IS THE UNSKILLED WORKER PROBLEM IN DEVELOPED COUNTRIES GOING AWAY?

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1 1 IS THE UNSKILLED WORKER PROBLEM IN DEVELOPED COUNTRIES GOING AWAY? Edward Anderson # Keele University, U.K. June 2001 Abstract Recent data suggest that the fortunes of unskilled workers in developed countries improved during the 1990s, after deteriorating significantly during the 1980s. Such a trend could be explained by a faster decline in the relative supply of unskilled labour, a slower decline in the relative demand for unskilled labour, or a shift in labour market institutions. This paper argues that the improvement almost always reflected a slower decline in relative demand. Further research will be required to discover why the decline in demand for unskilled labour decelerated. KEYWORDS: Wage Inequality, Human Capital. JEL CLASSIFICATION: J31, J21, F16. This work was partly funded by the UK Economic and Social Research Council under award R I am most grateful to Adrian Wood for many ideas, comments and suggestions; to David Autor, Susan Harkness and Jo Swaffield for lending me their data; and to Nick von Tunzelmann, Hugh Waddington and participants in a workshop at the Institute of Development Studies for useful suggestions. Appendices to this paper are available on request from the author. Alternatively, they can be downloaded from the following website: # Department of Economics, Keele University, Keele, Staffs. ST5 5BG. Tel: + 44 (0) ; fax: +44 (0) ;

2 2 1 Introduction The widening gaps in wages and unemployment rates between skilled and unskilled workers in almost all OECD countries since the 1970s have been the subject of much attention and research. However, recent data suggest that this widening might have slowed, or even stopped, during the 1990s. In the United States, for instance, the ratio of the 90 th to the 10 th percentile of the earnings distribution, and the college/high-school wage premium, both rose much less rapidly in the 1990s than in the 1980s (Bernstein and Mishel, 1997; Katz and Autor, 1999). Similar patterns are observed in the United Kingdom (Machin, 1998). 1 A slowdown of the rise in labour market inequality in developed countries should perhaps be expected. The two most widely suggested causes of the initial rise in inequality a skill-biased change in technology (e.g. Machin and Van Reenen 1998; Autor et al. 1998) and a reduction of trade barriers between developed and developing countries (e.g. Wood 1994, 1998; Leamer 1998) are arguably once-and-for-all changes. They would have caused a step decrease in the relative demand for unskilled workers in developed countries, but not a continuing decline (although the step decrease may have been spread out over a number of years). It may also be that further technological progress, or further increases in trade with developing countries, increasingly reduce the demand for more skilled workers in developed countries. Wood (2000), for example, shows how increased trade between

3 3 developed and developing countries initially displaces the production of labour-intensive goods in developed countries, but subsequently displaces the production of more skillintensive goods. The effect is that the relative demand for unskilled workers initially declines, but subsequently increases again. It may also be that the initial rise in inequality between skilled and unskilled workers has brought about a rise or more precisely, an acceleration of the long-term rise in the relative supply of skilled workers. By the 1990s individuals (either those already in the labour force or those about to enter) may have responded to the higher level of wage and unemployment inequality by acquiring more education and training than in the 1980s. The result would be a slower rise, or a fall, in inequality between skilled and unskilled workers, even if the relative demand for unskilled workers continued its rapid decline. As yet however, the evidence of a slowdown is not conclusive. First, little is known about other developed countries. It is generally agreed that in continental European countries, where the influence of institutions on wages is stronger than in North America or the UK, rising inequality during the 1980s mainly took the form of rising unemployment gaps between skilled and unskilled workers (Freeman and Katz, 1995; Nickell and Bell, 1995). Did these countries witness a slowdown or reversal of rise in unemployment inequality during the 1990s? Second, it is not known whether any slowdown in the rise in wage inequality in the US and UK was offset by a faster rise in unemployment inequality. It is often argued that a

4 4 shift to more flexible and competitive forms of wage-setting in the US and UK contributed to the observed rise in wage inequality during the 1980s (Dinardo et al. 1996; Lee 1999). Was there a slowdown or reversal of this shift during the 1990s perhaps associated with the election of more left-wing governments? 2 If so, the slower rise in wage inequality might have been offset by a faster rise in unemployment inequality. Third, while the rise in inequality during the 1980s occurred between and within observable skill groups, and in all parts of the skill distribution, it is not yet clear whether the same applies to the slowdown during the 1990s. In the US, for instance, there is little evidence of a slowdown in the widening of dispersion in the upper half of the earnings distribution. While models with only two skill groups may be able to capture the main features of the rise in inequality during the 1980s, explaining the 1990s may require a model with more than two groups, such as Wood (2000) or Howell and Wolff (1992). 3 There is even less evidence about what caused any improvement in the position of lessskilled workers during the 1990s. Two recent studies decomposing movements in the relative wage of college graduates into relative demand and relative supply shifts have yielded different conclusions. Autor et al. (1998) conclude that the slower rise of the relative wage of college graduates in the US was driven by a slower rise in relative demand. Machin (1998), by contrast, argues that the slower rise in the UK was driven mainly by a faster rise in relative supply. It is not immediately clear whether these differences are real, as the studies measure relative wages and relative supply in different

5 5 ways. 4 Furthermore, both studies assume perfect relative wage flexibility throughout the period, and therefore do not allow for the effects of any institutional shifts. This paper has two aims. The first is to establish the facts about any slowdown during the 1990s of the rise in labour market inequality in developed countries. The second is to further our understanding of what caused any slowdown. It follows Autor et al. (1998) and Machin (1998) in decomposing movements in wage inequality into the effects of shifts in relative supply and relative demand. However, it has three novel features. First, it uses an almost identical procedure for the US and UK, so the results are more directly comparable. Second, it consistently defines three, rather than two, skill groups, so the determinants of inequality in both the lower and upper half of the skill distribution can be analysed. Third, it analyses both wage and unemployment inequality, so the effects of shifts in labour market institutions can be separated out from the effects of shifts in market forces. The remainder of the paper proceeds as follows. Section 2 presents the theoretical framework on which the empirical analysis is based. It derives a composite measure of inequality between any two skill groups, which consists of differences in both their wages and the extent of mismatch (which in turn consists of differences in their unemployment and vacancy rates). The composition of this measure is determined by labour market institutions, while its overall level is determined by relative supply and relative demand.

6 6 Section 3 then discusses the evidence on movements in inequality between skilled and unskilled workers in OECD countries since the 1970s. Section 3.1 presents estimates of inequality in the US and UK, by gender, between groups of workers with different absolute levels of education. The results are neither simple nor uniform, because of often large differences, between the US and UK, between men and women, and between different pairs of education groups. Nevertheless, there was a slower rise, or even a fall, during the 1990s, in wage inequality between male college graduates and high-school graduates in the US, and between male and female high-school graduates and high-school dropouts in the UK. Mismatch between these groups also tended to rise by less, or fall, during the 1990s, suggesting that the slower rise, or fall, in wage inequality was not driven by a shift in labour market institutions. However, there is no evidence of a slowdown, during the 1990s, of the rise in inequality between college graduates and highschool graduates in the UK, nor between female college graduates and high-school graduates in the US. Section 3.2 then presents estimates of inequality between workers with different levels of education in other OECD countries. In much of continental Europe, mismatch between high and low-educated workers rose more slowly, or declined, between the mid-1980s and early-1990s, after rising sharply between the mid-1970s and mid-1980s. These estimates are not without their limitations, and there were some notable exceptions. Nevertheless, it does appear that the improvement in the position of less-educated workers since the mid-to-late 1980s, like the initial deterioration between the late-1970s and mid-to-late 1980s, was by no means confined to the US and UK.

7 7 Sections 3.3 and 3.4 look at trends in two other measures of inequality between skill groups, the level of wage dispersion and the aggregate unemployment rate. In the US, UK and Canada, the ratio of the 50 th to the 10 th percentile of hourly earnings rose more slowly, or fell, during the 1990s, after rising sharply between the late-1970s and mid- 1980s. In continental Europe, aggregate unemployment tended to rise sharply between the late 1970s and mid 1980s, followed in the late 1980s and 1990s by cyclical variations around a higher level. These data provide further support for an improvement in the position of less-skilled workers in developed countries since the mid-to-late 1980s. However, there were again certain notable exceptions:, in the US and Canada, for example, the ratio of the 90 th to the 50 th percentile continued to rise rapidly during the 1990s. Section 4 then decomposes the movements in inequality between more and less-educated workers into the effects of shifts in relative demand and relative supply. In the great majority of cases where inequality either rose less rapidly, or fell, during the 1990s, after rising rapidly during the 1980s, the change is accounted for by a deceleration of the rise in relative demand, rather than an acceleration of the rise in relative supply. In fact, the rise in relative supply was, in most of these cases, slower during the 1990s than during the 1980s. However, in certain cases the rise in relative demand accelerated during the 1990s, such as male college graduates relative to high-school graduates in the UK.

8 8 Section 5 concludes, and speculates about the most likely reason for a slowdown in the growth of relative demand for skilled workers in developed countries. Neither a onceand-for-all technological change, nor a once-and-for-all reduction of trade barriers with developing countries, appear convincing at first sight: as noted by Autor et al. (1998), both the spread of computers in the workplace, and the rapid growth of trade with developing countries, have continued in the 1990s, at least in the US. Further work possibly looking at changes in the skill-bias of technological progress, or at changes in the skill-intensity of goods traded between developed and developing countries will be required to pin down the exact cause of the demand slowdown.

9 9 2 Theoretical framework The simplest model for analysing inequality is one of two types of labour, skilled (subscript s) and unskilled (subscript u), whose supply in any one year (t) is fixed, i.e.: L st = L st (1) L ut = L ut (2) These two types of labour produce aggregate output of substitution (CES) production function: Q t according to a constant elasticity Q t ρ ρ 1 [ α ( a N ) + 1 α )( b N ) ] ρ = (3) t t st ( t t ut where N st and N ut are the quantities employed of skilled and unskilled labour in period t, a t and b t represent the current state of skilled and unskilled labour-augmenting technology, α t represents the share of work allocated to skilled labour, and the aggregate elasticity of substitution between skilled and unskilled workers is σ = 1 (1 ρ) (Autor et al. 1998, p.1176). If we assume perfect competition, workers are paid their marginal products, and the relative wage of skilled workers is:

10 10 w ln w st ut 1 = ln Dt σ 1 N ln σ N st ut (4) where ln D σ ln[ α (1 α )] + ( σ 1)ln( a b ) t t t t t. (The derivation of equation (4) is shown in Appendix A1). The relative wage adjusts to ensure that the relative employment of skilled labour N N ) is equal in each year to the relative supply of ( st ut skilled labour L L ). Thus if one also assumes a particular value of the substitution ( st ut elasticity σ, equation (4) can be used to decompose movements in the relative wage into the effects of shifts in relative demand ( ln ) and shifts in relative supply (ln L L ) ). Dt ( st ut If we assume the relative wage is fixed (because of labour market institutions), firms desired relative employment of skilled labour is no longer necessarily equal to the relative supply of skilled labour, but is: N st wst ln = ln D t σ ln (5) N ut wut where desired employment ( N ) consists of actual employment ( N ) plus any unfilled i vacancies ( V i ). (Equation (5) is simply the inverse of equation (4)). If one assumed a particular value of the elasticity of substitution, one could in principle use equation (5) to decompose movements in desired relative employment into the effects of shifts in relative demand ( ln ) and shifts in the relative wage ( ln( w w ) ). Dt st ut i

11 11 In the fixed wage scenario, the difference between firms desired relative employment of skilled labour and the relative supply of skilled labour is the extent of labour market mismatch (M): N st Lst ln M t ln ln, (6) Nut Lut which, given that the supply of each skill group ( L i ) consists of employment ( N i ) plus unemployment ( U ), can be written as i N st + Vst N st + U st 1+ vs 1+ us ln( M ) ln ln = ln ln (6a) Nut + Vut Nut + U ut 1+ vu 1+ uu where v i = Vi N i and i U i N i u =. Given also that ln( 1+ x) x (when x is small), mismatch is also roughly equal to the sum of the absolute differences between the skilled and unskilled vacancy rate and the unskilled and skilled unemployment rate: ln( M ) ( v v ) + ( u u ) (6b) S U U S Subtracting ln ( L st L ut ) from both sides of equation (5), we can express the determinants of mismatch as:

12 12 w st Lst ln M = t ln Dt σ ln ln (7) wut Lut One could use equation (7) to decompose movements in mismatch into the effects of shifts in relative demand, shifts in the relative wage, and shifts in relative supply. Neither the fixed nor flexible relative wage assumption may hold in practice - a more common occurrence might be semi-rigidity. In this case, both the relative wage and the amount of mismatch adjust when there are exogenous shifts in relative demand or relative supply. If we divide both sides of (7) by σ, and add ln ( w S w U ) to both sides, we are left with the expression: w ln w st ut 1 + ln M σ t 1 = ln Dt σ 1 L ln σ L st ut. (8) The left-hand side of equation (8) is a composite measure of inequality between skilled and unskilled workers. The nature of labour market institutions will affect its composition, between wage inequality and labour market mismatch, but not its overall level. 5 Given an assumption about the value of σ, one can use equation (8) to decompose the combination of movements in relative wages and mismatch into the effects of shifts in relative demand and relative supply. The above model contains only two skill categories. This is not necessarily unrealistic; although we observe more than two wage levels, individuals may simply possess

13 13 different amounts of each skill (or both skills), rather than different skills altogether. However, some models explicitly contain more than two skill categories; Wood (2000), for example, presents a model containing three types of workers: highly-skilled, mediumskilled and unskilled. In this case, a multi-factor production function is required, together with a set of assumptions about the elasticity of substitution between different pairs of inputs. The simplest approach is to consider a multi-factor CES function with K labour inputs, namely: 1 ρ ρ it ( ait Nit ) K Q t = α (9) i= 1 Here, the assumption is that the elasticity of substitution between any two inputs is the same (equal to σ = 1 (1 ρ) ). This implies that a rise in the supply of factor i has no effect on the demand for factor j relative to factor k. Equation (9) in turn implies a system of K-1 equations (one being redundant) linking movements in inequality between different groups of workers to relative demand and relative supply shifts, as follows: w ln w jt kt 1 + ln M σ jkt 1 = ln D σ jkt 1 L ln σ L jt kt (10) where ln M ln( N N ) ln( L L ); ln D ln( α α ) + ( σ 1)ln( a a ) jkt jt kt jt kt jkt σ. However, the assumption of a single substitution elasticity stretches credibility, especially jt kt jt kt as K increases. 6 An alternative is to use a production function which allows for more

14 14 general patterns of substitution between factors, such as the translog function (see Appendix A2). Ideally, the number of skill groups would be determined by the data. One would begin with a generalised production function of several skill groups, estimate elasticities of complementarity between each pair, and aggregate those groups whose elasticity of complementarity is zero (groups between which the elasticity of substitution is infinite). Unfortunately, the data requirements of such a procedure are prohibitive: it would require measuring, or finding proxies for, the relative demand for each pair of education groups. The approach used in this paper is to begin with three groups, and observe the extent to which trends in inequality between medium-skilled and low-skilled workers are similar to those between highly-skilled and medium-skilled workers. A problem with equations (8) and (10) is that in order to calculate mismatch, both unemployment rates and vacancy rates by skill are required, whereas in practice, only unemployment rates by skill are usually observable. If we ignore vacancy rates, or assume they are equal for skilled and unskilled workers, mismatch becomes the employment rate of skilled relative to unskilled labour (the employment rate being defined as employment divided by labour supply): 7 1+ uu ( NU + UU ) NU ( N S LS ) ns ln( M ') = ln = ln = ln = ln, (11) 1+ u S ( N S + U S ) N S ( NU LU ) nu

15 15 However, if we ignore vacancies we are likely to under-estimate both the level and changes in the level of mismatch. The degree of under-estimation may be large; in the numerical example contained in Wood (1988), for example, the shift in the relative employment rate is only 50% of the relative demand shift. A further problem is that movements in relative employment rates, and the absolute difference between unskilled and skilled unemployment rates, tend to be highly correlated with movements in aggregate unemployment rates (see Appendix A3). This suggests that the former are affected by neutral demand shifts, and therefore an unreliable indicator of relative demand shifts. 8 A solution is to make some assumption about the relationship between the vacancy rate and the unemployment rate within each skill group. It is widely held that the aggregate vacancy rate and the aggregate unemployment rate are inversely related (the relationship is known as the Beveridge curve). It is also widely held that this relationship shifted to the right in most developed countries during the 1980s (Jackman et al., 1990). However, if we assume that the relationship between unemployment and vacancies is constant over time within each skill group, we can estimate the vacancy rate of each skill group in each year, and calculate mismatch from readily observable data. 9 A general form of the Beveridge Curve within any skill group i can be written as: v = α u (12) i i β i

16 16 where α i reflects workers effectiveness of job search and firms costs of firing workers (both negatively: the higher workers job-search effectiveness, or the higher the costs of firing workers, the lower is α ), and β i (< 0) reflects the sensitivity of the hiring rate (or the exit rate from unemployment) to changes in the ratio of vacancies to unemployment. (See Appendix A4 for the derivation of this function). If we assume that β = 1, as is suggested by the evidence on aggregate vacancy and unemployment rates (Jackman and Roper, 1987), inserting equation (12) into equation (6a) yields the following expression for mismatch; uu 1+ uu α S + us ln( M ) = ln + ln + ln (13) us 1+ us αu + uu which reduces to just ln( u u ) if we further assume that α α = 1. However, it is u s S = U very unlikely that this latter assumption will ever hold in practice. 10 The value of α is instead likely to lie somewhere between and 0.01; this implies that Beveridge curves intersect the 45-degree line at values of unemployment and vacancy rates somewhere between 0.01 and 0.1, as is the case for the aggregate Beveridge curves in OECD countries plotted by Jackman et al. (1990). It may also be higher among unskilled workers, either because they have a lower job-search intensity when unemployed, or because the cost to firms of firing them is lower; it may also differ between countries with different labour market institutions. In this paper I estimate mismatch according to equation (13) under a series of assumptions about the value of α, and then test the sensitivity of results to the choice of this assumption.

17 17 3 Movements in inequality between skilled and unskilled workers since 1970 This section studies trends in wage and unemployment inequality between skilled and unskilled workers in OECD countries since the early 1970s. It first looks at the wages and unemployment rates of workers with different absolute levels of education. This is appropriate if education is correlated with skill because it directly increases workers productivity, as in human capital models of education. However, absolute levels of education are not an ideal measure of skill, for two reasons. First, many skills are acquired outside formal education. Second, if education is simply a device used by individuals to signal their skill, as in screening models of education, skill groups should be defined by their relative levels of education. For example, rather than defining unskilled workers as those a certain number of schooling years, we would define them as those in the lower part of the schooling distribution. This section therefore also uses an alternative measure of skill, the wage itself. This will reflect observed as well as unobserved skills, and although many factors other than skill affect wages, one can control for some of them, for instance by looking at male and female wage inequality separately. The wage is also necessarily a relative definition of skill (the unskilled typically being defined as either the bottom decile or bottom quintile of the earnings distribution), and is therefore a more appropriate measure of skill if education is more a screening device than a productive asset. 11

18 18 Unfortunately, we can typically only measure the wage component of inequality using wage information, as unemployment rates by wage level are not easily observed. If wages are inflexible, wage inequality may be only a small component of composite inequality. Finally therefore, this section uses the aggregate unemployment rate as a proxy for movements in labour market mismatch in countries with inflexible relative wages. An increase in mismatch will tend to raise the natural rate of unemployment (Nickell 1990). However, many other factors affect the natural rate of unemployment, and whether recent movements in aggregate unemployment rates have reflected mismatch is a matter of considerable controversy (Layard, Nickell and Jackman 1991; Wood 1994). 3.1 By education, US and UK Detailed data on wages and labour force status by educational attainment are available for the US and UK. For the US, the data come from the Census for 1970 and 1980, and the Current Population Survey (CPS) Outgoing Rotation Group files for 1980, 1990, 1996 and 1998 (kindly provided by David Autor); the measure of educational attainment is years of schooling. For the UK, the data come from the General Household Survey, and are available for each year between 1974 and 1996 (kindly provided by Susan Harkness); the measure of educational attainment is highest qualification held. Based on this information, I break the labour force into three groups in each country, according to their years of schooling. (The assignment of average years of schooling to

19 19 each qualification level in the UK is described in Appendix A5). The first is college graduates, who have roughly 16 or more years of schooling; the second is high-school graduates, who possess between 12 and 16 years of schooling, and the third is highschool dropouts, who have less than 12 years of schooling. 12 The proportion of the labour force in each group is shown in Table 3.1. On this evidence, levels of attainment have increased substantially in both countries since 1970, but remain significantly higher in the US. In fact, according to Barro and Lee (1993), the US population had the highest educational attainment in the world in 1990 (measured by average years of schooling); the UK was in 20 th position. Note, however, that despite this difference the ratio of college graduates to high-school graduates is in fact higher in the UK than the US. Table 3.1 Employment and labour force by educational attainment in the US and UK, US UK High-school High-school College High-school High-school College Dropouts Graduates graduates dropouts Graduates graduates Employment 1970* Labour force 1970* Notes: US figures for 1970 are from the Census, those for other years from the CPS ORG. The labour force is the defined as the population aged between 24 and 65. Data include men and women. *UK data refer to The US figures from the 1980 Census, the Feb 1990 CPS and the 1998 CPS ORG are shown in Appendix A11, Table A10. Source: UK General Household Survey, US Census and US Current Population Survey.

20 20 Table 3.2 shows estimates of the wage of college graduates relative to high-school graduates (referred to as the relative wage of college graduates), and of the wage of highschool graduates relative to high-school dropouts (referred to as the relative wage of high-school graduates). Each relative wage is estimated from cross-section log weekly earnings regressions which control for other influences on individuals wages (see Appendix A6.1), and is estimated separately for men and women (pooled estimates of relative wages are shown in Appendix A6.2). An identical procedure is used in each country to facilitate comparisons. Unfortunately, there is some doubt about the validity of the results for the US in the 1990s, because of changes in the education question in the CPS after 1992 (Katz and Autor 1999). In particular, it is argued that estimates of the growth of the wage of high-school graduates relative to high-school dropouts in the 1990s are upwardly biased. For this reason, these estimates are omitted from Table 3.2 (although they are shown in Appendix A11, Table A11). The results in Table 3.2 are not altogether simple or uniform, because both the level of, and changes in relative wages differ often substantially between the US and UK, between men and women, and between the two pairs of education classes. Turning first to the levels of relative wages, Table 3.2 shows that relative wages tend to be higher in the US than the UK, and higher between college graduates and high-school graduates than between high-school graduates and high-school dropouts. (The one exception is the relative wage of female high-school graduates in the UK, which is higher than the relative wage of female college graduates in the UK and the relative wage of female

21 21 high-school graduates in the US). The relative wage of college graduates is particularly higher in the US than the UK. Relative wages also tended to be higher among women than men during the 1970s (this is the case for the relative wage of high-school graduates in the UK, and the relative wage of college graduates in the US), but much of this gap had disappeared by the 1990s. Table 3.2 Relative wages between education groups, US and UK, US UK College / High-school / College / High-school / High-school Dropouts High-school Dropouts Men: levels (log ratio) Men: changes (annualised log changes * 100) Women: levels (log ratio) Women: changes (annualised log changes * 100) Notes: UK data are 3-year moving averages; 1970 is (data for UK begins in 1974), and 1996 is (data ends in 1996). US figures for 1970 are from the Census, those for other years from the CPS ORG; growth rates for are calculated using the 1980 Census, and for using the Feb 1990 CPS. Using 1998 figures for the US does not significantly alter the results. (The US figures from the 1980 Census, the Feb 1990 CPS and the 1998 CPS ORG are shown in Appendix A11, Table A11). Source: UK General Household Survey, US Census and US Current Population Survey.

22 22 Turning now to changes in relative wages, Table 3.2 shows that, in almost all cases, relative wages fell during the 1970s and then rose sharply during the 1980s. This broad pattern has been well documented in the literature (e.g. Katz and Murphy, 1992). Table 3.2 also shows, however, that there were certain exceptions to this pattern, and that there was a fair amount of variation in the magnitude of changes. During the 1970s, the relative wage of college graduates fell by more in the US, but in the UK, the relative wage of high-school graduates fell by more. The relative wage of male high-school graduates in fact rose in the US. During the 1980s, the rise in relative wages was much larger in the US than the UK. It was also larger in the US for college graduates, whereas in the UK it was larger for high-school graduates. In the US, the rise in relative wages was larger among women, whereas in the UK it tended to be larger among men. Similarly, there is evidence in both countries of a slower rise in relative wages during the 1990s, not between both pairs of education groups and not among both genders. In the UK, the relative wage of male and female high-school graduates in fact declined during the 1990s, but the relative wage of male college graduates grew more rapidly. In the US, the relative wage of male college graduates grew more slowly during the 1990s, but the relative wage of female college graduates kept increasing at the same rate. 13 Figure 3.1 shows the annual relative wage series for the UK, providing a more precise guide to the timing of changes in relative wage trends (the series for men and women combined is shown in Appendix A6.2, Figure A6).

23 23 Figure 3.1 Relative wages between education groups in the UK, Relative wages, men Log wage differential C/HS HS/HSD Relative wages, women Log wage differential C/HS HS/HSD All of the rise in the relative wage of male high-school graduates during the 1980s took place between 1979 and The relative wage of female high-school graduates continued falling between 1979 and 1984, but rose between 1984 and The relative wage of college graduates, by contrast, which is very similar among men and women, did

24 24 not begin rising until the late-1980s, and then stabilised in the mid-1990s. Annual estimates of the college/high-school graduate relative wage in the US (Katz and Autor 1999, Figure 5b) show that the rise began roughly in 1980, and that the slowdown of the rise had begun by the late-1980s. Table 3.3 presents estimates of the amount of mismatch between education groups in the US and UK since 1970, calculated according to equation (13) of the previous section, and assuming a value of α equal to for both skilled and unskilled workers. The sensitivity of results to this assumption is discussed further below. The figures are log ratios, so a value of zero implies that the relative demand for the two groups equals their relative supply. The calculations are made using a broad definition of unemployment, which includes all people not working (between the ages of 25 and 65). This definition is preferable to a narrow definition, which would include only those people actively seeking work, because some individuals are likely to respond to a lack of job opportunities by becoming inactive rather than unemployed and actively seeking work. The results are again shown for men and women separately; the pooled results are shown in Appendix A7.1, Table A2.

25 25 Table 3.3 Estimated mismatch between education groups in the US and UK, ( α = ) US UK College / High-school / College / High-school / High-school Dropouts High-school Dropouts Men, levels (log ratio) Men, changes (annualised log changes * 100) Women, levels (log ratio) Women, changes (annualised log changes * 100) Notes and sources: As Table 3.2. Data refers to those aged Using 1998 rather than 1996 figures for the US does not significantly alter the results, except for female high-school graduates relative to highschool dropouts in which case the acceleration of the rise in mismatch during the 1990s shown in Table 3.3 is replaced by a large deceleration (see Appendix A11, Table A12). In both countries, estimated mismatch is almost always higher between high-school graduates and high-school dropouts than between college graduates and high-school graduates. This is opposite to the pattern of relative wages, and suggests that there is more relative wage flexibility, and therefore less mismatch, when comparing groups with higher levels of education. However, estimated mismatch is higher in the US, in the same way as relative wages. This is surprising; given that relative wages appear more flexible in the US, we would expect more mismatch in the UK. One possible explanation

26 26 is that Table 3.3 over-estimates the amount of mismatch in the US compared to the UK, because α is in fact much lower in the US than the UK (which could be because jobsearch effectiveness is higher, or because the costs of firing workers are higher, in the US than the UK). 14 In both countries there were often large movements in mismatch, which sometimes reinforced and sometimes offset the changes in relative wages. During the 1970s for instance, there was a large fall in mismatch between female college and high-school graduates in the US and UK, which would have reinforced the fall in their relative wage, but a large rise in mismatch between high-school graduates and high-school dropouts which would have offset the fall in their relative wage. The implication is that the fall in the relative wage of female college graduates was driven by market forces, but that the fall in the relative wage of high-school graduates was driven by an institutional shift to less relative wage flexibility. During the 1980s, there was a small fall in mismatch between college graduates and highschool graduates, among both men and women and in both the US and UK, which would have offset the rise in their relative wage. Here the implication is that part of the rise in their relative wage was driven by an institutional shift to greater relative wage flexibility, although probably not all because the fall in mismatch was small compared to the rise in the relative wage. However, during the 1980s there was also a large rise in mismatch between high-school graduates and high-school dropouts, among both men and women and in both the US and UK, which would have reinforced the rise in their relative wage.

27 27 In this case, the implication is that the rise in their relative wage was wholly driven by market forces: a shift in relative demand or relative supply. Did a faster rise, or slower fall, in mismatch offset the slower rise of wage inequality during the 1990s, when observed? The evidence in Table 3.3 suggests not. In the UK, mismatch between high-school graduates and high-school dropouts either remained stable (among men) or rose less rapidly (among women) during the 1990s, while mismatch between female college and high-school graduates continued its slow decline. These movements would have reinforced, rather than offset, the fall or slower rise of relative wages during the 1990s. In the US, mismatch between male college and highschool graduates did begin to rise in the 1990s, after falling during the 1980s, which suggests that a shift to less relative wage flexibility did contribute to the slower growth of their relative wage during the 1990s. However, the magnitude of the reversal in mismatch was small, and unlikely to fully offset the deceleration of the rise in the relative wage. Figure 3.2 shows the annual relative employment series for the UK, again providing a more precise guide to the timing of changes in trends over the period (the series for men and women combined is shown in Appendix A7.1, Figure A7). It shows that, among men, the large rise in mismatch between high-school graduates and high-school dropouts occurred between 1977 and 1984, which closely matches the timing of the rise in their relative wage, although predating it by two years. Among women, the large fall in mismatch between college and high-school graduates took place between 1975 and 1977;

28 28 thereafter mismatch tended to increase until the late 1980s, before falling again during the 1990s. Figure 3.2 Estimated mismatch between education groups in the UK, ( α = ) Men Estimated mismatch (log point HS/HSD C/HS Women Mismatch (log point HS/HSD C/HS

29 29 The figures shown in Table 3.3 and Figure 3.2 are generally quite robust to the assumed value of α, and to the chosen measure of unemployment (see Appendix A7.2 and A7.3). When α = (which I regard as an upper-bound estimate), estimated mismatch is higher, but not substantially so. Similarly, when α = (which I regard as a lowerbound estimate), estimated mismatch is lower, but not substantially so. In both cases, trends over time are very similar to those shown above. A narrow definition of unemployment, including only those individuals who are officially categorised as unemployed, tends to yield lower estimates of the level of mismatch (see Appendix A7.2, Figure A10). This reflects the fact that the ratio of non-participation to employment, as well as that of official unemployment to employment, is higher among less-educated workers. The difference is particularly marked among women, which probably reflects the fact that, in the UK, women have tended to have lower access to unemployment benefits than men. The trends in estimated mismatch over time are, however, broadly similar to those in Figure 3.2. The above results are also consistent with the large fall in labour force participation rates amongst unskilled workers found by previous studies of these countries (e.g. Topel 1993; Nickell and Bell 1995). In the model underlying this paper, this decline is explained by an decrease in the relative demand for unskilled workers, or an increase in their relative supply, combined with less than perfect relative wage flexibility (the relative supply of unskilled workers being assumed to be completely inelastic). It might also be argued, however, that it is the result of a decrease in the relative demand for unskilled workers

30 30 combined with elastic relative supply: once the wage of unskilled workers falls below a certain level, unskilled workers voluntarily withdraw from the labour force, and the relative employment rate of skilled workers rises. 15 In the first case, unemployment is involuntary (the unemployed are willing to work at the current wage but unable to find an unfilled position); in the second case, unemployment is voluntary (the unemployed are unwilling to work at the current wage). However, it is not easy to observe, with the data at hand, into which of these categories unemployed or inactive workers fit. As a result, I am unable to distinguish between the two reasons why relative wages and relative employment rates both fell during the 1980s. While the observed facts are inconsistent with a model which assumes both perfect relative wage flexibility and inelastic relative supply, it is difficult to say which of these assumptions the data reject. 3.2 By education, other OECD countries Movements in the unemployment rates of low-education and high-education workers between the 1970s and 1990s in several OECD countries are available from Nickell and Bell (1995) and OECD (1997). Figure 3.3 shows estimates of mismatch between these groups, using the Nickell and Bell data, and again assuming a value of for α. The somewhat odd appearance of the lines, with flat segments connected by large changes, reflects the use of period averages by Nickell and Bell. Moreover, the lines for some of the countries have been scaled up or down by arbitrary amounts to make the figure more readable. The figures are repeated in Table 3.4 without the scaling.

31 31 Figure 3.3 Estimated mismatch between high- and low-educated male workers in OECD countries, mid-1970s to early 1990s ( α = ) Estimated mismatch (log poin Norway Sweden UK France Germany Netherlands Estimated mismatch (log poin US Canada Australia Japan Spain Italy Notes: To make the graph easier to read, 0.09 has been added to the figures for Norway, 0.07 to those for Sweden, 0.02 to those for the UK, and 0.05 to those for Italy, while 0.01 has been subtracted from those for Germany, 0.05 from those for the Netherlands, 0.09 from those for Spain, and 0.05 from those for Japan. Data mainly refer to males only. Source: Author s calculations using data from Nickell and Bell (1995)

32 32 We should be careful about making cross-country comparisons (especially between levels of mismatch), not only because of potential differences between countries in the value of α, but also because the definitions of high and low education vary by country. Nevertheless, Figure 3.3 and Table 3.4 suggest that in many OECD countries, mismatch tended to rise between the mid-1970s and mid-1980s, and then fall between the mid-tolate 1980s and the early 1990s. Mismatch also tended to rise by more, during the late 1970s and early 1980s, in continental Europe than in the US or the UK, which suggests a smaller degree of relative wage flexibility in continental Europe. Table 3.4 Estimated mismatch between high- and low-educated male workers in OECD countries, mid-1970s to early 1990s Levels Growth* Mid- 1970s Mid- 1980s Early 1990s Mid-1970s to mid- 1980s Mid-1980s to early 1990s Austria Finland France Germany Italy Netherlands Norway Spain Sweden UK Australia Canada Japan New Zealand US Notes: * annualised log changes multiplied by 100. For the exact years and definitions of high and low education for each country, see Appendix A8.1, Table A5. Source: Author s calculations from data in Nickell and Bell (1995)

33 33 There were certain exceptions to this pattern. In Italy, mismatch continued rising during the 1990s, while in Canada mismatch in fact tended to fall between the mid-1970s and mid-1980s, before rising between the mid-1980s and early 1990s. The reasons for these exceptions are not known, and require further research. But the overall pattern in Figure 3.3 and Table 3.4 does suggest that the slower rise, or fall, in inequality between skilled and unskilled workers witnessed during the 1990s in the US and UK extended to many other OECD countries. Furthermore, these results are again robust to a range of assumptions regarding the value of the parameter α (see Appendix A8.1, Figures A11 and A12), and the OECD (1997) data show a broadly similar pattern of movement (see Appendix A8.2). 16 It is possible that the fall in mismatch between high- and low-education workers in continental Europe after the mid-1980s reflected an institutional shift to more flexible relative wage setting. In this case, we would expect the fall in mismatch to be offset by a rise in relative wages, leaving composite inequality unchanged. I do not have the necessary data to carry out a formal test of this hypothesis (one would need the relative wage of high-education and low-education workers for each country and year contained in Figure 3.3 and Table 3.4), but it seems unlikely. Overall wage dispersion changed only modestly in the majority of continental European countries between the late 1970s and early 1990s, and in particular, we do not observe a faster rise, or slower fall, after the mid-1980s (Katz and Autor 1999, Table 10). It is more likely therefore that the fall or slower rise in mismatch reflected an improvement in the composite position of lesseducated workers, driven by a shift in relative demand or relative supply.

34 Inequality between high and low-wage workers Figure 3.4 shows the ratios of the 90 th to 50 th (90/50) and the 50 th to 10 th (50/10) percentiles of the US male and female earnings distribution, between 1973 and The data are from Bernstein and Mishel (1997); they refer to hourly earnings and include full-time and part-time workers. 17 Figure 3.5 shows the equivalent series in the UK; they are taken from Machin (1998), and also refer to hourly earnings and include full-time and part-time workers. In the US, the male 50/10 ratio rose gradually between 1973 and 1981, accelerated between 1981 and 1986, and then declined between 1987 and The female 50/10 ratio fell during the 1970s, before rising sharply between 1981 and 1986 and gradually declining thereafter. By contrast, among both men and women the 90/50 ratio rose at a roughly constant rate throughout the period, perhaps even accelerating during the 1990s. 18 In the UK, the male 50/10 ratio fell slightly between 1975 and 1979, rose sharply between 1979 and 1987, and then decelerated between 1987 and The 90/50 ratio also rose sharply, between 1981 and 1987, and then decelerated between 1987 and Among women, the 50/10 ratio fell between 1975 and 1979, rose between 1984 and 1992, and levelled out until The 90/50 ratio rose sharply, between 1979 and 1990, and then declined gradually until Similar findings for the US are reported by Katz and Autor (1999 Table 1 and Figure 3), using slightly different data in 1971, 1979, 1987 and In the lower half of the

35 35 male distribution, inequality rose during and , but was stable during In the upper half of the distribution, by contrast, relative wages were stable during , but rose during and Among women the trends were similar, except that during relative wages fell in the lower half of the distribution. Wolfson and Murphy (1998 Charts 3-5) apply a similar procedure to slightly different data for the US and Canada in 1975, 1985 and They use annual earnings, and include self-employment income, with higher top-coding levels than in the public-use datasets available to other researchers. Inequality among men, after rising during in both the lower and the upper halves of the distribution, fell during in the lower half of the distribution, but continued to rise in the upper half (particularly at the very top). There is a similar pattern among women, except that the rise between 1975 and 1985 in inequality among the lower half of the distribution is much smaller. Picot (1998, Chart 1) reports inequality among annual earnings of all workers in Canada in 1981, 1989 and Again the reported results are similar, at least among males: inequality rises in both the lower and upper halves of the male distribution during , but only in the upper half of the distribution during However, among women inequality falls in the lower half of the distribution during Other data for the UK, however, sometimes show a slightly different picture. Male 50/10 ratios from the New Earnings Survey (NES) fell between 1972 and 1977, and then rose at a roughly constant rate until 1995, before levelling off up to 1999 (see Appendix A9).

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