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The effect of tax-transfer policies on fertility in Canada, 1921-88.

I. Introduction

Fertility behavior is at the heart of many issues fundamental to the economic vitality of a society such as the growth and the aging of the population, and so remains a subject of great interest.(1) Many countries are facing declining fertility and are therefore searching for possible means to encourage births (Teitelbaum and Winter 1985). While explicit policies, such as relaxing immigration restrictions, have immediate effects on population growth, the effect of other policies implemented through fiscal redistribution remains to be seen. A recent study by Whittington, Alm, and Peters (1990) (hereafter, WAP) finds that the personal tax exemption for dependents has a significant positive effect on fertility in the United States.(2) Their study has generated some revitalized interest in the ability of governments to influence fertility. Given the critical importance of this issue in the policy arena, it would be worthwhile to examine the issue for other countries.

The purpose of this paper is to estimate the empirical effect on fertility of various federal tax-transfer policies in Canada. Since about 1972, the fertility rate has been below the replacement level in Canada. It is important to know whether or not pronatalist tax-transfer policies affect fertility and the magnitude of any effect. An estimate of the effect would provide useful information to the Canadian government on expenditures necessary to obtain replacement-level fertility. Our study will add to the limited literature on this topic, and perhaps, provide guidance to governments seeking appropriate solutions to increase fertility.

There exist major differences between Canada and the United States with respect to tax-transfer policies that provide relief to households with dependent children.(3) While the tax-transfer benefits provided in the United States are the personal tax exemption and child care credit, Canada has an extensive benefit package which includes family allowances, the child tax credit, and paid maternity leave in addition to the personal tax exemption for dependent children.(4) All of the benefits reduce the cost of having children and can thus be viewed as "subsidies" to childrearing. If the total subsidies are not negligible as compared to child costs, we would expect that they increase fertility. The magnitude of the response to these incentives is an empirical issue.

In this paper, we estimate an aggregate fertility equation for Canada for the period of 1921 to 1988. Fertility is modeled as a function of various economic variables, including the personal tax exemption, family allowances, child tax credit, and maternity leave. We find that the exemption, family allowances, and child tax credit have significant and positive effects on fertility; the effect of the allowances is robust to a variety of specifications. All the results also hold for the cumulative effect of the three tax-transfer programs. Maternity leave apparently does not have a significant effect.

This paper is organized as follows. Section II briefly reviews the federal tax-transfer policies in Canada. The magnitude of the benefit package is also compared with child costs in Canada. Section III briefly considers some theoretical issues. Section IV presents an empirical model which is similar to WAP but reflects the main features of the policies in Canada. Section V reports the estimation results. Section VI concludes the paper with some policy implications.

II. An Overview of the Tax-Transfer Policies in Canada, 1921-88(5)

In this section, we provide a brief overview of federal tax-transfer policies in Canada from 1921 to 1988. The discussion will be useful for model specifications and the analysis of estimation results. It should be pointed out that the following discussion is not intended to cover all specific details of policy changes over time.

The personal tax exemption was introduced into the Canadian tax system in 1918.(6) This exemption for dependents allows a taxpayer with children to deduct a fixed amount from his/her personal taxable income in order to reduce the total income tax paid.(7) Since the exemption is nonrefundable, it benefits mainly families in the middle and upper income classes. The actual benefit equals the amount of the exemption times the marginal tax rate. Hence, the higher one's marginal tax rate is, the more valuable is the exemption. We use aggregate average marginal tax rates to compute the tax value of the exemption. Beginning with the 1988 tax year the Canadian tax system shifted most exemptions, including the exemption for dependents, to nonrefundable tax credits which are subject to a fixed benefit rate of 17 percent. Thus, instead of using the average marginal tax rates for all other years, 17 percent is used for 1988.

The family allowance benefit came into existence in 1945 and is a universal social welfare benefit in the sense that it applies to all families with dependent children, regardless of the family's income level.(8) The allowance is distributed on a monthly basis in equal amounts per child to all families with dependent children under 18 years of age. (Before 1974, payments were made for children up to 16 years of age.) It is usually the mother who receives the family allowance payments. As of 1974, the family allowance benefit must be included in the taxable income of the spouse who claims the personal tax exemption.

In 1977, the federal government introduced the child tax credit.(9) Only the person (usually the mother) who receives the family allowance may claim the credit. Tax credits reduce a taxpayer's tax liability directly rather than through a reduction in taxable income. For this reason, unlike exemptions, credits do not provide larger benefits at higher marginal tax rates. Since 1978, the credit has been refundable. This credit is given to all families with dependent children who are eligible for the family allowance, provided that total net income of both spouses does not exceed a threshold level. However, if the taxpayer's income is above the threshold, the credit is subject to a 5 percent tax-back rate. (The credit is reduced by five percent of net family income in excess of the threshold level.) Consequently, this is a policy which generally benefits families at the lower to middle end of the income distribution. Since 1986, an additional child credit has been introduced in federal sales tax credits. Furthermore, a child care supplement credit was allowed in 1988.

Figure 1 shows the time profile of the three benefits in real terms.(10) The personal exemption has not changed very much. The family allowance has basically declined slightly from 1945 to the early 1970s, then increased and finally remained roughly constant. The child tax credit has steadily increased over time. Overall, the total benefits have risen over time except during the war years of 1942-46. In 1971 Canadian dollars, the average real values of the three programs and total benefits are $37.79, $64.68, $40.05, and $142.52, respectively. WAP report that the average real value of the personal exemption in the United States is US$101.01 for the period of 1913 to 1984.(11) Thus, although the value of each program in Canada is generally smaller than that in the United States, the total benefit package is larger in Canada.(12) (Unless otherwise indicated, dollar values are in Canadian currency.)

In Canada, maternity leave benefits have been available through the Unemployment Insurance program since 1971. Benefits equivalent to 60 percent of the mother's usual earnings (up to a maximum insurance earnings limit) are paid for 15 weeks to qualified employed women. Prior to January 1984, qualification requirements were so stringent that the majority of working mothers were excluded from benefits. In fact, officials within the Department of Employment and Immigration estimated that between 1971 and 1984, only about 45 percent of working women who were potentially eligible for maternity benefits actually received them. While it might be assumed that such a low percentage was largely attributable to stringent qualification requirements, officials suggested that many potentially eligible claimants did not even claim because they were not aware of the program or because they felt there was some stigma attached to the Unemployment Insurance program in general. In 1984 the regulations were changed to make the maternity leave benefit available to more people.

We should note that we focus on basic federal tax and ignore federal surtax and provincial taxes. In Canada, taxpayers are subject to both federal and provincial taxes. (Quebec continues to levy and collect its own personal income tax.) In 1983, nine provincial tax rates as a percent of federal tax payable range from 38.5 to 60.0 with the median at 52.5 (Boadway and Kitchen 1984, p. 41). Thus, if an individual benefits $200 from the personal exemption, the person would also pay about $100 less provincial tax. Another omitted complication is that provinces, especially Quebec, vary or supplement federal family allowances and child credits. For example, Quebec offers provincial family allowances to children under age 18 and "availability allowances" to children under age six, in addition to federal family allowances; Quebec also provides lump sum payments for newborn children (Mathews 1989, Kesselman 1992).

The value of the total benefits is not inconsequential relative to the annual cost of raising a child. Using the 1982 Family Expenditure Survey, Gauthier (1987) estimates that in 1982 the average annual direct costs of a child are slightly more than $5,000. (Subsequent children cost much less.) In 1982, the personal exemption, family allowance, and child tax credit are, respectively, 670, 343, and 323 dollars; the average marginal tax rate is 19 percent. Thus, the total value would be $497--about 10 percent of the child costs.

III. Some Theoretical Considerations

The empirical specification in the next section is in the spirit of previous work analyzing microeconomic determinants of fertility (see Becker 1992 for the theory and applications using micro or macro data).(13) We assume that leisure and child quality are fixed. Each family maximizes a utility function of the number of surviving children, N, and the amount of goods consumed, Z:

(1) U = U(N, Z).

Defining the prices of N and Z as |P.sub.n~ and |P.sub.z~, then a family's budget constraint equals

(2) |P.sub.n~N + |P.sub.z~Z = (1 - t)I,

where t is the income tax rate and I is total income.

The price (cost) of children depends on the opportunity cost of (mainly the mother's) time and other expenses incurred in bearing and rearing children. The various tax-transfer programs reduce the cost of children. Consider the personal exemption (PE), family allowances (FA), and the child tax credit (CTC). Then the cost of children will be reduced by the amount of tPE + (1 - t)FA + CTC (assuming that the family benefits from all the three programs).

Not all families qualify for and/or benefit from all the programs. As a result, the benefit to each family differs. More specifically, poor families may not benefit from the personal exemption because their total income may be below taxable income. On the other hand, rich families may not qualify for the child tax credit. Every family, however, receives family allowances.

In this simple model, the demand for children can be shown to be a function of prices of children and goods, family income, and taste and technology parameters. We estimate a birth equation using aggregate time-series data in the next section. Most of the explanatory variables in the empirical model are proxies that may affect family income and/or the cost of children.

If all individuals were identical, then parameter estimates from the aggregate birth equation can be used to infer individual behavior. In general, however, individuals are heterogenous. Unless certain (strong) assumptions are made regarding the utility functions for different individuals,(14) it would be difficult to infer individual behavior from aggregate estimates. In this sense, the following estimation results can only indicate aggregate relationships between fertility and other variables, or the average fertility behavior. Nevertheless, at least in the case of fertility rates, estimating aggregate relations may be quite important from a policy-effectiveness perspective.

Notice also that, as mentioned above, the population are heterogeneous in receiving benefits from the various tax-transfer programs. The various programs may have different effects on the birth rate in a model using aggregate data. In other words, even if individuals view benefits from the various programs as identical incomes, the use of aggregate data may show different effects for the different programs. In this case, it simply means that the different programs affect different population groups.

The foregoing formulation is based solely on a demand function for children. Due to child mortality, imperfect birth control, balance of sex ratio, and so on, however, the observed fertility rates do not represent points along the demand function. In general, observed fertility rates (births) will be a function of N, female education, birth control technique, child mortality, etc.

Finally, we note that the simple static model is an over-simplification to the real world. In particular, fertility decisions are sequential and dynamic (Wolpin 1984). We partly account for this by estimating an aggregate equation with different lag structures on explanatory variables.

IV. An Empirical Model

An extension of the WAP model is used in this paper. The reduced form aggregate fertility equation is as follows:(15)

|Mathematical Expression Omitted~

The dependent variable, the total fertility rate, is defined as the hypothetical number of children a woman would have if she is subject to the prevailing set of age-specific fertility rates in a particular calendar year. WAP use the general fertility rate in their study. The total fertility rate differs from the general fertility rate in that it is independent of age structure of the female population.(16)

The personal exemption, the family allowance and the child tax credit are considered as separate independent variables since they are distinct programs. In addition, the cumulative effect of the personal exemption, the family allowance, and the child tax credit will also be examined. As discussed earlier, these policy variables reduce the cost of having children and are therefore expected to have positive effects on fertility. The personal exemption variable is defined as the tax value of the personal exemption which is equal to the personal exemption multiplied by the average marginal tax rate.(17)

Maternity leave is defined as a dummy variable to reflect the introduction of the policy. For working women, the maternity leave benefit reduces the cost of having children and thus it may be expected to increase fertility. However, for nonworking women who specialize in household production, the leave benefit may create an incentive to enter the labor force, which has a negative impact on fertility. Consequently, the maternity benefit may have a negative effect on fertility for these women. Overall, maternity leave could have an ambiguous effect on fertility.

Other independent variables are factors that may affect demand for and supply of children (see also WAP). Canada is a multi-cultural society. Female immigration is included to control for cultural differences in birthrates between Canada and other countries. Unemployment results in at least lower transitory income, hence higher unemployment rates could reduce birthrates if children are a normal good. On the other hand, unemployment would also lower the opportunity cost of time in household production. It thus may have an ambiguous effect on fertility rates. Infant mortality also has two possible effects on fertility rates. The death of a child can result in another birth if families are concerned with completed (surviving) family size, which is usually referred to as the direct replacement effect. However, higher infant mortality increases the cost of producing a surviving child. The overall effect would be determined by the offsetting replacement and cost effects. Female wage captures the opportunity cost of having children, given that the production of children is more time intensive for women than for men. Male income is usually assumed to reflect the income effect on the demand for children.

Female education is not an independent variable in WAP (other than a proxy or instrument for female wage). Education is sometimes used as a proxy measure of potential wage. However, education is likely to be associated with every aspect of fertility determination. For example, it may affect individual preferences for children and parental productivity in childrearing and other activities; it may increase the ability to control the number of births and to reduce the incidence of child mortality. As a result, we include female education as an independent variable. Of course, one should be cautious in interpreting its effect.

The World War II dummy variable measures the effect on birthrates of the absence of men during the war years. The birth control pill is included to account for a possible reduction in fertility rates due to unwanted births. Finally, a time trend controls for any unobserved time-varying socioeconomic factors that may affect fertility rates.

The definition and summary statistics of all variables are given in Table 1. Procedures used to construct the marginal tax rates, female wage, and male income are described in the Appendix. All nominal values are converted into real terms using the CPI (equal to 100 in 1971).

Since birth usually lags the decision to have a child, a lag structure of some form is needed when estimating the fertility equation. Similar to WAP, we analyze a one-year lag structure, a two-year and a three-year rectangular lag structure, and a five-year inverted V pattern. We are prevented from developing a richer dynamic specification because of severe multicollinearity.

The rectangular lag structure gives a weighted average of the variable over a certain period. A three-year rectangular lag of a given variable X would be:

(4) | = |w.sub.1~|X.sub.t~ + |w.sub.2~|X.sub.t - 1~ + |w.sub.3~|X.sub.t - 2~ + |w.sub.4~|X.sub.t - 3~,

where | is the new constructed variable with weights |w.sub.1~ = |w.sub.2~ = |w.sub.3~ = |w.sub.4~. The five-year inverted V structure assumes that the variable lags four periods with peak in period t - 2. The constructed variable becomes:

(5) | = |w.sub.1~|X.sub.t~ + |w.sub.2~|X.sub.t - 1~ + |w.sub.3~|X.sub.t - 2~ + |w.sub.4~|X.sub.t - 3~ + |w.sub.5~|X.sub.t - 4~,

where | is the new constructed variable with weights |w.sub.1~ |is less than~ |w.sub.2~ |is less than~ |w.sub.3~, and |w.sub.3~ |is greater than~ |w.sub.4~ |is greater than~ |w.sub.5~.

V. Estimation Results and Analysis

Table 2 reports estimation results. Generalized least squares (GLS) estimation is performed with the Cochrane-Orcutt first-order autocorrelation correction using the Prais and Winsten's (1956) adjustment for the first observation.(18) TABULAR DATA OMITTED TABULAR DATA OMITTED High adjusted R squared(19) indicates a good fit of the model with the data. Figure 2 compares the actual fertility rate with the rate predicted from Model 4.

Regressions with the individual tax-transfer programs are shown in Columns 1 to 3 of Table 2. Family allowance has a positive and significant effect on birthrates. The result is robust to all the lag structures, and to the exclusion of a time trend (unreported). Personal exemption and child tax credit also have a positive effect, although their statistical significance is slightly sensitive to specifications. Our result strongly confirms the WAP finding for the personal exemption for the United States. Among the three policies, the family allowance has the most significant effect. This might be explained by the fact that almost every family qualifies for the family allowance and it is usually the mother who receives the benefit. One may argue that the mother is more concerned with the childbearing decision. Hence, any direct payments to mothers may be more effective to encourage births.

Maternity leave has a negative sign but its coefficient is never significantly different from zero at the 10 percent level. This is consistent with the theoretical discussion in Section III. As mentioned in Section II, while the maternity leave benefit was introduced in 1971, many restrictions had been imposed to qualify for the benefit for a long period. Thus, we used alternative definitions of the dummy variable (for example, equal to one after 1975, 1980, 1984, etc.); the maternity leave remains insignificant.(20)

As in WAP, the sign of female wage is sensitive to the lag structure and wage does not have a significant effect on fertility rates. We also estimated the models without female education and the wage remains insignificant. In contrast to female wage, female education has a highly significant and negative effect on fertility. Male income has some "unexpected" negative signs. WAP also note the perhaps surprising result that male income has a negative effect on birthrates in a time-series study.(21) Immigration appears to increase fertility rates. This is expected since the majority of immigrants have been Europeans and Asians who typically have larger family sizes than Canadians. Infant mortality has a positive effect on birthrates. This suggests that the replacement effect dominates the cost effect. The coefficient of the World War Il variable is negative, indicating that the absence of young men during the war years reduced birthrates in that period. Birth control pill seems to reduce fertility, although it is never statistically significant. Finally, perhaps surprisingly, the time trend has a positive effect on fertility. But notice that we are controlling for female education, which has a negative effect on fertility. The coefficient on time trend becomes negative when female education is dropped.

It may be argued that individuals care about the total benefits from the three distinct programs and thus the three tax-transfer variables should be considered as a combined variable. This hypothesis is tested formally. The last row of Table 2 gives the F-statistic for the null hypothesis that the coefficients of the personal exemption, family allowance and child tax credit are equal. The null hypothesis is not rejected at the 5 percent level. Thus, we reestimate Models 1-3 using the sum of the three variables as a single variable with results in Columns 4 to 6. The total benefits variable has a significant positive effect on fertility rates. This further increases our confidence in the earlier result in Columns 1 to 3. Note that there is virtually no significant difference in the sign and magnitude of the estimates for other variables between Columns 1-3 and Columns 4-6 in Table 2.

The elasticities of fertility with respect to the total benefits are also shown in Table 2. The estimated elasticity at the mean is about 0.05, although in unreported regressions the elasticities can be as high as 0.11. They are somewhat smaller than the estimates obtained by WAP for the United States. (WAP find the elasticity of fertility with respect to the personal exemption ranging from 0.127 to 0.248.) The presence of multiple programs in Canada may lead to different behavioral responses as compared with the United States.

Three more issues, not explicitly examined in WAP, regarding model validity deserve discussion at this stage. First, one may argue that the amount of the tax-transfer benefits has been affected by changes in fertility rates over time. The possible endogeneity in the total benefits is tested following the Hausman's (1978) two-step procedure (see Pindyck and Rubinfeld 1991, for a textbook discussion of the test procedure). Lagged and current independent variables in the fertility equation are used as the instrumental variables. The t-statistic on the residual of the total benefits equation is always less than one, indicating that endogeneity is not a problem.(22)

Second, multicollinearity problems may exist since so many variables are included in the models. The important thing to note here is that the tax-transfer variables stand significant in all specifications. Given the purpose of the paper, the relevant question is whether the multicollinearity problems have caused the strong and robust results on the tax-transfer variables. To examine this question, we have run regressions of the fertility rates on only the tax-transfer variables and a time trend. The results are that the tax-transfer variables still have significant and positive coefficients.

Third, there are concerns of whether each time-series is stationary(23) and, in particular, whether the very high R squared is a result of regressing "time against time." With respect to the R squared, we note that time trend is insignificant in all models except 1. Furthermore, even in the models without a time trend (unreported here), the result on the tax-transfer variables holds and R squared is virtually unchanged. As a further check on the robustness of the results of the tax-transfer variables, we run regressions in the form of the first-difference in all variables, which is normally stationary. The estimation results are reported in Columns 7 and 8 of Table 2. As expected, R squared drops significantly. However, the total benefits variable still has a significant positive effect on fertility rates.

We also estimated Equation 3 with a variety of other specifications, and the results are generally consistent with those reported in Table 2. These specifications include other lag structures, alternative measures of some variables, nonlinear terms of the policy variables, and the omission of a few independent variables from the regressions. There is some weak evidence that the marginal effect of any of the benefits is not constant. In fact, it decreases as the value of the benefit increases. This result is consistent with the current policy of increasing the personal exemption in Canada and family allowances in Quebec by birth order. Equation 3 is also estimated over different sub-periods (for example, before and after World War II). The coefficient on the policy variable is always positive and often significant. The results are also robust to the exclusion of some years that have large variations in the policy values. These sensitivity analyses increase our confidence in the results that the tax-transfer policies seem to have positive and significant effects on fertility rates.

VI. Conclusions and Policy Implications

Canada has had an extensive system of tax-transfer reliefs for childrearing for a few decades and thus provides a good opportunity to examine the empirical effects on birthrates of such incentives. In this paper, we find that the personal exemption, the family allowance and the child tax credit have significant positive effects on fertility rates when they are considered separately and jointly. Our results are consistent with those in WAP with respect to the personal exemption in the United States. The importance of the tax-transfer programs is further illuminated by noting that few other independent variables are statistically significant. While the three tax-transfer programs seem to be very distinct, the null hypothesis that they have no differential effects on fertility can hardly be rejected. This implies that individuals are concerned only with the cumulative value of the programs. Estimated elasticities of fertility with respect to the cumulative effect seem to be rather small, ranging from 0.05 to 0.11.

Our empirical results have some major policy implications. One important question is how much increase in the value of the tax-transfer programs is needed to increase fertility to a replacement-level. With allowances for sex ratio at birth and mortality rates in Canada, it is calculated that the replacement of a generation is only ensured when 1,000 women bring approximately 2,100 children into the world, or 2.1 children per woman (Statistics Canada 1990). The total fertility rate is 1690 in 1988 in Canada. Thus, an increase of 410 in total fertility rate would be required to reach the replacement-level. Using the estimate 1.132 in Table 2 (Model 4), this in turn means an increase of about $360 in the total benefits (in 1971 constant dollars). Adjusting for the inflation between 1971 and 1988, it would require family allowances in 1988 to rise from $389 (the actual value in 1988) to $1,982, holding other variables constant. This would require a considerable increase in federal outlays in the family allowance benefit.(24) However, increasing the family allowance benefit from $389 to $1,982 would just bring the benefit to a level similar to that in certain European countries. In France, for example, family allowances amount to approximately $1,400 for the first two children and $1,870 for the third and subsequent children (Mathews 1989, Beaujot 1991).

In conclusion, the tax-transfer programs in Canada may have alleviated, to some extent, the declining fertility rates. Our empirical results suggest that the replacement-level fertility rate could possibly be achieved if the government is willing to substantially increase the value of the tax-transfer programs.


Construction of Variables

Male Annual Income

Years 1921-45: The 1921, 1931, and 1941 Censuses of Canada provide average annual male earnings for the specific years. For years in between, the values are computed as the product of the actual values for 1921, 31 and 41 and the average annual growth rates, which are calculated for the periods 1921-31, 1931-41, 1941-51 as follows:

|G.sub.t~ = |(|MALEINC.sub.t~/|MALEINC.sub.t - 10~).sup.0.1~ - 1 for all t = 1931, 1941, 1951

where G is the estimated annual growth rate and MALEINC is male annual income.

Years 1946-64: Historical Statistics of Canada, Vol. II (Statistics Canada). Series D266-289 & Series E86-103. Series D266-289 publishes civilian employment by industry for both sexes. Series E86-103 reports the annual averages of weekly wages and salaries for selected industry groups. To estimate the male annual earnings for this period, the following formula is used:

|Y.sub.m~$ = 52* |summation over i~ (|W.sub.i*~ |N.sub.i~)/(|summation over i~ |N.sub.i~)

where |N.sub.i~ denotes the number of males employed in industry i and |W.sub.i~ is the average weekly wage for all employees in each industry.

Years 1963-88: Taxation Statistics (Revenue Canada). The total male income is divided by the total number of tax returns filed by males. This results in average annual male income.

Female Wage

Years 1934-69: Historical Statistics of Canada, Vol. II (Statistics Canada). Series E60-68. The hourly wage for females in the manufacturing sector is used.

Years 1970-88: Taxation Statistics (Revenue Canada): The average annual earnings for females is calculated by dividing total female income by total number of returns filed for females. This average is then converted to an hourly rate by dividing the average by 52 weeks and by 40 hours per week.

The overlap in the data from 1963-69 allows us to obtain a ratio of the female manufacturing wage over the estimated female wage. The female wage for 1970-88 computed above is then adjusted to the female manufacturing wage by multiplying it by this ratio.

Years 1921-33: The Canada Yearbook (Statistics Canada) reports annual industrial wage. The ratio of female wage over the wage for both sexes is calculated for 1934-88. An average of this ratio is multiplied by the annual industrial wage from 1921-33. The female manufacturing wage is then obtained by dividing this number by 52 weeks and 48 hours per week.

Marginal Tax Rate

Years 1946-88: Taxation Statistics (Revenue Canada). The median income class for each given year is determined. The average taxable income is calculated by dividing total taxable income by total number of taxable returns for this income bracket. This value represents the "median taxable income." Using the tax schedule for each given year, the marginal tax rate for this median income level is obtained.

Years 1921-45: The Canada Yearbook (Statistics Canada). The personal income assessed was divided by the total number of tax returns for each year to obtain the average annual individual income. In order to estimate the average taxable income for each year during this period, the average individual income is adjusted as follows. Taxation Statistics reports both taxable income and total income for the years 1946-88. The ratio of the taxable income over total income is calculated for each year between 1946-88. This ratio is then extrapolated back to 1921 (the trend is clearly increasing with time). The resulting estimated ratio is multiplied by the average income for the years 1921-45 to obtain the average taxable income for the years 1921-45. Finally, the average marginal tax rate is found for this average income taxpayer between 1921-45.

1. For example, Denton and Spencer (1976), and Fair and Dominguez (1991), among others, have examined demographic effects on several important economic variables.

2. Similar to WAP, Buttner and Lutz (1990) find a positive relationship between the introduction of several government policies and fertility in the German Democratic Republic. Whittington (1992) confirms WAP's finding using micro PSID data. However, Espenshade and Minarik (1987) argue that the increase in the tax value of the personal exemption is not likely to affect fertility in the United States.

3. In contrast to the United States, the Canadian personal income tax requires filing on an individual rather than a family basis. In households where both spouses have taxable incomes, each must file separately and be taxed as individuals.

4. We focus on explicit tax-transfer programs in this paper. There are welfare programs (for example, AFDC) and subsidies to child care in the United States that are not examined in WAP. Following WAP, we also ignore welfare programs in Canada here. However, a program such as the AFDC does not exist in Canada, although the Canada Assistance Plan covers income support for low income families with dependent children. Also ignored are social security programs (for example, old-age security) that might be relevant to the demand for children. We leave these issues for future research.

5. The Canadian tax system started in 1917. Our study focuses on the period 1921-88 because the total fertility rates are not available for the years 1917-21, and 1988 is the latest year all relevant data were available when the research was conducted. For discussions of more recent changes in tax-transfer policies in Canada, see Davies (1991) and Kesselman (1992, 1993).

6. Much of the following discussion is based on Kesselman (1979), Boadway and Kitchen (1984), Town-son (1985), Status of Women Canada (1986), and various issues of the National Finances published by the Canadian Tax Foundation.

7. The exception occurred from 1942-46 when tax credits were allowed.

8. From its inception in 1945 to 1946, the family allowance was subject to a tax-back recovery rate which varied with the income, marital status, and number of children in the family. The complexities of tax recovery were swept away from 1947.

9. In fact, the child tax credit started earlier: the personal tax exemption was replaced by child tax credits during the war years 1942-46 but was resumed from 1947. It is interesting to note that, beginning in 1993, the multiple programs (the nonrefundable child tax credit, family allowances and refundable tax credit) are combined into a single program, the child tax benefit program (Kesselman 1993).

10. The personal exemption became the nonrefundable child tax credit in 1988. In Figure 1 and subsequent estimations, our treatment of the nonrefundable child tax credit has been to include it in the personal exemption series (rather than in the refundable child tax credit series). Furthermore, as noted earlier, personal exemptions shifted to tax credits during 1942-46. In the reported results, the tax credits for these years have been included in the child tax credit series (rather than in the personal exemption series). The alternative treatment did not alter the main results of the paper.

11. In fact, WAP report an average of US$100.40 in 1967 dollars. We convert it to the 1971 value using information given in Appendix I of WAP (in other words, 100.40 * 133.80/132.99 = 101.01).

12. In the early 1970s, one Canadian dollar is worth approximately US$1.00. Since 1978, the Canadian dollar has depreciated. For example, one Canadian dollar is worth US$0.8767 and US$0.8444 in 1980 and 1988 respectively (Colombo 1992, p. 629).

13. For a survey of the economic literature on fertility, see also Schultz (1981). Our paper, like WAP, does not examine the impact of government policy on quality of children. Cigno (1986) theoretically analyzes the impact of various policies on quantity and quality of children.

14. Varian (1992, pp. 152-54) shows that in certain cases the aggregate behavior may look as though it were generated by a single "representative" individual. This would be the case if utility functions are homothetic or quasilinear. See also Theil (1954) for a systematical statistical analysis of aggregation problems.

15. For alternative empirical models of fertility, see Conger and Campbell (1978), Butz and Ward (1979), Joseph (1980), Biswas and Ram (1982), Shields and Tracy (1986), Blau and Robins (1989), Macunovich (1990), Schultz (1990), Whittington (1992), and references therein.

16. We also tried general fertility rates and found very similar results to those reported later in this paper.

17. While WAP use the average marginal tax rates reported by Barro and Sahasakul (1983), we construct our own average marginal tax rates for Canada. Appendix explains how we constructed the average marginal tax rates. The Barro and Sahasakul method cannot be implemented for Canada because of the lack of the necessary data for the first half century.

18. This estimation method is equivalent to what is sometimes called, as in WAP, a GLS method with a Yule-Walker first-order autocorrelation correction scheme (SAS/ETS User's Guide, Version 5, p. 191).

19. The R squared is defined in Judge et al. (1985, p. 32. eq. 2.3.16).

20. The impact on fertility of the maternity leave benefit may also be obscured by the fact that Canada liberalized abortion in 1970 (Statistics Canada 1980), which would be expected to reduce fertility. Furthermore, in 1972, child care expenses (up to a certain level) were introduced in the tax system as a deduction from total income (Boadway and Kitchen 1984, p. 65). The new child care expenses policy would be expected to increase fertility. Hence the dummy variable used in estimation for maternity leave may actually capture a mixture of maternity leave, abortion and child care expenses policies. Indeed, the sign of the coefficient of the dummy variable is sensitive to slight changes in the definition of the dummy variable. However, it always remains insignificant at even the 10 percent level. A separate dummy variable for the abortion policy was also used but it was never significant.

21. With a few exceptions, such as Nerlove and Schultz (1970), time-series studies generally found a positive effect (see, for example, Watcher 1975, Butz and Ward 1979, and Shields and Tracy 1986).

22. It might be argued that marginal tax rates are endogenous since they depend on female labor supply, which in turn is simultaneously determined with fertility (Whittington 1992). However, average (aggregate) marginal tax rates may be rather exogenous. Since average marginal tax rates are part of the total benefits variable, rejection of the endogeneity of total benefits also seems to suggest that this may be the case (in other words, endogeneity of marginal tax rates is not a severe problem).

23. There is a large literature on stationarity or unit root tests (for example, Phillips 1987). For a recent textbook treatment of the literature, see Pindyck and Rubinfeld (1991).

24. In 1988, there are 6,596,745 eligible children. The federal outlays in family allowances are 2564.4 million dollars. To reach the replacement-level fertility, a total of 13074.8 million dollars would be required in 1989.


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Junsen Zhang was an assistant professor of economics at the University of Western Ontario when the research for the article was conducted; he is currently a lecturer of economics at the Chinese University of Hong Kong. Jason Quan and Peter Van Meerbergen were both honors students of economics at the University of Western Ontario.
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Title Annotation:Communication; includes appendix
Author:Zhang, Junsen; Quan, Jason; Van Meerbergen, Peter
Publication:Journal of Human Resources
Date:Jan 1, 1994
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