Panel data from the United Kingdom are used to estimate a wage curve that allows simultaneously for time, individual, and spatial effects and which thus finesses the problem of grouped data bias. Once allowance is made for the multilevel and cross-classified nature of the data, estimates of the unemployment elasticity of the wage are seen to be volatile and imprecise.

Geraint Johnes

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
 
 
Lancaster University Management School 
Working Paper  
2005/062 
 
 
 
 
 
The wage curve revisited: estimates from a UK panel 
 
 
 
 
 
Geraint Johnes  
 
 
The Department of Economics                        
Lancaster University Management School 
Lancaster LA1 4YX 
UK 
 
 
© Geraint Johnes  
All rights reserved. Short sections of text, not to exceed 
two paragraphs, may be quoted without explicit permission, 
provided that full acknowledgement is given. 
 
The LUMS Working Papers series can be accessed at http://www.lums.lancs.ac.uk/publications/ 
LUMS home page: http://www.lums.lancs.ac.uk/  
 
 
 
 
 
THE WAGE CURVE REVISITED: ESTIMATES FROM A UK PANEL 
 
 
 
 
Geraint Johnes 
 
Department of Economics 
Lancaster University Management School 
Lancaster LA1 4YX 
United Kingdom 
 
 
T: +44 1524 594215 
F: +44 1524 594244 
E: G.Johnes@lancs.ac.uk
 
 
October 2005  
 
 
ABSTRACT 
 
Panel data from the United Kingdom are used to estimate a wage curve that allows 
simultaneously for time, individual, and spatial effects and which thus finesses the 
problem of grouped data bias. Once allowance is made for the multilevel and cross-
classified nature of the data, estimates of the unemployment elasticity of the wage are 
seen to be volatile and imprecise. 
 
 
 
JEL Classification:   J30 
Keywords:     wage curve, panel data 
 
 
The author is indebted, without implication, to David Blanchflower, Steve Bradley, 
Allan Little and David Peel for comments on an earlier draft.  1. Introduction 
 
Since the pioneering work of Blanchflower and Oswald (1994, 2005), the literature on 
the wage curve has developed along several lines (Nijkamp and Poot, 2005). 
Blanchard and Katz (1999) and Black and Fitzroy (2000), for example, have 
emphasised the importance of using (log) hourly wages (as opposed to annual 
earnings) as the dependent variable. Bell et al. (2002) have considered the relationship 
between wages, regional and aggregate unemployment, and migration. 
 
The developments of most interest in the present context concern two issues. First, the 
original wage curve estimates were subject to grouped data bias (Aitkin et al., 1981; 
Moulton, 1986) – since the data used in the analysis were collected at two levels of a 
hierarchy, namely individual (wages) and region (unemployment), a group effect bias 
is introduced. This problem was recognised by Blanchflower and Oswald (1994, pp. 
168-170) who finessed it by repeating their analysis at the more highly aggregated 
level using cell means for wage data. While this is a commonly used method, it 
suffers a major drawback in that it disposes of much individual level data. It also 
limits the extent to which issues of unobserved heterogeneity across regions can be 
investigated, although this drawback is mitigated in more recent studies that construct 
panels of regions across time (Baltagi et al., 2000; Wu, 2004; Iara and Traistaru, 
2004).  
 
The second development is related to the availablility of data. Since the original work 
on the wage curve was published, many more panel datasets have become available 
which allow exploration of the importance to the wage curve of unobserved 
heterogeneity across individuals. These include several German datasets (the German 
Socio-Economic Panel, studied by Pannenberg and Schearze, 1998, and the Institut 
fur Arbeitsmarkt und Berufsforschung panel, analysed by Baltagi and Blien, 1998, 
and by Bellman and Blien, 2001). In other European countries, the European 
Community Household Panel has been used by Montuenga et al. (2003) and by 
García-Mainar and Montuega-Gómez (2003). And for the US, the National 
Longitudinal Survey of Youth has provided a wealth of data for analysis by Bratsberg 
and Turunen (1996) and Turunen (1998). 
 
Several of the studies listed above use the panel data to control for both time and 
region effects, typically using a fixed effects methodology. Likewise, several studies 
make reference to grouped data bias as a caveat but do not correct for it. Some others 
do attempt a correction, but do not arrive at a fully satisfactory fix; for example, 
Turunen (1998) reports estimates both for equations including fixed effects for region 
and for those including fixed effects for individuals, but does not include both effects 
simultaneously.  García-Mainar and Montuega-Gómez (2003) are keenly aware of the 
issues here, and try two methods to fix the problem. The first method, which they 
deem unsatisfactory, adopts the two-stage approach suggested by Card (1995). Their 
second method introduces individual intercept shifts by modelling in differences 
(Arellano and Bond, 1991), which means that much information about the impact of 
time-invariant cofactors is lost.   
 
The aim of the present paper, therefore, is to evaluate wage curves using panel data 
which fully and simultaneously allow for time fixed effects, and both region and 
individual fixed effects in order to correct for grouped data bias. In so doing, we draw on the work of Goldstein (1987, 2003) on multi-level and cross-classified models. The 
method will be demonstrated using data for the United Kingdom, drawn from the 
British Household Panel Survey (BHPS).
1 The method also allows analysis of how 
the impact of variables other than unemployment on the wage can vary over time. A 
key finding of the paper is that allowing for the multilevel nature of the data much 
reduces the precision with which the unemployment elasticity of the wage is 
estimated, and thereby calls into question much of what we thought we knew about 
the wage curve.  
 
 
2. The wage function and data issues 
 
The method used here draws on the literature on multi-level modelling. We have a 
model where, within a region, measurements on individuals are taken at various 
points in time. This is not a standard hierarchical model, however, since individuals 
can move across regions over time. So the focus is on a two level model in which the 
first level represents occasions, while the second is a cross-classification between 
individuals and regions (Goldstein, 2003). Occasions (years) can be modelled as fixed 
effects, while both regions and individuals are associated with random effects. Hence 
all three sources of unobserved heterogeneity can simultaneously be modelled, with 
the wage curve taking the form 
 
ln wi(rt) = ai(rt) + fr + dt + bXi(rt) + β ln u(rt) + εirt      ( 1 )  
 
where wirt denotes the hourly wage obtained by individual i in region r at time t, urt is 
the unemployment rate in region r at time t, and Xirt is a vector of other individual-, 
region- and time-specific variables.   
 
The data are taken from the BHPS 1992-2003.
2 This is an unbalanced panel of 
152640 individuals, of whom 71011 have positive earnings. Of these we have location 
data for 65601, and this therefore forms the sample on which the analyses are 
conducted. The loss of more than one half of the observations due to zero earnings is 
not so much a concern as it might at first appear; since this is a household survey, 
much non-participation in the labor market is due to respondents’ age. But sample 
selection biases may remain; we note this as a caveat, but note also that standard 
solutions to this problem are not presently available for application in the context of a 
mixed hierarchical and cross-classified model of the type used here. 
 
Unemployment data (from www.nomisweb.co.uk) for October of each year are 
grafted onto the BHPS using region codes. Ideally one would wish to use more 
spatially disaggregated data than this, but software constraints preclude this – the 
modelling of cross-classified data requires us to set up a large number of auxilliary 
variables. For the same reason we are unable to disaggregate unemployment rates by 
worker group. Nevertheless, with 11 regions and a panel of length 11, the degrees of 
freedom on the unemployment variable are comparable with those available in several 
earlier studies based on panel data. 
 
                                                 
1 These data were kindly supplied by the UK Data Archive. 
2 The BHPS began in 1991; this year is omitted from the present analysis because unemployment data 
measured on a consistent basis with subsequent years are not available at regional level for that year. Control variables used in the analysis include sex (male=1, female=0), age, age 
squared, marital status (on its own and interacted with sex), number of dependent 
children (again on its own and interacted with sex), health status (measured on a 5 
point scale from excellent=1 to poor=5), union membership (member=1, non-
member=0) and binary variables indicating the highest educational qualification. 
These vary from higher degree (hidegree) through bachelor’s degree (degree), nursing 
qualification (nursingq), upper secondary school qualifications (alevels), lower 
secondary school qualifications (olevels) and other qualifications (othqual).  
 
 
3. Results 
 
Results, obtained using MLwiN 2.02, are reported in Table 1; these allow fully, both 
in estimation of coefficients and standard errors, for the grouped and cross-classified 
nature of the data. In column 1 we report an equation in which there are fixed effects 
for years and random effects for individuals, but where no allowance is made for a 
region effect, so that the group nature of the unemployment variable is not 
accommodated. It is readily seen that this specification yields a fairly conventional 
wage curve; the estimated unemployment elasticity of the wage is, in absolute terms, 
somewhat lower than the conventional value of –0.1 suggested by Blanchflower and 
Oswald’s ‘empirical law’, but it is negative and very highly significant. The values of 
the other coefficients all accord with the conventional wisdom. Some of the 
explanatory variables, in particular those referring to marital status and childrearing, 
are potentially endogenous; excluding them from the analysis makes no substantive 
difference to the coefficients on the remaining variables. 
 
Column 2 reports the results obtained once equation (1) is estimated, that is with 
individual and regional random effects and time fixed effects. While most of the 
estimated coefficients are robust to this change, the absolute value of the estimate of 
the unemployment elasticity of the wage drops, and, having previously been very 
highly significant, it is now significant only at levels in excess of 5 per cent. This 
finding echoes those of Bratsberg and Turunen (1996) and Turunen (1998). 
 
In column 3, we add dummies for (9) industries and (9) occupations. As might be 
expected, this reduces the magnitude on the coefficients on the education variables; it 
also reduces further both the estimate of the unemployment elasticity of the wage and 
its significance.  
 
Column 4 reports the outcome when the model is augmented further by a full set of 
interaction terms between years and (i) sex, (ii) degree, and (iii) logged 
unemployment. In each case, 1992 is the omitted interaction. These fixed effects are 
not reported in full for reasons of space, but the main findings may be summarised 
here.  The magnitude of the male wage premium declined over the period; while in 
1992 it amounted to 0.148, by 2003 it had declined to 0.097; the slope dummies are 
consistently significantly negative from 1998 on. Likewise the wage premium 
attached to degree-level educational qualifications (over and above no qualifications, 
and controlling, inter alia, for occupation) declined from 0.308 in 1992 to 0.260 in 
2003; these slope dummies are significant only from 2000 on. Note that these 
observations could not be made in the context of a model in which differencing is 
used to evaluate individual fixed effects, since amongst the employed sample changes in educational level would be rare and changes in sex (probably) nonexistent. Finally, 
and of most interest in the present context, the unemployment elasticity of the wage 
varied from a high of +0.017 in 1992 to a low of –0.054 in 1995.
3 This last finding 
reinforces observations made by Turunen (1998) about the instability of the wage 
curve over time.   
 
Some authors have raised concerns about the possible endogeneity of unemployment 
in wage curves models of the type estimated here (see, for example, Baltagi and 
Blien, 1998). To check for this, we rerun the model reported in column 3, this time 
instrumenting (on the lag of logged unemployment) for the unemployment variable. 
The effect of this is to increase somewhat the absolute value of the estimate of the 
unemployment elasticity of the wage, but the estimate remains insignificant at the 5 
per cent level. 
 
While it is not possible to estimate a wage curve for the whole of the UK using highly 
disaggregated unemployment data, it is possible to study smaller labor market areas if 
we restrict the sample to a single region, and then disaggregate the unemployment 
measure to the level of the local authority district. If this is done, similar findings to 
those reported above obtain. For example, the coefficients on logged unemployment 
that obtain in the London and South East regions corresponding to columns 1 and 2 of 
Table 1 are –0.017 (with a standard error of 0.007) and –0.027 (with a standard error 
of 0.019) respectively. The wage curve appears to be a context in which grouped data 
bias really matters. 
 
 
4. Conclusions 
 
 
The results reported above indicate that, once allowance is simultaneously made for 
unobserved heterogeneity at both the individual and region level and the grouped 
nature of the data are accommodated, the unemployment elasticity of the wage is both 
volatile and, in some specifications at least, imprecisely determined. The estimates 
reported here suggest that, while a wage curve appears to exist for the whole of the 
UK in some periods, its shape does not generally accord with any general ‘empirical 
law’. Further research using panels for other countries is clearly warranted.  
 
 
 
References 
 
Aitkin, Murray, Anderson, Dorothy and Hinde, John, 1981. Statistical modelling of data on teaching 
styles, Journal of the Royal Statistical Society A 144, 419-461. 
 
Arellano, Manuel and Bond, Stephen, 1991. Some tests of specification for panel data: Monte Carlo 
evidence and an application to employment equations. Review of Economic Studies 58, 277-297. 
 
Baltagi, Badi H. and Blien, Uwe, 1998. The German wage curve: evidence from the IAB employment 
sample. Economics Letters 61, 135-142. 
 
                                                 
3 Between 1993 and 1995, the slope dummy coefficients lie in the range –0.057 through –0.072; 
thereafter they lie in the range –0.030 through –0.046. All are significant. Baltagi, Badi H., Blien, Uwe and Wolf, Katja, 2000. The East German wage curve 1993-1998. 
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1996. Regional Studies 37, 929-945. 
 
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Econometrics 32, 385-397. 
 
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Surveys 19, 421-450. 
 
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 Table 1 Regression results: dependent variable is the log of the hourly wage 
 
variable  1 2 3 4 5 
sex  0.127 0.132 0.115 0.148 0.115 
  (0.005) (0.005) (0.005) (0.013) (0.005) 
       
age  0.070 0.069 0.055 0.055 0.055 
  (0.001) (0.001) (0.001) (0.001) (0.001) 
       
agesq  -0.001 -0.001 -0.001 -0.001 -0.001 
  (0.000) (0.000) (0.000) (0.000) (0.000) 
       
currently  married  -0.040 -0.029 -0.019 -0.019 -0.019 
  (0.005) (0.005) (0.005) (0.005) (0.005) 
       
married  x  sex  0.168 0.168 0.131 0.130 0.131 
  (0.007) (0.007) (0.007) (0.007) (0.007) 
       
number  of  children  -0.050 -0.045 -0.021 -0.022 -0.021 
  (0.003) (0.003) (0.003) (0.003) (0.003) 
       
number  of  children  x  sex  0.052 0.050 0.038 0.038 0.038 
  (0.004) (0.004) (0.003) (0.003) (0.003) 
       
health  -0.041 -0.042 -0.028 -0.027 -0.028 
  (0.002) (0.002) (0.002) (0.002) (0.002) 
       
union  0.157 0.170 0.153 0.154 0.153 
  (0.004) (0.004) (0.004) (0.004) (0.004) 
       
hidegree  0.807 0.771 0.436 0.435 0.436 
  (0.011) (0.011) (0.011) (0.011) (0.011) 
       
degree  0.496 0.476 0.277 0.308 0.277 
  (0.005) (0.005) (0.005) (0.014) (0.005) 
       
nursingq  0.473 0.457 0.234 0.235 0.234 
  (0.015) (0.015) (0.014) (0.014) (0.014) 
       
alevels  0.303 0.296 0.186 0.183 0.186 
  (0.007) (0.007) (0.006) (0.006) (0.006) 
       
olevels  0.212 0.205 0.135 0.133 0.135 
  (0.006) (0.006) (0.005) (0.005) (0.005) 
       
othqual  0.128 0.124 0.087 0.087 0.087 
  (0.008) (0.007) (0.007) (0.007) (0.007) 
       
ln  unemployment  -0.048 -0.035 -0.023 0.017 -0.052 
  (0.007) (0.018) (0.016) (0.018) (0.023) 
       
constant  1.644 1.623 1.534 1.379 1.586 
  (0.024) (0.048) (0.045) (0.112) (0.054) 
       
between  individual  variance  0.193 0.187 0.153 0.153 0.153 
  (0.001) (0.001) (0.001) (0.001) (0.001) 
       
between  region  variance    0.007 0.005 0.005 0.005 
    (0.003) (0.002) (0.002) (0.002) 
       
       
log  likelihood  -39109.25 -38063.17 -31533.32 -31441.26 -31531.82 
Note: Standard errors in parentheses. Coefficients on sex, degree, and lnu in column 4 refer to the year 
1992; interactions between these variables and year dummies are not reported for reasons of space, but 
are commented on in the text. All equations include year dummies. Columns 3-5 include occupation 
and industry dummies. Column 4 includes a variety of slope dummies discussed in the text. Column 5 
employs an instrumented measure of unemployment. 

and 1995, the slope dummy coefficients lie in the range –0.057 through –0.072; thereafter they lie in the range –0.030 through –0.046. All are significant. Baltagi,

Disaggregated wage curves in the United States: evidence from panel data of young workers.

Earnings curves and wage curves.

How flexible are wages in EU accession countries?

Labor market slack and the wage curve.

Multilevel covariance component models.

Multilevel statistical models (third edition),

Random group effects and the precision of regression estimates.

Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations.

Statistical modelling of data on teaching styles,

The German wage curve: evidence from the IAB employment sample.

The last word on the wage curve?

The Spanish wage curve 1994-1996.

The wage curve reloaded.

The wage curve,

The wage curve: a review.

Wage curve analyses of establishment data from

Wage curve evidence from panel data.

Wage curve for urban China: a panel data approach.

Wage equations, wage curves and all that.

Wage flexibility: evidence from five EU countries based on the wage curve.

The wage curve revisited: estimates from a UK panel

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The wage curve revisited: estimates from a UK panel

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