This paper presents a dynamic economic model of fertility behavior estimated with age-year-specific U.S. time-series data. The estimated model indicates that couples, on average, time their births to avoid periods when female wage rates are expected to be high, and that most of the observed effect of income and female wages on fertility rates is due to the indirect influence of these variables on couples' wage and income expectations. This paper also presents a decomposition of current fertility rates into timing and completed fertility components, allowing a comparison of current low fertility rates with couples' lifetime fertility plans. The estimates indicate that aggregate planned completed fertility is approximately equal to the fertility rate.

In this paper we investigate the reasons for the growth in the female labor force in America during the twentieth century. In our research, we study the longer-term trends since 1900 and conduct a more intensive examination of developments after the Second World War. On the basis of our work, we conclude that rising real wages accounted for 60% of the total growth in the female labor force. Half of this wage effect in expanding labor supply was the fertility-reducing consequence of a higher female wage.

At this time both professional and nonprofessional opinion concerning the cause of the present fertility decline in the U.S. has moved steadily away from the simple mechanism tying economic well-being to desired fertility. An alternative mechanism through which aggregate economic activity affects fertility rates is presented. The approach follows that of previous work which has analyzed the microeconomic determinants of fertility. The distinction between male and female earnings in affecting fertility and the distinction between families with employed and those with unemployed wives is emphasized. It is shown that post-World War 2 movements in fertility rates - a rapid increase throughout the 1950s and a sharp decline thereafter - can be reconciled within this framework. An empirical model is presented as are determinants of age-specific fertility rates for the 1947-1974 period. The 2 study conclusions are the following: 1) economic models of fertility behavior that stress the distinction between income and price effects - male income and female wage effects - are successful in explaining both important features of cross-sectional variations but also aggregate movements of U.S. fertility over time; and 2) the model proposed successfully predicts both procyclical and countercyclical variations in fertility in an unified framework across age groups and over a long period of time. The current level of employment among women and variations in their ages are more than high enough to induce continuing countercyclical fertility movements.

It is now standard practice in the enforcement of antidiscrimination legislation to use statistical analysis, especially in cases where the discriminatory practice is not observed directly, but must be inferred. In the classic example, the demographics of a firm's hiring might be compared to that of the county-wide work force. Plaintiffs in these actions would satisfy part of the requirement for a prima facie case by showing that the firm hired fewer protected group members than would be expected using the benchmark availability for that group. Similar calculations are made in promotion or termination investigations, but the benchmark would be the promotion or termination rates of the firm's own employees who are not charging discrimination. The logic of pay comparisons is the same: if the earnings of protected group members are statistically different from earnings of the benchmark group (usually white males), the defendant is presumed to have failed the statistical test. In each of these situations a defendant confronted with an adverse statistical finding will seek to explain differences in hiring, promotion, or pay by showing that they can be explained by productivity or availability factors.' The problem we draw attention to in this paper arises when dealing statistically with what remains unexplained or unquantifiable. The traditional analysis presumes that unquantifiable differences between protected and nonprotected groups are due to discrimination. Clearly, this presumption may place a difficult, and occasionally impossible, burden on defendants. In Section I we explore the use of regression as an analytical tool and critique the way its results are typically interpreted. In Section II we discuss the use of external availability calculations as benchmarks for the analysis of claims of discriminatory hiring. Using establishment-specific data filed with the federal government, we show that the variation in the representation of demographic groups across establishments greatly exceeds what would occur if all drew employees from the same pool. Judging all employers against a fixed pool implies an extreme assumption about a factor that is unquantifiable from aggregate data, specifically, that there is no underlying variation in availability. The main point of each of these sections is that, in performing statistical tests and giving opinions based on them, one necessarily makes assumptions in the form of maintained hypotheses. We believe that the movement by economists from data summary and presentation in professional journals to statistical inference for the courts has been simplistic. Before moving on to the body of our paper, we would like to mention two additional topics. First, as we have explained elsewhere,2 focusing statistical analysis on a subset of an employer's personnel actions may lead to incorrect inference if the prac* The authors are colleagues at Welch Associates. Robert S. Follett and Michael P. Ward are in Santa Monica, California (1640 Fifth Street, 90401) and Finis Welch is in Bryan, Texas (3833 S. Texas Avenue, #285, 77802) where he divides his time with Texas A&M University and Unicon Research. 'We use the term quantifiable instead of the traditional statistical term observable. In most employment litigation, decisions involving hiring, promotion and pay are rarely, if ever, random decisions. From the viewpoint of an outside observer, however, only a small fraction of observed variation is with employment records. 2Each practice by a large nondiscriminator has a probability of 0.95 that it will appear nondiscriminatory. If the practices are independent, these probabilities may be multiplied. For 14 practices, 0.95 raised to the 14th power is 0.4877, or less than half. (See Follett and Welch, 1983).

This paper presents a dynamic economic model of fertility behavior estimated with age-year-specific U.S. time-series data. The estimated model indicates that couples, on average, time their births to avoid periods when female wage rates are expected to be high, and that most of the observed effect of income and female wages on fertility rates is due to the indirect influence of these variables on couples' wage and income expectations. This paper also presents a decomposition of current fertility rates into timing and completed fertility components, allowing a comparison of current low fertility rates with couples' lifetime fertility plans. The estimates indicate that aggregate planned completed fertility is approximately equal to the fertility rate.