Author

A Simple Multivariate Test for Asymmetry

Keywords: Asymmetry, Multivariate, Aggregate Consumption, Model specification

Since many macroeconomic models are linear, it is not desirable to use them with an asymmetric dependent variable. In this paper we formulate a univariate test for symmetry, based on the third central moment, and extend it to a multivariate test; the test does not require modelling and it is robust against serial correlation, autoregressive conditional heteroscedasticity and non-normality. In the empirical application of the test it is found that orthodox theory seem to be supported; consumption expenditure on durable goods is found to be symmetric while consumption expenditure on nondurable goods is asymmetric for the US and UK, with peaks being higher than troughs are deep. Also, the empirical importance of the choice between the univariate and the multivariate test for possibly correlated series is underscored; the results from the two approaches clearly differ. Given the widespread practice of using consumption expenditure on nondurable goods as the dependent variable in linear models for the US and the UK, our results might be noteworthy.

Introduction

There has long been recognition that business cycles can be asymmetric, see e.g. [START_REF] Neftci | Are Economic Time Series Asymmetric Over the Business Cycle?[END_REF] and [START_REF] Potter | A Nonlinear Approach to U.S. GNP[END_REF]. Asymmetry of a macroeconomic times series is not a problem, though, unless it is modelled or treated as a symmetric series. However, since many macroeconomic models are linear, i.e. symmetric, we run the risk of trying to square the circle if we use them with an asymmetric dependent variable.

In this paper we propose a simple multivariate test for asymmetry, based on the third central moment. The test allow us to test for, using the terminology of [START_REF] Sichel | Business Cycle Asymmetry: A Deeper Look[END_REF], two types of asymmetry; steepness and deepness. Deepness considers peaks and troughs distance above and below trend, while steepness considers the speed at which the peaks and troughs are approached. Positive deepness is present when peaks are taller than troughs are deep and negative deepness is present when the converse is true. Positive steepness is when the peaks are approached faster than are the troughs and negative steepness is present when the converse is true. In order to obtain an intuitive idea of the meaning of these patterns, we present one symmetric cycle, one cycle with negative deepness and one cycle with negative steepness; see Figures 1(a)-1(c) below. 1 In applications where we test the dependent variable in a symmetric model for symmetry, our test can be viewed as a model specification test. Although in an economic setting in this paper, the proposed test is general in the sense that it can be applied to any stationary series. Also, the test does not require modeling and is robust against serial correlation, autoregressive conditional heteroscedasticity and non-normality. There are numerous proposed tests in the literature (using STAR-models for instance), that to a greater extent determine the finer characteristics of the asymmetry while modeling it, treatments that is 1 These stylized cycles are only intended to give an intuitive understanding of the two concepts; deepness and steepness. In reality, the series under investigation is usually much less well-behaved. For a more thorough presentation of the data series used in this paper, see the Appendix. Turning to empirical applications, one objection to this kind of diagnostic testing could be that such testing is superfluous since the question we are asking should already be answered by economic theory. However, it is not obvious to what degree a supposed asymmetry should be present. Moreover, the proposed diagnostic test could then be viewed as a way of testing theory regarding the 2 Examples of such models are found in [START_REF] Bradley | Are Business Cycle Dynamics the Same across Countries? Testing Linearity around the Globe[END_REF], for instance, where they fit non-linear time series models to output data for 26 countries. The result is a great deal of heterogeneity concerning the different countries' business cycles as the characteristics of the series are not easily classified into common groups as there is little unanimity concerning the non-linearity. In our context, however, this kind of precision is not needed as we are interested in the overall question of whether or not there are asymmetries. While it is of interest in other circumstances to model the possible nonlinearity with great precision, the verdict of a significant rejection (or not) of symmetry, is sufficient for our purposes. behavior of the dependent variable. Speaking in favor of our approach is also the fact that not all economic theory is unanimous. Regarding consumption as well as business cycle theory, to mention but a few, competing views do not agree on whether growth and consumption is symmetric or not.

The theoretical aim of the paper is twofold. First, we want to create a univariate test for asymmetry for which the statistical properties are clearly derived. Second, we want to develop the univariate test into a multivariate, thus being able to take into account the possible interdependence between two or more of the series to be tested.

The empirical aim is to test theories of consumption suggesting symmetric or asymmetric behavior, as well as testing the validity of common practices in empirical studies on aggregate consumption. Lastly, the empirical section contains a test of the difference between the univariate and the multivariate test. In the empirical application we use data from the United States, the United Kingdom, Canada and Sweden.

The disposition of the paper is as follows. Section 2 starts with a brief discussion on asymmetry, followed by the derivation of the univariate test as well as the multivariate test. Section 3 first looks at the data and methods of detrending, followed by the empirical testing and a summary of the results.

Section 4 comments and concludes. A more exhaustive graphical presentation of the data if found in the appendix.

Asymmetry

There are several ways in which a cycle may deviate from symmetry. [START_REF] Sichel | Business Cycle Asymmetry: A Deeper Look[END_REF] suggests two types of asymmetry of prime importance, as presented in the previous section, which he refers to as deepness and steepness, respectively.

Our main objective here is to detect deviations from symmetry of business cycles (i.e. to detect deviations from the pattern exemplified in Figure 1(a)). The series displayed in Figure 1 this is not to be recommended as the cycles are stylized, seldom occurring in economic data. We will therefore aim to find techniques for evaluation of asymmetry that do not rely on a parametric model.

The univariate test for asymmetry

Consider a variable Y t ≡ (X t -µ X ) 3 and define µ X ≡ E[X t ], µ Y ≡ E[Y t ] and γ j ≡ E [(Y t -µ Y )(Y t-j -µ Y )]. 3 Then consider a set of constants © ψ j ª ∞ j=0
such that P ∞ j=0 ¯ψj ¯< ∞ by assumption. By Wold's decomposition theorem [START_REF] Hamilton | Time Series Analysis[END_REF] p. 108), the variable Y t can be written in the form

Y t = µ Y + ∞ X j=0 ψ j ε t-j (1)
where ψ 0 = 1 and {ε t } is a sequence of i.i.d. random variables. The linear model in eq.( 1) is frequently referred to as the MA(∞) representation of Y t .

Our interest lies in assessing whether µ Y is zero or not. As µ Y is unknown, we need an estimate of it along with a known asymptotic null distribution.

Assuming that E[ε 2 t ] = σ 2 ε < ∞, it may be shown that

θ = √ T ( Ȳ -µ Y ) √ v 2 l → N (0, 1) (2)
where v ≡ P ∞ j=-∞ γ j (see e.g. Hamilton (1994), p. 195). Eq.(2) does not lead to a feasible test regarding µ Y since we assumed that v is known, which is usually not true. However, we may estimate v by Then, if q is chosen such that ¡ q/T 1/3 ¢ → 0, it follows that v p → v [START_REF] Hamilton | Time Series Analysis[END_REF] p. 283). Hence,

v2 = γ0 + 2 q X i=1 • 1 - i q + 1 ¸γ i . (3)
√ T ( Ȳ -µ Y ) √ v2 l → N (0, 1). (4) Definition 1 A test of H 0 : E(X t -µ X ) 3 = 0 against H A : E(X t -µ X ) 3 6 = 0 is
defined by the rejection area | θ| > q α where q α is the (1α) × 100 th percentile of the standard normal distribution. That is, H 0 is rejected for values of | θ| > q α .

The multivariate test for asymmetry

A multivariate version of the above may readily be constructed, the approach being analogous to the univariate case. Consider the P -dimensional random vector

Y t ≡ (X t -µ x ) 3 and let µ X t ≡ E[X t ] and µ Y t ≡ E[Y t ] and Γ j ≡ E [(Y t -µ Y )(Y t-j -µ Y ) 0 ]. Furthermore, consider a set of constants {Ψ j } ∞ j=0 such that P ∞ j=0 |Ψ j | < ∞
by assumption and Ψ 0 = I. Then, by Wold's decomposition theorem (Lütkepohl (1991), p. 20), the variable Y t can be written in the form

Y t = µ Y + ∞ X j=0 Ψ j ε t-j .
Again, our interest lies in assessing whether µ Y is equal to zero or not. As µ Y is unknown, we need an estimate of it along with an asymptotically known null [START_REF] Brockwell | Time Series: Theory and methods[END_REF]). A consistent estimate of v may be obtained by

distribution. Assuming that E[ε t ε 0 t ] = Σ ε < ∞, it may be shown that √ T v -1/2 ( Ȳ -µ Y ) l → N (0, I) 6
+ P ∞ j=1 ¡ Γ j + Γ 0 j ¢ (see, e.g.,
v = Γ0 + q X i=1 • 1 - i q + 1 ¸³Γ + Γ0 ´(5)
and hence

Θ = √ T v-1/2 ¡ Ȳ -µ Y ¢ l → N (0, I). Definition 2 A one-sided test of the hypothesis H 0 : E(X t -µ x ) 3 = 0 against H A : E(X t -µ x ) 3 6 = 0 is defined by the rejection area Θ0 Θ > Q α where Q α is the (1 -α) × 100 th percentile from the χ 2 (P ) distribution. That is, H 0 is rejected for values of Θ0 Θ > Q α .
3 Empirical application

Data

The data set comprises quarterly aggregate consumption data for four countries; the US, the UK, Canada and Sweden. 4 For the US, the three series are total personal consumption expenditure, personal expenditure on non-durable goods for total consumption expenditure, cd i t for consumption expenditure on durable goods and cnd i t for consumption expenditure on non-durable goods and services where the superscript i = US, UK, CAN or SW E for the US, the UK, Canada or Sweden respectively.

Since our empirical application of the test for asymmetry stems from an interest in whether the dependent variable in a linear model is linear, the starting point of our choice of data is the type of data used in such models. When estimating an aggregate consumption function, the dependent variable chosen is usually both seasonally adjusted and in natural logarithmic form. Thus, besides the seasonal adjustment, we have taken the natural logarithm of all series. From a statistical point of view, tampering with the original data as mentioned above might seem out of place. However, since the objective of, and motivation for, our application of the test is a macro consumption model and its empirical specification, such tampering is both motivated and necessary.

Detrending -obtaining a stationary series

A series that exhibits growth over time, as most macroeconomic time series, is asymmetric a priori which necessitates detrending of the variable of interest. This is obviously controversial as we are tampering with the original series. However, since we are only interested in one specific characteristic, we can adjust our requirements accordingly. As long as the choice of detrending process does not influence the proposed test for asymmetry, any possible concerns for undesired properties that might follow from the detrending process are a non-issue in the current context. Next, we consider a simple way of detrending a time series.

First differencing

We previously defined X t ≡ Z tτ t without paying any explicit attention to the trend component τ t . Now, in our case, since c t and ξ t have zero-means by construction, it follows that µ xt = [X t ] = 0, and hence our variable Y t is defined by Y t = X 3 t . However, we have not yet discussed how to obtain X t , i.e. how to remove the trend from Z t . In general, we assume the trend component to be defined by τ t = Z t-1 or by τ t = βt. Then, if τ t = Z t-1 , by taking the first difference of Z t , the trend is removed. But if τ t = βt, the first difference removes the trend but at the same time introduces a constant (since βtβ(t -1) = β) which in turn may be removed through differencing the data once more; i.e.

E[∆ 2 X t ] = 0.
First differencing is appropriate for the steepness test but since the deepness test requires a series in levels, another method must be adopted. A description of the filtering process of [START_REF] Hodrick | Post-war U.S. Business Cycles: An Empirical Investigation[END_REF] follows next.

The Hodrick-Prescott filter

Formally, the Hodrick-Prescott (HP hereafter) filter proposes a trend τ t for an original series Z t which is the solution to the problem

min T X t=1 {(Z t -τ t ) 2 + λ[(1 -L) 2 τ t ] 2 } (6)
where L is the lag operator. λ is known as the smoothing parameter and the choice of it will determine the characteristics of the filtered series. As an illustrative example, a choice of λ = 0 leads to τ t = Z t while a choice of λ = ∞ leads to a linear trend. Drawing upon earlier work in general, for instance [START_REF] Canova | Detrending and Turning Points[END_REF][START_REF] Canova | Detrending and Business Cycle Facts[END_REF] and [START_REF] Ravn | On Adjusting the Hodrick-Prescott Filter for the Frequency of Observations[END_REF], and the original in particular, we let λ = 1600 as we have quarterly data. A graphical illustration of the two variables, τ t and Z t , is found in Figure 2 under investigation, not a particularly desirable quality in several respects. This feature however, when combined with the test proposed here, is actually not negative but rather the contrary. If anything, it makes detection of asymmetry easier and is thus very much in line with the aim of the test. 5

3.2.3

The choice of detrending method and the series to be tested Thus, the variable X t that is the starting point in Section 2.1 and 2.2 where we derive the tests, is obtained in different ways for the two tests. 6 For the deepness test, we get the desired variable by subtracting the HP estimated trend, τ t , from the original series Z t . That is, for the deepness test X t = Z tτ t . For the steepness test we instead employ first differencing for detrending, followed by taking the first difference once more, this to get a series describing the rate of 5 The advantages and drawbacks of various methods of detrending have been an issue for quite some time, and Canova (1998), for instance, provides a good overview of the field. The HP filter is, for instance, found to perform best when it comes to identifying the turning point of business cycles [START_REF] Canova | Detrending and Turning Points[END_REF]). Also, none of the HP filter's drawbacks presented in [START_REF] Canova | Detrending and Business Cycle Facts[END_REF] poses a problem in the current context. All calculations for the HP filter have been done using PCGive 10.0.

6 For a graphical presentation of all series, see the appendix p.19.

Testing

Theories on consumption as well as empirical practices, imply symmetric or asymmetric properties of different measures of aggregate consumption, properties that will be tested for in this section.

Does cd t exhibit steepness?

It is fair to say that there is an established consensus that durable goods are to be viewed as investment goods and modelled accordingly, see e.g. [START_REF] Leahy | The Timing of Purchases and Aggregate Fluctuations[END_REF]. Furthermore, several theories agree on that cd t exhibit steepness: [START_REF] Leahy | The Timing of Purchases and Aggregate Fluctuations[END_REF] propose a model in which consumption expenditure on durable goods exhibits negative steepness while [START_REF] Gregorio | Inflation Stabilisation and the Consumption of Durable Goods[END_REF] presents a model where the steepness is positive.7 Using our univariate test, we can try these hypotheses using data for the four countries in question. Looking at Table 7 below, we find the results from the tests. Here we can see that we are not able to reject the null hypothesis of symmetry in any of the cases. Before commenting on the results, we also want to investigate whether it matters, in the current context, if the series are modeled as correlated or not.

10 Although this type of classification not is the main aim of the paper, we can conclude that that it is a positive deepness, by looking at the t -statistic which is positive; i.e. the peaks are higher than the troughs are deep for c UK From a theoretical point of view, given some correlation between the series, it is obvious that the univariate and the multivariate tests will yield different results. However, from an empirical point of view, these differences can of course vary in magnitude therefore a closer look at the two approaches is warranted.

More specifically, we are interested in whether the verdict of rejection differs or not between approaches. Before proceeding, it is important to stress that this section is intended only to highlight the possible difference between the two approaches and in that way underscore the importance of having chosen the right approach. The choice itself, however, is of course made on a theoretical basis depending on the situation and the data at hand. Here, we merely demonstrate the difference between the two options given the current context.

The novelty of the multivariate approach is that v in eq.( 5) captures the covariances of the series, something of course lacking in the univariate approach where the series are tested one at a time, independently of one another. In Table 11 below, the importance of the covariance is demonstrated in the current empirical application through a comparison between the two approaches. As we know from the previous section, we are not able to reject the null hypothesis of symmetry in any of the eight bivariate tests. If we instead turn to the disaggregated approach in the univariate setting, we find that we are able to reject the null hypothesis in three cases; the deepness test for cd CAN t , cnd UK t and cnd US t , corresponding to three out of the eight cases in the bivariate test.

Results

The models in [START_REF] Gregorio | Inflation Stabilisation and the Consumption of Durable Goods[END_REF] and [START_REF] Leahy | The Timing of Purchases and Aggregate Fluctuations[END_REF] imply that cd t exhibits positive and negative steepness, respectively, implications that not found support in our four-country sample. The null hypothesis of the test of symmetry was not even close of being rejected given that the lowest p-value was 0.37.

As for the alleged symmetry of cnd t , the results are different. For the two large Anglo-Saxon economies, the US and the UK, we can reject the null as both series exhibits positive deepness. Given the widespread use of cnd t in linear consumption models, we believe our results should be a cause of some Shea (1995a), Shea (1995b) and [START_REF] Bowman | Loss aversion in a consumptionsavings model[END_REF], yielding tentative evidence in favor of the loss-aversion model of [START_REF] Bowman | Loss aversion in a consumptionsavings model[END_REF].

The next hypothesis, that the three consumption measures, c t , cd t and cnd t , have the same symmetric properties, was difficult to reject. Again, we highlight that cd t and cnd t were tested jointly, in contrast to the previous hypothesis test where we tested cnd t in a univariate setting. Here, we could only reject the null hypothesis in one out of the sixteen tests, and then at the less conventional 10% significance level. Put differently, we could not reject it for three out four countries and in the case of the UK we could reject it, based on a rejection of the deepness test of c UK t at a 7% significance level.

Turning to the question of the importance of correlation between the series to be tested, we find it to be very important in the current context. In the bivariate case we could not reject the null hypothesis of symmetry in any of the eight cases. However, in 3 out of the 8 corresponding cases for the univariate test, we found that symmetry for one of the two series was rejected. Of course, the results for the difference between the two approaches will vary with the data, but the results here at least indicate that the potential for very different conclusions not is negligible. Again, we want to stress that this only is intended as a comment on the differences between the two alternatives, not the choice between them.

We also want to point out that the question of aggregation is highly nontrivial. In the current setting, we can take the example of the UK and the US.

For both economies, cnd t exhibits positive deepness while the aggregate c t only does for the UK. To address the possible explanation for such issues, quite a different type of analysis would have to be employed, an analysis beyond the scope of this paper. In the graphical presentation of the various series as used in the paper given below, we have chosen not to include the HP-trend in the diagrams in Figure 3, since the graphs have to be of considerable size to be meaningful

F

US Steepness

#88

#86

Figure 1 :

 1 Figure 1: Three different cycles in levels and first differences.

  , p.3, suggest that possible steepness (Figure 1(b))or deepness (Figure1(c)) may be analyzed with trigonometric models. However,

  and services and personal expenditure on durable goods for 1959:1-2002:4. All three series are seasonally adjusted, are in 1996 USD and have been obtained from the US Department of Commerce. For the UK, the three series are total domestic household consumption expenditure, households' domestic expenditure on non-durable goods and services and households' domestic expenditure on durable goods for 1963:1-2002:3. All three series are seasonally adjusted, are in 1995 GBP and have been obtained from the Office for National Statistics. For Canada, the three series are total personal consumption expenditure, personal expenditure on non-durable goods and services and personal expenditure on durable goods for 1961:1-2002:3. All three series are seasonally adjusted, are in 1997 CAD and have been obtained from Statistics Canada. For Sweden, the total household final consumption expenditure, household final consumption expenditure on non-durable goods and services and household final consumption expenditure on durable goods for 1963:1-2001:4. All three series are in 1991 SEK and have been obtained from Statistics Sweden and the National Institute for Economic Research. The Swedish series have been seasonally adjusted using the X12 ARIMA program. Henceforth, we will use c i t

Figure 2 :

 2 Figure 2: Swedish total private consumption 1970:2-2001:4, original series and estimated HP-trend with λ = 1600.

  impact of correlation -the univariate vs. the multivariate test

  . The example given in Figure 2, p.9, serves well as a general illustration of what the estimated HP-trend looks like. Since the test can be viewed as a test for the number of positive and negative observations we have included two numbers (#xx) in each of the graphs depicting the deepness and steepness series. The number above the zero line indicates the number of positive observations while the number below the zero line indicates the number of negative observations.

Figure 3 :

 3 Figure 3: The original series in logs for the three measures of consumption for all four countries.

Figure 4 :

 4 Figure 4: Deepness and steepness series for c SW E t

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  change in the detrended series. That is, for the steepness test X t = ∆ 2 Z t . In our application, we have that Z t is equal to c i t , cd i t or cnd i t for both tests.

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10 Page 10 of 23 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 7 :

 7 p-values from univariate testing of cd t

	H0 : Steepness 0.37 cd US t	cd UK t 0.64	cd CAN t 0.47	cd SW E t 0.88	(7)

As is evident from the table above, we cannot find any clear evidence of steepness for any of the four countries. Even applying significance levels that would be more generous than usual, does not help us since the lowest p-value is 0.37. Next, we to test if the widespread practice of using cnd t as the dependent variable in linear consumption functions is recommendable.

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Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK 8 The results can be found in Table

8

below.

Table 8 :

 8 p-values from univariate testing of cnd t , such use of c t carries the implicit assumption of c t , cd t and cnd t having the same symmetric properties. Using the univariate test we can test for the symmetry of c t , and using the multivariate (or in this case bivariate) we can test for the symmetry of cd t and cnd t . The bivariate test is in contrast to the previous section where no interdependence was possible given the setting. Here, however, cd t and cnd t are of interest given the use of them as an aggregate; c t .In Table9below, we see the results from the univariate testing of c t , that is the p-values from finite sample testing of eq.(4). The table reveals that, with a high probability, total consumption in the UK exhibits deepness.10

		cnd US t	cnd UK t	cnd CAN t	cnd SW E t
	Deepness	0.08*	0.09*	0.80	0.89
	Steepness 0.80	0.80	0.43	0.96

* denotes significance on the 10% level

(8)

Here we see that for the two larger economies, the UK and the US, cnd t display deepness while we cannot reject the hypothesis of normality for Canada and Sweden. The well-known similarities between the two Anglo-Saxon business cycles, are further supported by our findings since the two t-values are both positive, meaning that we have positive deepness; i.e. peaks are higher than troughs are deep. 9

3.3.3 Are all consumption series symmetric?

Using c t as the dependent variable in a linear consumption function is a practice that has grown more common over time; see e.g.

[START_REF] Bjellerup | Does the Measures of Consumption Measure Up?[END_REF]

. In our Page 12 of 23 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK context

Table 9 :

 9 p-values from univariate testing of c t

		c US t	c UK t	c CAN t	c SW E t
	Deepness	0.58 0.07* 0.17	0.87
	Steepness 0.36 0.40	0.32	0.97

* denotes significance on the 10% level

(9)

Apart from the deepness test for the UK, all the other tests stay well clear of any conventional significance levels. Turning to the two components of c t , cd t and cnd t , we can look at Table

10

where we find the p-values from the χ 2 -distributed bivariate test.

Table 10 :

 10 p-values from bivariate testing of cd t and cnd t

		US	UK	CAN SWE
	Deepness	0.245 0.408 0.315 0.923	(10)
	Steepness 0.446 0.780 0.291 0.952

Table 11 :

 11 p-values from the bivariate ('Joint') and the univariate tests (cdt and cndt)

			Deepness Steepness
		Joint	0.25	0.45
	US	cdt	0.11	0.37
		cnd t	0.08*	0.78
		Joint	0.41	0.71
	UK	cdt	0.13	0.64
		cnd t	0.09*	0.80	(11)
		Joint	0.32	0.29
	CAN cd t	0.04**	0.47
		cnd t	0.80	0.43
		Joint	0.92	0.95
	SWE cd t	0.67	0.88
		cnd t	0.89	0.62
	** denotes significance on the 5% level
	* denotes significance on the 10% level

  concern. Specifically, our results suggest that any linear consumption model of the UK or the US will consistently underestimate the height of the peaks in the business cycle. Thus, the results here are broadly in line with previous findings in model based tests of asymmetry in

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  In the empirical application of the test we focus on aggregate consumption.Theory, as well as its empirical applications, have several implications which the test allows us to test for. First, significant deviations from symmetry for cd t can not be found. Second, the alleged symmetry of the consumption of nondurable goods (cnd t ), does not find the expected support since the US and the UK series both exhibited positive deepness, i.e. the peaks are higher than the troughs are deep. For total consumption (c t ), no such asymmetry is found. Given the widespread use of cnd t in linear models, we believe our results should be a cause of some concern. Specifically, our results suggest that any linear consumption model of the UK or the US will consistently underestimate the height of the peaks in the business cycle. Third, the univariate and multivariate tests are used to test the hypothesis that c t , cd t and cnd t have the same symmetric properties. Out of the four countries in the sample (the US, the UK, Canada and Sweden), it is only for the UK that the hypothesis is rejected. Thus, from the point of symmetry, the use of c t as the dependent variable in a consumption

	Page 17 of 23	Submitted Manuscript
	4 Comments and conclusions Appendix
	In this paper we formulate a univariate test for symmetry based on the third Graphical illustration of the data
	central moment and extended it to a multivariate test. The test is robust in
	several aspects. First, it does not require modeling. Second, it is robust against
	serial correlation, autoregressive conditional heteroscedasticity as well as non-
	normality.
	o F o F o F o
	r r r r
	P e P e P e P e
		e e e e
		r r r r
		R e R e R e R e
	v i e w v i v i v i regression is given some support, although not unanimous. Fourth, the empirical importance of choosing whether to test possibly correlated series in a univariate or a multivariate setting is underscored. The results from the two approaches differs significantly, emphasizing why the importance of this choice should not be e w e w e w
	underestimated. However, such a choice is guided by theoretical considerations;
	the results here merely highlight the importance of that choice in the current
	empirical context.

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

Note that in our case, we know from our method of detrending that µ X = 0; see section 3.2, p.8.

For a graphical presentation of the data, see the appendix, p.19.

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

[START_REF] Gale | Delays and Cycles[END_REF] proposes a model for investment goods that share the characteristic of negative steepness with the model in[START_REF] Leahy | The Timing of Purchases and Aggregate Fluctuations[END_REF].

[START_REF] Bowman | Loss aversion in a consumptionsavings model[END_REF] also use c t , as mentioned in note 14, p.166. Their main measure of consumption, however, is cndt.

Although not as reliable as the test of course, this result can be viewed against the background of the number of positive and negative observations in the detrended series. In the two graphs on the left in figure 9, p.22 in the Appendix, we can see that the number of negative observations clearly outnumber the number of positive observations.

Page 19 of 23 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Ignacio Abásolo
email: iabasolo@ull.es

Aki Tsuchiya

Understanding preference for egalitarian policies in health: Are age and sex determinants?

Keywords:

Understanding preference for egalitarian policies in

health: Are age and sex determinants?

I. INTRODUCTION

Maximising average population health is a major objective of public health care systems.

However, modern health care systems have another objective: equality in the distribution of health. Various studies have explored how members of the public see the balance between these two objectives (see for example Johannesson & Gerdtham, 1996;Anderson & Lyttkens, 1998;[START_REF] Cuadras-Morato | Equity considerations in health care: The relevance of claims[END_REF][START_REF] Dolan | The measurement of preferences over the distribution of benefits: The importance of the reference point[END_REF][START_REF] Dolan | Determining the parameters in a social welfare function using stated preference data: an application to health[END_REF][START_REF] Abásolo | Exploring Social Welfare Functions and violation of monotonicity: An example from inequalities in health[END_REF]. A common feature of most studies is that neither maximisation nor equalisation of health alone is supported. However, what has been rarely investigated so far is what makes some people more egalitarian than others in health, that is, what factors determine preferences for egalitarian policies in health. An exception is [START_REF] Lindholm | Health maximization rejected -the view of Swedish health care politicians[END_REF], which found that support for different interpretations of equity in health is strongly associated with the respondent's sex and political affiliation: women, and those who support political parties on the left have relatively more sympathies towards equity. Another related study is the one of [START_REF] Hudson | In search of the good Samaritan: estimating the impact of 'altruism' on voter's preferences[END_REF] that shows with UK data that self-interest attitudes (together with public-interest attitudes) have a significant effect on preferences related to redistributive policies in health. In addition, the impact of age and education is such that as people get older and/or more educated they are less averse to higher taxes for health policy purposes.

Studies on people's attitudes and motivations outside the health economics literature have looked at attitudes over income inequalities, collective action, or moral and political orientation in general. Mainstream economics literature has assumed that self-interested preferences play a strong role in determining individual's attitudes towards income inequalities, as a direct consequence of the standard economic public choice argument of the self-interested median voter hypothesis [START_REF] Romer | Individual welfare, majority voting and the properties of a linear income tax[END_REF][START_REF] Meltzer | A rational theory of the size of government[END_REF]. [START_REF] Bénabou | Social mobility and the demand for redistribution: the POUM hypothesis[END_REF] has shown using an intergenerational model how the preferences of those with below average income to oppose redistributive policies can be consistent with self interest, if they expect to raise above mean income in the future, or the "prospect of upward mobility (POUM)" hypothesis (also see [START_REF] Ohtake | Who supports redistribution?[END_REF][START_REF] Ch | Social preferences, self-interest, and the demand for redistribution[END_REF], which has implications for the effect of age on such preferences. In their studies of the determinants of charitable donations in Canada, [START_REF] Kitchen | Determinants of charitable donations by families in Canada: a regional analysis[END_REF] and [START_REF] Kitchen | Determinants of charitable donations in Canada: a comparison over time[END_REF], show that family wealth and age of the household tend to be significant determinants of charitable giving. In addition to age, and going beyond self-interest, the effect of gender in moral and political orientation has been subject of analysis in a number of empirical studies. [START_REF] Beutel | Gender and values[END_REF] find that women are more likely than men to display group solidarity.

Similarly, [START_REF] Davies | The effect of dispositional empathy on emotional reactions and helping: a multi-dimensional approach[END_REF] shows that women display a greater ability to see things form the perspective of others. Gilligan (1993) shows that while men tend to base their moral arguments on concepts of justice and rights, women tend to appeal to notions of care and to a desire to minimise harm to others. However, [START_REF] Jaffee | Gender differences in moral orientation: a meta-analysis[END_REF] found evidence that do not offer support the claim that care orientation is used by women and justice orientation is used predominantly by men. Other researchers show that females support more policies like public protection, 'compassion' issues and traditional values [START_REF] Shapiro | Gender differences in policy preferences: a summary of trends from the 1960s to the 1980s[END_REF]. [START_REF] Eckel | Are women less selfish than men?: evidence from dictator experiments[END_REF] in their exploration of basic gender differences in economic behaviour show that women are more socially-orientated (selfless) and men more individually-orientated (selfish).

Finally, another interesting point raised in the literature is that people may prefer more redistribution to the poor if they believe that poverty is caused by circumstances beyond individual control. This implies a social perspective on distributive justice rather than (only) self-motivated preferences (see for example [START_REF] Ch | Social preferences, self-interest, and the demand for redistribution[END_REF]Charness & Rabin, 2002;[START_REF] Fehr | Why social preference matter -the impact of non-selfish motives on competition, cooperation and incentives[END_REF].

The motivation of this paper is to explore what factors can help us to understand social preferences for egalitarian policies in health in particular respondent age and sex. In addition, we will consider other factors that we anticipate to be relevant. To account for possible self-interest we will consider household income and education as proxies to capture that potential effect. We will also consider other controls such ideology or region of residence. Finally, the effect of framing the same question on responses and its interaction with respondent characteristics are investigated. Results from a survey in Spain that includes questions on preferences to reduce inequalities in health are used for this analysis (see Abasolo et al. 2001).

First, respondents were informed of a current health inequality across socio-economic groups, namely, that men from the highest social class have a longer life expectancy at . Then, respondents were asked to choose between two health programmes with the same cost: programme A, that extends the life expectancy of both these population groups by two years each (the "distribution neutral" programme), and programme B, that targets the disadvantaged group and increases their life expectancy by four years. Since, by targeting all the benefits to the disadvantaged group, programme B will reduce the inequality by the same amount, we will refer to this as the "targeting programme" or the "egalitarian programme". The aim of the questionnaire was to tap into the preferences of the respondent as a citizen, comparing public policies addressing issues of inequality and distribution, as opposed to a consumer, purchasing insurance policies for their own benefit. The survey question continued to identify the strength of inequality aversion by subjecting those respondents who choose the egalitarian policy to explicit trade offs between efficiency and equality; however, the present paper concentrates on the first exercise alone, where it is assumed that both programmes are equally efficient. At the end of the survey, socio-economic, demographic and ideological information were gathered to serve as the explanatory variables. Two different ways of presenting the options were used (a Pictorial variant and a Verbal variant), with the aim of testing whether or not these two different devices to present the same information lead to the same results.

II. THE MODEL AND ESTIMATION METHODS

We specify a model that explains the probability of a given respondent to target the disadvantaged group, as defined above. expected that all these variables are negatively related with the propensity to support the egalitarian health policy. Thirdly, political affiliation, or ideology (I), is also assumed to have a role in the model. After all, people's attitude towards egalitarianism is an ideological issue, which might be favoured more by a left wing person. Lastly, we include in the model another variable (Q) representing the questionnaire variant. The question could be presented to the respondents with the aid of pictures (P) or verbally with no visual aids (V). The aim of this regressor in the model is to determine whether there are significant differences in the estimated probabilities depending on the way the question is asked.

Thus, the model can be written as:

In model [eq.1], the i subscripts represent individual respondents, and i captures influences unobserved by the analyst, which we assume to have a standard normal distribution with zero mean and constant variance. In practice, * T is unobserved. Rather, we observe Ti, which is a dummy variable representing whether or not the individual actually chooses the targeting policy; therefore it is the realization of a binomial process defined by:

Ti = 1 if [ * i T > 0]
So, if the individual's propensity to target is positive ( * i T > 0) s/he will choose the egalitarian policy (Ti = 1), and if otherwise ( * i T 0) s/he will not (Ti = 0).

2 An additional variable "social class" was also available in the data set. However it was not used in this study due to two reasons. Firstly, because the definition of social class is not explicitly given (the respondent is simply asked whether s/he belongs to high, middle-high, middle, middle-low or low social class). So there is no correspondence at all with social class I and V referred in the main question. Actually 60% selfreported to belong to middle social class. Secondly, there is no correlation between the "social class" variable and other variables representative of socio-economic status such as education or family income. In order to select the functional form of the empirical model, socio-economic and statistical criteria are used. This has allowed us to consider the definitions of the set of dummy variables and whether the only continuous variable (age) enters the model in natural units, as logarithms or as higher-order powers. Interactions between regressors are also included and tested in the model. In particular, in order to test whether the mode of presenting the question (P or V) has a different effect on the propensity to target across the different background characteristics specified in the model, we will test the joint hypothesis that the interactions of Q with the rest of regressors are not significantly different from zero.

[eq. 1]

i Qi Ri Ii Li Yi Ei Ai Gi T T i + = ) , , , , , , , ( F o
The estimation process will be undertaken through non-linear probit regressions.

Likelihood ratio (LR) tests and Reset specification tests will be carried out to appraise the appropriateness of the different functional forms. Throughout, a 5% significance level is used.

Estimations of model [eq.1] will allow us to empirically assess the relevance of the different hypothesised explanatory variables and appraise whether the way in which the question is formulated does not account or it does, and if it does in which way.

Model [eq.1] may be subject to selection bias due to incomplete survey data. In surveys of this sort respondents do not always provide answers to all the questions of the survey. It is the so-called "item non-response". If the pattern of non-response is not at random, conventional estimators may be biased and inconsistent. Tests for selection bias and correction, if necessary, are undertaken estimating a probit with sample selection [START_REF] Greene | Econometric Analysis[END_REF]). The probit with sample selection works in a manner very similar to the Heckman model except that the response variable is binary. This method requires additional exogenous variables (or identifying variables), which should explain the probability of participating but have no direct impact on the probability to target. well as some identifying variables as follows:

The identifying variables include Mi, which represents the marital status of the individual (married, single, divorced or widow), and Hi, which represents whether the individual lives in a rural area. The main criteria used here for proposing both set of identifying variables are that the variables have an impact on the probability to participate but are unrelated to the individual's preference for egalitarian policies. ui is a random error term normally distributed with zero mean and constant variance.

Selection bias occurs when there is correlation between Y and (and therefore between and u); that is, when unobservable factors that influence the potentially selection are also influencing the probability to target. If so, selection bias will be corrected. To check whether selection bias is absent we will test, firstly, whether (the correlation of residuals) is significantly different from zero: if the covariance between and u is significantly different from zero, then we cannot reject that there is no selection bias. In addition, a comparison of the estimates of both the initial probit and the probit with selection is undertaken: a large change in the coefficients, a change of the sign of the coefficients or a change in the statistical significance of the coefficients between the initial probit and the probit with selection indicate the existence of selection bias.

III. DATA AND VARIABLES DEFINITION

The data were collected during 1999 in Spain. A survey of 1,209 individuals over 18 years of age was undertaken. Face to face interviews were assigned across the 17 "Comunidades Autónomas" ("Regions" for short), reflecting the local resident population proportionally.

Within each of the Regions, interviews were randomly allocated so that the achieved sample will be representative of the general Spanish population in terms of sociodemographic characteristics. Each of the two variants of the questionnaire was The binary dependent variable, target, takes the value 1 if individual i targets the worse off group, 0 if otherwise. Age is a continuous variable, which takes values between 18 and 94, and also enters the equation in quadratics. The binary variable female indicates whether the individual is female or male. Education is recorded by level of schooling and has been categorised in three dummy variables representing low education lowedu (those with primary school education or less), middle education midedu (those with secondary school education, the baseline category), and high education highedu (those with higher and university education). Household income is also categorised in three dummies high income (more than 1,653 euros per month), middle income (between 600 and 1,653 euros per month, the baseline category) and low income (less than 600 euros per month) 3 . Per capita income in the region of residence is captured by three dummies: high income regions highreg (those resident in Madrid, Navarra or País Vasco), low income regions lowreg (those who live in Andalucia or Extremadura) and middle income regions midreg (residents in the rest of Spain, the omitted category). The binary variable non-labour market (nonlabmkt) indicates whether the individual is not currently in the labour market (i.e. is retired, unemployed, homemaker or student) or whether s/he is. Political affiliation is recorded, by three categorical indicators, right (those who report as being centre-right, right or extreme right wing), left (those who report as being centre-left, left or extreme left wing), and centre (those who are in the political centre, the baseline category). Type is the dummy variable representing the type of question administered, taking value 1 if the V variant was provided, and 0 if the P variant was administered. Regarding the identifying variables, single, divorced and widowed are three dummy variables representing whether the individual belongs to one of such marital status (as opposed to the omitted category married); and the binary variable rural, representing whether the individual is resident in a rural area (of less than 10,000 residents). For descriptive statistics, see Table 1.

ui Hi Mi Ri Li Ai Gi Y Y i + = ) , , , , , ( F o
3 Although it would have been desirable to derive equivalent income, this has not been possible given the available information in the survey and also given that the household income was not available as a continuous variable. Descriptive statistics and estimation results are reported in table 1. Overall, 69% of full respondents chose to target the egalitarian policy. Model [eq.1] passes the Reset specification test, indicating that there is no evidence of functional form problems (table 2). In addition, when dealing with the issue of the relevance of the question variant in the model, likelihood ratio tests show that specification [eq.1] fits the data significantly better than other alternative specifications. The alternative equations considered include, on the one hand, a model that omits the type variable and, on the other hand, a model which includes the type variable together with interactions with the rest of independent variables.

Therefore model [eq.1] shows that the way in which the question is presented counts, although there are no differential effects across the individual characteristics considered in the model. Item non-response leads to 514 missing cases, which corresponds to 42.5% of the entire data, leaving 695 individuals as valid cases. Estimates for the probit with sample selection [eq.2] can be seen in table 4. The correlation coefficient (rho) is not statistically different from zero. It is also true that the confidence interval for the parameter estimate is wide. However, sign, magnitude and t-ratios of coefficients of the probit with selection are very similar to those of the initial probit estimation [eq.1]. Overall, the results suggest that we cannot reject the null hypothesis that there is no selection bias.

Probit average and marginal effects evaluated at sample means (table 3) show that: firstly, other things equal, age is a statistically significant explanatory variable of the probability to target the disadvantaged group. However, the marginal effect of age on targeting is not constant and changes with the age of the respondent. For young adults between 18 and 44 the probability of targeting increases with age at a diminishing rate. A maximum is reached, on average, at the age of 44, after which the probability of targeting starts to decrease with age at an increasing rate. Interactions between age and income or education were omitted on statistical grounds, showing that there was not a differential effect of age through different income (or education) groups.

Secondly, the existing literature suggests that female respondents will have a higher preference towards egalitarian policies, and thus, that more women will target than men. However, respondent sex did not have any statistically significant impact on the propensity to target. Thirdly, those who are politically right wing have a significantly 10 lower probability of targeting the egalitarian policy, as compared to those who are in the political centre (and consequently, as compared also to those who are left wing). In particular, the probability of a right wing individual targeting is on average 12% less than the reference individual, other things being equal. Finally, living in one of the richest regions such as Madrid, Navarra or País Vasco is associated with a lower probability of targeting the egalitarian policy, other things being equal, by 17.4%, compared to those living in average per capita income regions. There is no evidence that other demographic and socio-economic factors in the model have a significant influence in the attitudes towards health inequalities, including respondent sex.

Regarding the effect of the question variants, our model suggests that mode of presentation does make a difference. When individuals are administered the V-variant (as opposed to the P-variant), there is a 7% higher probability of targeting the egalitarian policy (at sample means). A comparison of this average effect with those of other variables shows that, at sample means, the average effect of the question variants is higher than that the marginal effect of age but lower than the average effect of being right wing or resident in a rich region. However, there is no evidence that the question variant has differential effects on the probability of targeting across the different demographic, socioeconomic and ideological characteristics, when these are taken jointly.

V. DISCUSSION

We found that a large majority of respondents (almost 70%) chose to target the egalitarian policy. This result, while interesting, should be interpreted with care and we discuss two points here. Firstly, we deliberately did not include efficiency issues in the question in order to isolate the equity issue alone. It may be the case that there is no reason to assume that, for instance, an extra $5 million put into program A would yield the same increase in health as the same expenditure in programme B and that, regardless of what the interviewers tell respondents, some of them would have made their own assumptions. In fact, the survey question of this study went on to identify the strength of inequality aversion by subjecting those respondents who choose the egalitarian policy to explicit but they suggest that the conclusions reached in this paper would not vary substantially if we had taken into account efficiency issues (for details, see Abasolo & Tsuchiya, 2004).

Secondly, we must be aware that the proportion of those who chose to target might be inflated by two effects. A) What could be called a "gap in life expectancy effect": in the question, the respondent is informed about current levels of health of both socioeconomic groups (70 vs 75 years). If this information had not been given to the respondent, we might have obtained a lower figure. Although this is an interesting issue that should deserve further research, it lies beyond the scope of this paper: the theoretical motivation behind the broader project that embraces the present piece of work was to estimate the inequality aversion parameter for a Health Related Social Welfare Function [START_REF] Dolan | The measurement of individual utility and social welfare[END_REF],

and therefore current levels of health needed to be explicit to the respondent. B) An "interviewer effect": if respondents feel that their preferences are less egalitarian than what they perceive as socially acceptable, then they may find it awkward to be seen by the interviewer not caring to target the worse off, therefore inflating the proportion of those who choose to target. The study design does not allow any explorations of this possibility, but even if it was a significant problem, insofar as they are random with respect to the determinants that we explore in this paper, conclusions would not be affected.

It should be pointed out that the main aim of the paper is not to measure the propensity to target but rather to understand how this happens. This is explored with reference to the predicted probability to target of a "standard Spaniard": an individual who is of average age (45 years old) and belongs to the baseline categories of our dummy variables, that is, male, with middle income and education levels, who is in the labour market, politically centred, resident in a middle per capita income region and has been administered the Pvariant of the question. This standard Spaniard has a 68% predicted probability of choosing the targeting policy. That is, two thirds of those with our standard features would support that resources ought to be devoted to the lowest (and unhealthiest) socio-economic group. 4 Starting with the same question as the one presented in this paper, the respondents were asked four more questions in which they had to choose between the same programme A (which was invariant across the four of them) and a modified pro-poor programme B in which overall health was diminished progressively. The results show that the vast majority (90%) of respondents, who chose B in the very first question, kept on choosing B despite the loss in efficiency. The results suggest that age has a role when explaining this (see figure 1): at age 18, the predicted probability that the standard Spaniard targets is 56%. Starting from here, it increases with age, reaching the maximum probability of 69% at age 44, after which this probability diminishes with additional years. This predicted profile is symmetric with respect to age so that, for example, probabilities at age 24 (= 44 -20) and at age 64 (= 44 + 20) are both 61%. The age at which the predicted probability of targeting is 50% is age 74. The fact that the age effect was not different across income (or education) groups suggests that the targeting preference of those with below average income is not affected by their future prospects of income and social status, which contradicts the POUM hypothesis which will predict an interaction effect of age and income.

There are two possible explanations on why there may be an age effect on the propensity to target, both concerning the way age affects the way people interpret the concept "social class". The first explanation is based on "age" as a life stage. To younger people, who are yet to establish their occupation or socio-economic status, the concept of social class may have less clear connotations than to older people whose occupation and socio-economic position is well established. The second explanation is based on "age" as a proxy for cohorts. In Spain, as in other modern societies, the concept of social class is becoming more and more obsolete in daily life, so that the younger generation may find it more difficult than the older generation to see the relevance of inequalities in health across the social classes. Whilst these explanations fall short of justifying the age profile in Figure 1, they are consistent with a profile that is not a straight flat line. Given the current cross sectional dataset, it is impossible to determine whether the effect of age is a life stage effect or a cohort effect, or a mixture of both.

Those who are politically right wing have a significantly lower probability of choosing the egalitarian policy, as compared to those of the centre (and consequently as compared to those left wing). Therefore, if the standard Spaniard became right wing (other things remaining equal) this would reduce the probability of targeting by 13%. This is consistent with prior expectations, that egalitarianism is associated with left wing ideology rather than right wing. However, the estimated average effect might be overestimated if, as it seems, right wing people are more reluctant to explicitly indicate their political affiliation Region) there would be, on average, a 18% lower probability of targeting the egalitarian policy. Given the decentralised Spanish health care system, regional differences in the residents' views towards health inequalities may be a matter of debate in the allocation of health care resources by regional health authorities.

Of the other demographic and socio-economic factors with possible association with respondents' propensity to target, none were statistically significantly associated.

Particularly, respondent sex and socio-economic background (approximated by education and household income variables) does not seem to affect propensity to choose the egalitarian policy. Rather, health inequalities seem to be a matter of concern for the general population, irrespective of their income or education level. Taking into account that we are dealing with socio-economic inequalities in health, these results are not consistent with selfish motivations. To the contrary, they seem to have picked up the respondents playing the role as citizens facing a policy rather than the role of consumers purchasing insurance policies, which was the intention of the questionnaire.

The way in which the question is presented is associated with the probability of a given respondent choosing the egalitarian policy. People have a higher propensity to target when they deal with the verbal variant than when they face the pictorial variant. A possible explanation for this is that the pictorial variant may have emphasised the gain more than the existing inequality. As was discussed under the effect of respondent sex, contrary to the consequentialist economist' conceptualisation, programme A, which gives equal amounts to both groups, might be perceived by the lay respondent as being more equal than programme B, which gives nothing to one group an all the benefits to the other. The illustrated P-variant seems to be at a higher risk of this happening, because it visualises the differences across the two programmes in terms of what the two population groups will gain. The current baseline inequality is the same across the two programmes, so they could be cancelled out from the cognitive process. Should this happen, then those respondents who, had they been given the V-variant may have chosen to target, may well 5 Only 21% of individuals report that they are centre-right or right, whilst 47% of respondents report a centre-left or left ideology. In 1999, the Spanish Popular Party was in government (a centre-right party) and Although the current data do not lead us to discriminate in favour of one particular mode of administration, we believe that this issue deserves more research in order to explore the reasons that lead people to choose differently under these two different formats.

It should also be noted that, despite this variant effect, the overall proportion of respondents who chose to target is roughly the same across the two questionnaire variants and the difference is not statistically significant (64% vs 69%). In certain research contexts, where the aim of the study is not to explain the variation in targeting behaviour by respondent background characteristics, this may be seen as sufficient justification to pool the data from the two variants.

VI. CONCLUSION

The impact of demographic characteristics has been largely investigated in the literature as motivations on people's attitudes over justice and rights in general and over income inequalities in particular. However, this has not been the case when we tackle attitudes towards redistributive or egalitarian policies in the health field. Stronger female traits towards solidarity observed in other areas was not observed in our example based on redistributive policies in health: respondent sex does not seem to have a significant impact when choosing egalitarian policies. On the other hand, results regarding respondent age suggest, in line with previous studies, changing levels of tolerance with aging towards socioeconomic health inequalities, but not lineally, so that younger and older individuals are significantly less likely to support egalitarian policies compared to middle age individuals. Analysis of other factors that have been controlled for show that right-wingers and/or those living in affluent regions are significantly less likely to support egalitarian policies; unexpectedly, other socioeconomic background characteristics such as individual's education or household's income do not seem to have a significant impact.

The evidence also shows that the way in which the question is administered also counts: the regression results indicate that on average, there is a significantly higher probability to target when people deal with numbers rather than with pictures.

the survey was undertaken just 3 months before general elections which the Popular Party won again with absolute majority.

  years) than men from the lowest social class (70 years) 1

  So, let us assume an underlying (unobserved) variable * i Y that determines selection into participating groups, i.e. Yi = 1 when * i Y > threshold, and Yi = 0 when * i Y threshold. * i Y would represent the inclination for the individual to participate answering all the relevant function of some of the exogenous variables in model [eq.1] as

  the same number of respondents: 602 for the P-variant and 607 for the V-variant. In terms of background characteristics, the distribution of these variables across the two variants is not statistically significantly different from each other.

  efficiency and equality 4 . The results are discussed in a separate paper,

  questions 5 . Finally, if a standard Spaniard was resident in one of the richest Regions like Madrid, Navarra or País Vasco (instead of living in a middle income

  target in the P-variant precisely because they regard themselves as egalitarian.

  Figure 1: Probability of chosing the "egalitarian" option of a standard Spaniard; by respondent age

TABLE 1 . MEAN VALUES AND STANDARD DEVIATIONS OF VARIABLES

 1

	Page 21 of 24		Submitted Manuscript
	VARIABLE	OBS.	MEAN	STD.DEV.	MIN	MAX
	Target	695	.6904674	.4626339	0	1
	Female	695	.485911	.5001614	0	1
	Age	695	45.26725	17.5467	18	91
	Agesq	695	2356.567	1709.339	324	8281
	Highedu	695	.2362348	.425074	0	1
	Midedu	695	.4139528	.492895	0	1
	Lowedu	695	.3498124	.477254	0	1
	Highinc	695	.2259842	.4185301	0	1
	Midinc	695	.4759503	.499781	0	1
	Lowinc	695	.2980655	.4577378	0	1
	Nonlabmkt	695	.5352979	.4991117	0	1
	Left	695	.4718532	.4995667	0	1
	Centre	695	.5377811	.4989296	0	1
	Right	695	.2190156	.4138771	0	1
	Reghigh	695	.1453269	.352684	0	1
	Regmid	695	.299272	.4582689	0	1
	Reglow	695	.223194	.4166872	0	1
	Type	695	.5006595	.5003597	0	1
	Single	695	.2614786	.4397565	0	1
	Divorced	695	.0256607	.1582349	0	1
	Married	695	.6236525	.4848178	0	1
	Widowed	695	.0892082	.2852493	0	1
	Rural	695	.2762375	.4474578	0	1

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

TABLE 2 . RESULTS PROBIT ESTIMATION

 2

	Number of obs	=	695
	Wald chi2(13)	=	35.60
	Prob > chi2	=	0.0007

TABLE 3 . PROBIT MARGINAL AND AVERAGE EFFECTS

 3 dF/dx is for discrete change of dummy variable from 0 to 1 z and P>|z| are the test of the underlying coefficient being 0

	Number of obs =	695
	Wald chi2(13) = 35.60
	Prob > chi2	= 0.0007

Page 23 of 24 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

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

The data are based on those for England[START_REF] Acheson | Independent Inquiry into Inequalities in health[END_REF]. Available data on life expectancy at age

by education groups in Madrid and Barcelona show similar patterns(Borrel et al. 1999).

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

Acknowledgements

We would like to thank Juan Diez-Nicolas, Paul Dolan, Roberto Gonzalez, Andrew Jones, Jaime Pinilla, Rebecca Shaw, Alan Williams, and the anonymous referee and the editor of Applied Economics for their input. We are also grateful to all the respondents who agreed to take part in the survey, and to the Spanish Instituto de Estudios Fiscales for financial support to undertake this research. The usual disclaimers apply.


A Dupuy
email: a.dupuy@roa.unimaas.nl.

Lex Borghans

Frank Cörvers

Bart Golsteyn

Ben Kriechel

Philip Marey

Christophe Meng

Inge Sieben

Wendy Smits

Bas Ter Weel

Will the skill-premium in the Netherlands rise in the next decades? *

Keywords: Skill premium, SBTC, Capital-skill complementarity

While the skill-premium has been rising sharply in the US and the UK for 20 years, the Dutch skill-premium decreased for much of that period and only started to rise in the early 90s. In this paper, we investigate whether the Dutch skill-premium will rise in the next decades. To answer this question, we forecasts the skill-premium using the Katz and Murphy (1992) and the Krusell et al. (2000) models. The Katz and Murphy model (KM) explains demand shifts by skill-biased technological change in unobservable variables captured by a time trend. In contrast,

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

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

	Page 25 of 29 Page 27 of 29	Submitted Manuscript Submitted Manuscript Submitted Manuscript	Page 26 of 29
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	F o r Wdeoh 5= Frpsdulvrq ri fkdqjhv lq wkh vnloo0suhplxp xqghu VEWF dqg Fdslwdo NP prgho *L} Ovw Oxw G ' U 2 dgm F o wlph G 2 ' f=f f=eb d 2=H. f=D. r Ef=fDH
	f=bS f=e e e Ef=f2 e P e r R v i w Shulrg NP/ frqwulexwlrq ri= d vlj dw I vnloo frpsohphqwdulw|1 NRUY/ frqwulexwlrq ri= 9<0;4 ;40<9 9<0<9 wlph *L} O vw Oxw e w 2 =.D ' =.D 2 2=. ' f=. 2 =22 ' =22 *L} N w *L} O vw Oxw |4i G 2 ' f =f2 f =Df d =Hb f =Sb Ef =fSH P wlph G 2 ' f=f f=. d =e f=.e e Ef=fH wlph G 2 ' f=fe f=Hb2 d =2 f=.S e e w =bb =D2 ' =De =Sb 2=DS ' f=H. =H =f ' =b Qrwh= wkh frqwulexwlrqv duh h{suhvvhg lq dqqxdo shufhqwdjh udwhv1 r NRUY prgho *L} O vw Oxw G ' U 2 dgm R *L} N w G ' f=f f=2He d =D2 f=ee Ef=fSf e *L} N w G ' f=2f f=ef2 d 2=eb f=eb v Ef=f.H i *L} k w G ' f =f f =D2f d =b2 f =eb e Ef =ff *L} N w G ' f=ef f=S. d =D. f=eH w Ef=2e	Gdwd w =fb f=Db f=H
	+Vwdqgdug0ghyldwlrq, d vlj dw I
	GZ Gxuelq0Zdwvrq +Vwdqgdug0ghyldwlrq,
	Qrwh= lv wkh hodvwlflw| ri vxevwlwxwlrq ehwzhhq vnloohg dqg Qrwh= lv wkh hodvwlflw| ri vxevwlwxwlrq ehwzhhq vnloohg dqg
	xqvnloohg oderu1 xqvnloohg oderu1
		58 59 5:
	Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

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