L Bettendorf
email: bettendorf@few.eur.nl

E Dijkgraaf
email: dijkgraaf@few.eur.nl

The bicausal relation between religion and income

Keywords: D31 -Personal Income, Wealth, Income, Religious Membership, Religious Participation Income, Religious Membership, Religious Participation JEL classification: Z12, D31

In this paper the relation between religion and income is investigated using a micro-dataset for the Netherlands. Religion is measured by religious membership and by participation. Instead of estimating a religion equation and an income equation separately, joint regression is preferred since this generally yields more efficient estimates. Following the single-equation approach, both religious measures are found to decrease income significantly and income is found to affect religion negatively. However, these cross-effects become insignificant once the equations are estimated simultaneously. In contrast, the effects of socio-economic characteristics on religion and income hardly differ between the approaches.

is summarized in Table 1. 4 Almost all studies focus on the differences in effect between denominations (Jewish, Catholic, Protestant, etc.). [START_REF] Crain | Economic growth regressions for the American states: a sensitivity analysis[END_REF] and [START_REF] Lipford | Religious participation and income[END_REF], however, analyze the effect of church membership without distinguishing denominations. With the exception of [START_REF] Steen | Religion and earnings: evidence from the NLS Youth Cohort[END_REF], only recently has the participation effect of religious behavior been empirically tested [START_REF] Cornwell | Religious background and the labor supply and wages of young women[END_REF][START_REF] Barro | Religion and economic growth across countries[END_REF][START_REF] Mangeloja | Economic growth and religious production efficiency[END_REF]. Until the cross-country studies of [START_REF] Barro | Religion and economic growth across countries[END_REF] and [START_REF] Mangeloja | Economic growth and religious production efficiency[END_REF], all results were based on data for Canada and the USA. The results are always positive for the Jewish belief. More mixed results are found for other denominations and for participation. Interestingly, Mangeloja (2005) also presents estimations with time series for eight OECD countries. He finds that the effect of religion on income growth is not consistent between countries. While he finds an insignificant effect of religion on income growth for five countries, other countries show a negative or positive effect.

A second strand of the literature analyzes the reverse relation, i.e. the effect of income (and other socio-economic characteristics) on religion. According to [START_REF] Iannaccone | Introduction to the economics of religion[END_REF] this literature finds a strong positive relation between income and financial contributions to churches, but often a weak relation with other religious variables (attendance, membership, frequency of prayer and beliefs). [START_REF] Sawkins | Church attendance in Great Britain: an ordered logit approach[END_REF], for instance, find an insignificant relationship between non-labor income and church attendance using micro-data for Great Britain. The coefficients for labor earnings variables, however, imply higher church attendance for middle-income earners.

Although these two types of analyses suggest that there might be a bicausal relationship between religion and income, most studies ignore the endogeneity of religion. As long as the role of endogeneity is unclear, the general conclusions of the literature can be questioned, as neglect of endogeneity might result in biased estimations. One exception is [START_REF] Lipford | Religious participation and income[END_REF]. They estimate a system of equations to account for the effect of church membership on income but also for the reverse effect. They find that not only the estimated effect of church membership on income is negative, but also the effect of income on church membership. Furthermore, the estimate of the former effect is twice that with single-equation estimation. [START_REF] Barro | Religion and economic growth across countries[END_REF] also take the endogeneity issue seriously. 5 They account for this problem by using instrumental variables in a three-stage least squares estimation. Again they find that endogeneity is important and that correcting for this problem results in larger coefficients with the same sign. They find that religion influences income growth negatively when measured by church attendance and positively when measured by beliefs (in hell and heaven).

While [START_REF] Lipford | Religious participation and income[END_REF] use a state-level database with 153 observations for the USA, [START_REF] Barro | Religion and economic growth across countries[END_REF] use a panel database with 181 observations for 59 countries. This paper analyzes a micro-dataset for the Netherlands with observations for 27,908 households. We find that whether we estimate the income and the religion equations separately or simultaneously matters for the results. While religiousness is found to reduce income significantly when single equations are estimated, joint estimation results in an insignificant effect.6

The contribution to the literature of this paper is threefold. First, we estimate the bicausal relation between religion and income for the Netherlands while the literature is dominated by results for the USA and Canada. Second, our dataset allows us to discriminate between the effects of religious membership and of religious participation. Third, we show with micro-data that the equations should be estimated jointly to explain the relation between religion and income.

The next two sections discuss the estimation methodology and the data. Section IV describes the estimation results. The last section concludes.

II Methodology

We start by estimating the relation between religion measured by church membership and income.

As both variables are measured as discrete variables, a probit estimator is applied. Membership is denoted by the dummy y 1i with the value 1 if household i is a member of a church. As income is available only in deciles,7 y 2i denotes the after-tax income class of household i. The system of structural equations is expressed in terms of the latent variables. This specification assumes that households have complete flexibility in their decisions but that the researcher can only observe the choices as discrete variables (see [START_REF] Blundell | Coherency and estimation in simultaneous models with censored or qualitative dependent variables[END_REF]. 8 The structural model written in terms of the latent variables (y * 1 and y * 2 ) and vectors of socio-economic control variables (x 1 and

x 2 ) is:

y * 1i = α 1 y * 2i + β 0 1 x 1i + u 1i y 1i = 1 if y * 1i > 0, = 0 otherwise y * 2i = α 2 y * 1i + β 0 2 x 2i + u 2i y 2i = j if μ j-1 < y * 2i ≤ μ j j = 1, ., J (II.1)
The second equation contains J +1 cutoffs μ j . Assuming that y * 2 has an infinite support yields that μ 0 = -∞ and μ J = ∞. Since x 2 includes a constant, μ 1 = 0 has to be imposed. The remaining J -2 cutoffs are estimated.

Model (II.1) cannot be directly estimated since it contains non-observables on the right-hand side.

Therefore, the reduced form equations are derived as, with D ≡ (1α 1 α 2 ),

y * 1i = β0 1 x i + v 1i β0 1 x i = ¡ β 0 1 x 1i + α 1 β 0 2 x 2i ¢ /D v 1i = (u 1i + α 1 u 2i ) /D y * 2i = β0 2 x i + v 2i β0 2 x i = ¡ α 2 β 0 1 x 1i + β 0 2 x 2i ¢ /D v 2i = (α 2 u 1i + u 2i ) /D (II.2)
where x i = x 1i ∪x 2i . A variable that occurs in both structural equations thus has a coefficient equal with means 0, variances 1, and covariance ρ.9 To compare the results of the system estimation, we also apply a probit regression to each equation separately. The single equations are specified similarly to (II.1), where the latent variable y * k on the right-hand side is replaced by the observed y k . 10 The estimation procedure is explained in Appendix A.

to (β 1 + α 1 β 2 ) /D and (α 2 β 1 + β 2 ) /D
In the estimation of a second system, religiousness is measured by church attendance. The binary y 1 is replaced by a dummy with the value 1 if the household attends church services at least once a week. The vector of control variables (x) in this system contains dummies indicating the denomination to which the respondent belongs. One could argue that the choice of denomination should also be treated as an endogenous decision. However, this last option implies in our case simultaneous estimation of three equations (two ordered probits for income and denomination membership and one probit for participation). As this clearly results in econometric complexities, simplification is desirable. This is motivated by the intuitive observation that endogeneity is a more serious problem with participation than with membership choice, as most people stick to the church membership they are born with, while participation is changed far more often. Indeed, [START_REF] Tomes | The effects of religion and denomination on earnings and the returns to human capital[END_REF] shows that more than 75% of Canadians keep the religion they are raised in (this figure is 86% for Protestants and 81% for Catholics). In contrast, a majority of the people that are not raised in a religion become members of a church later on (53%). Figures for the Netherlands are in accordance with this observation [START_REF] Becker | Secularisatie in de Jaren Negentig (Secularisation in the Nineties), Social and Cultural Planning Office of the Netherlands[END_REF].11 While membership did not change much between 1991 (43%) and 1999 (37%), religious participation (defined as the share of members attending services at least once a week) decreased by 26%. This was especially the case for Roman Catholics, for whom this share decreased by 53% to a level of 14% in 1999. 12It should be noted that one can doubt the quality of the answers on the membership question because official but inactive members, who make up a large part of total members, might answer this question arbitrarily with yes or no. Answers on questions about participation are considered to be more precise. We therefore believe that the participation variable is a more reliable measure of religiousness.

III Data

Data are from 2000 for 27,908 Dutch households. These data are based on a survey of Statistics Netherlands (CBS), which gives, according to the CBS, a reliable picture of the total Dutch population. In this survey households are questioned about socio-economic characteristics (such as age, education level and composition of households), the level of after-tax household income13 and church membership.

The income tax is in principle levied on individual income. However, fiscal partners can transfer joint income components between them for their tax return. Benefits that are means tested are based on household income.14 Specific church taxes are not levied in the Netherlands. Tax refunds arising from contributions to churches are not included in our income concept.

Households can choose between no membership of a denomination or membership of the following denominations: Roman Catholic, two types of Protestants (Reformed and 'Gereformeerd'), Islam and non-specified other denominations. 15 Furthermore, members of a denomination are asked how many times per year they attend a service of that denomination. Membership and frequency

F o r P e e r R e v i e w
of attendance are unfortunately not reported for individual family members, but only for the respondent (always an adult). This study therefore focuses on the question of whether household income is different when at least the respondent is religious. Ideally, we would need information on the religious behavior of all household members, but these data are not available. In our opinion this limitation is not crucial for our estimations as homogeneous religiousness within households is still the rule, especially for membership. [START_REF] Kalmijn | Intermarriage and homogamy: causes, patterns, trends[END_REF] concludes on the basis of several studies for western countries that both Catholics and Protestants have a tendency to marry within rather than outside their group. [START_REF] Hendrickx | Religious and educational assortive marriage patterns in the Netherlands, 1940-1985[END_REF] confirms this for the Netherlands.

Our estimations are based on two different datasets (Table 2). The full dataset (27,908 observations) is used to estimate the system with membership as endogenous variable. As here religion is defined as membership of a church, we include observations for church members (16,758) as well as for non-church members (11,150). These latter observations are excluded in the second system estimation, with participation as endogenous variable, as non-church members have zero participation by definition. Since the non-church-member dummy would be perfectly correlated with participation (=0), estimation of the corresponding coefficient in the first equation is impossible.

Estimation of the income equation would suffer from multicollinearity for the same reason.

In total 16,758 respondents are members of some denomination (see Table 3). This is 60% of all households, which is comparable to the figure for the USA according to [START_REF] Iannaccone | Progress in the economics of religion[END_REF]. Roman

Catholic membership applies for 52% of all members, while 36% are members of a Protestant church. Finally, 4% are members of the Islamic faith and 9% of some non-specified denomination.

Comparing the number of church members who seldom or never attend services (7,366) with total membership of denominations makes it clear that many members are not religiously active. While this comprises 44% of total church members, the differences between denominations are large, with members of the Roman Catholic, Reformed and Islamic denominations having the lowest participation levels. Only 21% of church members attend a church service often (once or more per week). This is somewhat lower than in Canada and much lower than in the USA, according to

IV Results

First we discuss the estimation results for the bicausal relation between religious membership and income. The second subsection presents the results for religious participation. The third subsection discusses results for the socio-economic characteristics.

IV.1 Membership and income

Table 5 presents the estimation results for religion defined as membership of a denomination. In panel A the results are given for the membership equation, while in panel B the results are shown for the income equation. Columns two and three present the structural coefficients and the standard errors, while the fourth column gives marginal effects. 18 The system results can be compared with the results for the single-equation estimations, presented in the last two columns. The choice of the identifying restrictions is motivated by the single-equation results. In the system estimation, the Male dummy is excluded from the membership equation, while the Child 12-18 dummy is dropped 18 Marginal effects on income are calculated in euros using the average income per decile from Table 4 and expressed as a % of the sample average income. The marginal effects of age are multiplied by its standard deviation (=15) for a better scaling. See [START_REF] Bettendorf | The bicausal relation between religion and income[END_REF] for details on the computation and for individual decile effects. These results are also available on request. A first finding is that ρ is significant (at 1%). 20 The results of the system estimation are therefore preferred to the single-equation estimations. The single-equation approach results in highly significant, negative cross-effects between membership and income. The significant bicausal relation is no longer found with the more efficient simultaneous estimation. The structural estimates show that for given socio-economic variables income has no effect on membership. The negative coefficient in the single membership equation incorrectly identifies part of the non-income effects as pure income effects. A similar interpretation holds for the income equation. The rejection of bicausality might suggest that system estimation is not required. However, system estimation still yields more efficient estimates than single-equation estimation since it accounts for the correlation between the disturbance terms of both equations.

In contrast, [START_REF] Lipford | Religious participation and income[END_REF] found that system estimation did not change the significant, negative effect of income on membership, but that the negative coefficient for the opposite effect doubled. The negative relation between membership and income in both directions is not found in our dataset.

IV.2 Participation and income

Table 6 presents the estimation results for religious participation. The identifying restrictions are the same as in the first system (with membership as religious measure). Again, ρ is significant.

With single-equation estimation, both the coefficient for the effect of income on participation and the coefficient for the opposite effect are significantly negative. However, estimating a system again yields insignificant cross-effects, suggesting that households who attend church services frequently do not have a significantly lower income. Concerning the reverse effect, Iannaccone (1998) reports that most studies find that income is a weak predictor of church attendance. 19 Sensitivity analyses with other restrictions show that our main conclusions do not depend on this choice. Alternative identifying restrictions are motivated by the significance level or the magnitude of marginal effects in the single-equation estimation. Results are available upon request. 20 For both the membership and participation estimations this result is confirmed by a log likelihood ratio test. Interestingly, we find an effect of Islamic membership on income after controlling for religious participation. Compared with the benchmark (a Reformed household), Islamic households have less income (-25%). This effect is in accordance with results found by [START_REF] Barro | Religion and economic growth across countries[END_REF], although our effects are much larger. It should be kept in mind that part of this large effect probably has to do with the specific labor market position of persons coming from Islamic countries. 21 The insignificant effect of Catholic membership on income is in line with [START_REF] Cornwell | Religious background and the labor supply and wages of young women[END_REF].

However, [START_REF] Heath | Religion and economic welfare: an empirical analysis of state per capita income[END_REF] found a negative effect and [START_REF] Steen | Religion and earnings: evidence from the NLS Youth Cohort[END_REF] found a positive effect for this variable.

Summarizing, our analysis shows that estimating a single equation may lead to erroneous conclusions about the effect of religion on income. Clearly, the conclusions of [START_REF] Lipford | Religious participation and income[END_REF] and [START_REF] Barro | Religion and economic growth across countries[END_REF] cannot be confirmed for our data as in their cases the effect remains significantly negative after correcting for endogeneity. The significant effects found in [START_REF] Cornwell | Religious background and the labor supply and wages of young women[END_REF] and [START_REF] Steen | Religion and earnings: evidence from the NLS Youth Cohort[END_REF] might be misleading since they follow the single-equation approach. Our results are more in line with [START_REF] Mangeloja | Economic growth and religious production efficiency[END_REF] as he finds insignificant effects for five out of eight countries using country-level data. The effect of religion on income probably differs between countries, making cross-country analysis a troublesome route to follow.

IV.3 Effects of socio-economic characteristics

In contrast to the former findings, system estimation hardly affects the coefficients representing the effects of socio-economic characteristics. This is illustrated by way of the marginal effects calculated for the case with religious participation (Figures 1 and2). 22 Two features can be observed. First, the marginal effects obtained for the structural system hardly differ from the ones for the reduced system (if the corresponding coefficient is significantly estimated). In other words, the direct effect of the socio-economic characteristics dominates the indirect effects for both endogenous variables. 21 Sensitivity analysis shows that all conclusions are robust when data from Islamic members are excluded. Results are available on request.

22 See [START_REF] Bettendorf | The bicausal relation between religion and income[END_REF] for details on the computation and for detailed effects. These results are also available on request. Second, system estimation yields effects comparable to those from single-equation estimation. In the following we discuss in detail the structural coefficients of the socio-economic variables.

The effects of socio-economic control variables on income are in general as expected (see Panel B in Tables 5 and6). Income increases with the level of education and the age profile has an inverted U-shape (with a peak at 46 and 44 years, respectively). 23 Households with a male breadwinner have higher income levels (only significant in Table 5). Larger households have a lower level of income, although there is some indication that households with children under 12 have more.

Households with one adult have less income than households with two grown-ups without children (remember that our endogenous variable is household income). Finally, there is some indication that Dutch households have more income than non-Dutch households and that households living in more densely populated areas have higher incomes. and education level. According to Table 6, single-adult households have 46% less income than households with two grown-ups, while a high education level increases income by 47%.

More interesting are the effects of socio-economic variables on the religious variables (see Panel A in Tables 5 and6). While Roman Catholic households have a lower religious participation than Reformed households (-9%: see Table 6), the 'Gereformeerden' and other church members show a higher religious participation (30% and 32%, respectively). In contrast, [START_REF] Barro | Religion and economic growth across countries[END_REF] find a higher church attendance for the Roman Catholics than for Protestants, while Sawkins et al.

(1997) also find that Catholics have the highest attendance level in Great Britain. The situation in the Netherlands seems to be different from that in other countries. This stresses the point that the dominance of empirical studies based on data for Canada and the USA might be misleading.

Furthermore, it questions the soundness of cross-country estimations such as that of [START_REF] Barro | Religion and economic growth across countries[END_REF], as members of the same religion might behave differently in different countries.

The relation between age and religious variables is U-shaped, but this effect is only significant for in Table 6). [START_REF] Sawkins | Church attendance in Great Britain: an ordered logit approach[END_REF] find a comparable pattern for Great Britain. However, this conflicts with the results of [START_REF] Barro | Religion and economic growth across countries[END_REF] as they find a positive effect for the share of population younger than 15 on church attendance and an insignificant effect for the share of people older than 65.

The size of the household has positive effects: larger households are more often members of a church and they also have greater religious participation. These effects are, however, reduced when young children are present. The marginal effects on church membership in Table 5 show that the net effect, when we increase the household size with one and assume that this increase stems from an extra child, is even negative when the youngest child is between 4 and 18 years old. Single-adult households do not attend services more often, nor are they more frequently church members (the coefficients for this variable are not significantly different from zero).

None of the education dummies has a significant effect on membership or participation. [START_REF] Barro | Religion and economic growth across countries[END_REF] find that higher education levels lead to higher levels of religious belief and more church attendance. [START_REF] Sacerdote | Education and religion[END_REF] argue that households with higher education more often choose to leave the church, but also intensify their religious behavior when they decide to stay. [START_REF] Sawkins | Church attendance in Great Britain: an ordered logit approach[END_REF] find also a positive effect of education on church attendance. However, we do not find this pattern for the Netherlands. Dutch households are less often members of a church (note that the marginal effect is -23%), although Dutch members attend services as often as non-Dutch members. Finally, households living in less densely populated areas participate more and are also more often members of a church.

V Conclusions

This paper focuses on the estimation of the effect of religion on income, using a large micro-dataset for the Netherlands. Religion is captured by two measures: church membership and attendance.

We find that the estimates of the cross-effects following the single-equation approach differ greatly from the ones obtained from the more efficient system approach.

When religion is measured by membership, we find with the single-equation approach that membership reduces the income level significantly and that income has a negative effect on membership.

However, both coefficients become insignificant under simultaneous estimation. The bicausal relation is also rejected when religion is measured by church attendance (for the subset of church members). In contrast, the effects of the socio-economic characteristics on religion and income hardly differ between the estimation approaches.

The conclusion that religion does not affect income, when properly estimated, might be specific for the Dutch situation. For future research we plan to investigate, using micro-datasets, whether the impact of religious behavior differs between countries. where I indicates a dummy variable that equals 1 when observation i matches the combination of y 1 and y 2 . Maximizing (A.3) gives the estimates of the structural coefficients (α k , β k ), the cutoff points (μ j ) and the correlation (ρ).

Notice that in the special case with ρ = 0, the bivariate system separates into the binary Probit

Figure 1 :

 1 Figure 1: Marginal effects of Income equation for Participation case (% of average income)

Figure 2 :

 2 Figure 2: Marginal effects of Participation equation (%)

  equation estimations. The negative effect of children is larger for households with young children as the coefficients for the Child dummies are significantly negative (except for Child <4 years

  1i = 1, y 2i = j) ln Pr(y 1i = 1, y 2i = j) + I(y 1i = 0, y 2i = j) ln Pr(y 1i = 0, y 2i = j)}(A.3)

  and the ordered Probit since Φ 2 (a, b, 0) = Φ(a)Φ(b). The log likelihood (A.3) simplifies to the sum of the log likelihood functions of the single equations.

Table 1 :

 1 Literature income and religion

	No. Country	Level of data	Measure of religion Effect on income
	1.	USA	Micro: men	Membership	Positive (Jewish)
	2.	Canada	Micro: men	Membership	Insignificant (within memberships)
	3.

  of the structural coefficients requires that x 1 contains at least one variable that is not included in x 2 and vice versa. The reduced form disturbances v k are assumed to have a joint normal distribution

	F o r
	P
	e
	e r
	R e v
	i e
	w
	in the reduced form equations, respectively. Identification

Table 2 :

 2 Descriptive statistics: income and socio-economic characteristics

			Sample members			Full sample
		Ave. St. dev. Max. Min.	Ave. St. dev. Max. Min.
	Income (decile)	5.43	2.81	10	1	5.57	2.84	10	1
	Member Catholic	0.52	0.50	1	0	0.31	0.46	1	0
	Member Ref ormed	0.24	0.42	1	0	0.14	0.35	1	0
	Member Geref ormeerd	0.12	0.32	1	0	0.08	0.25	1	0
	Member Islam	0.04	0.20	1	0	0.02	0.15	1	0
	Member Other	0.09	0.28	1	0	0.05	0.22	1	0
	Age	49.42	15.35	85	15	47.57	14.97	85	15
	Male	0.82	0.38	1	0	0.81	0.39	1	0
	Household size	2.91	1.38	6	1	2.86	1.34	6	1
	Child<4 years	0.16	0.37	1	0	0.17	0.37	1	0
	Child 4-12 years	0.16	0.36	1	0	0.16	0.37	1	0
	Child12-18 years	0.11	0.31	1	0	0.10	0.31	1	0
	Single-adult household	0.18	0.38	1	0	0.19	0.39	1	0
	Education low	0.06	0.24	1	0	0.06	0.24	1	0
	Education mid	0.34	0.47	1	0	0.34	0.47	1	0
	Education high	0.22	0.41	1	0	0.25	0.43	1	0
	Dutch	0.97	0.18	1	0	0.97	0.16	1	0
	Surface per inhabitant	3.25	1.25	5	1	3.08	1.29	5	1

Table 3 :

 3 Descriptive statistics: number of denomination members[START_REF] Iannaccone | Deregulating religion: the economics of church and state[END_REF]. Countries such as Switzerland, Australia, Germany, New Zealand and the UK have a somewhat lower attendance rate, while Scandinavian countries especially have a very low religious participation rate (less than 10%). In our estimations the participation dummy is based on the category of church visits of at least once per week. Our results do not depend on this definition. When participation is defined as church attendance at least twice per month, results are comparable. In another alternative, we treat households that never attend services as non-church members. This reclassification also hardly affects our conclusions.16

			Participation: minimum number of services attended per year
	Membership Roman Catholic	All 8,655	52 882	24 641	12 1,043	< 12 1,979	≈ 0 4,110
	Reformed	4,041	860	376	287	502	2,016
	'Gereformeerd'	1,944	951	259	134	167	433
	Islam	678	212	35	35	78	318
	Other	1,440	608	131	74	138	489
	Total	16,758	3,513	1,442	1,573	2,864	7,366
				10

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

Table 4

 4 area and 5 for a sparsely populated country village). Dummies are available for four types of family composition (benchmark is households with two adults and no children under 18 years old), for four education levels (benchmark is households with an education level less than low) and for the breadwinner being of Dutch nationality (benchmark is households with breadwinner not of Dutch nationality).

	16 Results for both sensitivity analyses are available on request and are also included in Bettendorf and Dijkgraaf
	(2005).

gives more information about the income deciles. Although we only have information on which decile households are in, average and maximum decile figures in euros are available.

The average income for our sample is 24,800 euro per year. The distribution of households over the deciles is quite equal with a minimum of 2,508 and a maximum of 2,872 households per decile. The table also shows the number of non-church-member households per decile (column with Membership=0) and the number of households that are church members (Membership=1), divided into members who participate less than once a week (Part=0) and members who participate at least once a week (Part=1).

Data are available for the most important socio-economic characteristics (see Appendix B for definitions). For most characteristics information is expressed as a dummy variable. Exceptions are age (available for the breadwinner and included in years and its square), household size (the number of persons in the household)

17

and surface per inhabitant (ordered variable with value 1 for a densely populated 17 Statistics Netherlands does not report data for households consisting of more than 6 persons for privacy reasons. 11 Page 11 of 26 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 4 :

 4 Income deciles

			Number of households		Income in euros per year
	Income	Membership=1	Member-
	decile	Part=1	Part=0	ship=0	Total	Average	Maximum
	1	357	1,137	1,014	2,508	4,900	10,000
	2	465	1,315	897	2,677	11,500	12,900
	3	502	1,296	1,018	2,816	14,300	15,700
	4	416	1,348	1,082	2,846	17,100	18,700
	5	386	1,372	1,095	2,853	20,500	22,200
	6	320	1,397	1,155	2,872	24,100	25,900
	7	308	1,386	1,178	2,872	27,900	29,900
	8	276	1,408	1,150	2,834	32,400	35,100
	9	275	1,309	1,252	2,836	38,700	43,200
	10	208	1,277	1,309	2,794	56,500	na
	Total	3,513	13,245	11,150	27,908

Table 5 :

 5 Estimation results: religious membership

		Structural System		Single
		Coeff.	St. error Marg. 1	Coeff.	St. error
	A. Membership
	Income	0.245	(0.548)	8.99	-0.015 * * *	(0.003)
	Age	-0.032	(0.039)	6.25	-0.012 * * *	(0.004)
	Age 2 (*1000)	0.463	(0.411)		0.257 * * *	(0.036)
	Male	(-)		(-)	0.012	(0.024)
	Household size	0.174 * * *	(0.042)	6.21	0.153 * * *	(0.012)
	Child <4 years	-0.156 * * *	(0.053)	-5.65	-0.135 * * *	(0.032)
	Child 4-12 years	-0.270 * * *	(0.065)	-9.84	-0.242 * * *	(0.033)
	Child 12-18 years	-0.193 * * *	(0.036)	-7.03	-0.200 * * *	(0.033)
	Single-adult household	0.407	(0.701)	13.50	0.056 *	(0.029)
	Education low	-0.169	(0.189)	-6.08	-0.073 * *	(0.034)
	Education mid	-0.172	(0.253)	-6.19	-0.043 * *	(0.020)
	Education high	-0.445	(0.569)	-16.47	-0.154 * * *	(0.022)
	Dutch	-0.710 * * *	(0.175)	-22.62	-0.625 * * *	(0.053)
	Surface per inhabitant	0.152 * * *	(0.006)	5.45	0.153 * * *	(0.006)
	B. Income
	Membership	0.117	(0.120)	5.20	-0.058 * * *	(0.013)
	Age	0.071 * * *	(0.004)	-1.00	0.070 * * *	(0.003)
	Age 2 (*1000)	-0.777 * * *	(0.046)		-0.739 * * *	(0.028)
	Male	0.042 * *	(0.018)	1.88	0.044 * *	(0.019)
	Household size	-0.092 * * *	(0.016)	-4.02	-0.070 * * *	(0.009)
	Child<4 years	0.093 * * *	(0.023)	4.43	0.074 * * *	(0.025)
	Child 4-12 years	0.132 * * *	(0.026)	6.29	0.098 * * *	(0.026)
	Child 12-18 years	(-)		(-)	-0.027	(0.026)
	Single-adult household	-1.268 * * *	(0.023)	-49.82	-1.255 * * *	(0.022)
	Education low	0.353 * * *	(0.029)	14.67	0.341 * * *	(0.027)
	Education mid	0.467 * * *	(0.017)	19.78	0.459 * * *	(0.015)
	Education high	1.061 * * *	(0.028)	48.56	1.035 * * *	(0.017)
	Dutch	0.379 * * *	(0.085)	16.06	0.292 * * *	(0.039)
	Surface per inhabitant	-0.016	(0.019)	-0.69	0.005	(0.005)
	Rho	-0.036 * * *	(0.008)		0
	Log L	-76,675			-76,665
	Observations	27,908			27,908
	1. Marginal effects in %-point change of base value for Membership (60.34%) and
	% change of base value for Income (24.8 thousand euro). Quadratic and linear
	effect of age are combined in one marginal effect.
	Coefficients with */**/*** are significant at the 10%/5%/1% level.

Table 6 :

 6 Estimation results: participation (once or more per week)

		Structural System		Single
		Coeff.	St. error Marg. 1	Coeff.	St. error
	A. Participation
	Income	1.475	(1.859)	35.51	-0.030 * * *	(0.005)
	Member Catholic	-0.450 * * *	(0.045)	-9.20	-0.440 * * *	(0.030)
	Member Geref ormeerd	0.908 * * *	(0.095)	29.54	0.846 * * *	(0.037)
	Member Islam	1.393	(1.111)	47.04	0.473 * * *	(0.067)
	Member Other	0.971 * * *	(0.306)	31.87	0.726 * * *	(0.042)
	Age	-0.106	(0.105)	12.89	-0.019 * * *	(0.006)
	Age 2 (*1000)	1.348	(1.161)		0.393 * * *	(0.052)
	Male	(-)		(-)	0.046	(0.041)
	Household size	0.256 * * *	(0.094)	6.67	0.181 * * *	(0.016)
	Child <4 years	-0.215	(0.149)	-4.35	-0.110 * *	(0.054)
	Child4-12 years	-0.351 * *	(0.160)	-6.76	-0.234 * * *	(0.053)
	Child12-18 years	-0.179 * *	(0.077)	-3.67	-0.199 * * *	(0.051)
	Single-adult household	1.927	(2.224)	52.58	0.112 * *	(0.046)
	Education low	-0.467	(0.581)	-12.73	0.014	(0.051)
	Education mid	-0.671	(0.849)	-17.48	0.032	(0.030)
	Education high	-1.573	(1.943)	-31.74	0.039	(0.036)
	Dutch	-0.277	(0.250)	-7.23	-0.085	(0.070)
	Surface per inhabitant	0.075 *	(0.039)	1.85	0.045 * * *	(0.010)
	B. Income
	Part	0.068	(0.156)	2.95	-0.109 * * *	(0.021)
	Member Catholic	0.037	(0.071)	1.62	-0.003	(0.020)
	Member Geref ormeerd	-0.099	(0.135)	-4.28	-0.010	(0.029)
	Member Islam	-0.631 * * *	(0.095)	-25.21	-0.581 * * *	(0.050)
	Member Other	-0.210 *	(0.119)	-8.94	-0.135 * * *	(0.032)
	Age	0.058 * * *	(0.005)	-3.38	0.055 * * *	(0.004)
	Age 2 (*1000)	-0.651 * * *	(0.079)		-0.607 * * *	(0.036)
	Male	0.027	(0.026)	1.17	0.032	(0.026)
	Household size	-0.062 * *	(0.024)	-2.65	-0.044 * * *	(0.011)
	Child <4 years	0.077 * *	(0.030)	3.57	0.067 * *	(0.034)
	Child 4-12 years	0.093 * * *	(0.034)	4.30	0.071 * *	(0.034)
	Child 12-18 years	(-)		(-)	-0.019	(0.034)
	Single-adult household	-1.192 * * *	(0.039)	-45.65	-1.175 * * *	(0.030)
	Education low	0.312 * * *	(0.035)	12.67	0.311 * * *	(0.034)
	Education mid	0.454 * * *	(0.020)	18.90	0.455 * * *	(0.019)
	Education high	1.046 * * *	(0.023)	47.12	1.043 * * *	(0.023)
	Dutch	0.131 * *	(0.051)	5.58	0.123 * *	(0.050)
	Surface per inhabitant	-0.023 * *	(0.010)	-0.98	-0.018 * * *	(0.007)
	Rho	-0.067 * * *	(0.012)		0
	Log L	-42,547			-42,532
	Observations	16,758			16,758
	1. Marginal effects in %-point change of base value for Part (20.83%) and
	% change of base value for Income (24.8 thousand euro). Quadratic and linear
	effect of age are combined in one marginal effect.
	Coefficients with */**/*** are significant at the 10%/5%/1% level.

Page 16 of 26 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Other effects are also analyzed in the literature such as effects on mental and physical health, crime and divorce. See[START_REF] Iannaccone | Introduction to the economics of religion[END_REF] for an excellent overview.

See alsoMcCleary and Barro (2006).

Notice that even in the absence of a serious endogeneity problem, system estimation yields generally more efficient estimates by using the correlation of the disturbance terms. 5 Page 5 of 26 Editorial Office, Dept of Economics, Warwick University, Coventry CV4

7AL, UKSubmitted Manuscript

Statistics Netherlands calculates deciles from the original level of data for privacy reasons.

Maddala (1983, p. 124) interprets a latent variable as a measure of intentions.[START_REF] Blundell | Coherency and estimation in simultaneous models with censored or qualitative dependent variables[END_REF] consider a class of structural models that are simultaneous in the observed dependent variables. As a consequence, the reduced form cannot be derived explicitly and extra coherency restrictions have to be imposed.

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

This implies that the structural disturbancesu k = v kα k v k 0 (k 6 = k 0 ) are normally distributed with means 0, variances (1 + α 2 k -2α k ρ) and covariance (1 + α 1 α 2 ) ρα 1α 2 .

Note that the rejection of the hypothesis ρ = 0 means that system estimation is preferred to single-equation regressions.

Our dataset contains no information about the religion in which a person was raised.

This is in line with the conclusion of[START_REF] Iannaccone | Introduction to the economics of religion[END_REF]Iannaccone ( , p. 1470) that the empirical literature shows that for religious membership, 'income or wage effects are almost always dwarfed by those of age, gender, and religious upbringing.'

We have no information on the wage rate or hours of work.

Detailed information can be found in DeMooij (2006, Section 3.4) and on the Ministry of Finance website (www.minfin.nl/en/subjects,taxation/income-tax).

The Reformed Church and the 'Gereformeerde' Church are both Protestant churches. Although they are alike in some respects, the differences are large in others. Tests show that it is not appropriate to combine them in one Protestant dummy (orthodox Protestants are included in the dummy for the Reformed Church). Reformed households are taken as benchmark in the estimation, so the dummy for this religion is excluded.

In all tables, the coefficient of Age 2 is multiplied by 1000 for a better scaling.

This appendix is based onHall et al. (2000, Appendix B),[START_REF] Greene | Econometric Analysis[END_REF] and[START_REF] Maddala | Limited-Dependent and Qualitative Variables in Econometrics[END_REF].

In this research, data have been used from "Permanent Onderzoek Leefsituatie

The probability that y 1i = 1 and y 2i = j for observation i is given by

where Φ 2 (a, b, ρ) is the cumulative unit bivariate normal distribution with correlation coefficient ρ evaluated at cutoff points a and b. Notice that for the two outside classes (j = 1 or j = J), the expression simplifies to

where Φ denotes the univariate standard normal cdf. Analogously, the probability that y 1i = 0 and y 2i = j is given by

The log likelihood function over all observations is obtained by combining the logarithms of the probabilities (A.1) and (A.


O47 -Measurement of Economic Growth|Aggregate Productivity < O4 -Economic Growth and Aggregate Productivity < O -Economic Development, Technological Change, and

Keywords: Production function, Total factor productivity, European manufacturing, Cyclical adjustment, panel data

How different are the production functions of the European manufacturing sectors? New empirical evidence

Carmen López-Pueyo, Jaime J.

INTRODUCTION

During the course of recent years we have witnessed a renewal of interest in cross-country comparisons of productivity and its explanatory factors, this being the case in both the academic and the political sphere.

Among the reasons that have motivated this line of work, emphasis needs to be placed on the desire to improve our knowledge of the restructuring of the industrialised economies, a process that took place during the crisis of the 1970s and the recession of the early 1980s. This was a time when there was a fall in the demand for labour on the part of the manufacturing sector, when it came to represent around a quarter of total employment in the majority of industrialised countries. At the same time, a number of important changes took place in the distribution of labour in this sector, which led, at least in part, to changes in weight from the traditional industries towards more innovative ones.

The aim of this paper is to present empirical evidence on the estimation of industry production functions in the manufacturing sectors of the European Union, accepting that national technologies can be different and that economies of scale can be present.

When considering that the total factor productivity (TFP) in a given sector is equal for all countries and that there are constant returns to scale, the postulate is that the sectoral product of the countries differs only with respect to the different factor endowments. This is very important, given that the Neo-classical model of international trade makes such assumptions in order to forecast a country's pattern of trade and to derive the equalisation of factor prices of those countries that trade among themselves.

Such equalisation implies an identical technological matrix between countries and that for each sector the capital per worker, the output per worker and the profits per worker will be equal between countries. The accumulation of physical capital will increase the aggregate output and the output per worker, but will only increase the income of the owners of the new capital; the capital/labour ratio and the labour productivity in each sector will not change and neither will the remuneration of the labour factor for each level of qualification or the average wage. However, there will be a change in the distribution of the output between sectors due to a reorientation towards those sectors that are more intensive in physical capital.

In response to these formulations, an increasing number of studies have made clear that the different levels of sectoral production across countries cannot be explained exclusively by reference to differences in factor endowments; rather, consideration must be given to economies of scale in national industries and to technological differences across countries 1 .

Furthermore, these two assumptions can prevent factor prices from being equal, although international trade tends to equal goods prices. If we suppose a general equilibrium framework, the conditions of full employment and of null profits may be expressed as:

h h h v x A = F o r P e e r R e v i e w 2 p w A h h = '
where A is the technological matrix m x n with m factors and n goods, x is the n x 1 vector of outputs, v is the m x 1 vector of factor endowments, w is the m x 1 vector of factor prices and p is the n x 1 vector of goods prices. The super-index h indicates that the technology, the technique, the supply of factors and of goods and the factor prices can be different in each country, whilst the goods prices will equal between countries.

The elements of the matrix A, given that they depend on the factor prices and on the scale of production, can be different in each country, either because there is access to different technologies or because the technique employed differs by virtue of economies (or diseconomies) of scale. Factor prices in each country will be obtained from the joint resolution of the two above expressions and, therefore, they will be a function of factor endowment of each country and of the commodity prices.

Following [START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF], in this paper we set out to estimate sectoral production functions, allowing for the existence of different technologies between countries and not imposing constant returns to scale.

In order to test the model, we have gathered information on all the manufacturing industry of eight EU countries for the period 1978-1992, sub-dividing the sample into eight productive sectors. Faced with the choice of using either production or value added as the measurement of output, we have opted for the latter, given the lack of appropriate data on intermediate costs and their deflators.

The most important contributions of our study are that it extends earlier contributions in two directions. First, it tests the above hypotheses using all the manufacturing sectors, as compared to only the machinery and mechanical equipment sectors. The second main contribution is that it analyses a more extensive time period than that considered in [START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF] and for a sample of exclusively European countries (Germany, France, Italy, Sweden, the United Kingdom, Spain, Finland and Denmark) that is more homogenous in economic, technological and institutional terms2 . These are the only European countries for which we have been able to form a balanced panel with the manufacturing variables we employ for the period in question. Furthermore, we have also carried out a cyclical adjustment by way of the Hodrick-Prescott filter.

The rest of the paper is organised as follows. Section 2 is devoted to the empirical model. The data are described in Section 3 and the results considered in Section 4. Section 5 closes the paper with a review of the main conclusions.

EMPIRICAL MODEL

The general Neo-classical production function assumes: y t = a t F(k t , l t )

(1) where y t is the aggregate output, k t and l t represent the contributions of capital and labour inputs and a t is the level of technology or total factor productivity3 . Therefore, an aggregate production function is the maximum output that can be produced given the In order to explain national productivity differences and to test the hypotheses in the introduction, we have carried out an econometric estimation of sectoral production functions, following [START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF]. Our study extends Harrigan's contribution testing his model to the eight manufacturing sectors in eight European countries over the period 1978-1992 (a more homogenous sample than the one used by Harrigan).

The econometric procedure has the advantage of requiring assumptions that are less restrictive than international comparisons with TFP indices.

We assume that for each country c and year t, the real value added y of a sector j is a function of the stock of real physical capital and the quantity of labour :

) , ( * ) , (

cjt cjt cjt cjt cjt cjt cjt cjt l k g l k f y = =
(2) Considering that the technological differences are neutral in the sense of Hicks, cjt can be interpreted as an index of TFP. If we adopt the Cobb-Douglas functional form, we have:

cjt cjt cjt cjt l k y ln ln ln ln 2 1 + + = (3) Introducing 1 2 1 + =
(where +1 denotes the degree of returns to scale), subtracting ln l ctj from both sides of the equation, and reordering, we see that the value added per worker depends on the capital per worker, the total labour and the TFP:

cjt cjt cjt cjt cjt cjt l l k l y ln ) / ln( ln ) / ln( 1 + + =
(4) Drawing on earlier studies, we will consider that the TFP varies between countries and over time, including country effects and time trends. More specifically, we will assume that the differences in TFP are common to the sectors of one and the same country and that the time trends are specific to each sector and common across countries, thereby obtaining the following statistical model:

cjt cjt j cjt cjt j j c cjt cjt l l k t l y + + + + = ln ) / ln( ) / ln( / 1 1 0
(5) One of the problems that may arise is the cyclical variation in the use of productive capacity, this being caused by the non-proportional change of inputs and outputs in the short term which has its origin in the invariability of physical capital and the accumulation of labour factor.

To mitigate this the dependent variable was ajusted by the output gap, defined as µ = observed GVA/potential GVA4 . In this way, the generic equation to be estimated takes the following form:

cjt cjt j cjt cjt j j c ct cjt cjt l l k t l y µ + + + + = ln ) / ln( ln ) / ln( / 1 1 0 (6)
We have estimated three models. The first (without restrictions) assumes different coefficients for each of the sectors in the exogenous technical progress ( j 1 ), elasticity of GVA with respect to capital ( j 1 ) and level of economies of scale (1+ j ) variables, as well as a different average TFP for each country ( oc ).

In the second, the national variations in the production functions are maintained, but we have imposed constant returns to scale ( j =0).

The third model considers again the possibility of economies (diseconomies) of scale, at the same time as imposing the equality of the ( 0 = oc ) across countries. We have chosen the weighted least squares estimator, which is appropriate when there is unknown heteroscedasticity among individuals. The weightings are the inverses of the variances of the estimated equation and are obtained from the estimation without weightings of the parameters. Furthermore, the inclusion of the time trends makes improbable the existence of auto-correlation in the residuals. Nevertheless, a correlation between the explanatory variables and the error terms may remain, either due to measurement errors or because of simultaneity5 . Although this problem is mitigated, in part, by correcting the phase of the cycle, the solution comes from working with instrumental variables. However, given that we have not been able to find appropriate instruments and that the incorrect introduction of them would give rise to additional distortions, we have decided to forgo this type of estimation.

THE DATA

The data of the gross value added (GVA), physical capital and total employment used to estimate the model are drawn from the International Sectoral Data Base (ISDB) (1997) for all the sample countries, save for Spain. For this country, the GVA and employment data come from the Structural Analysis Data Base (STAN) (1998), and that of the physical capital variable from [START_REF] Mas | El stock de capital en España y su distribución territorial, 1964-1998[END_REF]. It is certainly the case that the use of net capital stock would be a much more appropriate measurement to estimate the effects of technology in the increase of production, but unfortunately the OECD does not publish estimations for all the countries.

In order to compare the data of the different countries and years, we have homogenised the monetary units of the different countries with the purchasing power parity (PPP) of the GVA or of the gross formation of physical capital (in the case of the physical capital).

In order to adjust the labour productivity for the cycle, we have obtained the potential GVA by applying the Hodrick-Prescott (1997) filter, a smoothing methodology which allows us to obtain the long-term trend component of a series. With the aim of avoiding the possible inadequacy of the trend values in the final years of the sample, we have applied the filter for a longer period (1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997) than that used in the panel (1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992), following the recommendations of [START_REF] Scarpetta | Economic Growth in the OECD Area. Recent Trends at the Aggregate and Sectoral level[END_REF].

As total employment does not capture the force applied by labour, the equivalent to the number of workers that have worked a forty-hour week during the year has been calculated. The information on the effective hours per worker/week has been taken from the Yearbook of Labour Statistics of the International Labor Organisation.

A prior analysis of the data offers some interesting hypotheses to be tested. First, we see in Table 1 that in 1990 there was a considerable variation in labour productivity across sectors in the average of the countries analysed. We likewise observe that for each branch the ratio between the productivity of the country with the highest value and that of the country with the lowest oscillates between 2.55 and 1.31. These differences among countries which might be due to the behaviour of one of them, are also maintained (albeit in a somewhat smooth form) if we compare the data of France and Germany. The differences in labour productivity among countries are not compatible with the equality of productivities (and factor prices) predicted by the Neo-classical model. Table 3 offers the correlation between the capital/labour ratio in aggregate manufacture and the labour productivity of one sector in 1990, again taking the countries as individuals. In this case, the high coefficients indicate that those countries with a high capital intensity in total manufacturing similarly tend to have high capital intensity in most sectors. This contradicts the equality of the Neo-classical model, according to which those countries with a greater relative abundance of capital will specialise in more capital-intensive sectors (which does not predict that they will be more capital-intensive in all their sectors).

F

Finally, Table 4 reflects two manufacturing labour productivity indices for each country in 1990, taking the UK value as the base figure of 100. The first index is the result of calculating the average productivity of the country, weighing the productivity of each sector by the proportion of labour really used in it, whilst the second uses the proportion of labour used in France as the weighing for all countries. The country ranking proves to be the same, with the exception of Spain.

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

6 The explanation for this similarity is that the national differences in aggregate labour productivity are due to differences in sectoral labour productivity rather than to discrepancies in the sectoral distribution of employment. Once again, this would appear to contradict the Neo-classical model, according to which national divergencies are due to disparities in the distribution of employment, which is orientated towards activities that are more capital or labour intensive, and not to systematic variations in sectoral productivity.

In short, the results invite us to estimate three alternative models when seeking to explain the variations in labour productivity across sectors and countries.

RESULTS

Table 5 contains the estimations of the three models specified on the basis of equation ( 6).

Those in the first two columns correspond to model 1 (non-restricted), which considers different coefficients for each sector in the four variables. According to this specification, the labour productivity of the sectors differs not only because countries have different TFPs (assuming that all the sectors of a given country have the same TFP) and distinct sectoral technical progress rates, but also because the levels of economies of scale and the elasticities of the GVA with respect to the capital also vary from sector to sector.

Indeed, these elasticities have values ranging between 0.101 in the chemical sector and 0.272 in other manufacturing industries. All the sectors present decreasing returns to scale and the rate of technical progress oscillates between 0.9% in the textile sector and 3.2% in basic metalss industries. Finally, the TFP of each country gives rise to a ranking that places France at its head, followed by Germany and Italy. The United Kingdom and Spain follow at some distance, whilst the Nordic countries of Denmark, Sweden and Finland occupy the final positions.

The fact of France occupying the first position (amongst the EU countries) is a result also obtained by [START_REF] Mas | Capitalización y crecimiento de la economía española (1970-1997). Una perspectiva internacional comparada[END_REF] when they estimated the production function for the total economy of various OECD countries (including the USA, which leads the TFPs).

Note that our model explains a larger percentage of sectoral product than that of [START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF] with a smaller range of values in the TFP. This would appear to indicate that when we estimate the model for broader industrial aggregations, the differences in the TFPs of the countries are reduced.

Here, we should bear in mind that Harrigan estimates his model with an imibalanced panel of data for the period 1981-1989 for countries such as Australia, Canada, Japan, Norway and the USA. These are countries whose economies not only differ significantly from those of Europe but also among themselves. This is the case both in the technologies employed as well as in the institutions and the endowments of certain variables not considered, such as infrastructures, human capital or economic size.

The second model assumes that the production (technology) function differs across countries, but imposes constant returns to scale as a restriction. These assumptions give rise to a generalised increase in the values of the elasticity estimated with respect to physical capital (with the sole exception of other manufacturing industries), which are now placed between 0.120 for basic metalss industries and 0.267 for the textile sector. The rates of technical progress remain very similar to those of the earlier model and result in the same sectoral ranking. Furthermore, we can appreciate a relative improvement in the TFP of France with respect to Germany, followed by Italy and Denmark, with a second block composed by the United Kingdom, Sweden, Finland, and Spain. Once again, the range of values of the country TFPs is smaller than that reported by [START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF] although the coefficients of this variable continue to present high statistical significance.

The third model imposes the equality of the TFP across countries, although permitting non-constant returns to scale. It is supposed that the countries have equal production functions but use different techniques: the economies of scale do not lead to the equality of the productive factor prices and, as a consequence, different production technologies are employed even though the same production function is available. The estimation of the elasticity with respect to capital increases in all the sectors, now lying between 0.278 for the paper sector and 0.494 in mechanical industries. The rates of technical progress are again similar to those of the two earlier models and there appears to be a certain level of economies of scale in all the sectors except for basic metalss industries (whose coefficient has a reduced statistical significance).

The appearance of increasing economies of scale when excluding technological differences between countries is a result also obtained by [START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF] for the 1980s and for other countries in which the size effect is more evident (Canada, Japan, Australia), as well as by [START_REF] Maskus | Comparing International Trade Data and Product and National Characteristics Data for the Analysis of Trade Models[END_REF] for 1984, using information for twenty eight countries and twenty eight sectors.

This result would appear to indicate that country size is related to economies of scale. When the fixed country effects (Model 3) are excluded, economies of scale appear, but when no restrictions are imposed in the coefficients (Model 1), the reduced sample with which we are working does not allow to distinguish the economies of scale and the country effects, giving negative coefficients (diseconomies of scale) to them. In support of our interpretation we can point to the fact that in Model 2 (in which constant returns to scale are imposed), the values of the country effects are more reduced than in Model 1 6 .

In Table 6 we present the statistics that allow us to draw comparisons between the three models. According to the F-tests, the restrictions imposed in both Model 2 and Model 3 are rejected, but these two models cannot be compared. However, in order to make such a comparison we can make use of the posterior odds ratios7 . These ratios indicate that the data support Model 2 as compared to Model 1 and Model 3, whilst Model 1 has a better fit to the data than Model 3.

In slim, they show that to explain the behaviour of labour productivity it is necessary to include the assumption of different TFPs across countries. Bear in mind that this TFP reflects not only technology but also a number of variables that, with much less mobility, act in the national sphere and explain labour productivity. In any event, the results of our study are much more favourable to the constant returns hypothesis, given that Model 2 is preferred to Model 1, in clear contrast to [START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF] where the opposite is the case.

CONCLUSIONS

In this paper we have carried out a descriptive analysis of the data corresponding to the productive factors and gross value added of the different manufacturing branches of various EU Member States from the end of the 1970s until the beginning of the 1990s. A first conclusion that can be drawn is that there is a certain inadequacy in the prescriptions provided by the Neo-classical model of equality of productive factor prices. The differences found across countries in terms of sectoral labour productivity are such that they question the use of this model when seeking to explain the behaviour of this variable.

In turn, countries with relatively high labour productivity in one sector tend to exhibit it in all the sectors; similarly, a country with a relative abundance of capital tends to have greater capital intensity in all its manufacturing branches, against the model's forecast of specialisation in more capital intensive sectors. Furthermore, national differences in aggregate labour productivity are the result of national differences in sectoral productivity rather than of differences in the national distribution of employment between the different branches.

In the light of all this, we have proposed three models which combine different hypotheses on the existence of economies of scale and of technological differences across countries. Although the variation in labour productivity is explained, in great Having said that, we must be aware of the fact that these differences in TFP can be interpreted not only as differences in the technology employed, but also as differences in national variables which have not been considered (such as infrastructures, legal and social institutions or human capital) or, simply, as measurement errors.

Given that technology is a factor capable of being transferred by way of multinational firms, technological transactions and imitation, our contention is that the technological differences of the countries analysed in this paper could be less relevant than the above-mentioned second type of national variables.

Consequently, economic policies must head for an improvement of human capital, of infrastructures, of the legal institutions that minimize transaction costs and the development of social capital as a catalyst of economic relations. Similarly, the generation of a national technological capital able to assimilate foreign technology or to develop new technological advances is another aspect to be encouraged so that a frame can be created that makes better conditions possible for growth to take place.

The challenge of future research rests on the improvement in the measurement of the variables used, as well as on the incorporation of new variables like human technological capital, infrastructures and social capital. The database which is currently being built within the Euklems project will no doubt allow a step forward in this respect.

  factors of production. Technology can be assumed Hicks neutral (output augmenting) or can also be specified as Harrod neutral (labour augmenting).

  the differences in capital intensity, the results nevertheless support the existence of a distinct TFP in the EU Member States.

Table 1 Sectoral productivity of manufacturing in 1990 (Average of the eight countries considered)

 1 Table2presents the correlation between the labour productivity of each pair of sectors in 1990, taking the countries as individuals. If the basic metalss industries are excluded, these coefficients are positive and indicate that labour productivity in one sector tends to be correlated with labour productivity in the other sectors.

		Participation in	GVA/employee	Productivity ratios
	Sector	Manufacturing
		employment	(US dollars PPP) Max/min France/Germany
	Food	11.7%	42,188	1.6	1.0
	Textile	10.3%	22,958	1.6	1.2
	Paper	10.0%	37,060	1.3	1.2
	Chemical	10.0%	57,154	2.0	1.3
	Non-metalslic mineral	4.4%	40,417	2.1	1.4
	Basic metalss industries	4.1%	48,046	2.6	1.2
	Other manufacturing
	industries	8.9%	25,517	1.8	1.1
	Mechanical industries	40.7%	33,748	2.1	1.2
	o r
		P
		e
		e r
			R e v
			i e
			w

Table 2 Correlation coefficients of labour productivity of the different sectors in 1990

 2

				Non-	Basic	Other
				metalslic	metalss	manufacturing	Mechanical
	Sector	Textile Paper Chemical	minerals	industries	industries	Industries
	Food	0.73 0.27	0.49	0.57	0.02	0.21	0.66
	Textile	0.56	0.30	0.74	-0.38	0.65	0.77
	Paper		0.28	0.74	-0.35	0.78	0.80
	Chemical			0.76	-0.01	-0.23	0.44
	Non-metalslic minerals				-0.36	0.43	0.84
	Basic metalss industries					-0.51	-0.48
	Other manufacturing
	industries						0.67

Table 3 Correlation coefficients between capital/labour ratio in the aggregate manufacture and the labour productivity of one sector in 1990

 3

	Sector	Coefficients
	Food	0.90
	Textile	0.83
	Paper	0.76
	Chemical	0.93
	Non-metalslic minerals	0.64
	Basic metalss industries	0.69
	Other manufacturing industries	0.44
	Mechanical industries	0.84

Table 4 Labour productivity indices in the aggregate manufacture in 1990

 4

	Country	Index 1	Index 2
	France	159.1	154.6
	Germany	138.2	132.4
	Italy	135.4	131.9
	Spain	134.9	139.7
	Finland	123.1	119.5
	Denmark	120.9	117.3
	Sweden	109.9	109.2
	United Kingdom	100.0	100.0
	Notes: Index 1 has been calculated with the labour participation of the country itself.
	Index 2 has been calculated with the labour participation of France.
	In both cases, the United Kingdom has been taken as the base figure of 100.

Table 5 . Dependent variable: log (GVA per employee, adjusted by the use of capacity) Period 1978-1992. Estimation by weighted least squares Logarithm of capital per

 5

		Model 1	Model 2	Model 3
	employee	Coefficient	t-statistic	Coefficient t-statistic Coefficient	t-statistic
	Food	0.146	7.184	0.236	10.103	0.303	16.785
	Textile	0.197	6.639	0.267	10.322	0.413	13.497
	Paper	0.195	11.820	0.200	12.218	0.278	15.157
	Chemical	0.101	5.053	0.194	9.813	0.284	13.198
	Non-metalslic minerals	0.189	15.667	0.240	18.616	0.347	36.423
	Basic metalss industries	0.118	4.533	0.120	3.549	0.295	16.093
	Other manufacturing
	industries	0.272	10.896	0.231	10.191	0.355	21.494
	Mechanical industries	0.194	6.673	0.259	11.635	0.494	17.553
	Logarithm of employment	Model 1			Model 3
		Coefficient	t-statistic			Coefficient	t-statistic
	Food	-0.114	-7.662			0.114	19.821
	Textile	-0.126	-10.802			0.031	4.886
	Paper	-0.163	-8.348			0.100	7.930
	Chemical	-0.119	-8.706			0.064	7.124
	Non-metalslic minerals	-0.143	-10.397			0.060	13.598
	Basic metalss industries	-0.193	-10.969			-0.020	-1.585
	Other manufacturing
	industries	-0.223	-12.061			0.025	2.393
	Mechanical industries	-0.161	-10.585			0.004	0.542
	Exogenous technical
	progress	Model 1	Model 2	Model 3
		Coefficient	t-statistic Coefficient t-statistic Coefficient	t-statistic
	Food	0.019	9.799	0.020	7.965	0.014	6.847
	Textile	0.009	3.28	0.011	4.642	0.008	2.555
	Paper	0.019	8.155	0.024	12.539	0.018	5.965
	Chemical	0.028	14.145	0.027	12.98	0.025	9.671
	Non-metalslic minerals	0.015	13.037	0.019	16.837	0.016	12.964
	Basic metals industries	0.032	11.511	0.034	7.543	0.033	14.725
	Other manufacturing
	industries	0.014	7.081	0.017	7.976	0.017	8.481
	Mechanical industries	0.021	8.875	0.016	7.364	0.004	1.679
	National fixed effects	Model 1	Model 2
	France = 100	Coefficient	t-statistic Coefficient t-statistic
	Germany	96.5	34.578	90.720	49.302
	France	100.00	35.21	100.00	48.359
	Italy	91.41	34.395	90.690	48.019
	Sweden	57.14	36.284	76.75	47.944
	United Kingdom	76.98	34.676	78.360	50.069
	Spain	72.05	35.426	70.570	52.265
	Finland	54.27	36.403	75.75	45.875
	Denmark	59.08	37.292	85.74	48.158
	Number of observations R 2	900 0.856		900 0.855		900 0.825

Note: 1 plus the coefficient of the logarithm of employment indicates the degree of returns to scale. So as not to overload the Table, the sectoral dummies has been omitted. Specific dummies have been introduced for Spain (to reflect that its data do not come from the ISDB) and for the other manufacturing industries sector in Italy (which also includes the Paper).

  All test statistics are calculated using the estimates of Table5.

	Table 6
	Test statistics
	_______________________________________________________________________
	F-tests__________________________________________________________________
	Null hypothesis: Model 2
	F (8.860) = 5.298	Critical value at 1% = 2.51
	Null hypothesis: Model 3
	F (7.860) = 28.900	Critical value at 1% = 2.64
	____________________________________________________________
	Relative odd ratios________________________________________________________
	Pr (model 2\data)/Pr(model 1\data) = 259.619	Model 2
	Pr (model 3\data)/Pr(model 1\data) = 1.1302 E -31	Model 1
	Pr (model 2\data)/Pr(model 3\data) = 2.2972 E 33	Model 2
	________________________________________________________________________
	Note:

[START_REF] Harrigan | Estimation of cross-country differences in industry production functions[END_REF] does not include France, Denmark or Spain. His results are obtained with information for Germany, Italy, the United Kingdom, Finland, the Netherlands (a country for which we do not have the necessary data), Norway (which does not belong to the UE), as well as for four non-European countries, namely Australia, Canada, Japan and the USA.

Among the numerous empirical resarch papers that use the aggregate production function, we can mention[START_REF] Bairam | The form of the production function for the Chinese regional economy[END_REF],[START_REF] Tzanidakis | A test of a modern version of the Solow model[END_REF],[START_REF] Casler | Applied production theory: explicit, flexible, and general functional forms[END_REF],[START_REF] Kaskaleris | Aggregate returns to scale in Greek manufacturing[END_REF],[START_REF] Felipe | Does the aggregate production function imply anything about the laws of production? A comment[END_REF],[START_REF] Segoura | Return to scale and external economies; empirical evidence from Greek two-digit manufacturing industries[END_REF],[START_REF] Duffy | A Cross-Country Empirical Investigation of the Aggregate Production Function Specification[END_REF],[START_REF] Moss | Estimation of the Cobb-Douglas with zero input levels: bootstrapping and substitution[END_REF],[START_REF] Mccombie | The CES Production Function, the accounting identity, and Occam's razor[END_REF],[START_REF] Graham | Productivity growth in British manufacturing: Spatial variation in the role of scale economies, technological growth and industrial structure[END_REF] and[START_REF] Kumbhakar | Factor productivity and technical change[END_REF].

The potential GVA has been estimated by way of the Hodrick-Prescott filter applied to the GVA data for manufacturing corresponding to each country for the period 1978-1997 as this appears in the STAN data base

If, in the face of a productivity shock, there is an increase in the use of factors, this may be an indication of a strong positive correlation between employment and the error term.

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

In Model 1 the decreasing economies of scale appear with negative coefficients so that, when excluding them from Model 2, they explain the lower value of the TFP in all the countries.

For details of their development and a discussion, seeLeamer (1983:157-159)

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