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Does female employment affect fertility? Evidence from the United Kingdom
The Social Science Journal 41 (2004) 235–249
Does female employment affect fertility? Evidence from the United Kingdom Evangelia Papapetrou a,b,∗,1 a
b
University of Athens, Athens, Greece Bank of Greece, Economic Research Department, Athens, Greece
Abstract This paper tests the validity of the proposition that there is a causal relationship between fertility choice and female employment in a multivariate framework during the period 1958–1998 in the United Kingdom. Following recent advances in economic and demographic theory the nexus between female employment and fertility is reexamined taking into account changes in the labor market and the overall real economic activity. Our key finding is that expanding the estimating equations to control for the influences of changes in real wages and real output creates a positive relationship between fertility and female employment and a negative relationship between fertility and real wages. Finally, fertility choice should not be considered exogenous to the female employment, the labor market or the growth process. © 2004 Elsevier Inc. All rights reserved.
1. Introduction The theory of the allocation of time in Becker (1965) implies the importance of labor supply and fertility decisions. In his framework fertility decision is viewed as an economic one, and that one of the costs of having a child is the forgone earnings of the person caring for the child at home, in most cases the mother. The development within this framework of the new microeconomic theory in Willis (1973) formally modeled this joint fertility–labor supply decision. In the model of household behavior the family is maximizing utility defined over market goods, leisure and child services. In the household the wife’s time and market goods are used as inputs to produce child services. So the participation and procreation decisions are mutually exclusive. If the woman devotes most of her time to market work, then she should decrease her leisure time and/or the number of children. This implication is especially ∗
Tel.: +30-10-320-2429; fax: +30-10-323-3025. E-mail address: [email protected] (E. Papapetrou). 1 Present address: Economic Research Department, Bank of Greece, El. Venizelou 21, 102 50 Athens, Greece.
0362-3319/$ – see front matter © 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.soscij.2004.01.003
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important, as we need to explain the trends in fertility and female labor supply over the last 30 years. However, in the labor supply literature, most empirical work has analyzed fertility and female labor supply decisions separately. Some economists have treated fertility as an exogenous determinant of labor supply and others have assumed that labor supply is an exogenous determinant of fertility. Other researchers have estimated simultaneous models of fertility and labor supply and have showed the interdependency over the life cycle of fertility and female employment rates (Cain & Dooley, 1976; Cigno, 1991; Fleisher & Rhodes, 1976; Hotz & Miller, 1988; Kalwij, 2000; Mahdavi, 1990; Moffit, 1984). Several studies have tried to test the existence and the direction of causality between fertility and female employment applying methods of time series analysis. Among others, Cheng (1996), Cheng, Hsu, and Chu (1997), Klijzing, Sieger, Keilman, and Groot (1988), and Michael (1985) apply Granger-causality tests to study the relationship among female labor force participation and fertility. These studies provide mixed results on the existence and direction of causality between fertility and female employment. The advance of econometric techniques in recent years stimulated further empirical research on the interdependence of fertility and female employment. However, to resolve the issue of the direction of causality in a bivariate context, the previous studies have applied causality tests based on the standard Granger–Sims, the modified Sims and Hsiao tests. But the studies applying these tests suffered from methodological deficiencies. First, the basic time series properties of the variables were not examined implying that the findings of their analysis may be spurious. Second, if the variables are cointegrated, then tests incorporating differenced variables will be misspecified unless the lagged error-correction term is included (Cheng, 1996; Cheng et al., 1997; Klijzing et al., 1988; Michael, 1985). So, the application of vector error-correction model (VECM) estimation, derived from the cointegration equations by introducing the lagged error-term, incorporates all the long-run information that was initially lost through differencing the variables (Granger, 1988). Finally, the inclusion in the bivariate relation analysis of other economic factors such as the wage rate and real economic activity, may influence the fertility and female employment relationship and may reveal additional channels of causality initially ignored in the bivariate context analysis. The lack of unequivocal evidence on the relationship between fertility and female employment creates an obvious deficiency that may affect applied research and policy making in employment and economic development. In light, of these contradicting results the detailed investigation of the nexus between female employment and fertility deserves particular attention. In addition, recent development in economic and demographic theory supports the notion that in OECD countries increasing female participation rates do not depress fertility rates for those countries that have succeeded in minimizing the incurred costs of childbearing and work (McDonald, 2000; Rindfuss & Brewester, 1996; Rindfuss, Brewster, & Kavee, 1996). According to the argument of Chesnais (1996) and Esping-Andersen (1999) if women are provided with opportunities nearly equivalent to those of men, such as in market employment and in education, but these opportunities are severely curtailed by having children, then, on average, women will restrict the number of children that they have to an extent which leaves fertility at a precariously low, long-term level. So, as long as there is an improvement in the
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childcare availability this might reduce the incompatibility between childbearing and female employment and enable woman to combine work and childrearing. The primary purpose of this paper is to address the causality issue between fertility and female employment in a temporal causal framework, taking into account changes in the labor market and in the overall economic activity, with the aid of multivariate cointegration and the application of VECM estimation for United Kingdom for the period 1958–1998. In the empirical investigation of the dynamic interaction between fertility choice, female employment other economic variables are employed, such as the real wage rate and real output, and the nexus between fertility and female employment is reexamined in a multivariate framework. U.K. serves as a good example since the demographic developments closely resemble the general trend in most OECD countries. The paper utilizes the recently developed technique of VECM estimation. This technique has several advantages over other methods used in the past by various researchers, since this type of multivariate analysis clearly can distinguish between exogenous and endogenous variables. Our key finding is that expanding the estimating equations to control for the influences of changes in real wages and real output creates a positive relationship between fertility and female employment and a negative relationship between fertility and real wages. Fertility choice should not be considered exogenous to the female employment, the labor market or the growth process. Lastly, estimation of the four-variable vector autoregression model supports the finding that changes in the fertility choice are not responsible for changes in female employment. The remainder of the paper is organized as follows. Section 2 briefly reviews empirical evidence on the relationship among fertility and female employment. Section 3 discusses the methodological issues and the data. Section 4 reports the empirical results. Section 5 presents the concluding remarks.
2. Fertility choice and female employment: empirical and theoretical considerations Several studies have tried to test the existence and the direction of causality between fertility and female employment applying methods of time series analysis. Most of these studies examine the nexus between fertility and female employment in a bivariate context and provide mixed results on the direction of causality among the two variables. Michael (1985) uses a model to study the bivariate relationship among female employment and fertility in the USA over the period 1948–1980. By applying standard Granger-causality tests he shows that female labor force participation positively causes fertility. However, his conclusion is sensitive to the definition of fertility. Klijzing et al. (1988) use monthly data from a Dutch survey for 1977–1984. They apply Sim’s indirect Granger-causality tests to find that labor force participation has no influence on fertility decisions and vice versa. However, when they apply standard Granger-causality tests there is evidence of bi-directional causality among the fertility and female employment. Cheng (1996) applies Hsiao’s version of the Granger-causality method to examine the causality between fertility and female labor participation using transformed U.S. data for the period 1948–1993. He argues that there is unidirectional causality running from fertility to female labor force participation with no feedback.
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Most work have used data for the U.S. (Cain & Dooley, 1976; Cheng, 1996; Hoffman, 1985; Moffit, 1984; Schultz, 1978) a few for Japan (Cheng et al., 1997; Osawa, 1988; Yamada & Yamada, 1986) and the main OECD countries (Gustafsson, Wetzels, Vlasblom, & Dex, 1996; Kalwij, 2000; Mahdavi, 1990; Sprague, 1988; Tanda, 1994). Recent advances in demographic theory suggest that a reduction in the incompitability between childrearing and female employment, as a result of changes in social norms and in childcare availability has affected fertility decision. The demographic theory supports the idea that in some OECD countries increasing participation rates do not depress fertility rates if these societies manage to minimize the incurred costs of childbearing and work. Rindfuss et al. (1996) show, using attitudinal data, that since the 1970s in the United States that there has been a substantial weakening of the norm that mothers of preschool children should stay at home. This change in measured attitudes is pervasive and appears to have been led by well-diffused behavioral change. The authors argue that this change in attitudes has played an important role in the stabilizing of U.S. fertility levels and might explain a positive association fertility rate and female labor market participation rates. Chesnais (1996) and Esping-Andersen (1999) claim that if women are provided with opportunities similar to those of men in education and market employment, but women have to bear the costs of child raising, then women will restrict the number of children that they have. McDonald (2000) claims that for societies that the breadwinner model prevails women are left with choices between children and employment, which in turn leads to having fewer children and low fertility.1 He suggests that societies that advance gender equity in social institutions related to the family, women and men are able to combine market employment with having children and fertility will be higher. So, as long as structural obstacles are restricted through the provision of social organization and support for families with children, women will be able to combine work with children.
3. Methodological issues and data In the empirical analysis we test for the existence of a dynamic relationship between fertility choice and female employment in the context of an extended model to account for the contribution of economic forces to this bivariate relationship. In order to account for influences on the fertility–female employment relationship of changes in medical technology, literacy, standard of living, overall economic performance, opportunity cost of time devoted to childcare and the labor market, real GDP per capita and real wages are added to the VAR model. In particular, we employ the VECM estimation to investigate empirically the endogeneity of fertility and female employment and their linkage with economic variables, such as real wage and real output. In addition, we examine the responses of fertility and female employment to labor market and overall economic activity, in order to capture the short-run dynamics of the variables. The four macroeconomic variables employed in the empirical analysis are the fertility rate, female employment, real wage and real per capita gross domestic product. Testing for the existence of statistical relationship among the variables is done in three steps. The first step is to verify the order of integration of the variables since the causality tests are
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valid only if the variables have the same order of integration. Standard tests for the presence of a unit root based on the work of Dickey and Fuller (1979, 1981), ADF test; Perron (1988), Phillips (1987), Phillips and Perron (1988), PP test; Kwiatkowski, Phillips, Schmidt, and Shin (1992), KPSS test; and Zivot and Andrews (1992), ZA test, are used to investigate the degree of integration of the variables used in the empirical analysis. The second step involves testing for cointegration using the Johansen maximum likelihood approach (Johansen, 1988; Johansen & Juselius, 1990, 1992). The Johansen–Juselius estimation method is based on the error-correction representation of the VAR model with Gaussian errors.2 Evidence of cointegration rules out the possibility that the estimated relationship is spurious (Granger, 1986, 1988).3 The third step involves utilization of the vector error-correction modeling and testing for exogeneity of variables. Engle and Granger (1987) show that in the presence of cointegration, there always exists a corresponding error-correction representation which implies that changes in the dependent variable are a function of the level of disequilibrium in the cointegrating relationship, captured by the error-correction term (ECT), as well as changes in other explanatory variables. Thus through ECT, the VECM modeling establishes an additional way to examine the Granger-causality ignored initially from the Granger–Sims tests. The Wald-test applied to the joint significance of the sum of the lags of each explanatory variable and the t-test of the lagged error-correction term will imply statistically the Granger-exogeneity or endogeneity of the dependent variable. The non-significance of ECT is referred as long-run non-causality, which is equivalent to saying that the variable is weakly exogenous with respect to long-run parameters. The absence of short-run causality (Grangercausality in the strict sense) is established from the non-significance of the sums of the lags of each explanatory variable. Finally, the non-significance of all explanatory variables including the ECT term in the VECM indicates the econometric strong-exogeneity of the dependent variable, that is the absence of Granger-causality. The proposed three steps are presented and outlined in Fig. 1. The empirical analysis has been carried out using annual data for the period 1958–1998 for United Kingdom. LFERT is the fertility rate, LFEM is the female employment as a percentage of the labor force, LRWAGE is the real wage and LRCGDP is the real GDP per capita. Fertility and employment rate are obtained from the Labor Force Statistics published by the OECD. Real wage and real GDP per capita are obtained from the International Financial Statistics tape. All variables are expressed in logarithmic form.
4. Empirical results Table 1 presents the ADF, PP and KPSS tests for the four variables, fertility rate, female employment, real wage and real per capita output used in the analysis in levels and first differences. The ADF statistic suggests that all variables are integrated of order 1, I(1), whereas the first differences of all the variables are integrated of order 0, I(0). Therefore, the hypothesis that the time series contain an autoregressive unit root is accepted in all cases. Also, the Phillips–Perron test based on the 5 and 1% critical values supports the hypothesis that all series contain a unit root. Finally, the KPSS statistics tests for lag-truncation parameters one and four
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Fig. 1. The procedure for testing for cointegration and Granger-causality.
(l = 1 and 4)4 since it is unknown how many lagged residuals should be used to construct a consistent estimator of the residual variance. The KPSS test rejects the null hypothesis of level and trend stationarity for both lag truncation parameters. The KPSS statistics does not reject the I(0) hypothesis for the first differences of the series at various levels of significance. Therefore, the combined results from all the tests (ADF, PP, KPSS) suggest that all the series under consideration appear to be I(1) processes. Next the Zivot–Andrews test is estimated for the four variables used in the analysis to ensure that all the series are I(1). Table 2 reports the minimum t-statistics from testing the stationarity assuming a shift in mean and broken trend for the levels and first differences of all the variables. The minimum t-statistics reported is the minimum overall break point regressions from 1958 to 1998. The results suggest that at 5% level of significance none of the estimated variables are stationary around a broken trend or a shift in the mean, while their differences are I(0). The Zivot–Andrews test confirms that all the variables are I(1). Since both the fertility and employment levels are integrated of the same order, it is appropriate to look for a relationship between fertility choice and female labor decision. In order to account for influences on the fertility rate–female employment relationship of changes in labor market and income of the households, real wage (LRWAGE) and the real per capita output (LRCGDP) variables are added to the extended VAR model. Table 3 summarizes the results of cointegration analysis among the four variables using the Johansen maximum likelihood approach employing both the maximum eigenvalue and trace statistic. To determine the lag length of the VAR three versions of system were initially estimated: a four, a three and a two-lag version. Then, an Akaike Information criterion (AIC), a Schwarz Bayesian Criterion (SBC) and a likelihood ratio test (Sims’ test) were used to test that all
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Table 1 Tests of unit roots hypothesis Variable
LFERT LFEM LRWAGE LRCGDP LFERT LFEM LRWAGE LRCGDP
Augmented Dickey–Fuller
Phillips–Perron
KPSS
τµ
ττ
k
τµ
ττ
k
−1.10 −0.93 −1.53 −0.52 −3.32∗ −4.62∗∗ −5.68∗∗ −4.63∗∗
−2.13 −0.86 −1.98 −2.67 −3.28∗ −4.67∗∗ −5.58∗∗ −4.58∗∗
1 1 1 2 0 0 0 0
−0.91 −0.89 −2.16 −1.00 −3.35∗ −4.69∗∗ −5.68∗∗ −4.48∗∗
−1.67 −0.95 −2.43 −3.01 −3.32∗ −4.72∗∗ −5.83∗∗ −4.41∗∗
3 3 3 3 3 3 3 3
l=1
l=4
ηµ
ητ
ηµ
ητ
1.503∗∗ 2.124∗∗ 2.082∗∗ 2.100∗∗ 0.139 0.280 0.323 0.084
0.309∗∗ 0.224∗∗ 0.266∗∗ 0.132 0.145 0.220∗ 0.061 0.049
0.659∗∗ 0.906∗∗ 0.913∗∗ 0.927∗∗ 0.092 0.215 0.302 0.117
0.146∗ 0.123 0.146∗ 0.091 0.095 0.170∗ 0.066 0.070
Notes. The relevant tests are derived from the OLS estimation of the following autoregression for the variable involved: xt = δ0 + δ1 (time)t − δ2 xt−1 +
k φi xt−i + ut
(1)
i=1
where τ µ is the t-statistic for testing the significance of δ2 when a time trend is not included in Eq. (1) and τ τ is the t-statistic for testing the significance of δ2 when a time trend is included in Eq. (1). The calculated statistics are those reported in Dickey and Fuller (1981). The critical values at 5 and 1% for N = 50 are −2.93 and −3.58 for τ µ and −3.5 and −4.15 for τ τ , respectively. The lag length structure of φi of the dependent variable xt is determined using a recursive procedure in the light of a Lagrange multiplier (LM) autocorrelation test (for orders up to 4) which is asymptotically distributed as chi-squared distribution and the value of t-statistic of the coefficient associated with the last lag in the estimated autoregression. The critical values for the Phillips–Perron unit root tests are obtained from Dickey and Fuller (1981). ηµ and ητ are the KPSS statistics for testing the null hypothesis that the series are I(0) when the residuals are computed from a regression equation with only an intercept and intercept and time trend, respectively. The critical values for ηµ and ητ at 5% are 0.463 and 0.146 and at 1% are 0.739 and 0.216, respectively (Kwiatkowski et al., 1992, Table 1). Asterisks (**, *) indicate significance at the 1 and 5% levels, respectively.
three specifications are statistically equivalent. All tests reject the null hypothesis that all specifications are equivalent. In particular, the tests suggest that VAR = 2 should be used in the estimation procedure of cointegration to avoid over-parameterization of the estimated models. Finally, a log-likelihood ratio test is used for testing the deletion of a dummy variable Table 2 Zivot–Andrews minimum t-statistics Variables
t-statistic
Year
LFERT LFEM LRWAGE LRCGDP LFERT LFEM LRWAGE LRCGDP
−5.07 −3.28 −3.82 −4.87 −6.27∗∗ −5.96∗∗ −6.21∗∗ −5.95∗∗
1971 1990 1976 1979 1976 1971 1972 1989
Notes. All t-statistics estimated from a break in intercept and trend model. Critical values are those reported in Table 4 of Zivot and Andrews (1992). The 1 and 5% critical values are −5.57 and −5.08, respectively. Asterisks (**) indicate significance at the 1% level.
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Table 3 Johansen and Juselius cointegration test: fertility rate, female employment, real wage, real per capita output in United Kingdom, 1958–1998 VAR = 2, variables: LFERT, LFEM, LRWAGE, LRCGDP Null
Alternative
Maximum eigenvalues r=0 r=1 r≤1 r=2 r≤2 r=3 r≤3 r=4
Eigenvalue
41.26∗∗ 16.60 8.46 1.18
Critical values 95%
90%
27.42 21.12 14.88 8.07
24.99 19.02 12.98 6.5
48.88 31.54 17.86 8.07
45.70 28.78 15.75 6.50
Trace Trace statistic r=0 r≤1 r≤2 r≤3
r r r r
≥1 ≥2 ≥3 ≥4
67.50∗∗ 26.24 9.64 1.18
Z = LFERT − 0.81LFEM + 0.87LRWAGE − 0.45LRCGDP Note. The variable r indicates the number of cointegrating relationships. Maximum eigenvalue and trace test statistics are compared with the critical values almost identical with those reported in Johansen and Juselius (1992, Table 2). These differences are explained in Pesaran, Shin, and Smith (2000). When the two statistics are eignevalues and the trace statistics are adjusted for the degrees of freedom the estimated values are for eignevalues: 32.8∗ , 13.19, 6.73, 0.94 and for trace statistics: 53.65∗ , 20.85, 7.66, 0.94 (Reimers, 1992). Asterisks (**) indicate rejection of the null hypothesis at 95% critical value.
from the VAR model. The dummy variable accounts for the sharp decline in real output due to the oil crisis in 1973. The test rejects the null hypothesis of the deletion of the dummy variable from the VAR model. The estimation procedure assumes unrestricted intercepts and no trends in the VAR estimation. The two test statistics give similar results. Both tests provide evidence to reject the null of zero cointegrating vectors in favor of one cointegrating vector at 5% level.5 On the basis of the results, the long-run relationship between fertility rate female employment, real wages and real per capita output finds statistical support in U.K. over the period under examination. Subsequently, we investigate whether all the variables, fertility rate, female employment, real wage and real per capita output enter into the cointegrating vector in a statistically significant way. Table 4 reports the likelihood ratio tests as described in Johansen (1992) and Johansen and Juselius (1992). The results suggest that all the variables enter in a statistically significant way into the cointegrating vector. In addition, Table 4 reports the statistics testing for the stationarity hypothesis of all variables. In particular, we investigate whether all the variables except 1, which takes the value 1, are equal to 0. The tests, which follow chi-square distribution with three degrees of freedom, reject the stationarity hypothesis for all variables at 1% level of significance. These findings are in accordance with the rejection of the unit root hypothesis, from the four tests (ADF, PP, KPSS and ZA), implying that all variables employed in the analysis are not stationary.
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Table 4 Long-run hypothesis testing Variables LFERT LFEM LRWAGE LRCGDP
LR test of restrictions that each variable does not enter in the cointegrating vector 7.80∗∗∗ 19.28∗∗∗ 20.95∗∗∗ 10.14∗∗∗
Weak exogeneity test
Stationarity test
52.15∗∗∗ 0.27 1.99 1.26
33.55∗∗∗ 39.24∗∗∗ 38.45∗∗∗ 39.07∗∗∗
Notes. The reported statistics are distributed as chi-square distribution with degrees of freedom the number of cointegrating vectors for the first two tests and the number of restrictions for the third test. Asterisks (***) indicate rejection of the null hypothesis at 1% level of significance.
The estimated cointegration relationship is presented in Table 3. This equation can be rewritten as LFERT = 0.81LFEM − 0.87LRWAGE + 0.45LRCGDP + Z From the above estimated equation three main points can be concluded. First, an upward shock to female employment leads to higher fertility. This result suggests that, when we account for wage effects and output changes, a positive relationship among female employment and fertility emerges. Second, an upward shock in real wages, due for example to technological change, leads to lower fertility. This implies that the opportunity cost of time devoted to childcare has increased and consequently fertility has declined. Finally, an upward shock in real GDP per capita, due for example to an improvement in the terms of trade, leads to higher fertility. This implies a positive income effect on the demand for children. Overall, the estimated cointegrating vector suggests that the fertility is affected by changes in female employment, real wage and real per capita output in the long run. Next, we estimate the long-run relationship recursively and we test for the stability of the long-run relationship using the recursive estimation of one-step Chow test, break point Chow test and forecast Chow test at 5% level of significance. The results indicate that none of the break point Chow statistics is significant at their one-off 5% level.6 This result suggests that the long-run relationship remained unchanged during the estimation period.7 Turning to the persistence profile (Fig. 2) presents the persistence profile for the long-run relationship Z.8 It is important to notice that the relationship has the tendency to converge
Fig. 2. Persistent profile of the effect of a system-wide shock to cointegrating vector Z.
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Equations Test of restrictions Short-run dynamics non-causality
Weak exogeneity (ECT coefficient)
LFERT LFEM LRWAGE LRCGDP Z = 0 LFERT LFEM 0.08
0.65
3.84∗∗ 0.36
0.002 0.96
−0.13∗∗∗ 0.04
Tests for Granger non-causality (joint short-run dynamics and ECT) LFERT and ECT 0.99
LFEM and ECT
LRWAGE and ECT
LRCGDP and ECT
52.67∗∗∗
56.46∗∗∗ 1.30
57.59∗∗∗ 1.02
Tests for strong exogeneity
60.02∗∗∗ 2.86
Note. The lagged ECT is derived by normalizing the cointegrating vector on fertility. The statistics reported are distributed as chi-square distribution with degrees of freedom the number of restrictions. In the short-run dynamics asterisks indicate rejection of the H0 that there is short-run non-causal relationship between the two variables. The coefficients of the lagged ECTs are negative. Asterisks indicate rejection of the null hypothesis that the estimated coefficient is equal to 0 (weak exogeneity). Finally, in the tests for Granger-non-causality and strong exogeneity, asterisks denote rejection of the null hypothesis of Granger-non-causality and strong exogeneity, respectively. Asterisk (***, **) indicate significance at the 1 and 5% levels, respectively.
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Table 5 Summary of tests for weak and strong exogeneity of variables based on vector error-correction models
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relatively fast (4 years after the shock) to equilibria. This suggests that the cointegrating relationship tends to respond quickly to changes in the fertility rate, the female employment, the real wage and real economic changes. Having verified that the variables are cointegrated, vector error-correction models can be applied. The lagged residuals from the cointegrating regression with the appropriate number of lags are included in the Granger-causality test structure. The lag lengths structure depends on the restricted error-correction models. The restricted error-correction models pass a series of diagnostic tests including serial correlation based on the inspection of the autocorrelation functions of the residuals as well as the reported Lagrange multiplier. Table 5 reports the findings for the endogeneity of fertility choice and female employment variables, based on the error-correction equations. Estimates of the parameters show that the error-correction term measuring the long-run disequilibrium is significant for the fertility equations. This implies that the fertility variable have a tendency to restore equilibrium and take the brunt of any shock to the system. The t-tests for the error-correction terms indicate, at the 1% level of significance, that fertility is not weakly exogenous variables. In addition, the results imply at different levels of significance that female employment is weakly exogenous variable. Table 5 confirms the above results employing the Wald test. In the short-run dynamics (Granger-causality in the strict sense), the Wald-tests indicate that there is a relationship between the fertility rate and real wage. In particular, the results suggest that in the short-term fertility choice is affected by changes in the real wage variable. Finally, the significance levels associated with the Wald-tests of joint significance of the sum of the lags of the explanatory variable and the error-correction term, provide more information on the impact of economic variables on fertility choice and female employment variables as a further channel of Granger-causality is exposed. For the fertility variable the results imply the Granger-endogeneity of the variable. The empirical results reject the hypothesis of strong exogeneity of fertility choice variable supporting the proposition that there is a relationship between fertility choice, female employment, real wage and real per capita output in U.K. From the empirical analysis five conclusions can be drawn. First, when we account for real wage and real output effects, a positive relationship among female employment and fertility exists in the long-run while in the short-run employment seems not to affect fertility. Second, fertility choice should not be considered exogenous to the female employment, the labor market or the growth process. Third, higher real wages are responsible for the deterioration of fertility, since time is reallocated from childbearing toward labor, increasing the opportunity cost of time devoted to childcare. Fourth, an upward shock in real GDP per capita leads to higher fertility. Fifth, changes in the fertility choice are not responsible for changes in female employment. So, we can conclude that the declining fertility rates are associated not with the choice of women to participate in the labor force but with higher wages.
5. Conclusions This paper provides an empirical model that examines the validity of the proposition that there is a causal relationship between female employment and fertility choice in a multivariate framework for the United Kingdom over the period 1958–1998. Previous empirical research
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has provided inconclusive results on the relationship between female employment and fertility. Moreover, recent demographic findings suggest a reduction in the incompatibility between childrearing and female employment, as a result of changes in social norms and in childcare availability. Therefore, following recent advances in economic and demographic theory the nexus between female employment and fertility is reexamined taking into account changes in the labor market and the overall real economic activity. In order to account for influences on the fertility–female employment relationship of changes in medical technology, literacy, standard of living, overall economic performance and the labor market, real GDP and real wages are added to the VAR model. Initially, the paper examines the existence of a relationship between fertility, female employment, real wages and real per capita GDP. The empirical results of cointegration, within this multivariate cointegrated system, derived from the Johansen and Juselius maximum likelihood estimation technique of cointegrating vectors, rules out the possibility that the estimated relationships are spurious and supports the hypothesis of the existence of a long-run relationship among the variables. This implies that these variables although they may have occasional short-term or transitory deviations from their long-term equilibrium, eventually forces will prevail that will drive them together. In the long-run, when we account for wage effects and output changes, an upward shock in female employment leads to higher fertility. Second, an upward shock in real wages, due for example to technological change, leads to lower fertility. Finally, an upward shock in real GDP per capita leads to higher fertility. In short, the results from the long-run analysis suggest that fertility is affected by changes in female employment, real wage and real per capita output in the long-run. The results of the empirical models using the VECM estimation suggest that fertility should be considered as endogenous variable to the female employment, the labor market and the growth process relationship rejecting the hypothesis of weak and strong exogeneity of fertility. In the short-term fertility choice is affected by wages implying that higher real wages are responsible for the deterioration of fertility, since time is reallocated from childbearing toward labor, increasing the opportunity cost of time devoted to child care. To sum up, although in recent years econometric advances have stimulated further research on the interdependence of fertility and employment the evidence in a bivariate context has produced mixed results. When we account for the role of wages and output, there are grounds for believing that fertility is affected by changes in female employment, real wage and real per capita output. Both in the short- and long-term fertility choice is affected by wages implying that higher real wages are responsible for the deterioration of fertility. In the long-run, when we account for wage effects and output changes, an upward shock in female employment leads to higher fertility and an upward shock in real GDP per capita leads to higher fertility. Notes 1. The male breadwinner, or family wage model, assumes that the father goes out to work while the mother stays at home to look after the children. According to the model the man is the provider and protector of the family and the woman is the one who cares and reproduces children.
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2. This approach has several advantages over the Engle and Granger (1987) technique employed in other empirical studies. First, the Johansen and Juselius method tests for the number of cointegrating vectors between the variables. These tests are based on the trace statistic test and the maximum eigenvalue test. Second, it treats all variables as endogenous thus avoiding an arbitrary choice of dependent variable. Third, it provides a unified framework for estimating and testing cointegrating relations within the framework of a vector error-correction model. 3. For other applications of this technique in different topics, see Masih and Masih (1996) and Hondroyiannis and Papapetrou (2000, 2001). 4. The KPSS statistics are known to be sensitive to the choice of truncation parameter l and tend to decline monotonically as l increases. 5. It is known that the Johansen cointegration procedure is biased towards the rejection of the null hypothesis in a small sample (Cheung & Lai, 1993). Therefore, in the estimation procedure we used the critical values obtained from Johansen and Juselius (1990) and the critical values adjusted for small sample (see note to Table 3). Both values reject the null of zero cointegrating vectors in favor of one cointegrating vector at 5 and 10% level of significance. 6. The results are available from the author upon request. 7. The results for the Chow test are obtained using PcFiml 9.0 (see Doornik & Hendry, 1997). 8. Pesaran and Shin (1996) have proposed the estimation of persistence profile to estimate the speed with which the effect of system-wide shocks on cointegrating relationship disappears. In particular, the persistence profile at n periods after a shock can be viewed as the variance of the difference between the forecast for n periods if a shock had occurred and the forecast for n periods if no shock had occurred.
Acknowledgments The views expressed in this paper are those of the author and not those of the Bank of Greece. The author wishes to thank an anonymous referee for his valuable comments in a previous version of this paper. All remaining errors and deficiencies are the responsibility of the author.
References Becker, G. (1965). A theory of allocation of time. Economic Journal, 75, 493–517. Cain, G., & Dooley, M. D. (1976). Estimation of a model of labor supply, fertility and wages of married women. Journal of Political Economy, 84, S179–S201. Cheng, B. S. (1996). An investigation of cointegration and causality between fertility and female labour force participation. Applied Economics Letters, 3, 29–32. Cheng, B. S., Hsu, R. C., & Chu, Q. (1997). The causality between fertility and female labour force participation in Japan. Applied Economics Letters, 4, 113–116.
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Chesnais, J.-C. (1996). Fertility, family and social policy in contemporary western Europe. Population and Development Review, 22(4), 729–739. Cheung, Y. W., & Lai, K. S. (1993). Finite-sample sizes of Johansen’s likelihood ratio tests for cointegration. Oxford Bulletin of Economics and Statistics, 55, 313–328. Cigno, A. (1991). Economics of the family. Oxford: Clarendon Press. Dickey, D. A., & Fuller, W. A. (1979). Distributions of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431. Dickey, D. A., & Fuller, W. A. (1981). The likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057–1072. Doornik, J. A., & Hendry, D. F. (1997). Modeling dynamic systems using PcFiml 9.0 for Windows. London: International Thomson Business Press. Engle, R. F., & Granger, C. W. J. (1987). Cointegration and error-correction: Representation. Econometrica, 55, 251–276. Esping-Andersen, G. (1999). Social foundations of postindustrial economics. Oxford: Oxford University Press. Fleisher, B. M., Jr., & Rhodes, G. F. (1976). Unemployment and the labor force participation of married men and women: A simultaneous model. Review of Economics and Statistics, 58, 398–406. Granger, C. W. J. (1986). Developments in the study of cointegrated economics variables. Oxford Bulletin of Economics and Statistics, 48, 213–228. Granger, C. W. J. (1988). Developments in a concept of causality. Journal of Econometrics, 39, 199–211. Gustafsson, S. S, Wetzels, M. M. P. C., Vlasblom, J. D., & Dex, S. (1996). Women’s labor force transitions in connection with childbirth: A panel data comparison between Germany, Sweden and Great Britain. Journal of Population Economics, 9, 223–246. Hoffman, E. P. (1985). Fertility and female employment. Quarterly Review of Economics and Business, 25, 85– 95. Hondroyiannis, G., & Papapetrou, E. (2000). Do Demographic changes affect fiscal developments? Public Finance Review, 28(5), 468–488. Hondroyiannis, G., & Papapetrou, E. (2001). Demographic changes, labour effort and economic growth: Empirical evidence from Greece. Journal of Policy Modeling, 23, 169–188. Hotz, V. J., & Miller, R. A. (1988). An empirical analysis of life cycle fertility and female labor supply. Econometrica, 56, 91–118. Johansen, S. (1988). Statistical and hypothesis testing of cointegration vectors. Journal of Economic Dynamics and Control, 12, 231–254. Johansen, S. (1992). Cointegration in partial systems and the efficiency of single equation analysis. Journal of Econometrics, 52, 389–402. Johansen, S., & Juselius, K. (1990). Maximum likelihood estimation and inference on cointegration—With applications to the demand for money. Oxford Bulletin of Economics, 52, 169–210. Johansen, S., & Juselius, K. (1992). Testing structural hypotheses in a multivariate cointegration analysis at the purchasing power parity and the uncovered interest parity for the UK. Journal of Econometrics, 53, 211– 244. Kalwij, A. S. (2000). The Effects of female employment status on the presence and number of children. Journal of Population Economics, 13(2), 221–239. Klijzing, E., Sieger, X., Keilman, J. N., & Groot, L. (1988). Static versus dynamic analysis of the interaction between female labour force participation and fertility. European Journal of Population, 4, 97–116. Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54, 159–178. Mahdavi, S. (1990). A simultaneous-equations model of cross-national differentials in fertility labor force participation rates. Journal of Economic Studies, 17, 32–49. Masih, A. M. M., & Masih, R. (1996). Empirical tests to discern causal chain in macroeconomic activity: New evidence from Thailand and Malaysia based on a multivariate cointegration/vector error-correction. Journal of Policy Modeling, 18(5), 531–560. McDonald, P. (2000). Gender equity, social institutions and the future of fertility. Journal of Population Research, 17(1), 1–12.
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Michael, R. T. (1985). Consequences of the rise in female labor force participation rates: Questions and probes. Journal of Labor Economics, 3, 117–157. Moffit, R. (1984). Profiles of fertility, labour supply and wages of married women: A Complete life-cycle model. Review of Economic Studies, 51, 263–278. Osawa, M. (1988). Working mother: Changing patterns of employment and fertility in Japan. Economic Development and Cultural Changes, 36, 623–650. Perron, P. (1988). Trends and random walks in macroeconomic time: Series further evidence from a new approach. Journal of Economics Dynamic and Control, 12, 297–332. Pesaran, M. H., & Shin, Y. (1996). Cointegration and speed of convergence to equilibrium. Journal of Econometrics, 71, 117–143. Pesaran, M. H., Shin, Y., & Smith, R. J. (2000). Structural analysis of vector error correction models with exogenous I(1) variables. Journal of Econometrics, 97, 293–343. Phillips, P. C. B. (1987). Time series regression with a unit root. Econometrica, 55, 277–346. Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrica, 75, 335–346. Reimers, H. E. (1992). Comparisons of tests for multivariate cointegration. Statistical Papers, 33, 335–359. Rindfuss, R. J., & Brewester, K. L. (1996). Childrearing and fertility. Population and Development Review, 22(Supplement), 258–289. Rindfuss, R. J., Brewester, K. L., & Kavee, A. L. (1996). Women, work, and children: Behavioural and attitudinal change in the United States. Population and Development Review, 22(3), 457–482. Schultz, T. P. (1978). The influence of fertility on labour supply of married women: Simultaneous equation estimates. In R. G. Ehrenberg (Ed.), Research in labor economics (Vol. 2, pp. 273–351). Greenwich, CT: JAI Press. Sprague, A. (1988). Post-war fertility and female labor force participation rates. Economic Journal, 98, 682–700. Tanda, P. (1994). Marital instability, reproductive behavior and women’s labour force participation decisions. Labour, 8, 279–301. Willis, R. (1973). A new approach to the economic theory of fertility behavior. Journal of Political Economy, 81, S14–S64. Yamada, T., & Yamada, T. (1986). Fertility and labor force participation of married women: Empirical evidence from the 1980 population census of Japan. Quarterly Review of Economics and Business, 26, 35–46. Zivot, E., & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business and Economic Statistics, 10(3), 251–270.
Does female employment affect fertility? Evidence from the United Kingdom Evangelia Papapetrou a,b,∗,1 a
b
University of Athens, Athens, Greece Bank of Greece, Economic Research Department, Athens, Greece
Abstract This paper tests the validity of the proposition that there is a causal relationship between fertility choice and female employment in a multivariate framework during the period 1958–1998 in the United Kingdom. Following recent advances in economic and demographic theory the nexus between female employment and fertility is reexamined taking into account changes in the labor market and the overall real economic activity. Our key finding is that expanding the estimating equations to control for the influences of changes in real wages and real output creates a positive relationship between fertility and female employment and a negative relationship between fertility and real wages. Finally, fertility choice should not be considered exogenous to the female employment, the labor market or the growth process. © 2004 Elsevier Inc. All rights reserved.
1. Introduction The theory of the allocation of time in Becker (1965) implies the importance of labor supply and fertility decisions. In his framework fertility decision is viewed as an economic one, and that one of the costs of having a child is the forgone earnings of the person caring for the child at home, in most cases the mother. The development within this framework of the new microeconomic theory in Willis (1973) formally modeled this joint fertility–labor supply decision. In the model of household behavior the family is maximizing utility defined over market goods, leisure and child services. In the household the wife’s time and market goods are used as inputs to produce child services. So the participation and procreation decisions are mutually exclusive. If the woman devotes most of her time to market work, then she should decrease her leisure time and/or the number of children. This implication is especially ∗
Tel.: +30-10-320-2429; fax: +30-10-323-3025. E-mail address: [email protected] (E. Papapetrou). 1 Present address: Economic Research Department, Bank of Greece, El. Venizelou 21, 102 50 Athens, Greece.
0362-3319/$ – see front matter © 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.soscij.2004.01.003
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important, as we need to explain the trends in fertility and female labor supply over the last 30 years. However, in the labor supply literature, most empirical work has analyzed fertility and female labor supply decisions separately. Some economists have treated fertility as an exogenous determinant of labor supply and others have assumed that labor supply is an exogenous determinant of fertility. Other researchers have estimated simultaneous models of fertility and labor supply and have showed the interdependency over the life cycle of fertility and female employment rates (Cain & Dooley, 1976; Cigno, 1991; Fleisher & Rhodes, 1976; Hotz & Miller, 1988; Kalwij, 2000; Mahdavi, 1990; Moffit, 1984). Several studies have tried to test the existence and the direction of causality between fertility and female employment applying methods of time series analysis. Among others, Cheng (1996), Cheng, Hsu, and Chu (1997), Klijzing, Sieger, Keilman, and Groot (1988), and Michael (1985) apply Granger-causality tests to study the relationship among female labor force participation and fertility. These studies provide mixed results on the existence and direction of causality between fertility and female employment. The advance of econometric techniques in recent years stimulated further empirical research on the interdependence of fertility and female employment. However, to resolve the issue of the direction of causality in a bivariate context, the previous studies have applied causality tests based on the standard Granger–Sims, the modified Sims and Hsiao tests. But the studies applying these tests suffered from methodological deficiencies. First, the basic time series properties of the variables were not examined implying that the findings of their analysis may be spurious. Second, if the variables are cointegrated, then tests incorporating differenced variables will be misspecified unless the lagged error-correction term is included (Cheng, 1996; Cheng et al., 1997; Klijzing et al., 1988; Michael, 1985). So, the application of vector error-correction model (VECM) estimation, derived from the cointegration equations by introducing the lagged error-term, incorporates all the long-run information that was initially lost through differencing the variables (Granger, 1988). Finally, the inclusion in the bivariate relation analysis of other economic factors such as the wage rate and real economic activity, may influence the fertility and female employment relationship and may reveal additional channels of causality initially ignored in the bivariate context analysis. The lack of unequivocal evidence on the relationship between fertility and female employment creates an obvious deficiency that may affect applied research and policy making in employment and economic development. In light, of these contradicting results the detailed investigation of the nexus between female employment and fertility deserves particular attention. In addition, recent development in economic and demographic theory supports the notion that in OECD countries increasing female participation rates do not depress fertility rates for those countries that have succeeded in minimizing the incurred costs of childbearing and work (McDonald, 2000; Rindfuss & Brewester, 1996; Rindfuss, Brewster, & Kavee, 1996). According to the argument of Chesnais (1996) and Esping-Andersen (1999) if women are provided with opportunities nearly equivalent to those of men, such as in market employment and in education, but these opportunities are severely curtailed by having children, then, on average, women will restrict the number of children that they have to an extent which leaves fertility at a precariously low, long-term level. So, as long as there is an improvement in the
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childcare availability this might reduce the incompatibility between childbearing and female employment and enable woman to combine work and childrearing. The primary purpose of this paper is to address the causality issue between fertility and female employment in a temporal causal framework, taking into account changes in the labor market and in the overall economic activity, with the aid of multivariate cointegration and the application of VECM estimation for United Kingdom for the period 1958–1998. In the empirical investigation of the dynamic interaction between fertility choice, female employment other economic variables are employed, such as the real wage rate and real output, and the nexus between fertility and female employment is reexamined in a multivariate framework. U.K. serves as a good example since the demographic developments closely resemble the general trend in most OECD countries. The paper utilizes the recently developed technique of VECM estimation. This technique has several advantages over other methods used in the past by various researchers, since this type of multivariate analysis clearly can distinguish between exogenous and endogenous variables. Our key finding is that expanding the estimating equations to control for the influences of changes in real wages and real output creates a positive relationship between fertility and female employment and a negative relationship between fertility and real wages. Fertility choice should not be considered exogenous to the female employment, the labor market or the growth process. Lastly, estimation of the four-variable vector autoregression model supports the finding that changes in the fertility choice are not responsible for changes in female employment. The remainder of the paper is organized as follows. Section 2 briefly reviews empirical evidence on the relationship among fertility and female employment. Section 3 discusses the methodological issues and the data. Section 4 reports the empirical results. Section 5 presents the concluding remarks.
2. Fertility choice and female employment: empirical and theoretical considerations Several studies have tried to test the existence and the direction of causality between fertility and female employment applying methods of time series analysis. Most of these studies examine the nexus between fertility and female employment in a bivariate context and provide mixed results on the direction of causality among the two variables. Michael (1985) uses a model to study the bivariate relationship among female employment and fertility in the USA over the period 1948–1980. By applying standard Granger-causality tests he shows that female labor force participation positively causes fertility. However, his conclusion is sensitive to the definition of fertility. Klijzing et al. (1988) use monthly data from a Dutch survey for 1977–1984. They apply Sim’s indirect Granger-causality tests to find that labor force participation has no influence on fertility decisions and vice versa. However, when they apply standard Granger-causality tests there is evidence of bi-directional causality among the fertility and female employment. Cheng (1996) applies Hsiao’s version of the Granger-causality method to examine the causality between fertility and female labor participation using transformed U.S. data for the period 1948–1993. He argues that there is unidirectional causality running from fertility to female labor force participation with no feedback.
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Most work have used data for the U.S. (Cain & Dooley, 1976; Cheng, 1996; Hoffman, 1985; Moffit, 1984; Schultz, 1978) a few for Japan (Cheng et al., 1997; Osawa, 1988; Yamada & Yamada, 1986) and the main OECD countries (Gustafsson, Wetzels, Vlasblom, & Dex, 1996; Kalwij, 2000; Mahdavi, 1990; Sprague, 1988; Tanda, 1994). Recent advances in demographic theory suggest that a reduction in the incompitability between childrearing and female employment, as a result of changes in social norms and in childcare availability has affected fertility decision. The demographic theory supports the idea that in some OECD countries increasing participation rates do not depress fertility rates if these societies manage to minimize the incurred costs of childbearing and work. Rindfuss et al. (1996) show, using attitudinal data, that since the 1970s in the United States that there has been a substantial weakening of the norm that mothers of preschool children should stay at home. This change in measured attitudes is pervasive and appears to have been led by well-diffused behavioral change. The authors argue that this change in attitudes has played an important role in the stabilizing of U.S. fertility levels and might explain a positive association fertility rate and female labor market participation rates. Chesnais (1996) and Esping-Andersen (1999) claim that if women are provided with opportunities similar to those of men in education and market employment, but women have to bear the costs of child raising, then women will restrict the number of children that they have. McDonald (2000) claims that for societies that the breadwinner model prevails women are left with choices between children and employment, which in turn leads to having fewer children and low fertility.1 He suggests that societies that advance gender equity in social institutions related to the family, women and men are able to combine market employment with having children and fertility will be higher. So, as long as structural obstacles are restricted through the provision of social organization and support for families with children, women will be able to combine work with children.
3. Methodological issues and data In the empirical analysis we test for the existence of a dynamic relationship between fertility choice and female employment in the context of an extended model to account for the contribution of economic forces to this bivariate relationship. In order to account for influences on the fertility–female employment relationship of changes in medical technology, literacy, standard of living, overall economic performance, opportunity cost of time devoted to childcare and the labor market, real GDP per capita and real wages are added to the VAR model. In particular, we employ the VECM estimation to investigate empirically the endogeneity of fertility and female employment and their linkage with economic variables, such as real wage and real output. In addition, we examine the responses of fertility and female employment to labor market and overall economic activity, in order to capture the short-run dynamics of the variables. The four macroeconomic variables employed in the empirical analysis are the fertility rate, female employment, real wage and real per capita gross domestic product. Testing for the existence of statistical relationship among the variables is done in three steps. The first step is to verify the order of integration of the variables since the causality tests are
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valid only if the variables have the same order of integration. Standard tests for the presence of a unit root based on the work of Dickey and Fuller (1979, 1981), ADF test; Perron (1988), Phillips (1987), Phillips and Perron (1988), PP test; Kwiatkowski, Phillips, Schmidt, and Shin (1992), KPSS test; and Zivot and Andrews (1992), ZA test, are used to investigate the degree of integration of the variables used in the empirical analysis. The second step involves testing for cointegration using the Johansen maximum likelihood approach (Johansen, 1988; Johansen & Juselius, 1990, 1992). The Johansen–Juselius estimation method is based on the error-correction representation of the VAR model with Gaussian errors.2 Evidence of cointegration rules out the possibility that the estimated relationship is spurious (Granger, 1986, 1988).3 The third step involves utilization of the vector error-correction modeling and testing for exogeneity of variables. Engle and Granger (1987) show that in the presence of cointegration, there always exists a corresponding error-correction representation which implies that changes in the dependent variable are a function of the level of disequilibrium in the cointegrating relationship, captured by the error-correction term (ECT), as well as changes in other explanatory variables. Thus through ECT, the VECM modeling establishes an additional way to examine the Granger-causality ignored initially from the Granger–Sims tests. The Wald-test applied to the joint significance of the sum of the lags of each explanatory variable and the t-test of the lagged error-correction term will imply statistically the Granger-exogeneity or endogeneity of the dependent variable. The non-significance of ECT is referred as long-run non-causality, which is equivalent to saying that the variable is weakly exogenous with respect to long-run parameters. The absence of short-run causality (Grangercausality in the strict sense) is established from the non-significance of the sums of the lags of each explanatory variable. Finally, the non-significance of all explanatory variables including the ECT term in the VECM indicates the econometric strong-exogeneity of the dependent variable, that is the absence of Granger-causality. The proposed three steps are presented and outlined in Fig. 1. The empirical analysis has been carried out using annual data for the period 1958–1998 for United Kingdom. LFERT is the fertility rate, LFEM is the female employment as a percentage of the labor force, LRWAGE is the real wage and LRCGDP is the real GDP per capita. Fertility and employment rate are obtained from the Labor Force Statistics published by the OECD. Real wage and real GDP per capita are obtained from the International Financial Statistics tape. All variables are expressed in logarithmic form.
4. Empirical results Table 1 presents the ADF, PP and KPSS tests for the four variables, fertility rate, female employment, real wage and real per capita output used in the analysis in levels and first differences. The ADF statistic suggests that all variables are integrated of order 1, I(1), whereas the first differences of all the variables are integrated of order 0, I(0). Therefore, the hypothesis that the time series contain an autoregressive unit root is accepted in all cases. Also, the Phillips–Perron test based on the 5 and 1% critical values supports the hypothesis that all series contain a unit root. Finally, the KPSS statistics tests for lag-truncation parameters one and four
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Fig. 1. The procedure for testing for cointegration and Granger-causality.
(l = 1 and 4)4 since it is unknown how many lagged residuals should be used to construct a consistent estimator of the residual variance. The KPSS test rejects the null hypothesis of level and trend stationarity for both lag truncation parameters. The KPSS statistics does not reject the I(0) hypothesis for the first differences of the series at various levels of significance. Therefore, the combined results from all the tests (ADF, PP, KPSS) suggest that all the series under consideration appear to be I(1) processes. Next the Zivot–Andrews test is estimated for the four variables used in the analysis to ensure that all the series are I(1). Table 2 reports the minimum t-statistics from testing the stationarity assuming a shift in mean and broken trend for the levels and first differences of all the variables. The minimum t-statistics reported is the minimum overall break point regressions from 1958 to 1998. The results suggest that at 5% level of significance none of the estimated variables are stationary around a broken trend or a shift in the mean, while their differences are I(0). The Zivot–Andrews test confirms that all the variables are I(1). Since both the fertility and employment levels are integrated of the same order, it is appropriate to look for a relationship between fertility choice and female labor decision. In order to account for influences on the fertility rate–female employment relationship of changes in labor market and income of the households, real wage (LRWAGE) and the real per capita output (LRCGDP) variables are added to the extended VAR model. Table 3 summarizes the results of cointegration analysis among the four variables using the Johansen maximum likelihood approach employing both the maximum eigenvalue and trace statistic. To determine the lag length of the VAR three versions of system were initially estimated: a four, a three and a two-lag version. Then, an Akaike Information criterion (AIC), a Schwarz Bayesian Criterion (SBC) and a likelihood ratio test (Sims’ test) were used to test that all
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Table 1 Tests of unit roots hypothesis Variable
LFERT LFEM LRWAGE LRCGDP LFERT LFEM LRWAGE LRCGDP
Augmented Dickey–Fuller
Phillips–Perron
KPSS
τµ
ττ
k
τµ
ττ
k
−1.10 −0.93 −1.53 −0.52 −3.32∗ −4.62∗∗ −5.68∗∗ −4.63∗∗
−2.13 −0.86 −1.98 −2.67 −3.28∗ −4.67∗∗ −5.58∗∗ −4.58∗∗
1 1 1 2 0 0 0 0
−0.91 −0.89 −2.16 −1.00 −3.35∗ −4.69∗∗ −5.68∗∗ −4.48∗∗
−1.67 −0.95 −2.43 −3.01 −3.32∗ −4.72∗∗ −5.83∗∗ −4.41∗∗
3 3 3 3 3 3 3 3
l=1
l=4
ηµ
ητ
ηµ
ητ
1.503∗∗ 2.124∗∗ 2.082∗∗ 2.100∗∗ 0.139 0.280 0.323 0.084
0.309∗∗ 0.224∗∗ 0.266∗∗ 0.132 0.145 0.220∗ 0.061 0.049
0.659∗∗ 0.906∗∗ 0.913∗∗ 0.927∗∗ 0.092 0.215 0.302 0.117
0.146∗ 0.123 0.146∗ 0.091 0.095 0.170∗ 0.066 0.070
Notes. The relevant tests are derived from the OLS estimation of the following autoregression for the variable involved: xt = δ0 + δ1 (time)t − δ2 xt−1 +
k φi xt−i + ut
(1)
i=1
where τ µ is the t-statistic for testing the significance of δ2 when a time trend is not included in Eq. (1) and τ τ is the t-statistic for testing the significance of δ2 when a time trend is included in Eq. (1). The calculated statistics are those reported in Dickey and Fuller (1981). The critical values at 5 and 1% for N = 50 are −2.93 and −3.58 for τ µ and −3.5 and −4.15 for τ τ , respectively. The lag length structure of φi of the dependent variable xt is determined using a recursive procedure in the light of a Lagrange multiplier (LM) autocorrelation test (for orders up to 4) which is asymptotically distributed as chi-squared distribution and the value of t-statistic of the coefficient associated with the last lag in the estimated autoregression. The critical values for the Phillips–Perron unit root tests are obtained from Dickey and Fuller (1981). ηµ and ητ are the KPSS statistics for testing the null hypothesis that the series are I(0) when the residuals are computed from a regression equation with only an intercept and intercept and time trend, respectively. The critical values for ηµ and ητ at 5% are 0.463 and 0.146 and at 1% are 0.739 and 0.216, respectively (Kwiatkowski et al., 1992, Table 1). Asterisks (**, *) indicate significance at the 1 and 5% levels, respectively.
three specifications are statistically equivalent. All tests reject the null hypothesis that all specifications are equivalent. In particular, the tests suggest that VAR = 2 should be used in the estimation procedure of cointegration to avoid over-parameterization of the estimated models. Finally, a log-likelihood ratio test is used for testing the deletion of a dummy variable Table 2 Zivot–Andrews minimum t-statistics Variables
t-statistic
Year
LFERT LFEM LRWAGE LRCGDP LFERT LFEM LRWAGE LRCGDP
−5.07 −3.28 −3.82 −4.87 −6.27∗∗ −5.96∗∗ −6.21∗∗ −5.95∗∗
1971 1990 1976 1979 1976 1971 1972 1989
Notes. All t-statistics estimated from a break in intercept and trend model. Critical values are those reported in Table 4 of Zivot and Andrews (1992). The 1 and 5% critical values are −5.57 and −5.08, respectively. Asterisks (**) indicate significance at the 1% level.
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Table 3 Johansen and Juselius cointegration test: fertility rate, female employment, real wage, real per capita output in United Kingdom, 1958–1998 VAR = 2, variables: LFERT, LFEM, LRWAGE, LRCGDP Null
Alternative
Maximum eigenvalues r=0 r=1 r≤1 r=2 r≤2 r=3 r≤3 r=4
Eigenvalue
41.26∗∗ 16.60 8.46 1.18
Critical values 95%
90%
27.42 21.12 14.88 8.07
24.99 19.02 12.98 6.5
48.88 31.54 17.86 8.07
45.70 28.78 15.75 6.50
Trace Trace statistic r=0 r≤1 r≤2 r≤3
r r r r
≥1 ≥2 ≥3 ≥4
67.50∗∗ 26.24 9.64 1.18
Z = LFERT − 0.81LFEM + 0.87LRWAGE − 0.45LRCGDP Note. The variable r indicates the number of cointegrating relationships. Maximum eigenvalue and trace test statistics are compared with the critical values almost identical with those reported in Johansen and Juselius (1992, Table 2). These differences are explained in Pesaran, Shin, and Smith (2000). When the two statistics are eignevalues and the trace statistics are adjusted for the degrees of freedom the estimated values are for eignevalues: 32.8∗ , 13.19, 6.73, 0.94 and for trace statistics: 53.65∗ , 20.85, 7.66, 0.94 (Reimers, 1992). Asterisks (**) indicate rejection of the null hypothesis at 95% critical value.
from the VAR model. The dummy variable accounts for the sharp decline in real output due to the oil crisis in 1973. The test rejects the null hypothesis of the deletion of the dummy variable from the VAR model. The estimation procedure assumes unrestricted intercepts and no trends in the VAR estimation. The two test statistics give similar results. Both tests provide evidence to reject the null of zero cointegrating vectors in favor of one cointegrating vector at 5% level.5 On the basis of the results, the long-run relationship between fertility rate female employment, real wages and real per capita output finds statistical support in U.K. over the period under examination. Subsequently, we investigate whether all the variables, fertility rate, female employment, real wage and real per capita output enter into the cointegrating vector in a statistically significant way. Table 4 reports the likelihood ratio tests as described in Johansen (1992) and Johansen and Juselius (1992). The results suggest that all the variables enter in a statistically significant way into the cointegrating vector. In addition, Table 4 reports the statistics testing for the stationarity hypothesis of all variables. In particular, we investigate whether all the variables except 1, which takes the value 1, are equal to 0. The tests, which follow chi-square distribution with three degrees of freedom, reject the stationarity hypothesis for all variables at 1% level of significance. These findings are in accordance with the rejection of the unit root hypothesis, from the four tests (ADF, PP, KPSS and ZA), implying that all variables employed in the analysis are not stationary.
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Table 4 Long-run hypothesis testing Variables LFERT LFEM LRWAGE LRCGDP
LR test of restrictions that each variable does not enter in the cointegrating vector 7.80∗∗∗ 19.28∗∗∗ 20.95∗∗∗ 10.14∗∗∗
Weak exogeneity test
Stationarity test
52.15∗∗∗ 0.27 1.99 1.26
33.55∗∗∗ 39.24∗∗∗ 38.45∗∗∗ 39.07∗∗∗
Notes. The reported statistics are distributed as chi-square distribution with degrees of freedom the number of cointegrating vectors for the first two tests and the number of restrictions for the third test. Asterisks (***) indicate rejection of the null hypothesis at 1% level of significance.
The estimated cointegration relationship is presented in Table 3. This equation can be rewritten as LFERT = 0.81LFEM − 0.87LRWAGE + 0.45LRCGDP + Z From the above estimated equation three main points can be concluded. First, an upward shock to female employment leads to higher fertility. This result suggests that, when we account for wage effects and output changes, a positive relationship among female employment and fertility emerges. Second, an upward shock in real wages, due for example to technological change, leads to lower fertility. This implies that the opportunity cost of time devoted to childcare has increased and consequently fertility has declined. Finally, an upward shock in real GDP per capita, due for example to an improvement in the terms of trade, leads to higher fertility. This implies a positive income effect on the demand for children. Overall, the estimated cointegrating vector suggests that the fertility is affected by changes in female employment, real wage and real per capita output in the long run. Next, we estimate the long-run relationship recursively and we test for the stability of the long-run relationship using the recursive estimation of one-step Chow test, break point Chow test and forecast Chow test at 5% level of significance. The results indicate that none of the break point Chow statistics is significant at their one-off 5% level.6 This result suggests that the long-run relationship remained unchanged during the estimation period.7 Turning to the persistence profile (Fig. 2) presents the persistence profile for the long-run relationship Z.8 It is important to notice that the relationship has the tendency to converge
Fig. 2. Persistent profile of the effect of a system-wide shock to cointegrating vector Z.
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Equations Test of restrictions Short-run dynamics non-causality
Weak exogeneity (ECT coefficient)
LFERT LFEM LRWAGE LRCGDP Z = 0 LFERT LFEM 0.08
0.65
3.84∗∗ 0.36
0.002 0.96
−0.13∗∗∗ 0.04
Tests for Granger non-causality (joint short-run dynamics and ECT) LFERT and ECT 0.99
LFEM and ECT
LRWAGE and ECT
LRCGDP and ECT
52.67∗∗∗
56.46∗∗∗ 1.30
57.59∗∗∗ 1.02
Tests for strong exogeneity
60.02∗∗∗ 2.86
Note. The lagged ECT is derived by normalizing the cointegrating vector on fertility. The statistics reported are distributed as chi-square distribution with degrees of freedom the number of restrictions. In the short-run dynamics asterisks indicate rejection of the H0 that there is short-run non-causal relationship between the two variables. The coefficients of the lagged ECTs are negative. Asterisks indicate rejection of the null hypothesis that the estimated coefficient is equal to 0 (weak exogeneity). Finally, in the tests for Granger-non-causality and strong exogeneity, asterisks denote rejection of the null hypothesis of Granger-non-causality and strong exogeneity, respectively. Asterisk (***, **) indicate significance at the 1 and 5% levels, respectively.
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Table 5 Summary of tests for weak and strong exogeneity of variables based on vector error-correction models
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relatively fast (4 years after the shock) to equilibria. This suggests that the cointegrating relationship tends to respond quickly to changes in the fertility rate, the female employment, the real wage and real economic changes. Having verified that the variables are cointegrated, vector error-correction models can be applied. The lagged residuals from the cointegrating regression with the appropriate number of lags are included in the Granger-causality test structure. The lag lengths structure depends on the restricted error-correction models. The restricted error-correction models pass a series of diagnostic tests including serial correlation based on the inspection of the autocorrelation functions of the residuals as well as the reported Lagrange multiplier. Table 5 reports the findings for the endogeneity of fertility choice and female employment variables, based on the error-correction equations. Estimates of the parameters show that the error-correction term measuring the long-run disequilibrium is significant for the fertility equations. This implies that the fertility variable have a tendency to restore equilibrium and take the brunt of any shock to the system. The t-tests for the error-correction terms indicate, at the 1% level of significance, that fertility is not weakly exogenous variables. In addition, the results imply at different levels of significance that female employment is weakly exogenous variable. Table 5 confirms the above results employing the Wald test. In the short-run dynamics (Granger-causality in the strict sense), the Wald-tests indicate that there is a relationship between the fertility rate and real wage. In particular, the results suggest that in the short-term fertility choice is affected by changes in the real wage variable. Finally, the significance levels associated with the Wald-tests of joint significance of the sum of the lags of the explanatory variable and the error-correction term, provide more information on the impact of economic variables on fertility choice and female employment variables as a further channel of Granger-causality is exposed. For the fertility variable the results imply the Granger-endogeneity of the variable. The empirical results reject the hypothesis of strong exogeneity of fertility choice variable supporting the proposition that there is a relationship between fertility choice, female employment, real wage and real per capita output in U.K. From the empirical analysis five conclusions can be drawn. First, when we account for real wage and real output effects, a positive relationship among female employment and fertility exists in the long-run while in the short-run employment seems not to affect fertility. Second, fertility choice should not be considered exogenous to the female employment, the labor market or the growth process. Third, higher real wages are responsible for the deterioration of fertility, since time is reallocated from childbearing toward labor, increasing the opportunity cost of time devoted to childcare. Fourth, an upward shock in real GDP per capita leads to higher fertility. Fifth, changes in the fertility choice are not responsible for changes in female employment. So, we can conclude that the declining fertility rates are associated not with the choice of women to participate in the labor force but with higher wages.
5. Conclusions This paper provides an empirical model that examines the validity of the proposition that there is a causal relationship between female employment and fertility choice in a multivariate framework for the United Kingdom over the period 1958–1998. Previous empirical research
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has provided inconclusive results on the relationship between female employment and fertility. Moreover, recent demographic findings suggest a reduction in the incompatibility between childrearing and female employment, as a result of changes in social norms and in childcare availability. Therefore, following recent advances in economic and demographic theory the nexus between female employment and fertility is reexamined taking into account changes in the labor market and the overall real economic activity. In order to account for influences on the fertility–female employment relationship of changes in medical technology, literacy, standard of living, overall economic performance and the labor market, real GDP and real wages are added to the VAR model. Initially, the paper examines the existence of a relationship between fertility, female employment, real wages and real per capita GDP. The empirical results of cointegration, within this multivariate cointegrated system, derived from the Johansen and Juselius maximum likelihood estimation technique of cointegrating vectors, rules out the possibility that the estimated relationships are spurious and supports the hypothesis of the existence of a long-run relationship among the variables. This implies that these variables although they may have occasional short-term or transitory deviations from their long-term equilibrium, eventually forces will prevail that will drive them together. In the long-run, when we account for wage effects and output changes, an upward shock in female employment leads to higher fertility. Second, an upward shock in real wages, due for example to technological change, leads to lower fertility. Finally, an upward shock in real GDP per capita leads to higher fertility. In short, the results from the long-run analysis suggest that fertility is affected by changes in female employment, real wage and real per capita output in the long-run. The results of the empirical models using the VECM estimation suggest that fertility should be considered as endogenous variable to the female employment, the labor market and the growth process relationship rejecting the hypothesis of weak and strong exogeneity of fertility. In the short-term fertility choice is affected by wages implying that higher real wages are responsible for the deterioration of fertility, since time is reallocated from childbearing toward labor, increasing the opportunity cost of time devoted to child care. To sum up, although in recent years econometric advances have stimulated further research on the interdependence of fertility and employment the evidence in a bivariate context has produced mixed results. When we account for the role of wages and output, there are grounds for believing that fertility is affected by changes in female employment, real wage and real per capita output. Both in the short- and long-term fertility choice is affected by wages implying that higher real wages are responsible for the deterioration of fertility. In the long-run, when we account for wage effects and output changes, an upward shock in female employment leads to higher fertility and an upward shock in real GDP per capita leads to higher fertility. Notes 1. The male breadwinner, or family wage model, assumes that the father goes out to work while the mother stays at home to look after the children. According to the model the man is the provider and protector of the family and the woman is the one who cares and reproduces children.
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2. This approach has several advantages over the Engle and Granger (1987) technique employed in other empirical studies. First, the Johansen and Juselius method tests for the number of cointegrating vectors between the variables. These tests are based on the trace statistic test and the maximum eigenvalue test. Second, it treats all variables as endogenous thus avoiding an arbitrary choice of dependent variable. Third, it provides a unified framework for estimating and testing cointegrating relations within the framework of a vector error-correction model. 3. For other applications of this technique in different topics, see Masih and Masih (1996) and Hondroyiannis and Papapetrou (2000, 2001). 4. The KPSS statistics are known to be sensitive to the choice of truncation parameter l and tend to decline monotonically as l increases. 5. It is known that the Johansen cointegration procedure is biased towards the rejection of the null hypothesis in a small sample (Cheung & Lai, 1993). Therefore, in the estimation procedure we used the critical values obtained from Johansen and Juselius (1990) and the critical values adjusted for small sample (see note to Table 3). Both values reject the null of zero cointegrating vectors in favor of one cointegrating vector at 5 and 10% level of significance. 6. The results are available from the author upon request. 7. The results for the Chow test are obtained using PcFiml 9.0 (see Doornik & Hendry, 1997). 8. Pesaran and Shin (1996) have proposed the estimation of persistence profile to estimate the speed with which the effect of system-wide shocks on cointegrating relationship disappears. In particular, the persistence profile at n periods after a shock can be viewed as the variance of the difference between the forecast for n periods if a shock had occurred and the forecast for n periods if no shock had occurred.
Acknowledgments The views expressed in this paper are those of the author and not those of the Bank of Greece. The author wishes to thank an anonymous referee for his valuable comments in a previous version of this paper. All remaining errors and deficiencies are the responsibility of the author.
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