted with unobservable and observable shocks, respectively, on the prime age male unemployment rate, and on youth unemployment rates by gender, in levels, relative to the unemployment rate of prime age men, and in terms of the unemployment rate diferential. Each Table has two panels reporting the results from estimation with annual data and with five-year averages.

The second column of Table 4a shows the efects of labour market institutions on the unemployment rate of men aged 25-54 (um2554). Higher replacement rates (Rrate), longer duration benefits (Benefit ), stricter protection legislation (EPL), higher union density (Udensity), a higher tax wedge (Twedge), and lower coordination (Coord) all lead to higher unemployment of prime-age men, while the coeficients of expenditures on active labour market policies (Almp) and union coverage (Ucoverage) are not statistically significant.¹⁰ With the exception of the efect of active labour market policies, these results are very much in line with the results in Blanchard and Wolfers (2000) referred to the aggregate unemployment rate from five-year averages, which are replicated here in the second column of Table 4b. It turns out that when we estimate the equation with the observations grouped in five-year averages (as in Blanchard and Wolfersí (2000)), the efects of labour market institutions on the prime age male unemployment are qualitatively similar (see the third column in Table 4b), although standard errors are higher by the significantly lower number of observations (i.e., 404 observations in the regressions with annual data and 90 observations in the regressions with five-year averages).

^{(ln u}1 −ln ^u2⁾

⁹Alternatively, one could think of models in which the labour market equilibrium is defined in terms of relative unemployment rates, instead of absolute diferences in unemployment rates (which are the focus of this paper). This would call for the estimation of unemployment equations in which the dependent variable is the (ln) of the youth relative unemployment rate . To avoid a rather lengthy set of results we report only the results from estimation of the first specification. Results for relative unemployment rates are available from the authors on request.

Table 4a. Institutions interacted with unobservable shocks Annual data

¹⁰The variables ALMP and Coord are defined with a negative sign, so that increases in all institutional variables are expected to increase unemployment.

The rest of the columns in Tables 4a and 4b report the estimated efects of labour market institutions interacted with unobservable shocks on youth unemployment rates (um1524, for men, and uf1524, for women) and on the diferential between youth unemployment rates and the unemployment rate of prime-aged men (um1524 um2554 and uf1524 um2554, respectively). In these regressions we also include the relative size of the youth population (Ypop, measured as the (log) ratio of the population aged 15-24 over the population aged 25-54) and two additional labour market institutions: the degree of strictness of regulation of temporary employment (Temp, taken from OECD, 1994) and the (log) ratio of the minimum wage applying to young workers over the minimum wage applying to prime-aged workers (Rwmin, also from OECD, 1994 ). In most countries this ratio is equal to one, since there are not sub-minimum wages for young workers, but it is below one in Australia (0.7), Belgium (0.9), France (0.8), Ireland (0.7) Netherlands (0.8) and Portugal (0.8).

Notes: Unsigned statistics in parentheses. Regressions include country and time

fixed efects. The estimates for the total unemployment rate are from Blanchard and Wolfers (2000).

As for the efects on the level of youth unemployment, we find some diferential efects of the institutions on male and female youth unemployment rates. Young mení unemployment rates are significantly increased by the duration of unemployment benefits, union density, the tax wedge and lower coordination. For young women, unemployment rates are increased by higher levels in union coverage, stricter employment protection legislation the tax wedge and by lower coordination. Furthermore, the sixth and seventh columns in Table 4a show that the youth unemployment diferential increases with the strictness of employment protection legislation (EPL), union density, tax wedge and decreases with coordination, in the case of males. As for females, the diferential increases with union coverage strictness of EPL, the tax wedge and the degree of strictness of temporary employment, and decreases with union density. When estimating with five-year averages we find that youth unemployment diferentials increase with union density and the tax wedge, in the case of young men, and with the strictness of EPL and the tax wedge, in the case of young women.

We also investigate the relevance of the interactions between labour market institutions and some observable shocks at explaining cross-country diferences in aggregate and youth unemployment rates, as in Blanchard and Wolfers (2000). As for observable shocks we consider the demographic shifts (Y pop), measured as the relative size of the population aged 15-24 over the population aged 25-54, and:

1. Shifts in labour demand (LD shift).

2. Ex-post real interest rates (RIrate), and

3. Productivity growth (TFP).

Equations (4) and (5) are useful to illustrate why these shocks may have a diferent impact on the youth unemployment rate with respect to the unemployment rate of prime aged men. First, shifts in labour demand translate into lower employment if real wages do not adjust, and, even if these shifts are evenly distributed across sectors and occupations, there are no reasons to expect that the wages of youth workers respond similarly to the wages of adult workers, particularly if collective bargaining, and concerns about wage compression, are widespread. Secondly, productivity growth may afect the relative eficiency of ìyoungî versus ìadultî workers (δ in Section 2). Higher productivity growth may result in lower employment opportunities for young, unskilled workers, if educational systems are not flexible enough to adjust for providing better professional qualifications. Finally, higher ex-post real interest rates imply a higher cost of capital, and, hence, lower employment creation and, possibly, also higher gross rates of employment destruction, afecting most to capital intensive sectors. Thus, higher real interest rates are likely to have diferent efects on prime-age and younger, as workers diferent ages tend not to be evenly distributed across sector and occupations.

Tables 5a and 5b report the results from both annual data and five-year averages regressions on the efects of the interactions between labour market institutions and observable shocks on unemployment rates of young and prime age workers.

Notes: t-statistics (in absolute value) in parenthesis. Regressions include country and time fixed efects.

Both for prime aged men and young workers, the unemployment rate increases with negative shifts in labour demand, the real interest rate, and TFP growth in the regressions with annual data.¹¹. These efects are larger for young men, so that the diference between the unemployment rate of young men and that of prime aged men increases with negative labour demand shifts, interest rates and TFP growth in the short-run. Over five year periods, youth unemployment diferentials increase with the real interest rate and decreases with TFP growth, while labour demand shifts become barely statistically significant. As for the coeficients on labour market institutions, in this specification the only variable with a consistently positive efect on the youth unemployment diferential, both with annual data and five-year averages, is the tax wedge. As for the demographic variable, in this specification we find much lower coeficients, which are statistically significant only in the case of women. While the results from estimation with five-year averages are similar for labour demand shifts and real interest rates, the coeficient of TFP growth changes sign indicating a positive efect of TFP growth on unemployment. This is consistent with some macroeconomic evidence from Structural VAR estimation which finds that productivity growth raises unemployment at high frequencies, while this efect vanishes or become negative at low frequencies (see, for instance, GalÌ, 1999)

¹¹TFP growth is multiplied by -1, so that a negative coeficient implies unemployment increasing with TFP growth.

Notes: t-statistics (in absolute value) in parenthesis. Regressions include country and time fixed efects. The estimates for the total unemployment rate are from Blanchard and Wolfers (2000).

Finally, to further examine the efects of labour market institutions and macroeconomic shocks on youth unemployment we estimate additional regressions without imposing any specific forms of interaction between both. Table 6 reports the results from linear regressions including labour market institutions, macroeconomic shocks, the relative size of the youth population and time fixed efects. As for macroeconomic shocks, we continue finding that TFP growth increases the diference between the unemployment rate of young men and the unemployment rate of adult males at the annual frequency. And the relative size of youth population increases youth unemployment, with the corresponding elasticity of the same order of magnitude both at annual and five year period frequencies.

Notes: Unsigned t-statistics in parenthesis. Regressions include time fixed efects.

As regards the efects of labour market institutions, higher replacement rates and longer duration of unemployment benefits decrease the youth unemployment diferential. This efect of the generosity of unemployment benefits on youth unemployment diferentials could be expected from the fact that in some EU countries young unemployed workers without previous employment spells are non-eligible for unemployment benefits. That is, in this regard, these institutional factors would be primarily related to wage formation by prime age workers and only secondarily to wage developments of younger workers. This, together with the fact that these workers are mutually substitutes, could explain the efect of unemployment benefits on the relative unemployment rate. This precisely corresponds to the intuition derived from the model laid out above.

Notes: Unsigned t-statistics in parenthesis. Regressions include time fixed efects.

Regarding the institutional variables related to wage determination, higher incidence of unions and of collective bargaining increase the relative youth unemployment rate and the youth unemployment diferential, something which Kahn (2000) also finds in a panel of 15 OECD countries over the period 1985-94. As unions compress wages, low productivity, unskilled, young workers are priced out of employment. This is also confirmed by the positive efect of relative statutory minimum wages (Rwmin) on the youth unemployment diferential.¹² Moreover, a similar relative wage efect also appears through the tax wedge variable. Increases in the tax wedge have the strongest impact on the employment opportunities of workers at the bottom of the wage distribution, where restrictions from minimum wage legislation are frequently binding. Hence, as the tax wedge rises, youth unemployment rates ought to be expected to rise by more than prime age male unemployment, as it is the case according to the corresponding coeficients in Tables 4 and 5. As for EPL and the strictness of regulation afecting temporary employment, the ranking measures included in the regression do not seem to be associated with higher relative youth unemployment. As shown by Dolado, Felgueroso, and Jimeno (2002), countries with stricter employment protection legislation liberalised ìatypicalî employment contracts (temporary, fixed-term contracts) to a larger extent, which have resulted in a higher hiring rates for young workers. In fact, we find that the youth unemployment diferential (in some specifications) is higher the stricter the regulation afecting temporary employment, although admittedly the estimated coeficients are not statistically significant in all our specifications.

Overall, we draw two main conclusions from the evidence presented in this paper. First, wage-compressing institutions increase the youth unemployment diferential, in the spirit of the model in Section 2. Secondly, there is a large and significant efect of the relative size of the youth population both on youth unemployment rates and youth unemployment diferentials with respect to the unemployment rate of prime age men. In this case, this efect seems to be of a similar order of magnitude in the short-run (annual data) and in the medium run (five-year period), suggesting that the efects of demographic shifts on youth unemployment diferentials are not short-lived and that relative wages by age take time to adjust.

5 Concluding remarks

In recent work Korenman and Neumark (2000) explain cross-country diferences in youth unemployment rates by demographic shifts causing fluctuations in the relative size of the youth population. Blanchard and Wolfers (2000) explain cross-country diferences in aggregate unemployment rates by appealing to diferent labour market institutions, the diferent incidence of macroeconomic shocks, and the interaction between both. In this paper we have combined all these factors (demographic, institutional, and macroeconomic) to gauge their relative relevance at explaining cross-country diferences in relative youth unemployment rates. Our data set is a non-balanced panel of 19 OECD countries over the 1960- 1996 period. We perform estimation on a extensive number of specifications involving demographic, institutional and macroeconomic variables. Our results show that: i) the relative size of the youth population is a non-negligible factor at explaining cross-country diferences in youth unemployment, ii) labour market institutions and macroeconomic shocks have had diferential efects on age-specific unemployment rates, and iii) ìmoreî rigid labour markets imply higher relative youth unemployment rates. We rationalise these results as the composition of imperfect substitution of workers of diferent ages in production and imperfect competition in the labour market delivering less than full adjustment of relative wages to relative supply.

¹²The measure of relative minimum wages is the ratio of young minimum wages to adult minimum wages as provided by OECD.

References

1. [1] Ahn, Izquierdo and Jimeno (2000): ìYouth cohort size and unemployment in Spain: An exploration of national, regional and micro dataî, FEDEA, mimeo.
2. [2] Belot, M. J.C. van Ours (2000): ìDoes the recent success of some OECD countries in lowering their unemployment rates lie in the clever design of their labour market reforms?î, CEPR working paper no. 2492.
3. [3] Bentolila, S. and A. Ichino (2000): ì_Unemployment and Consumption. Are Job Losses Less Painful Near the Mediterranean?î, CEMFI, working paper 0010.
4. [4] Bertola, G. F.D. Blau and L.M. Kahn (2002): ìComparative Analysis of Labour Market Outcomes: Lessons for the US from the International Long-Run Evidenceî, in A. Krueger and R. Solow, eds. The Roaring Nineties: Can Full Employment Be Sustined?, New York: Russell Sage.
5. [5] Blanchard, O. and J. Wolfers (2000): ìThe role of shocks and institutions in the rise of European unemployment: The aggregate evidenceî, The Economic Journal, 110 (March), C1-33.
6. [6] Brunello, G., C. Lupi, P. Ordine, and M.L. Parsi (2001): ìBeyond National Institutions: Labor Taxes and Regional Unemployment in Italyî, mimeo.
7. [7] Dolado, J.J., F. Felgueroso, and J.F. Jimeno (2000): ìExplaining youth labour market problems in Spain: Crowding-out, institutions or technology shiftsî, FEDEA, working paper 2000-09.
8. [8] Dolado, J.J., F. Felgueroso, and J.F. Jimeno (2001): ìFemale Employment and Occupational Changes in the 1990s: How is the EU performing relative to the USî, European Economic Review 45, 875-889.
9. [9] Dolado, J.J., F. Felgueroso, and J.F. Jimeno (2002): ìDrawing Lessons from the Boom of Temporary Employment in Spainî, Economic Journal, vol. 112 (June), F1-F24.
10. [10] GalÏ, J. (1999): ìTechnology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuationsî, American Economic Review, March, 249-271.
11. [11] Gruber, J., and D. Wise (1998), Social Security and Retirement Around the World, NBER, The University of Chicago Press.
12. [12] Jimeno, J.F. and S. Bentolila (1998): ìRegional unemployment persistence (Spain, 1976-1994)î, Labour Economics, 5, 25-52.
13. [13] Kahn, L.M. (2000): ìWage inequality, Collective Bargaining , and relative employment, 1985-94: Evidence from 15 OECD countriesî,The Review of Economics and Statistics, 82, no. 4 (November), 564-579.
14. [14] Korenman, S. and D. Neumark (2000): ìCohort crowding and youth labor markets: A cross-national analysis.î in D.G. Blanchflower and R.B. Freeman, eds. Youth Employment and Joblessness in Advanced Countries, NBER: Chicago University Press.
15. [15] Nickell, S. and R. Layard (1999): ìLabour market institutions and economic performanceî in Ashenfelter, O. and D. Card, eds., Handbook of Labor Economics, Amsterdam: North Holland
16. [16] Nickell, S. and J.C. van Ours (2000): ìThe Netherlands and the United Kingdom: A European unemployment miracleî, Economic Policy, 30 (April), 137-180.
17. [17] Nunziata, L. (2001): ìLabour cost determination in OECD countriesî, Nufield College, Oxford University, mimeo.
18. [18] OECD (1994), The OECD Jobs Study, OECD, Paris.
19. [19] OECD (2000), From Initial Education to Working Life. Making Transition Works, OECD: Paris.
20. [20] Scarpetta, S. (1996): ìAssessing the role of labour market policies and institutional settings on unemployment: A cross-country studyî, OECD Economic Studies, 2(26), 43-82.
21. [21] Shimer, R. (2001): ìThe impact of young workers on the aggregate labor market.î Quarterly Journal of Economics, vol. XVI, August, 969-1007.

Appendix A: Data sources.

Our data set is constructed from three sources of information:

1. EUROSTAT (for EU countries) and UN Population Statistics Yearbook give annual information on the composition of population by ages and gender. For the US we took the information provided in the web page of the US Bureau of Labor Statistics (www.bls.org)

2. Data on age-specific unemployment and employment rates are from the OECD Labour Force Statistics.

3. Data on labour market institutions and macroeconomics shocks are from Blanchard and Wolfersí (2000) data set.

The following table gives the countries, period and number of observations included in our sample.

Table A1. Sample composition

Appendix B: Proof of proposition 1

Equation (5) in the text is:

\[\frac {w _ {1}}{w _ {1} - \overline {{w}} _ {1}} - \sigma = \gamma \delta^ {- \sigma} \left(\frac {w _ {2}}{w _ {2} - \overline {{w}} _ {2}} - \sigma\right) \left(\frac {w _ {1}}{w _ {2}}\right) ^ {1 - \sigma}\]

From the first order conditions of the bargaining problem it follows that for , since the associated shadow variable is positive. Moreover, this equation can be rewritten as:

\[\frac {h \left(w _ {1} , \overline {{w}} _ {1}\right)}{h \left(w _ {2} , \overline {{w}} _ {2}\right)} = \gamma \delta^ {- \sigma}\tag{7}\]

where , which implicitly defines . It is easy to show (using the previous inequality) that and

To see for instance the first partial derivative, notice:

\[\begin{array}{r c l} \frac {\partial h}{\partial w _ {s}} & = & \frac {\partial}{\partial w _ {s}} \left(\left(\frac {w _ {s}}{w _ {s} - \overline {{w}} _ {s}} - \sigma\right) w _ {s} ^ {\sigma - 1}\right) \\ & = & - \frac {\overline {{w}} _ {s}}{\left(w _ {s} - \overline {{w}} _ {s}\right) ^ {2}} + (\sigma - 1) \left(\frac {1}{w _ {s} - \overline {{w}} _ {s}} - \frac {\sigma}{w _ {s}}\right) \end{array}\]

Moreover, since 2

\[s i g n \left(- \frac {\overline {{w}} _ {s}}{\left(w _ {s} - \overline {{w}} _ {s}\right) ^ {2}} + (\sigma - 1) \frac {1}{w _ {s}} \left(\frac {w _ {s}}{w _ {s} - \overline {{w}} _ {s}} - \sigma\right)\right) =\]

\[= \operatorname{sign} \left(- \frac {\overline {{w}} _ {s}}{w _ {s} - \overline {{w}} _ {s}} + (\sigma - 1) \left(1 - \sigma \frac {w _ {s} - \overline {{w}} _ {s}}{w _ {s}}\right)\right)\]

The latter expression is bounded above:

\[\Rightarrow - \frac {\overline {{w}} _ {s}}{w _ {s} - \overline {{w}} _ {s}} + (\sigma - 1) \left(1 - \sigma \frac {w _ {s} - \overline {{w}} _ {s}}{w _ {s}}\right) < - \sigma + (\sigma - 1) \left(1 - \sigma \frac {w _ {s} - \overline {{w}} _ {s}}{w _ {s}}\right)\]

and since

\[= - \sigma + \sigma - \sigma^ {2} \frac {w _ {s} - \overline {{w}} _ {s}}{w _ {s}} - 1 + \sigma \frac {w _ {s} - \overline {{w}} _ {s}}{w _ {s}} < 0\]

so that the partial derivative is negative in the relevant range.

From this, and since and , it is immediate that

With these results it then follows that:

\[\begin{array}{r c l} \frac {d w _ {2}}{d w _ {1}} & = & - \frac {\partial h / \partial w _ {1}}{(- \gamma \delta^ {- \sigma}) \partial h / \partial w _ {2}} > 0 \\ \frac {d ^ {2} w _ {2}}{d w _ {1} ^ {2}} & = & \frac {\partial^ {2} h / \partial w _ {1} ^ {2} \cdot \partial h / \partial w _ {2} - \partial^ {2} h / \partial w _ {2} ^ {2} \cdot \partial h / \partial w _ {1}}{(\gamma \delta^ {- \sigma} \cdot \partial h / \partial w _ {2}) ^ {2}} < 0 \end{array}\]

which proves claim 1. Claim 4 follows from this and the fact that aggregate wage increases shift the restriction away from the origin in the space. Finally, Claims 2 and 3 follow from (7). •

Appendix C: Proportion of youth population and groupspecific unemployment rates in sample of countries.

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