Siegers, 'The Macroeconomics of Fertility in Small Open Economies: A Test of the Becker-Barro Model for the Netherlands and New Zealand. THE MACROECONOMICS OF FERTILITY IN SMALL OPEN ECONOMICS: A TEST OF THE BECKER-BARRO MODEL FOR THE. At the same time, a renewed interest in the economic determinants of population growth arose, with the book by Razin and Sadka (1995) representative of the modern approach to population economics.

The two driving forces of the steady growth rate of output in the standard neoclassical model - technological change and. Becker and Barro (1988) were the first to combine these ideas and techniques in a reformulation of the economic theory of fertility. The long-run level of consumption in the Becker-Barro type model can be shown to be independent of the interest rate.

Of course, the essential features required for the specification of the empirical model are maintained. Each adult i works a given time and earns an income Wi.4 The income Wi is determined by the reward for effort ei and the return on human capital. The term in the first set of brackets represents the growth factor of the net cost of child rearing (excluding human capital investment).

We will therefore consider the expected annual compound growth rate of the real net cost of child rearing, g{.

## Fertility and long-run macroeconomic trends

Therefore, the baby boom after World War II was much more pronounced in the Netherlands. However, the birth rate in New Zealand at the time was, on average, 1,104 children per woman higher than in the Netherlands. The subsequent decline took place in both countries at about the same speed, which led to a minimum birth rate in this century of 1.92 and 1.47 respectively and in the same year (1983).

Since then, fertility has increased in both countries to reach a modest peak of 1.62 in the Netherlands in 1990 and 2.20 in New Zealand in 1993 (not shown in figure). Moreover, the econometric evidence reported in the next section suggests that changes in social security payments, and possibly higher real interest rates, have also contributed to the increase in fertility. 1983 Dutch guilders by purchasing power parity exchange rates published in the Penn World Table (see Summers and Heston 1991).

The actual 1983 exchange rate was 1.88 guilders to one New Zealand dollar, but the higher price level in the Netherlands meant the PKM exchange rate was 2.31 guilders to the dollar. In terms of purchasing power, earnings per working-age person in New Zealand were slightly higher than in the Netherlands, except from about 1926 to 1932 and 1978-1979. If real income per working-age adult is interpreted as an indicator of productivity, the acceleration of productivity growth until the late 1960s would have a negative effect on the birth rate in the Becker-Barr model.

11 The working-age population is equal to the population aged 15 to 60 in New Zealand and 15 to 65 in the Netherlands. The introduction and rapid growth of child benefits in the early post-war period would have encouraged higher fertility in both countries. Since then, the family allowance has fluctuated around the equivalent of 1,000 guilders per child per year in New Zealand and 1600 guilders in the Netherlands. 13.

The acceleration of real welfare payments for the elderly did not begin in the latter country until the 1970s, when a universal pension called the National Superannuation was introduced in 1975. Thus, the trends in real social security payments to the elderly are similar to those made to children: rapid post-war growth as the welfare state grew in importance, with the subsequent dissolution of the welfare state into a more "targeted" approach to needs" that began in the 1980s. The theoretical model of section 2 suggests that this may have been a contributing factor to the country's higher average fertility rate, but to disentangle such an effect from other possible ones require the use of econometric models.

The regression models fit very well, especially in the case of the Netherlands, but - as expected - all four equations show significant autocorrelation. However, in the two comparisons for the Netherlands, the DW statistic is close to one and the Phillips-Perron tests of the stationarity of the residuals in the OLS regression are close to the critical values (and in fact exceed them in the case of the t -ratio test). However, even in the case of the largest t-ratio (2.34) the coefficient becomes insignificant at the conventional levels when a correction.

The downward trend can be explained in terms of the Becker-Barro model as a decrease in the parameter a, which measures the degree of altruism in relation to offspring. At levels there appears to be a possibly negative effect of real income on fertility in the Netherlands, but a significantly positive effect in New Zealand. This is a rather surprising result since an increase in real income would mean an increase in the real cost of raising children, which includes a time cost.

The nuptial number sequences behave similarly, but the effect becomes more noticeable in the error correction models discussed below. Since the equations of Table 3 are based on differentiated variables (except for the error correction term), the constants now indicate the linear trend in the original series and indeed the constants are both negative and significant in the case of the Netherlands. Given the corresponding number of observations and variables, the Durbin-Watson statistics are in the inconclusive range.

As can be expected, the fit of the ECMs is not very close, but somewhat better in the case of the Netherlands. However, real income per person of working age and the real interest rate are not significant in the Table 3 regression models. The earlier detected positive effect of the family advantage on fertility in Table 2 is reinforced by Table 3, although the t-statistics are not significant in the New Zealand case.

Similarly, the introduction of social security for the elderly had a negative effect on the birth rate in the Netherlands. Finally, the error correction term has the expected sign in the case of the Netherlands and is also statistically significant. Although similar in size, the parameter estimates in the models discussed so far differ significantly between the Netherlands and New Zealand.

## 5 . Conclusions

For brevity, models that include country effects in coefficients are not included, but inspection of coefficients and standard errors in Tables 2 and 3 suggests that such country effects are generally significant. As indicated in section 2, differences between corresponding coefficients of the regression models may be due to country differences in preferences or in expectation formation. In addition, there may be country-specific phenomena affecting the growth in the net real cost of children, which we could not capture in our model.

Malthus TP (1798) An Essay on the Principle of Population and a Summary View of the Principle of Population.

ANNEX

The data consist of annual observations from 1901 to 1993 for the Netherlands and 1912 to 1990 for New Zealand, excluding the social security variables.

The Cross-Section Heteroscedastic Time-Wise Autoregressive

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