Pär Österholm
email: par.osterholm@nek.uu.se

-Time-Series Models < C3 -Econometric Methods: Multiple/Simultaneous Equation Models < C -Mathematical and Quantitative Methods, E31 -Price Level|Inflation|Deflation < E3 -Prices, Business Fluctuations, and Cycles < E -Macroeconomics and Monetary Economics, E43 -Determination of Interest Rates|Term Structure of Interest Rates < E4 -Money and Interest Rates < E -Macroeconomics and Monetary Economics

Keywords: Unit root, Mean reversion, Fisher hypothesis JEL Classification: C22, C32, E31, E43 Unit root, Mean reversion, Fisher hypothesis

This paper investigates the time-series properties of Norwegian inflation and nominal interest rate using annual data from 1850 to 2004. A number of different univariate unitroot tests are employed to examine whether the time series are mean reverting or generated by unit-root processes. Results show very strong evidence in favour of mean reversion in inflation but a unit root in the nominal interest rate. This implies that there exists no long-run relationship between these two variables, a conclusion which is further supported by cointegration tests and estimated vector error correction models. The cointegration analysis also points to an important potential pitfall when using cointegration techniques on systems where some variables are stationary processes.

Introduction

The time-series properties of nominal interest rates and inflation have been a field of much empirical research. This focus is not surprising since the time-series properties in many cases can provide important information regarding the relevance of different economic hypotheses. For example, with a foundation in the efficient market hypothesis, it can be argued that the nominal interest rate should be generated by a unit-root process. A potential unit root in the nominal interest rate also raises the question of a unit root in inflation. As it is commonly assumed in the literature -see, for example, [START_REF] Fama | Short-Term Interest Rates as Predictors of Inflation[END_REF] and [START_REF] Crowder | The Long-Run Relationship between Nominal Interest Rates and Inflation: The Fisher Equation Revisited[END_REF] -that the real interest rate is either constant or a stationary process, the nominal interest rate and inflation need to be integrated of the same order for the Fisher hypothesis to be empirically relevant. 1 However, the time-series properties of these variables are not only interesting for distinguishing between different economic hypotheses, they can also determine which methodological approaches could be employed to test a particular hypothesis. For example, cointegration techniques -which are associated with a number of advantages -can be used when variables are generated by unit-root processes. Accordingly, knowledge about the presence or absence of unit roots in inflation and interest rates are important from several perspectives. This paper aims to establish the time-series properties of Norwegian inflation and nominal interest rate. There is little previous research addressing this question but given the interesting historical features of the Norwegian economy -for example, the low rate of unemployment during the 1970s and 1980s when making international comparisons and the development of a substantial oil sector since the early 1970s -there are reasons to investigate the behaviour of these key variables more closely. In particular, we will focus on whether inflation and the nominal interest rate are mean reverting or unit-root processes. This will be done by employing a range of univariate unit-root tests to the two series. Relying on unit-root tests for inference, this paper is similar to a reasonably large literature in this field; see, for example, [START_REF] Campbell | Yield Spreads and Interest Rate Movements: A Bird's Eye View[END_REF], [START_REF] Culver | Is there a Unit Root in the Inflation Rate? Evidence from Sequential Break and Panel Data Models[END_REF], [START_REF] Wu | Mean Reversion of Interest Rates in the Eurocurrency Market[END_REF], [START_REF] Charemza | Is Inflation Stationary?[END_REF] and [START_REF] Basher | Is there Really a Unit Root in the Inflation Rate? More Evidence from Panel Data Models[END_REF].

A novelty of this paper is the dataset used; we apply the unit-root tests to a very long 1 Whilst a constant or mean-reverting real interest rate has found plenty of support in the literature and is a common modelling choice, this assumption has also been questioned; see, for example, [START_REF] Mills | An Empirical Analysis of the UK Treasury Bill Market[END_REF] and [START_REF] Rose | Is the Real Interest Rate Stable?[END_REF]. long sample has benefits from an econometric point of view. It is well-known that for the sample sizes typically available in macroeconomics, the power of Dickey-Fuller type unitroot tests is generally low for highly persistent, but stationary, time series; see, for example, [START_REF] Froot | Perspectives on PPP and Long-Run Real Exchange Rates[END_REF]. By using longer series, we should hence improve the power of the tests. This point is particularly interesting when considering the commonly stated claim that it is the span of the data -rather than sampling frequency -that is most important for being able to distinguish if a time series has a unit root or is stationary. 2 Apart from establishing the univariate time-series properties of the two variables, this paper also aims to relate the two variables to each other. The main question in this aspect will be the relevance of the Fisher hypothesis. Both the unit-root tests and cointegration analysis will be used for this purpose.

Results from the unit-root tests unambiguously support the conclusion that the nominal interest rate is generated by a unit-root process, whereas inflation is stationary. These results are further confirmed by the cointegration analysis and estimated vector error correction models. This implies that the traditional Fisher hypothesis is not supported by the Norwegian data. 3 Moreover, the analysis based on vector error correction models also points to an important potential pitfall: Using cointegration techniques on systems where some variables may be stationary processes, both the number of cointegrating vectors and restrictions on these vectors should be carefully investigated.

The rest of this paper is organised as follows. In Section two, data are presented and unitroot tests and cointegration analysis are conducted. Section three concludes.

Empirical analysis

The empirical analysis uses annual data on Norwegian nominal interest rate and CPI inflationt i and t respectively -from 1850 to 2004. The nominal interest rate is given by the yield on the most actively traded maturities of long-term government bonds;

2 An early reference pointing this out is [START_REF] Shiller | Testing the Random Walk Hypothesis: Power versus Frequency of Observation[END_REF] 3 As a comparison to the results based on the Norwegian dataset, we also conduct the same analysis using monthly US data ranging from April 1953 to July 2005.

Unit roots or mean reversion

Turning to the empirical analysis of the data, we initially investigate the time series using five different unit-root tests: The Augmented Dickey-Fuller test [START_REF] Said | Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order[END_REF], the [START_REF] Phillips | Testing for Unit Roots in Time Series Regression[END_REF] (PP) test, the [START_REF] Kapetanios | Testing for a Unit Root in the Nonlinear STAR Framework[END_REF] test, the [START_REF] Zivot | Further Evidence on the Great Crash, the Oil-Price Shock and the Unit Root Hypothesis[END_REF] test and the KPSS [START_REF] Kwiatkowski | Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure are We That Economic Time Series Have a Unit Root?[END_REF] test. The number of unitroot tests available for an empirical analysis of this kind is very large and the choice of which to use is clearly arbitrary. However, we believe that the five tests chosen here provide a sensible range as they address three different issues that could be important. [START_REF] Michael | Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation[END_REF]. Third, by employing the Zivot and Andrews test -where we allow for an endogenously determined breakpoint in the intercept -the poor power of Dickey-Fuller type tests when structural breaks are present is addressed. 4 As a general principle, we do believe that structural breaks too often are used with the benefit of hindsight to control for something that was difficult to anticipate and that it therefore should be used very restrictively in empirical work. 5 We will, however, nevertheless allow for a break in the intercept of the time series in question to ensure that our conclusions are robust to that possibility. Taken together, we conclude that the tests actually employed in this paper appear well-suited for our purpose.

F

As all tests -except the [START_REF] Kapetanios | Testing for a Unit Root in the Nonlinear STAR Framework[END_REF] (KSS) test -have been standard tools in the macroeconomic literature for more than a decade now, they will not be presented to the reader. We will, however, describe the KSS test a little more closely. This tests the null hypothesis of a unit root against the alternative hypothesis of a globally stationary exponential smooth-transition autoregressive (ESTAR) process. 6 The test is based on estimation of ,

1 3 1 = + + = s j t j t j t t x x x
(1) 4 See, for example, [START_REF] Perron | The Great Crash, the Oil-Price Shock, and the Unit Root Hypothesis[END_REF]. 5 Moreover, unit-root tests that allow for structural breaks -such as [START_REF] Perron | The Great Crash, the Oil-Price Shock, and the Unit Root Hypothesis[END_REF], [START_REF] Zivot | Further Evidence on the Great Crash, the Oil-Price Shock and the Unit Root Hypothesis[END_REF] and [START_REF] Vogelsang | Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time[END_REF] -have some well-documented shortcomings. One well-known problem is the risk of spurious rejection of the null hypothesis when the breakpoint is chosen endogenously; see, for example, [START_REF] Nunes | Testing for Unit Roots with Breaks: Evindence on the Great Crash and the Unit Root Hypothesis Reconsidered[END_REF] and [START_REF] Lee | Break Point Estimation and Spurious Rejections with Enodgenous Unit Root Tests[END_REF]. 6 In an ESTAR model, the speed of mean reversion is not constant. Instead, the process can display unit root behaviour in the region close to its equilibrium but strong mean reversion when the process is far from its mean. interest rate and inflation appear to be integrated of different orders is interesting as we relate it to the Fisher hypothesis. As pointed out by, for example, Crowder and Hoffman (1996, p. 103), such a finding implies that "… the textbook representation of the Fisher hypothesis may be rejected out of hand".

F

The results for the United States are equally conclusive regarding the nominal interest rate -all five tests conclude that this is a unit root process. For the inflation rate though, we find that the US data have very different properties to the Norwegian. Whilst the results are a touch less conclusive, since only four out of five tests agree, we still believe that there is fairly strong evidence in favour of a unit root in the US inflation rate. 8 Given that the nominal interest rate and inflation appear to be integrated of the same order, there is clearly a possibility that the Fisher hypothesis is valid in the United States. With these findings in mind we next turn to a closer inspection of how nominal interest rates and inflation relate to each other, with a particular focus on the Fisher hypothesis.

The Fisher hypothesis

A traditional formulation of the Fisher hypothesis is that the expected nominal interest rate over the period is equal to the expected real interest rate plus expected inflation. Relying on the commonly made assumption of a constant or mean-reverting real interest rate, an empirical version of the Fisher hypothesis can be written as

t t t v r i + + = * , ( 2
)
where the constant * r has the interpretation of the equilibrium real interest rate, the error term t v is assumed to be a stationary ARMA process and should be equal to unity; see, for example, MacDonald and Murphy (1989).9 Given the high persistence of nominal interest rates and inflation in many countries, a popular approach to test the Fisher hypothesis in more recent years has been to employ cointegration techniques; see, for example, [START_REF] Atkins | Co-Integration, Error Correction and the Fisher Effect[END_REF], [START_REF] Macdonald | Testing the Long Run Relationship between Nominal Interest Rates and Inflation Using Cointegration Techniques[END_REF], [START_REF] Mishkin | Is the Fisher Effect for Real?[END_REF], [START_REF] Wallace | The Fisher Effect and the Term Structure of Interest Rates: Test of Cointegration[END_REF], [START_REF] Evans | Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation?[END_REF]Lewis (1995), Crowder and[START_REF] Crowder | The Long-Run Relationship between Nominal Interest Rates and Inflation: The Fisher Equation Revisited[END_REF], [START_REF] Payne | Evidence from Lesser Developed Countries on the Fisher Hypothesis: A Cointegration Analysis[END_REF], [START_REF] Junttila | Testing an Augmented Fisher Hypothesis for a Small Open Economy: The Case of Finland[END_REF] and [START_REF] Rogoff | Fisher Hypothesis: UK Evidence over a Century[END_REF]. Usage of cointegration techniques makes sense to some extent as it has been pointed out that the Fisher hypothesis is better interpreted as a long-run equilibrium condition [START_REF] Summers | The Nonadjustment of Nominal Interest Rates: A Study of the Fisher Effect[END_REF]). As stated above, a necessary condition for this modelling choice to be relevant is that both inflation and the nominal interest rate are unit root processes. The results presented above indicate that this appears to be true for the United

States, but for Norway there is extremely strong evidence that the nominal interest rate and inflation have different orders of integration. Let us nevertheless turn to cointegration analysis to see if this can provide us with further information.

A cointegrated vector autoregression (VAR) can be written as

t p j j t j t t y F y y + + + = = 1 1 1 , (3)
where t y is an nx1 vector of variables that are assumed to be integrated of order one and t is a nx1 vector of innovations. Particular attention is paid to the rank of the matrix as this matrix will have reduced rank if the variables of the system are cointegrated; the rank will be equal to the number of cointegrating vectors. It should also be noted that only can have full rank if all variables in the system are stationary; see [START_REF] Taylor | The Behaviour of Real Exchange Rates During the Post-Bretton Woods Period[END_REF] and Österholm (2004).

Turning to our particular application, we can -if the nominal interest rate and inflation both are integrated of order one, and moreover, cointegrated -write the system as

+ + + = = t i t p j j t j t j ij j i iij t t t t i f f f f i i 1 1 1 1 (4)

=

. Regarding the constant, , a restriction has been imposed such that we do allow for an intercept in the cointegrating relationship but no drift in the variables.

Before estimating a cointegrated VAR though, we must first establish i) lag length for the VAR and ii) the number of cointegrating vectors. Lag length was determined by employing the [START_REF] Akaike | A New Look at the Statistical Model Identification[END_REF] information criterion to the bivariate VAR in levels. Testing for cointegration using the [START_REF] Johansen | Statistical Analysis of Cointegration Vectors[END_REF][START_REF] Johansen | Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models[END_REF] trace and maximum eigenvalue tests, we find that both the trace and maximum eigenvalue tests conclude that there is one cointegrating vector for Norway as well as the United States. Test statistics are reported in Table 2. Note also that these cointegration tests show that both variables cannot be stationary in either country as the rank then would be equal to two. . This yields an estimate of the cointegrating vector 10 of ( )

466 . 1 1 ˆ =
. This estimate appears encouraging, as it is not very far from the most traditional interpretation of the Fisher hypothesis which suggests the cointegrating vector ( )

1 1 =
. We therefore next impose this restriction on the cointegrating vector and test whether the restriction is rejected by the data using a likelihood ratio test. Doing this, we find that the test statistic is 0.708; since the test statistic follows a 2 -distribution with one degree of freedom, the restriction is not rejected at the five percent level. 10 The constant term has been omitted for notational convenience. ( )

1 0 =
, which are shown in Table 3, are both clearly larger than the critical value from a 2 -distribution with one degree of freedom.

Summing up, it hence seems that cointegration techniques provide an appropriate tool for the empirical analysis of the US data, since both the nominal interest rate and inflation appear to be I(1). In addition to cointegration between US nominal interest rate and inflation providing support for the Fisher hypothesis, we also find that the most traditional interpretation cannot be rejected by the data.

Conclusions

This paper has investigated the time-series properties of Norwegian inflation and nominal interest rate using annual data from 1850 to 2004, employing both univariate unit-root tests and cointegration analysis. Our results unequivocally support the conclusion that Norwegian inflation is mean reverting whereas the interest rate is a unit-root process. This implies that the real interest rate is not a mean-reverting process -a finding in line with those of [START_REF] Rose | Is the Real Interest Rate Stable?[END_REF]. The findings in this paper also raise questions regarding previous studies that have relied on cointegrating methods despite having found evidence of stationarity of the included variables; see, for example [START_REF] Crowder | The Long-Run Relationship between Nominal Interest Rates and Inflation: The Fisher Equation Revisited[END_REF] and [START_REF] Rogoff | Fisher Hypothesis: UK Evidence over a Century[END_REF]. We have shown that great care should be taken when cointegration techniques are applied to systems where some variables may be stationary processes. In particular, the cointegrating rank of the system, estimates of the cointegrating vectors and potential restrictions on these vectors are issues that all should be carefully scrutinised.

  data from 1850 to 2004 of the variables in question. Usage of such a

  Figure 2.

Figure 1 .Figure 2 .

 12 Figure 1. Time-series plots of Norwegian interest rate and inflation 1850 to 2004.

  for Norway and the United States respectively.

  First, the first four tests test whether the time series in question has a unit root versus the alternative hypothesis of stationarity; the KPSS test on the other hand reverses the burden of proof as it has mean reversion under the null hypothesis. Second, the KSS test offers a method to test for potential non-linear mean reversion, a data generating process which standard unit root tests tend to have poor power properties against; see, for example,

	o r
	P
	e
	e r
	R
	e
	v i e
	w
	6

  -statistic on ˆ. The null hypothesis of a unit root is rejected for large negative values of the test statistic; critical values can be found in Kapetanios et al.In the ADF, Zivot and Andrews and KSS tests, we must first determine lag length in the test equations. For the ADF and Zivot and Andrews tests, we employed the[START_REF] Akaike | A New Look at the Statistical Model Identification[END_REF] information criterion for this purpose. Regarding lag length in the KSS test regressions,

	where t x refers to demeaned values of the original time series, t x ~ and t	iid	( ) 2 , 0	. 7 For
	all time series under investigation, the null hypothesis	H	0	:	=	0	is then tested versus
	0 using the t(2003). : 1 < H
	o r
			P
			e
			e r
	i	t	Norway	R e t		i	t	United States	t
	ADF PP KSS ZA KPSS 0.491 Turning to the results for Norway first, Table 1 presents what must be described as -2.406 -6.298 * -1.904 -3.072 * v -1.988 -6.259 * -1.706 -2.432 i -2.873 -6.446 * -2.836 -2.529 e -2.300 -6.913 * -3.105 -4.004 w 0.553 * 0.395 0.813 *
	overwhelming evidence in favour of a unit root in the nominal interest rate and mean
	reversion in inflation. It is interesting to note that all five tests reach the same conclusion
	regarding each time series; such conclusive evidence is only rarely presented when

this was set equal to that of the ADF test.

[START_REF] Kapetanios | Testing for a Unit Root in the Nonlinear STAR Framework[END_REF]

pointed out that linear dynamics can be seen as a first-order approximation if the true augmentations are nonlinear in nature. For the PP and KPSS tests, a Newey-West estimator was employed to correct for serial correlation in the residuals. All tests are conducted allowing for mean reversion around a constant level different from zero. We do not allow for any time trends, as we argue that linear time trends in nominal interest rates or inflation are inconsistent with economic theory. Results from the unit-root tests can be found in Table

1

. Table 1. Results from unit-root tests. * ADF, PP, KSS, ZA and KPSS are the test statistics from the Augmented Dickey-Fuller, Phillips and Perron, Kapetanios et al., Zivot and Andrews and KPSS tests respectively. * significant at the 5% level different tests are applied to a macroeconomic time series. The finding that the nominal 7 The value of the delay parameter has been set to 1 = d

. Just like

[START_REF] Taylor | Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles[END_REF]

, we believe that that the delay parameter should be small.

Table 2 .

 2 Results from cointegration tests.

											Norway	United States
								J	trace	J	max	J	trace	J	max
	H	0	:	r	=	0		41.296 *	38.015 *	23.156 *	18.168 *
	H	0	:	r	=	1		3.281	3.281	4.988	4.988
	significant at the 5% level
	We next estimate the model in equation (4) for Norway, with one cointegrating vector and
	lag length set to	p	1 =	1

trace J is the test statistic from Johansen's trace test for cointegrating rank. max J is the test statistic from Johansen's maximum eigenvalue test for cointegrating rank. *

Table 3 .

 3 Results from testing restrictions on the cointegrating vector.

	= = =	( 1 ( ) 1 ) 0 1 ( ) 1 0	Norway 0.708 34.728 * 3.006	United States 1.555 13.155 * 6.441 *

* significant at the 5% level

This finding would be consistent with the viewpoint of, for example,[START_REF] Cogley | Evolving Post-World War II U.S. Inflation Dynamics[END_REF] and[START_REF] Stock | Has Inflation Become Harder to Forecast?[END_REF] that US inflation is a unit root process.

Note that even though the constant is interpreted as the equilibrium real interest rate in this setting, this does not mean that this variable needs to be stationary in practice. A unit root in the equilibrium real interest rate could accordingly be one reason for failing to find cointegration between the nominal interest rate and inflation.

So far it seems that the cointegration analysis has lent strong support for the Fisher hypothesis on the Norwegian data. One cointegrating vector was found in the system and we could not reject the hypothesis that this vector is ( )

. However, in this particular application we have -based on the unit-root tests -very strong reason to suspect that inflation is not a unit-root process. As stated above, this leads us to question the above finding that there is cointegration between inflation and the nominal interest rate above.

In order to establish whether the above finding of cointegration between Norwegian nominal interest rate and inflation is for real, we suggest that a final restriction should be tested. If the nominal interest rate is a unit-root process and inflation truly is stationary, we should not only find -which has been done above -that the matrix has rank one but also be unable to reject the restriction ( )

. This restriction implies that inflation alone provides a cointegrating vector and the interpretation accordingly that it is stationary. Estimating the model with the restriction ( )

imposed, we find a test statistic of 3.006. As the test statistic follows a 2 -distribution with one degree of freedom, the null hypothesis can not be rejected at the five percent level. 11 Our conclusion is hence that the above result of cointegration between the nominal interest rate and inflation in Norway is not a relevant finding. All evidence support that the nominal interest rate and inflation are integrated of different orders; no long-run equilibrium relationship can therefore exist between the two.

Finally, the model in equation ( 4), with one cointegrating vector and a lag length of

, is estimated on the US data. The estimated cointegrating vector is

and when the restriction ( )

is tested, the null hypothesis cannot be rejected. Recalling that we found some evidence of stationarity of the US inflation rate though, we should obviously scrutinise these results further. However, unlike what we found using the Norwegian data, stationarity of both US nominal interest rate and 11 We could -despite the overwhelming evidence from the unit root tests -also test the hypothesis ( )

to investigate whether the nominal interest rate is judged stationary. Doing this, we get a test statistic of 34.728; this null hypothesis is hence forcefully rejected by the data.


Santiago Budría
email: sbudria@uma.pt.

Rita Asplund

Ali Skalli

Earling Barth

Grijander Mor

Peter Dolton

IN THE EUROPEAN PRIVATE AND PUBLIC SECTORS Santiago

Keywords: D31 -Personal Income, Wealth, and Their Distributions &lt, D3 -Distribution &lt, Returns to schooling, Quantile regression, Within-groups wage inequality Returns to schooling, Quantile regression, Within-groups wage inequality. JEL classification: D31, I21, J45

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. Introduction

This paper intends to shed further light on the interplay between schooling and within-groups wage dispersion using recent data from eight European countries: Finland, France, Germany, Italy, Norway, Portugal, Sweden and the UK. Up to date, the inequality implications of schooling have not been compared between the private and public sectors: while the impact of schooling on within-groups dispersion has been well documented for the private sector, evidence for the public sector is mostly lacking 2 . This paper takes a step towards filling this gap by asking: does the conditional wage distribution of education groups, and thus the impact of schooling on within-groups dispersion, differ across sectors?

The public sector has always attracted policy attention. The government is typically the largest employer in the economy and, as such, its wage settlements can exert a strong influence on those in the private sector. Despite recent efforts to increase both competition and efficiency of the public sector, most economies still see significant differences between the two sectors regarding the criteria adopted to select, recruit and promote workers, the adjustment of wage levels, the degree of regulation, and the role of collective bargaining and trade unions, thus resulting into a different distribution of earnings across sectors. As the public and the private sector compete on the labour market, differences in the wage structure may have important implications for the sorting of workers across sectors, the demand for certain types of qualifications, and the overall wage inequality.

The existing literature on wage distributions in the public and private sectors is predominantly based on the public sector pay premium [START_REF] Terrell | Public-Private Wage Differentials in Haiti: Do Public Servants Earn a Rent?[END_REF], Hartog and Oosterbeck, 1993[START_REF] Poterba | The Distribution of Public Sector Wage Premia: New Evidence Using Quantile Regression Methods[END_REF][START_REF] Dustmann | Wage Structures in the Private and Public Sectors in West Germany[END_REF], 1998, Disney and Gosling, 1998, Mueller, 2 [START_REF] Buchinsky | Changes in the US Wage Structure 1963-1987: Application of Quantile Regression[END_REF] pools together private and public servants and, therefore, does not differentiate between sectors. [START_REF] Hartog | Changing Returns to Education in Portugal during the 1980s and Early 1990s: OLS and Quantile Regression Estimators[END_REF], [START_REF] Machado | Counterfactual Decomposition of Changes in Wage Distributions using Quantile Regression[END_REF], [START_REF] Martins | Does Education Reduce Wage Inequality? Quantile Regressions Evidence from Fifteen European Countries[END_REF], and [START_REF] Budría | The Impact of Educational Qualifications on Wage Inequality: Evidence for Europe[END_REF], in turn, restrict the analysis to private sector workers. [START_REF] Tansel | Public-Private Employment Choice, Wage Differentials and Gender in Turkey[END_REF][START_REF] Melly | Public-Private Sector Wage Differentials in Germany: Evidence from Quantile Regression[END_REF]. The perspective of this paper is slightly different. Rather than calculating the wage differential between private and public sector workers for the total working population or for specific population groups, the paper examines wage differences within education groups in the private and the public sector. Unlike previous work, this paper does not attempt to examine the impact of public sector status on the conditional wage distribution.

Rather, it describes and compares the effects of schooling on the conditional distribution of each sector.

To that purpose, the paper exploits the following idea: schooling, rather than assuring a certain amount of earnings, gives access to a distribution of earnings. That distribution is characterized using Ordinary Least Squares (OLS) and Quantile Regression (QR) methods. Estimation by OLS assumes that the marginal impact of schooling on wages is constant over the wage distribution. In this case, the effect of having one additional year of schooling can be represented by a shift (to the right) of the conditional wage distribution. Quantile returns, in turn, measure the wage effects of schooling at different points of the distribution, thus describing changes not only in the location but also in the shape of the distribution. By combining OLS with quantile regression, we can assess the impact of education on wage inequality between and within groups: while OLS returns measure the average differential between education groups, differences in quantile returns represent the wage differential between individuals that are in the same group but located at different quantiles.

The rest of the paper is organized as follows. Section II describes the countries, datasets and variables used for the analysis. Overall wage inequality in Europe is described by reporting several measures of unconditional dispersion for the surveyed countries. Section III presents the quantile regression model. Section IV presents average and quantile estimates of the returns to schooling. Differences between sectors regarding the impact of schooling on wage dispersion Section VI presents the concluding remarks. The paper includes an Appendix that describes the national data sources and estimating samples.

II. Countries, datasets and variables

We collect data on earnings and education for Finland, France, Germany, Italy, Norway, Portugal, Sweden and the UK. This was achieved under the framework of a research project, 'Education and Wage Inequality in Europe' (EDWIN), where each country team analyzed their country datasets3 . In the Appendix, we briefly describe such datasets, including the years for which the information applies, the number of observations used, and additional information concerning country-specific definitions of variables.

We use the same estimation procedure and population group for all countries. We have restricted the sample to male wage earners, aged between 18 and 60, who work normally between 35 and 85 hours a week, and are not employed in the agricultural sector. Self-employed individuals, as well as those whose main activity status is paid apprenticeship, training, and unpaid family worker have been excluded from the sample. The case of women is disregarded on account of the extra complication of potential selectivity bias. Workers with a monthly wage rate that is less than 10% or over 10 times the average wage have also been excluded.

The dependent variable is the logarithm of hourly wages. Wages are measured before taxes in Finland, France, Germany, Norway, Sweden and the UK, and after taxes in Italy and Portugal.

Even though the aim of the paper is not to conduct a thorough comparison across countries, differences in the dependent variable should be taken into account when comparing the results. professional experience. Average schooling years are well above ten years, with the exception of Portugal, while experience levels are about 20 years in all countries. The last four columns report the ratios between wages at different deciles of the wage distribution and the Gini indexes. Wages at the 9 th decile are between two and three times larger than wages at the 1 st decile. The 9/5 ratio is higher than the 5/1 ratio in most cases, indicating that in Europe wage dispersion is relatively larger in the top part of the wage distribution. Relative to workers in the private sector, public sector servants are more educated, have more experience, and with the exception of Portugal and Sweden, show lower wage dispersion.

----------Insert Table 1 about here -------

III. The model

The quantile regression model can be written as where X i is the vector of exogenous variables and is the vector of parameters 4 . Quant (ln w i | X i ) denotes the th conditional quantile of ln w given X. The th regression quantile, 0< <1, is defined as a solution to the problem 4 For a survey of quantile regression models and some applications, see [START_REF] Buchinsky | Recent advances in quantile regression models: a practical guideline for empirical research[END_REF][START_REF] Fitzenberger | Economic Applications of Quantile Regression[END_REF], and [START_REF] Koenker | Quantile regression: An Introduction[END_REF].

(1) with

i i i i i i X ) |X w ln ( Quant e X w ln = + = F o r P e e r R e v i e w 6
This problem is solved using linear programming methods. Standard errors for the vector of coefficients are obtainable by using the bootstrap method described in [START_REF] Buchinsky | Recent advances in quantile regression models: a practical guideline for empirical research[END_REF]. Our wage equation includes years of schooling, experience and experience squared, where = .1, .2, …, .9 is the quantile being analyzed. This parsimonious specification is a working compromise to have a common equation for all countries, as some typical variables in wage equations -such as tenure, occupation and part-time job-were not available in some of the national datasets. Moreover, according to the meta-analysis conducted by [START_REF] Pereira | Returns to education and wage equations[END_REF], the simplest Mincer specification suffices to provide a good approximation of the value for the total return to education. Finally, using years of schooling rather than levels of education facilitates the comparison with previous works, as most other papers are based on the former variable.

IV. Empirical results

In this section we calculate OLS returns to schooling as well as conditional returns at five representative quantiles: .10, .25, .50, .75, and .90. Henceforth, we will denote these quantiles by 10q, 25q, 50q, 75q and 90q.

Before presenting our results, it must be pointed out that some authors attempt to instrument (3)

2 i i 1 i 2 i i ln w years exp exp e = + + + + ) 2 ( X w ln ) (1 X w ln Min i i i i k x w ln : i x w ln : i i i i i R + < F o r P e e r R e v i e w
sector choice using some observable characteristics that are related to the sector status but unrelated to wages. Workers might be heterogeneous across sectors with respect to some unmeasured characteristics in a non-random way, such as risk aversion, motivation, preferences for public sector work, etc., and self-select themselves according to those features. If this is the case and these characteristics are related to wages, then standard estimates of the returns to observable characteristics may be biased. However, there is no consisting evidence that controlling for selection yields more reliable estimates. In general, the validity of the instruments is questionable, as it is not clear whether the variables that explain sector choice are excludable from the wage equation. Probably due to differences in the quality of the instruments, the magnitude of selection effects is found to vary considerably across studies.

With this in mind and given the impossibility to find valid instruments that are common to the surveyed countries, this paper disregards selection effects5 .

A. The private sector…

The first set of results is presented in Table 2. As expected, education gives a substantial reward in the labour market. The average return to an additional year of schooling ranges from 5.67% in Italy to 8.98% in Finland, at an average of 7.13%. In all countries, the estimated return is significant at the 1% level. However, the impact of schooling on wages is not constant over the wage distribution. The schooling coefficient is higher at the upper parts of the distribution than at the lower parts, meaning that workers at high-pay jobs earn substantially higher returns from schooling than workers at low-pay jobs. France and Portugal are two illustrative examples. In France an average return of 7.39% masks a return of only 4.10% in the first quantile and 9.77% in the top quantile. In Portugal, the average return is 7.31%. However, the returns at the bottom and the top of the distribution are, respectively, 5.17% and 8.10%.

----------Insert Table 2 about here -------This upward profile has two clear implications. First, the conditional wage distribution of more educated workers is more dispersed than the conditional wage distribution of less educated workers. This has been called 'the inequality increasing effect of education' (Machado and Mata, 2005, p. 457): if we give more education to workers who have the same observable characteristics but are located at different quantiles of the wage distribution, then their wages will become more dispersed. We show that, without exception, this phenomenon is regular across European countries. It may be the case, therefore, that by raising the weight of the highspread group, an educational expansion in Europe increases overall wage inequality through the within-dimension.

The second implication has to do with schooling as a risky investment. The unexplained component or earnings variation is frequently regarded in the literature as the amount of wage risk. In our setting, that risk can be measured by the differences in the returns across quantiles, as such differences are residual inequalities of pay after controlling for the effect of skill differences by regression results. Our results show that to the extent that prospective students are not aware of the characteristics which will place them at some point of the wage distribution, the returns to their educational investment are largely unpredictable 6 . 6 Including additional controls in the wage equation does not change the estimated wage risk by much. [START_REF] Hartog | Changing Returns to Education in Portugal during the 1980s and Early 1990s: OLS and Quantile Regression Estimators[END_REF] show that, even after controlling for a large set of observed individual and job characteristics, the variation of returns across quantiles is still large. This uncertainty has recently attracted the attention of researchers, as it may have important consequences on individual earnings levels and earnings growth [START_REF] Shaw | An empirical Analysis of Risk Aversion and Income Growth[END_REF][START_REF] Bonin | Cross-sectional Earnings Risk and Occupational Sorting: The Role of Risk Attitudes[END_REF], the wage structure (Hartog andVijverberg, 2002, Hartog et al., 2003) and the decision on extended schooling [START_REF] Hogan | Education Choice under Uncertainty: Implications for Public Policy[END_REF]Walker, 2003, Hartog and[START_REF] Hartog | Earnings Risk and Demand for Higher Education: A Cross-Section Test for Spain[END_REF]. To provide a more illuminating view, in Table 3 we report several measures of wage inequality based on different parts of the distribution. As mentioned above, dispersion across quantiles is substantial. Thus, for example, the return differential between the 90q and the 10q quantiles ranges from 6.01 percentage points in Sweden to 1.88 percentage points in Finland. This means that, relative to workers at low-pay jobs (10q), workers at high-pay jobs (90q) earn from university education (approximately 15 years of schooling) an additional return of 90 percentage points in Sweden and 28 percentage points in Finland. This excess return represents the inequality increasing effect of education or, alternatively, the amount of wage risk associated to schooling.

----------Insert Table 3 about here -------Using the information reported in Table 3, we can inspect to what extent the contribution to overall within-groups dispersion differs across segments of the wage distribution. Two patterns are apparent. First, in most countries, the 90q-10q differential more than doubles the 90q-50q differential. Thus, for example, in the UK and Portugal the 90q-10q spread is 6.1 and 4.6 times larger, respectively, than the 90q-50q spread. This indicates that conditional wage dispersion is higher at the bottom part of the wage distribution than at the upper part or, to put it different, that a significant amount of the wage dispersion within the educated arises from differences within individuals earning below-average returns. Italy and Norway, where dispersion is relatively larger at the top part of the wage distribution, are exceptions to the general pattern.

Second, with the exception of Germany, in all countries the 75q-25q spread accounts for a large fraction of the 90q-10q spread. Excluding Germany, this fraction ranges from 52% in France up to 91% in Finland. According to this, a substantial amount of the total wage dispersion among the educated takes place in the middle part rather than in the tails of the wage distribution.

B. …and the public sector

Next, we turn to the estimates for the public sector. As Table 4 shows, the average return to an additional year of schooling in the public sector ranges from 4.44% in Italy to 9.73% in Finland, and is statistically significant in all cases. Averaging across countries, the estimated return is 6.40%, a value that is 0.73 percentage points lower than in the private sector. This result is in line with Psacharopoulos' (1994) finding that, worldwide, returns to schooling are somewhat higher in the private sector than in the public sector.

----------Insert Table 4 about here -------More interestingly, we find that the tendency of education to be more valued at high-pay jobs is much less apparent in the public sector than in the private sector. As Table 5 shows, only in one country, Italy, returns at the upper quantiles are significantly higher than at the lower quantiles regardless of the quantiles selected. In Finland, France and Sweden, differences across quantiles are significant only when certain parts of the distribution are considered. In the remaining countries, Germany, Norway, Portugal and the UK, the estimated returns are fairly uniform over the conditional wage distribution, indicating that differences in wage dispersion across education groups are small and non-significant.

----------Insert Table 5 about here -------

C. Differences in wage dispersion and the shape of the conditional wage distributions

As is apparent from the previous analysis, the association between schooling and within-groups dispersion is much sharper in the private sector than in the public sector. To provide a quantitative assessment on this issue, we average across countries and find that while in the private sector the 90q-10q, 90q-50q, 75q-25q, and 75q-50q spreads are, respectively, 3.38, 1.58, 2.07 and 1.04, in the public sector these spreads fall to 1.50, 1.08, 0.58 and 0.54. Taking the 90q-10q as a reference, we can conclude that in Europe the effect of schooling on within-groups dispersion is, on average, more than two times larger in the private sector than in the public sector. It must be noted that Italy is an exception to the general pattern, as in this country wage inequality within the educated is larger in the public sector than in the private sector.

Next, we examine differences in the shape of the conditional distributions. To that purpose, Figure 1 plots the quantile-return profile in each sector. We detect two groups of countries. In France, Germany, Norway and Sweden the higher dispersion in the private sector is due to relatively large returns at the top part of the distribution. As opposite, in Finland, Portugal and the UK the higher dispersion within private sector workers is due to relatively low returns at the bottom part of the distribution.

----------Insert Figure 1 about here -------Institutional differences across countries seem to indicate that "a glass ceiling effect" characterizes the public sector in the first group of countries, while in the second group the public sector is better described by a "high floor effect". [START_REF] Poterba | The Distribution of Public Sector Wage Premia: New Evidence Using Quantile Regression Methods[END_REF], Disney and Gosling (1998), [START_REF] Mueller | Public-Private Sector Wage Differentials in Canada: Evidence from Quantile Regressions[END_REF], [START_REF] Melly | Public-Private Sector Wage Differentials in Germany: Evidence from Quantile Regression[END_REF] and, more recently, [START_REF] Papapetrou | The unequal distribution of the public-private sector wage gap in Greece: evidence from quantile regression[END_REF], use quantile regression to analyze the wage effects of having a public sector job. They show that, by offering a higher floor for the low skilled (those located at the lower quantiles) and imposing a lower ceiling to the high skilled (those located at the upper quantiles), the public sector compresses wages. Our results offer a complementary and novel view: as far as education is concerned, the public sector compresses wages by offering to the high-skilled (upper quantiles) a lower return to education and a higher return to the low-skilled (lower quantiles).

V. Discussion

Even though testing hypotheses is beyond the scope of this paper, we may advance some explanations that account for the lower dispersion in the public sector. Conditional on observable characteristics, those individuals that are located at higher quantiles of the earnings distribution have, presumably, more skills, where skills include ability, motivation, better academic credentials and other unobservable characteristics affecting productivity. The estimates show that while these favourable characteristics interact positively with schooling in the private sector, they are mostly innocuous in the public sector. A candidate explanation is that relative to the private sector, the public sector has a wider union presence and a more effective use of union power, less incentives relating wages to productivity, smaller monopsony and discrimination effects, and less flexibility in wage determination. Arguably, these factors conduct to a much flatter wage structure and, more specifically, to a more homogeneous reward to education.

A complementary view is that unobserved skills may be more evenly spread within the public sector, thus resulting into smaller differences within groups. The State may have some interest to be perceived as a "good employer" and, consequently, end up offering (relatively) high wages to unskilled workers and (relatively) low wages to the high-skilled. Such mechanism would create incentives for the most skilled to move on to the private sector and for the less skilled to enter in the public sector. Given the limited access to public sector jobs, these effects would result into a homogenization of skills in the public sector rather than in the private sector. This view is consistent with the evidence reported in [START_REF] Borjas | The Wage Structure and the Sorting of Workers into the Public Sector, in For the People: Can We Fix Public Service[END_REF], who shows that despite higher average wages, the US public sector finds it difficult to attract high-quality workforce due to lower earnings at the top part of the wage distribution.

VI. Conclusions

According to the international evidence, schooling exerts a positive impact on within-groups wage dispersion. This finding raises serious concerns about the inequality-reducing scope that is commonly attributed to schooling, as it suggests that an educational expansion may raise overall wage inequality. Most studies, however, are based on private sector data and, up to date, the inequality implications of schooling among public servants are mostly unknown. This is somewhat surprising, as more than one fifth of the European labour force works in public sector jobs.

In this paper we asked: does the conditional wage distribution of education groups differ between the private and public sectors? To answer this question, we used recent comparable data from eight European countries. Drawing on quantile regression, we showed that in the private sector schooling has an effect on the location as well as on the shape of the conditional wage distribution: conditional on observable characteristics, educated workers display higher wages and higher wage dispersion. In the public sector, in turn, the effect of schooling is on the location rather than on the shape of the distribution: conditional on observable characteristics, educated workers display higher wages but not necessarily higher wage dispersion. This result warns that the positive association between education and within-groups wage inequality reported by previous work does not generally apply to the public sector.

A limitation of our study is that, given the international coverage of the paper, we do not explore selection effects nor do we control for the endogeneity of schooling. These extensions are considered outside the scope of the present paper, which concentrates on distributional aspects.

Our results have several implications. First, the allocation of qualified workers between the private and the public sector is important in shaping overall wage inequality. It has been documented that a large fraction of university graduates end up in public sector employment [START_REF] Blank | An analysis of workers' choice between employment in the public sector and private sectors[END_REF][START_REF] Terrell | Public-Private Wage Differentials in Haiti: Do Public Servants Earn a Rent?[END_REF][START_REF] Disney | Does It Pay to Work in the Public Sector?[END_REF]. Given the lower dispersion in this sector, the effects of the European educational expansion on overall wage dispersion may be smaller than previously thought 7 . We think that it is high time that sector effects were explicitly taken into account when inspecting how changes in education groups and the market price of education have affected the European earnings distribution over the last years. Second, differences in the shape of the distributions may importantly affect the sorting of workers across sectors. [START_REF] Belman | Government wage differentials: a sample selection approach[END_REF] find evidence that workers self select by systematically locating in the sector that offers them the higher expected wage. In the same vein, [START_REF] Borjas | The Wage Structure and the Sorting of Workers into the Public Sector, in For the People: Can We Fix Public Service[END_REF] shows that transitions between the public and private sectors are strongly influenced by the distribution of wages in each sector. In this paper we showed that high-skill individuals -further to the right of the conditional wage distribution-obtain larger returns from their educational investment. This effect is large in the private sector and small in the public sector. It is likely, therefore, that the European Union public sector finds it difficult to attract high-skill workers and to prevent high-skill workers from quitting and moving on to the private sector. Extending Borjas's analysis to European countries would prove fruitful to evaluate the size of these filter effects.

The third implication has to do with the demand for education. [START_REF] Bonin | Cross-sectional Earnings Risk and Occupational Sorting: The Role of Risk Attitudes[END_REF]

  Section V outlines some hypothesis that may account for the observed patterns.

FiguresFigure

  Figures

  Table 1 presents descriptive statistics for each country. The first column reports the proportion of the sample individuals working in each sector. Public servants account for 17.3% in Finland up to 26.7% in Norway. The next columns report the average number of schooling years and

Table 1 . Descriptive statistics

 1 find strong evidence that risk averse individuals have preferences for occupations with less dispersion.According to this, risk averse individuals may be inclined to choose education careers that are oriented towards public sector work.

	F o r
	P
	e
	e r
	R e v
	i e
	w

Table 2 . Average and quantile returns to schooling -Private sector

 2

		OLS	10q	25q	50q	75q	90q
	Finland	8.98 ***	7.95 ***	7.95 ***	8.85 ***	9.66 ***	9.83 ***
		(.33)	(.74)	(.41)	(.22)	(.33)	(.52)
	France	7.39 ***	4.10 ***	5.78 ***	7.30 ***	8.72 ***	9.77 ***
		(.11)	(.16)	(.14)	(.10)	(.14)	(.18)
	Germany	7.04 ***	4.66 ***	6.24 ***	6.53 ***	7.25 ***	7.87 ***
		(.33)	(.82)	(.51)	(.34)	(.27)	(.46)
	Italy	5.67 ***	5.01 ***	4.45 ***	4.80 ***	5.74 ***	6.99 ***
		(.25)	(.51)	(.38)	(.28)	(.33)	(.38)
	Norway	7.95 ***	6.24 ***	6.30 ***	7.04 ***	8.59 ***	9.29 ***
		(.50)	(.79)	(.63)	(.40)	(.71)	(1.19)
	Portugal	7.31 ***	5.17 ***	5.92 ***	7.46 ***	8.00 ***	8.10 ***
		(.14)	(.23)	(.24)	(.19)	(.15)	(.19)
	Sweden	6.08 ***	2.19 ***	3.89 ***	5.79 ***	7.53 ***	8.20 ***
		(.42)	(.83)	(.64)	(.41)	(.61)	(.87)
	UK	6.58 ***	4.89 ***	5.85 ***	6.84 ***	7.45 ***	7.22 ***
		(.13)	(.25)	(.22)	(.16)	(.17)	(.18)

Note: i) * signals significant at the 10% level, ** signals significant at the 5% level, and *** signals significant at the 1% level; ii) standard errors in parenthesis; iii) OLS estimation is heteroskedasticrobust.

Table 3 . Within-groups wage inequality -Private sector

 3

		90q-10q	90q-50q	75q-25q	75q-50q
	Finland	1.88 **	0.98 *	1.71 ***	0.81 **
	France	5.67 ***	2.47 ***	2.94 ***	1.42 ***
	Germany	3.21 ***	1.34 ***	1.01 ***	0.72 **
	Italy	1.98 ***	2.19 ***	1.29 ***	0.94 ***
	Norway	3.05 **	2.25 ***	2.29 ***	1.55 ***
	Portugal	2.93 ***	0.64 *	2.08 ***	0.54 **
	Sweden	6.01 ***	2.41 ***	3.64 ***	1.74 ***
	UK	2.33 ***	0.38 *	1.60 ***	0.61 **
	Note: i) * signals significant at the 10% level, ** signals significant at the 5%
	level, and *** signals significant at the 1% level.

Table 4 . Average and quantile returns to schooling -Public sector

 4 signals significant at the 10% level, ** signals significant at the 5% level, and *** signals significant at the 1% level; ii) standard errors in parenthesis; iii) OLS estimation is heteroskedasticrobust.

		OLS	10q	25q	50q	75q	90q
	Finland	9.73 ***	9.35 ***	9.42 ***	8.52 ***	9.63 ***	10.09 ***
		(.45)	(.74)	(.59)	(.38)	(.46)	(.76)
	France	5.88 ***	4.37 ***	5.25 ***	5.10 ***	5.44 ***	7.18 ***
		(.15)	(.25)	(.16)	(.16)	(.14)	(.25)
	Germany	5.80 ***	4.83 ***	5.39 ***	5.62 ***	5.54 ***	5.93 ***
		(.45)	(.81)	(.40)	(.36)	(.43)	(1.06)
	Italy	4.44 ***	3.04 ***	3.13 ***	2.79 ***	4.67 ***	5.53 ***
		(.49)	(1.10)	(.51)	(.57)	(.65)	(.88)
	Norway	4.91 ***	4.95 ***	4.17 ***	4.13 ***	4.15 ***	4.53 ***
		(.45)	(.78)	(.31)	(.29)	(.32)	(1.01)
	Portugal	8.25 ***	7.37 ***	8.46 ***	8.38 ***	8.19 ***	8.48 ***
		(.24)	(.64)	(.38)	(.31)	(.28)	(.57)
	Sweden	5.06 ***	2.40 ***	3.04 ***	4.84 ***	5.95 ***	6.22 ***
		(.51)	(.54)	(.46)	(.62)	(.82)	(1.36)
	UK	7.09 ***	6.75 ***	7.25 ***	7.03 ***	7.15 ***	7.06 ***
		(.23)	(.67)	(.31)	(.23)	(.26)	(.38)

Note: i) *

Table 5 . Within-groups wage inequality -Public sector

 5 signals significant at the 10% level, ** signals significant at the 5% level, and *** signals significant at the 1% level.

	Page 21 of 22	Submitted Manuscript
		90q-10q	90q-50q	75q-25q	75q-50q
	Finland	0.74	1.57 **	0.21	1.11 ***
	France	2.81 ***	2.08 ***	0.19	0.34
	Germany	1.10	0.31	0.15	-0.08
	Italy	2.49 **	2.74 ***	1.54 **	1.88 ***
	Norway	-0.42	0.40	-0.02	0.02
	Portugal	1.11	0.10	-0.27	-0.19
	Sweden	3.82 ***	1.38 **	2.91 ***	1.11
	UK	0.31	0.03	-0.10	0.12

Note: i) *

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Due to contractual reasons, the national datasets could not be transferred across countries. For a detailed description of the EDWIN project and the national datasets, see http://www.etla.fi/edwin and Budria and[START_REF] Budría | The Impact of Educational Qualifications on Wage Inequality: Evidence for Europe[END_REF].

This is also the perspective in[START_REF] Dustmann | Wage Structures in the Private and Public Sectors in West Germany[END_REF],[START_REF] Disney | Does It Pay to Work in the Public Sector?[END_REF] and[START_REF] Melly | Public-Private Sector Wage Differentials in Germany: Evidence from Quantile Regression[END_REF].

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The educational update was intense during the nineties. In Europe, the proportion of individuals with less than upper secondary education fell from 45% in 1991 to 33% in 2001, while the proportion of individuals with upper secondary or tertiary education rose from 55% in 1991 to 77% in 2001(OECD, 2004).

1 Financial support of the European Commission, EDWIN project HPSE-CT-2002-00108, and the FCT of the Portuguese Ministry of Science and Higher Education is gratefully acknowledged.

Appendix A. Description of data sources and estimating samples