Interpreting Aggregate Wage Growth: the Role of Labor Market Participation Richard Blundell; Howard Reed; Thomas M. Stoker the American Economic Review, Vol

Interpreting Aggregate Wage Growth: The Role of Labor Market Participation

Richard Blundell; Howard Reed; Thomas M. Stoker

The American Economic Review, Vol. 93, No. 4. (Nov., 2003), pp. 1114-1131.

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VOL. 93 NO. 4 BLUNDELL ET AL.: INTERPRETING AGGREGATE WAGE GROWTH 1115 changes within the (selected) sample of workers from which measured wages are recorded. As in the selection bias literature,2 this second factor depends on the covariance between participation and wages. The final term measures the adjustment for composition changes in hours and depends on the size of the covariance between wages and hours. These bias terms are then investigated using data for male wages from the British economy in the 1980's and 1990's. These data analyses point to significant 78 80 82 84 86 88 90 92 94 96 year deviations between aggregate measures and individual measures, that give a substantively different picture of actual real wage growth over this period. There are at least three reasons why the Brit- ish labor market experience during the last two decades is particularly attractive for this analy- recession and another sharp decline in partici- sis. First, there have been strong secular and pation. In contrast, log average wages show cyclical movements in male employment over reasonably steady increase from 1978 through this period. Second, there exists a long and the 1990's. growing more than 30 percent in representative time series of individual survey real terms over this period and even displaying data, collected at the household level, that growth during the severe recession of the early records detailed information on individual 1990's. hourly wages as well as many other individual The analysis presented in this paper shows characteristics and income sources. Finally, this picture of the evolution of real wages to be over this period, there has been a systematic highly misleading. Making our three corrections change in the level of real out-of-work income. reveals no evidence of real growth whatsoever The household survey data utilized in this study in the early 1990's, and that over the whole allows an accurate measure of this income vari- period, real wage growth was no more than 20 able which, in turn, acts as an informative in- percent. We show this corrected series is pre- strument in controlling for participation in our cisely estimated and robust to parametric spec- analysis of wages. ification. With our micro-level data, we can Labor market behavior in Britain over the directly measure the large discrepancy in the recent past serves to reinforce the importance level and growth between the aggregate and of these issues. Indeed the relationship between individual wage paths, and we find that it is wage growth and employment in Britain has almost completely captured by the aggregation often been the focus of headline news3 Fig- factors we develop. This validates our model ure 1 displays the time series of aggregate specification and supports our interpretation of hourly wages and aggregate employment for the overall aggregation biases involved. The men in the United Kingdom over two busi- large discrepancy is clearly associated with an ness cycles between 1978 and 1996. In 1978- important upward bias in the aggregate trend of 1979, over 90 percent of men aged between 19 real wages and a reduction in the degree of and 59 were employed. The participation rate procyclicality. fell dramatically in the recession of the The picture of employment fluctuations is early 1980's and then recovered somewhat in even more dramatic between education groups the late 1980's (although not to its initial and date-of-birth cohorts. Given the strong in- level). In the early 1990's there was a further terest in the economics literature on returns to education across education and cohort groups (see Amanda Gosling et al., 2000 and David See Heckman (1979). Card and Thomas Lernieux, 2001, for example), For example, "Rise in Earnings and Jobless Sparks it is important to study how these employment Concern," Financial Times,front page, June 18th, 1998. fluctuations impact estimated returns to education 1116 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003

0 left education atlbefore 16 0 left education 17-18 + left education I9or older

78 80 82 84 86 88 90 92 94 96 06 year 76 60 82 84 86 68 90 92 94 96 year FIGURE2. BRITISHMALES: LABORMARKET PARTICIPATION RATE, 1978-1996 FIGURE4. MALE COHORT,BORN 1945-1954: LABORMARKETPARTIC~PATION RATE

0 left educat~onatlbefore 16 0 left education 17-18 + left education 19 or older 1.0- 200 - ? 09- ! 180- $ 41

0.8 ' 8 1604 Y

07- $e 140- -3

0 6 - 120 - 78 80 82 84 66 88 90 92 94 96 78 80 82 84 86 88 90 92 94 96 year year

FIGURE3. MALECOHORT,BORN1935-1944: LABORMARKETPARTICIPATION RATE

age, and other observed wage determinants. For across these groups. Figures 2-4 present the this we use another feature of recent British picture of employment by education level for experience: the large changes in the real value two central cohorts. For the cohort born be- of benefit (transfer) income which individuals tween 1945-1954, the steep fall in employment receive (or would receive) when out of work.4 experienced by the lower-education group in Figure 5 shows the time-series variation of out- the early 1980's is not matched in the employ- of-work benefit income for a particularly rele- ment patterns of the higher-educated groups. vant group-married low-education men in Indeed, the level and growth in dispersion also rented housing. The housing component of ben- differs substantially across cohort and education efit income5 increased sharply in real terms over groups. Our results show that the selection ef- the period 1978 to 1996, an increase which was fect is often substantial and suggests a large largely dnven by a policy shift from subsidized underestimate in the level and growth in educa- public sector rents and rent controls in the pri- tion returns. However, when aggregated across vate rented sector toward a system where rent groups, this selection effect can be offset by levels more closely reflected the market value of differences in wage dispersion across education and cohort groups. To identify these corrections to the aggregate 4 The out-of-work income measure is constructed for series we need some that affects male each household using a tax and benefit simulation model. employment decisions but does not affect the s This is a means-tested benefit covering a large propor- distribution of wages conditional on education, tion of rental costs. VOL. 93 NO.4 BLUNDELL ET AL.: INTERPREl 'ING AGGREGATE WAGE GROWTH housing. This increase in this housing compo- I. Aggregation and Selection nent is a major contributory factor in the rise in benefit income for the "low-education" families A. A Model for Real Wages depicted in Figure 3. Although it is unlikely that variation in real The approach we use for modeling individual value of benefit income can explain all of wages follows Andrew Roy (1951) in basing the variation in participation rates, we argue wages on human capital or skill levels, assum- that changes in real benefits serve as an im- ing that any two workers with the same human portant instrument in the participation deci- capital level are paid the same wage. Thus we sion, which therefore affect the endogenous assume that there is no comparative advantage, selection in real wages. Moreover, we can and no sectoral differences in wages for workers isolate the selection effects in part because with the same human capital level. We assume the housing benefit varies strongly across that the mapping of skills to human capital is time, location, and cohort group. This varia- time invariant, and that the price or return to tion occurs because individuals with low lev- human capital is not a function of human capital els of education in the older cohorts had a endowments. In particular, we begin with a much higher chance of spending their lives in framework consistent with the proportionality public housing. We take this variation to be hypothesis of Heckman and Sedlacek (1990). exogenous to the individual decision to work The simplest version of the framework as- (conditional on cohort, education, region, sumes that each worker i possesses a human trend, and cycle effects), and find evidence capital (skill) level Hit, which is nondifferenti- of substantial selection effects that vary over ated in that it commands a single price r, in time the economic cycle and across education period t. Worker i's wage is the value of his groups. human capital, which may differ across cohorts The layout of the remainder of this paper is j and education groups s. Suppose we assume as follows. Section I gives the modeling human capital Hit is lognormally distributed7 framework that underlies the empirical work, with mean a,, and variance 2,then log wages and presents the aggregation bias terms.6 are given by the additive equation As discussed above, these terms are particularly informative when there have been dramatic and systematic changes in the distributions of hourly wages, hours of work, and where ei, is NO, g).*In this model the sys- in participation rates-features that have oc- tematic growth in wages is common across curred both secularly and cyclically in Britain workers (through r,); below we allow growth to as well as Europe as a whole. Our application differ across groups (e.g., by education) over to real wages of men in Britain, presented in time. Section 11, well illustrates this value. We find Reservation wages w;, are also assumed to be important impacts of wage heterogeneity and lognormal, with labor participation on the interpretation of observed aggregate wages-impacts that differ in magnitude and direction. For example, changes in the dispersion of individual wages where 5, is NO, at). Here bit is the exogenous lead to a secular increase in the bias of ag- benefit level (out-of-work income) available to gregate wages; in contrast, compositional worker i, that varies with individual characteris- changes induced by labor market participa- tics and time. Participation occurs if wit r wz and tion lead to a countercyclical bias in the ag- we represent the participation decision by the gregate measure. Section I11 draws some conclusions. 'We utilize lognormality assumptions extensively in our derivations and their validity is assessed in the empirical analysis that follows. The bias terms are derived from new results on aggre- * Clearly, there is an indeterminacy in the scaling of r,. gation with lognormal distributions, as spelled out in the In our empirical work we normalize the value of r, for some Appendix. year t = 0 (say, to r, = 1). 1118 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003 indicator I, = 1[wit r w:]. This is our base-level Here, education can have a time-varying impact specification that maintains the proportionality on wages. The second extension is to allow the hypothesis. There are no trend or cycle interac- different stock of labor market experience that tions with cohort or education level in either is associated with each cohort at any specific equation. calender time to have an impact on returns. This We are interested in how aggregate wages generalizes the basic model to allow log wages depend on the distribution of hours of work. to display different trend behavior for each date- One approach is to assume that the distribution of-birth cohort group. of hours worked (when working) is uncorrelated To summarize our discussion, the underlying with the participation decision. Alternatively, individual model is comprised of the following we can use a labor supply model where hours log wage equation, an hours equation, and an worked correlate with the incentives to partici- employment selection equation. We express pate. To see how aggregation bias is structured these equations in compact form as in that case, we consider the following simple model. Assume that desired hours hit are chosen by utility maximization, where reservation wages are defined as hit(w*) = h, and h, is the minimum h = h, + y. (a, + a'z + v), number of hours available for full-time work.9 Assume that hit(w)is normally distributed for each I = l[a, + a'z + v > 01, w, and approximate desired hours by where x refers to predictors in the log wage (3) h,, = ho + y(ln wir - In w:) equation, such as the variables that represent aj, in (1) or the predictors in the extended versions of the model such as (4), and where z refers to predictors in the participation equation, including log benefit income. The disturbances E and v are normally distributed, each with mean 0. This model is used in our bias form~lation.'~ Two extensions of this basic framework are made necessary by our empirical findings. First, B. Bias in Aggregate Wages suppose that education produces a differentiated type of human capital. That is, a high-education Measured wages at the individual level are worker i has a skill price f and a low-education represented by an entire distribution. Therefore, worker i skill price 6.As before, similar there are many ways to pose the question of workers with a particular skill level are paid the whether aggregate wage movements adequately same in all sectors. If d, is the high-education reflect movements in individual wages. The ag- dummy, the log wage equation has the form gregate wage is measured by = el,

where i E (I = 1) denotes a labor market participant and where e,, = hi,w,, is the earnings of individual i in period t, and where pit are the hours weights This allows for a simple characterization of fixed costs; see John F. Cogan (1981). 'O We could easily nest labor supply model with the situation of hours uncorrelated with participation, by adding another error term ui,to (3), which is uncorrelated with participation error but possibly correlated with the log wage error. This adds a further term to the hours adjustment given We take the population of participating workers in the Appendix. as sufficiently large so that we can ignore VOL. 93 NO. 4 BLUNDELL ET AL.: INTERPRETING;AGGREGATE WAGE GROWTH 1119 sampling variation in average earnings and av- Jacob Mincer (1972), and Heckman (1974), erage hours; modeling the aggregate wage as among many others]. We have extensive individual-level data on wages, and so we could examine aspects of how aggregate wage compares to average log wage empirically. Part of the contribution of this where E[.] refers to the mean across the work is to give explicit representations of the population. biases in interpreting aggregate wages, using The basic framework suggests one natural the indvidual model (5). To start, note that the comparison for interpreting w,. From (I), we mean log wage is simply could ask whether movements in the aggregate wage w, accurately reflect movements in the skill price r,. For instance, if aggregate produc- tion in the economy has total human capital This equation reflects the key parameters of (XiHi,) as an input, then the appropriate price interest: the mean log wage and the f3 coeffi- for that input is r,, and so this comparison cients. It also captures how the /3 coefficients would ask whether i?, accurately reflects the are relevant to aggregates; changes in the mean relevant (quality-adjusted) price of labor. With predictor variables E(xi,) are multiplied by the differentiated skills, we could ask whether the p's for associated changes in mean log wage aggregate wage iit, reflects an average of the E(ln wit). various skill prices-for instance, if (4) applies, To analyze the observed aggregate wage, we then we could compare iit, to a weighted aver- characterize the large sample approximation (7) age of < and $. Such comparisons of aggre- by applying some new results on aggregation gate wages to skill prices are very natural, but with nonlinear models. For that purpose, we require a human capital framework as the foun- assume that the indexes Po + plx and a, + dation of labor value. a'z are (bivariate) normally distributed in each Other interpretable comparisons arise on time period t. We can clearly apply our results purely statistical grounds, such as comparing to any population segment where this normality the aggregate wage I?, to the unweighted mean assumption is valid. wage E(wi,). Following the tradition of mea- Our main result is summarized as follows. suring "returns" from coefficients in estimated For each time period t, we have log wage equations, we focus on the "log" version of this comparison, namely to compare

In G, versus E(ln wit). = E(ln wi,) + DSP, + SEL, + HR,. This approach is adopted by Gary Solon et al. (1994), as well as in our empirical work be- These are the three bias terms; DSP, for bias low." We note that our choice of In wit follows from wage dispersion, SEL, for bias deriving one of the longest established traditions in em- from compositional changes in the (selected) pirical economics, where log wage is the pri- sample of workers, and HR, for bias from het- mary object of analysis in studying individual erogeneity in hours worked. earnings data [see Bany R. Chiswick (1970), The simplest term is DSP,, for wage dispersion, and it is equal to ?htimes the variance of log wages at time t. This arises because the standard micro model is for log wages (with I' This statistical comparison captures the simplest skill variance associated with proportional variation price interpretation as well-if our basic framework applies, across workers), but for observed aggregate and if the log mean of Hi,is constant over time in our basic framework, then the mean log wage comparison matches the "Cv, versus r," comparison (in log form). We have raised these comparisons separately because one might be interested in the log wage comparison even without a framework This assumption as well as all derivations are spelled tracing wages to human capital. out in the Appendix.

THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003

Single Married Year Number Percent Number Percent Total 1978 99 1 22.98 3,322 77.02 4,313 1979 978 23.60 3,166 76.40 4,144 1980 964 22.75 3,274 77.25 4,258 1981 1,124 24.55 3,454 75.45 4,578 1982 1,189 25.90 3,401 74.10 4,590

Total 19,813 27.56 52,089 72.44 7 1,902

participation separately from the wage.19 We have argued that this variable is exogenous Education group for wages, conditional on the other included (i) (ii) (iii) variables (age, region, etc.). This is an iden- Left school Left 17-18 Left 19+ tifying restriction which is not directly test- 5 16 Total able. We do carry out specification testing by Single 13,607 3,232 2,974 19,813 conducting joint significance tests for sets of (percent) 68.68 16.31 15.01 100.00 regressors and interactions between them. Married 38,627 6,763 6,699 52,089 (percent) 74.16 12.98 12.86 100.00 These are presented in the remaining rows of TOTAL 52,234 9,995 9,673 71,902 Table 3 for the participation probit and the (percent) 72.65 13.90 13.45 100.00 wage equation with the selectivity correction via the inverse Mills ratio. In estimation we are unable to use data on housing benefit for the year 1983. This is be- B. Results cause the system of benefit assistance for ten- ants was reformed in 1983 and the information We consider a number of possible speci- on rent levels and benefit receipts was not col- fications for our individual-level participa- lected properly by Family Expenditure Survey tion and wage equations which relate to the interviewers. We do, however, have a consistent various specifications discussed in Section series for 1978-1982 and 1984-1996. Below I. Our model of participation includes the we present results for the complete period out-of-work income (the simulated benefit 1978-1996 omitting 1983 data. income variable) interacted with marital sta- The chosen specification, which the results tus, as well as the variables included in the below focus on, models participation and wages log wage equation. The X2 test reported in the first row of Table 3 shows that the benefit income variable is strongly significant in l9 The full results are available on the AER web site the participation (probit) equation. This is (http://www.aeaweb.org/aer/contents/) as Supplement B to important as it is our key source of identifying the paper. VOL. 93 NO. 4 BLUNDELL ET AL.: INTERPRETING AGGREGATE WAGE GROWTH

TABLE~--SIGN~CANCETESTS FOR REGRESSIONSPECIFICATION

Participation equation Wage equation Coefficients ,$ (d.0.f.) p-value F-test (k, n) p-value Instruments:

Out-of-work income X marital status Education (left 17-18, left 19+) Trend (3rd-order polynomial) Cohort (b.1919-1934, b.1935-1944, b.1955-1964, b.1965-1977) Education X trend Education X cohort Trend X cohort Education X trend (1st order) X cohort Region (1 1 standard regions) Region X trend, region X trendZ Mills ratio X marital status Married (single coefficient) Spouse's education (single coefficient)

as a function of the three education groupings, and second, it is quite possible that selection cohort dummies, a cubic trend, and region, plus may have different effects at different skill lev- interactions between the cubic trend and educa- els. For example, an increase in the level of tion, cubic trend and cohort, education and co- out-of-work income which families can expect hort, linear trend by education and cohort, and a to receive when unemployed might have a quadratic trend times region. This specification larger impact among lower-educated groups, was chosen in comparison to a number of alter- where the financial net returns to working are natives through a standard specification search. lower, than among graduates or other highly Further details of the validation of this model educated groups, where the ratio of out-of-work are presented in the model validation section income to in-work income may still be very below. low. As Table 3 shows, the benefit income The necessity of the inclusion of the interac- terms are strongly significant in the participation terms means that our preferred specification tion equation and the selectivity correction, ed- of the log wage equation departs from the full ucation, cohort, and trend terms are all proportionality hypothesis as set out in Section significant in the wage equation. I. The additional interactions between cohort and education and trend which we introduce Aggregate Wages and Corrections: Overall could reflect many differences in minimum Sample Measures.-We now consider aggre- educational standkds across cohorts such as gate wages and the corrections due to heteroge- the systematic raising of the minimum school- neity, the distribution of hours, and labor leaving age over the postwar period in the participation.20 These correction terms are con- United Kingdom. Meanwhile the prices of dif- structed separately for each year as described in ferent (education-level) skills are allowed to Section I. We plot the values over time to allow evolve in different ways, by including an inter- a quick assessment of the path of aggregate action between the education dummies and the wages and the relative importance of the cor- trend terms. The selectivity correction using the rections, as well as how well the corrected inverse Mills ratio from the participation equation is interacted with marital status and by education group, because first, the way out-of- 20 The disturbance "variance" terms are computed by work income is defined implies that it attains standard variance estimates from the structure of the esti- different levels for single and married people, mated truncated regression. 1124 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003

/ +-- J ..,,.,,,,,,,....,,, 78 78 BO 81 82 83 61 85 LXI 87 BI) 88 90 81 92 83 B1 85 gB year

FIGURE7. WAGEPREDICTIONS FROM MICROMODEL, AGGREGATEWAGE AND CORRECTIONS:REBASED TO 1978

aggregate wage after all corrections, and shows aggregate vage matches up with the mean log a growth over the period of only 20 percent. wage implied by the micro-level wage equa- In order to see the relative growth of the tions. We have found this graphical approach various series more clearly, Figure 7 shows much more straightforward than trying to di- exactly the same aggregate wage measure and rectly analyze the numerous estimated coeffi- the fully corrected aggregate series, but rebased cients underlying the graphs. to 1978.~~Plotting each series starting at the Overall aggregate wages and the various cor- 1978 level makes it easier to see what the im- rection terms are plotted in Figure 6. This dis- plementation of the adjustment formula does to plays the behavior of all the measures of wages the measured aggregate hourly earnings growth. we look at over the entire period. The raw For comparison, we also plot the mean log wage aggregate earnings index is the aggregate mea- (8) implied by the bias-corrected micro regres- sure of wages calculated as the log of average sions (adjusted for participation, or omitting the wages for those in work; this shows an increase selection term). A key evaluation of our frame- of 34 percent over the period 1978-1997.~' The work is whether the fully corrected aggregate remaining three lines shown on the figure give series lines up with this selectivity-adjusted mi- the (cumulative) application of the correction cromodel prediction. The figure shows that terms to aggregate wages. First is the correction there is a very close correspondence between for the distribution of hours [HR, in (9)]. As we the series. Later on we use bootstrap methods to may have expected given the relatively stable check whether any difference which does arise pattern of hours worked, this has little impact on between the micromodel and the corrected ag- the time-series evolution of wages. Second is gregate series is statistically significant. the selection correction for covariance between Several features of this figure are noteworthy. wages and participation [SEL, in (9)]. This has For instance, the direction of movement of the a more dramatic effect, with growing gaps over uncorrected log aggregate wage does not always time associated with large decreases in partici- mirror that of the mean micro log wage. During pation-it reduces the estimated increase in the recession of the early 1980's, aggregate wages over the period to around 28 percent. wages grow rather more than the corrected mi- Finally, we apply the correction for the hetero- cromodel wage. While there is a reasonably geneity (dispersion) of individual wages [DSP, close correspondence between the trend of the in (9)]. This gives the impact of the increasing two lines in the latter half of the 1980's, in the heterogeneity in wages that is separated from 1990's we find that there is a reasonably sub- participation effects. This final series gives the stantial increase in log aggregate wages but essentially no growth in the corrected measure.

2' This is also calculated from the FES and corresponds closely to the measure of "average earnings," which media 22 That is, the 1978 values are subtracted from all values commentators in the United Kingdom have focused on. in the series. VOL. 93 NO. 4 BLUNDELL ET AL.: INTERPRETING AGGREGATE WAGE GROWTH 1125

-8-IOW WD(1Ie@. 8ml"g. I&X

+mmx sner all mnas~ns

1990's reduces our estimate of average wage growth for this group from over 20 percent to around 10 percent. The corrected aggregate series and the selectivity-adjusted micromodel prediction appear to line up very well here. For those individuals with more schooling, presented in the subsequent Figures 9 and 10, the fit between the two series is less good largely because these are smaller subsarnples, and so the data on wages for them is more noisy. Nevertheless, there appears to be evidence that selection effects do bias measured FIGURE9. WAGEPREDICTIONS BY EDUCATIONGROUP: wage growth estimates upwards for both of the LEFTEDUCATIONAGED17-18 better-educated groups.

Education Returns by Cohort.-Disaggregat- Figure 7, which rebases to 1978, shows these ing wages by education and cohort reveals an- patterns even more vividly. Correcting for se- other important aspect of the impact of lection over the period reduces our estimate of participation on aggregate wages. As we noted real aggregate wage growth from over 30 per- in the introduction, the employment rate fell cent to around 20 percent. sharply over this period with strong cohort differences. Figures 11-13 graph the estimated Wage Measures by Education Group.-Next returns with and without the correction factors we break our sample up by the three education for three different cohorts: those born between groups used in the analysis. We plot the wage 1935 and 1944 (who were the oldest cohort with series defined just as before but this time we are representatives in every sample year), those taking the rnicromodel prediction, the "aggre- born between 1945 and 1954, and those born gate" wage series and the corrections to the between 1955 and 1964 (who were the young- aggregate series within education group for est). It is very noticeable how strongly the re- each year. Hence we have three plots in Figures turns increased in the early 1980's but equally 8-10, which present the path of the series for interesting how the increase is only maintained each education group. into the 1990's for the youngest cohort. For the low-education group-those that left The impact of selection effects on returns is full-time education at age 16 or younger-the clearly important. In Figures 14-16 the time- picture is particularly clear. This is presented in series variation in the selection bias term is Figure 8. Controlling for the biases induced by presented for each cohort. This follows the cy- shifts in participation rates over the 1980's and clical pattern of employment-as one might 1126 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003

0-i 1 +WL.onT*n I 0.01 4, , , , , , , , , , 78 80 82 84 88 88 90 92 94 96 0 30 rn i87080BIIY81WBS~BiW8B~81929394P586 year war

FIGURE 1 1. RETURNTO EDUCATION: COHORTBORN1935-1944

0.01~, , , , , , , , , , 78 80 82 84 86 88 90 92 94 96 year

0 0 , . , , , , . . . . , . . . 78 79 80 81 82 83 84 85 86 81 $8 BS 10 91 Pi I1 94 95 9s year year FIGURE16. SELECTIONBIAS IN RETURNSTO EDUCATION, FIGURE13. RETURNTO EDUCATION: COHORTBORN1955-1964 COHORTBORN1955-1964 expect given the analysis presented so far. But lection biases the aggregate wage downward. what is rather more interesting is how disper- For groups with greater dispersion, such as the sion effects often operate in the opposite direc- higher educated, those effects can be substan- tion to selection effects. Increasing dispersion tial. For instance, in the case of the older cohort biases the aggregate wage upward, whereas se- illustrated in Figure 14, those two impacts VOL. 93 NO. 4 BLUNDELL ET AL: INTERPRETING AGGREGATE WAGE GROWTH 1127

series.23The figure shows that the two measures are not significantly different over the period roughly cancel each other from the late 1980's covered by the sample. Occasionally the cor- through the 1990's. rected aggregate measure is higher than the 95 percent upper bound on the micromodel prediction, but in general the two series line up very C. Model Validation well. This provides a very positive validation of the model framework. Our model and its underlying econometric assumptions have been tested as far as is Semiparametric Estimation.--Our model, as possible in order to ascertain their plausibil- set out in Section I, makes the assumption that ity. The validation procedures undertaken the unobservable factors affecting participation include (a) a check to see whether the correc- and wages are normally distributed. This can of tions to aggregate wages line them up suffi- course be called into question. The properties of ciently well with the predictions from the the estimator rely on the parametric distribu- selectivity-adjusted micromodel, (b) relaxing tional assumptions on the joint distribution of the normality assumption on the unobserv- the errors. However, given our exclusion as- ables by estimating an analogous model using sumption on the continuous out-of-work in- semiparametric methods, and (c) plots of the come variable, semiparametric estimation can predicted indices from the probit and the proceed in a fairly straightforward manner. To wage equation to assess whether the dis- estimate the slope parameters we follow the tributions of observable attributes conform to suggestion of Peter M. Robinson (1988) which normality. We now assess each of these in is developed in Hyungtaik Ahn and James L. turn. Powell (1993). These techniques are explored in a useful application to labor supply by Whitney Bootstrapping the Accuracy of the Model K. Newey et al. (1990). In Figure 18 we graph Fit.-To assess the accuracy with which the a comparison between the predicted wages corrections which we make to the aggregate estimated using semiparametric techniques average male log wage series "line up" against and the wage predictions from the selectivity- the prediction from our micromodel of wages adjusted micromodel which we use. Bootstrap (with the selectivity correction included), we confidence bands (95 percent) refer to the para- used bootstrap methods to simulate the differ- metric selectivity model. There is a very close ence between the two measures. This involved correspondence between the predictions from sampling with replacement from the Family Ex- the parametric micromodel and the semipara- penditure Survey data and reestimating the mi- metric version. We conclude that the assumption cromodel a total of 500 times. The 95-percent confidence intervals on the bootstrapped micromodel prediction are shown in Figure 17 to- 23 Very similar results, broken down by educational gether with the corrected aggregate wage group, are available from the authors on request. I128 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003

-5 0 4 -2 o i i Prsdicted index Standardized predb

of normality of the unobservables in the model III. Conclusion is not unduly restrictive. This aim of this paper has been to provide a Normality of the Wage and Participation Zn- systematic assessment of the way changes in labor dexes.-In addition to checking the validity of market participation affect our interpretation of the normality assumption on the unobserv- aggregate real wages. We have developed and able~,we are also interested in the normality implemented an empirical framework for under- of the probit index and of the fitted wage standing this relationship which reduces to the distribution from the selectivity-adjusted calculation of three aggregation factors. These can wage equation. Taking the participation pro- be interpreted as correction terms reflecting bit first of all, Figure 19 plots the distribution changes in the distribution of retums, changes in of the standardized probit index &'z over all selection due to participation, and changes in years of the sample (plots for individual years hours of work, respectively. We have shown that are all quite similar). The index is distributed they do a remarkably good job of explaining the roughly normally although with a slight neg- differences between individual and aggregate ative skew.24 wages in the British context. We also checked the validity of the normal- British data was used for three reasons. First, ity assumption on log wages by plotting the there have been significant changes in labor standardized wage predictions from the model market participation over the last two decades. overlaid with a standard normal curve. This is Participation rates for men have seen a secular shown in Figure 20. The distribution is not decline and have displayed strong cyclical vari- obviously skewed left or right, and there ap- ation. The secular decline is largely reflected in pears to be a higher density of observations increasing decline in participation among older around the mean than is the case with a stan- men across cohorts while the cyclical variation dard normal. In any case, while these plots do shows strong regional variation. This phenom- not show exact concordance with the normal enon is common to many other developed econ- distribution assumptions, we feel that the omies. Second, in Britain, there are strong proximity of the empirical distributions to changes in real wages and the distribution of normal helps explain the close correspon- real wages over this sample period. Third, there dence between corrected aggregate wages is important exogenous variation in certain and the mean wages implied by the micro components of out-of-work incomes across regressions.25 time and across individuals that allows the iden- tification of the correction terms. "For further validation, kernel regressions of participation on &'z show a normal shape, details of which are available from the authors on request. summarized in the difference between the plots from the 25 While there are some visible departures from normal- corrected aggregate measure and the micromodel. As we ity, the entire impact of those departures on the analysis is have noted above these plots are extremely close. VOL 93 NO. 4 BLUNDELL ET AL :INTERPRETING AGGREGATE WAGE GROWTH 1129

The empirical analysis of aggregate wages is sion and for selection in characterizing the shown to provide a coherent picture of the re- distortion in the measurement of wage growth lationship between individual male wages and from aggregate data. Most noteworthy is how aggregated wages over this period. Moreover, mean individual log wages are largely flat the statistical model adopted appears to ac- throughout the early 1990's, whereas measured cord well with the empirical facts. The correc- aggregate wages are rising. As such, we see tion terms explain the differences between log our estimates as giving clear evidence that aggregate wages and the average of log wages the biases in log aggregate real wages are sub- implied by our analysis. The differences are stantial and can lead to misleading depictions interesting and have valuable implications. of the progress of wages of individual male They show an important role for wage disper- workers.

This Appendix presents the explicit formulations of biases in aggregate wages, as well as the aggregation results on which they are based. The mathematical details are provided on the AER web site as Supplement A (see http://www.aeaweb.org/aer/contents/) and draw on the work of Daniel McFadden and Fred Reid (1975) and Thomas E. MaCurdy (1987). The aggregation results apply to aggregate of nonlinear relationships over normal and lognormal distributions. We make use of standard formulae familiar from the analysis of selection bias, as well as some further results that we present in Lemma Al. A proof of Lemma A1 is given in Supplement A. Assume that (U, v)are jointly normal random variables: namely

and denote I = 1 [v<01 and ln w = U. The formulations of aggregate participation utilize the "probit" formula

-PI' E[I] = @ [-] U-V where @[.I is the standard normal cumulative distribution function (c.d.f.). The impact of participation on mean log wage makes use of the "selection" formula

where A[*] = $[.]/@[.I is the inverse Mill's ratio, with $[-I the standard normal density function. In addition to these ex ressions, for analyzing the wage level we use the following results for the lognormal variable %= exp U. LEMMA Al: We have that: THE AMERICAN ECONOMIC REVIEW SEPTEMBER 2003

To apply the above relationships to the model (5), we require the following assumption:

DISTRIBUTIONAL ASSUMPTION: The indices determining log wages and participation are joint normally distributed: namely

(PO+ P'x + &) - N(( PfXXXP+u: fflZ:,P+ (I..)) (Yo + a'z + v ~'X,Za+uE,afZZza+u: '

The following correspondence allows application of the results:

where U is the log wage and wis the wage (level). The assumption establishes normality as in (Al), with parameters given as

The bias results follow from working out (lo), (ll), and (12) using the aggregation results with this correspondence. The results are as follows: For (lo), we have

1 DSP - [PfZxxP+ ui]. for (1 I), we have

and for (12), we have VOL. 93 NO. 4 BLUNDELL ET AL.: INTERPRETING AGGREGATE WAGE GROWTH

(A51

a,, + cufE(z)+ a,, ho + yao + ycufE(z)+ yflfZxzcu+ ya,, + y , / m .h HR = In a, + cufE(z) h, + yn, + ycufE(z)+ y~mo:.h(cuf~,,a-) + 4

Finally, our remarks in Section I, subsection C, are substantiated by noting that an increase in skill price r, reduces the selection bias term; we have

with the term in brackets negative when PfZ,,a + a,, > 0. REFERENCES December 1985,93(6), pp. 1077-125. ."Self-selection and the Distribution of Ahn, Hyungtaik and Powell, James L. "Semipa- Hourly Wages." Journal of Labor Econom- rametric Estimation of Censored Selection ics, January 1990, 8(1), pp. S329-63. Models with a Nonparametric Selection MaCurdy, Thomas E. "A Framework for Relating Mechanism." Journal of Econometrics, July Microeconomic and Macroeconomic Evidence 1993, 58(1-2), pp. 3-29. on Intertemporal Substitution," in T. F. Bewley, Bik, Mark J. "Real Wages over the Business Cycle: ed., Advances in econometrics, F$h World Evidence from Panel Data" Joumal of Political Congress, Vol. 11. 1987, pp. 149-76. Economy, August 1985,93(4),p~. 666-89. McFadden, Daniel and Reid, Fred. "Aggregate Card, David and Lemieux, Thomas. "Can Falling Travel Demand Forecasting From Disaggre- Supply Explain the Rising Return to College gated Behavioral Models." Transportation for Younger Men? A Cohort-Based Analy- Research Record, No. 534, 1975. sis." Quarterly Journal of Economics, May Mincer, Jacob. Schooling, experience and earn- 2001, 116(2), pp. 705-46. ings. New York: National Bureau of Eco- Chiswick,Barry R "An Inter-Regional Analysis of nomic Research, 1972. Schooling and the Skewness of Income," in Newey, Whitney K; Powell, James L. and Walker, W. L. Hansen, ed., Education, income and hu- James R "Semiparametric Estimation of Selec- man capital. New York: National Bureau of tion Models: Some Empirical Results." Ameri- Economic Research, 1970, pp. 157- 84. can Economic Review, May 1990 (Papers and Cogan, John F. "Fixed Costs and Labor Supply." Proceedings), 80(2), pp. 324-28. Econometrica, June 198 1,49(4), pp. 945-63. Robinson, Peter M. "Root-N-Consistent Semipa- Gosling, Amanda; Machin, Stephen and Meghir, rametric Regression." Econometrica, July Costas. "The Changing Distribution of Male 1988, 56(4), pp. 931-54. Wages in the UK." Review of Economic Stud- Roy, Andrew. "Some Thoughts on the Distribu- ies, October 2000, 67(4), pp. 635-66. tion of Earnings." Oxford Economic Papers, Heckman, James J. "Shadow Prices, Market 1951, 3, pp. 135-46. Wages, and Labor Supply." Econometrica, Schmi#, John. 'me Changing Structure of Male July 1974, 42(4), pp. 679-94. Earnings in Britain, 1974-1988," in Di$erences . "Sample Selection Bias as a Specifi- and changes in wage structures. Chicago: Univer- cation Error." Econometrica, January 1979, sity of Chicago Press, 1995. 47(1), pp. 153-61. Solon, Gary; Barsky, Robert and Parker, Heckman, James J. and Sedlacek, Guilberme "Heter- Jonathan A. "Measuring the Cyclicality of ogeneity, Aggregation, and Market Wage Func- Real Wages: How Important Is Composition tions: An Fhnpirical Model of Self-selection in the Bias?" Quarterly Journal of Economics, Feb- Labor Market." Joumal of Political Economy, ruary 1994, I09(1), pp. 1-25. http://www.jstor.org

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You have printed the following article: Interpreting Aggregate Wage Growth: The Role of Labor Market Participation Richard Blundell; Howard Reed; Thomas M. Stoker The American Economic Review, Vol. 93, No. 4. (Nov., 2003), pp. 1114-1131. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28200311%2993%3A4%3C1114%3AIAWGTR%3E2.0.CO%3B2-1

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[Footnotes]

2 Sample Selection Bias as a Specification Error James J. Heckman Econometrica, Vol. 47, No. 1. (Jan., 1979), pp. 153-161. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28197901%2947%3A1%3C153%3ASSBAAS%3E2.0.CO%3B2-J

9 Fixed Costs and Labor Supply John F. Cogan Econometrica, Vol. 49, No. 4. (Jul., 1981), pp. 945-963. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28198107%2949%3A4%3C945%3AFCALS%3E2.0.CO%3B2-O

16 The Changing Distribution of Male Wages in the U.K. Amanda Gosling; Stephen Machin; Costas Meghir The Review of Economic Studies, Vol. 67, No. 4. (Oct., 2000), pp. 635-666. Stable URL: http://links.jstor.org/sici?sici=0034-6527%28200010%2967%3A4%3C635%3ATCDOMW%3E2.0.CO%3B2-S

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Real Wages over the Business Cycle: Evidence from Panel Data Mark J. Bils The Journal of Political Economy, Vol. 93, No. 4. (Aug., 1985), pp. 666-689. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198508%2993%3A4%3C666%3ARWOTBC%3E2.0.CO%3B2-K

Can Falling Supply Explain the Rising Return to College for Younger Men? A Cohort-Based Analysis David Card; Thomas Lemieux The Quarterly Journal of Economics, Vol. 116, No. 2. (May, 2001), pp. 705-746. Stable URL: http://links.jstor.org/sici?sici=0033-5533%28200105%29116%3A2%3C705%3ACFSETR%3E2.0.CO%3B2-A

Fixed Costs and Labor Supply John F. Cogan Econometrica, Vol. 49, No. 4. (Jul., 1981), pp. 945-963. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28198107%2949%3A4%3C945%3AFCALS%3E2.0.CO%3B2-O

The Changing Distribution of Male Wages in the U.K. Amanda Gosling; Stephen Machin; Costas Meghir The Review of Economic Studies, Vol. 67, No. 4. (Oct., 2000), pp. 635-666. Stable URL: http://links.jstor.org/sici?sici=0034-6527%28200010%2967%3A4%3C635%3ATCDOMW%3E2.0.CO%3B2-S

Shadow Prices, Market Wages, and Labor Supply James Heckman Econometrica, Vol. 42, No. 4. (Jul., 1974), pp. 679-694. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28197407%2942%3A4%3C679%3ASPMWAL%3E2.0.CO%3B2-S

Sample Selection Bias as a Specification Error James J. Heckman Econometrica, Vol. 47, No. 1. (Jan., 1979), pp. 153-161. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28197901%2947%3A1%3C153%3ASSBAAS%3E2.0.CO%3B2-J

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Heterogeneity, Aggregation, and Market Wage Functions: An Empirical Model of Self-Selection in the Labor Market James J. Heckman; Guilherme Sedlacek The Journal of Political Economy, Vol. 93, No. 6. (Dec., 1985), pp. 1077-1125. Stable URL: http://links.jstor.org/sici?sici=0022-3808%28198512%2993%3A6%3C1077%3AHAAMWF%3E2.0.CO%3B2-P

Self-Selection and the Distribution of Hourly Wages James J. Heckman; Guilherme L. Sedlacek Journal of Labor Economics, Vol. 8, No. 1, Part 2: Essays in Honor of Albert Rees. (Jan., 1990), pp. S329-S363. Stable URL: http://links.jstor.org/sici?sici=0734-306X%28199001%298%3A1%3CS329%3ASATDOH%3E2.0.CO%3B2-3

Semiparametric Estimation of Selection Models: Some Empirical Results Whitney K. Newey; James L. Powell; James R. Walker The American Economic Review, Vol. 80, No. 2, Papers and Proceedings of the Hundred and Second Annual Meeting of the American Economic Association. (May, 1990), pp. 324-328. Stable URL: http://links.jstor.org/sici?sici=0002-8282%28199005%2980%3A2%3C324%3ASEOSMS%3E2.0.CO%3B2-3

Root-N-Consistent Semiparametric Regression P. M. Robinson Econometrica, Vol. 56, No. 4. (Jul., 1988), pp. 931-954. Stable URL: http://links.jstor.org/sici?sici=0012-9682%28198807%2956%3A4%3C931%3ARSR%3E2.0.CO%3B2-3

Some Thoughts on the Distribution of Earnings A. D. Roy Oxford Economic Papers, New Series, Vol. 3, No. 2. (Jun., 1951), pp. 135-146. Stable URL: http://links.jstor.org/sici?sici=0030-7653%28195106%292%3A3%3A2%3C135%3ASTOTDO%3E2.0.CO%3B2-Q

Measuring the Cyclicality of Real Wages: How Important is Composition Bias Gary Solon; Robert Barsky; Jonathan A. Parker The Quarterly Journal of Economics, Vol. 109, No. 1. (Feb., 1994), pp. 1-25. Stable URL: http://links.jstor.org/sici?sici=0033-5533%28199402%29109%3A1%3C1%3AMTCORW%3E2.0.CO%3B2-L NOTE: The reference numbering from the original has been maintained in this citation list.