## THE IMMIGRANTS: Counterfactual Density Estimates 2

In addition, the data in the 1970 Census, particularly on the operational definition of Hispanic, is more comparable with the 1980 and 1990 Census than is the 1960 Census. For these reasons, we will perform our comparisons in this section between recent immigrants in 1970 and recent immigrants in 1990. However, we have completed all comparisons using the 1960 Census data as well, and these results are very similar. (See Appendix figure 1 for an example).

Methods

In this section w7e consider the following thought experiment: What would the distribution of 1970 recent immigrant wages look like if they were treated (on the basis of observable X’s only) as 1990 recent immigrants. To do so we adapt the method discussed in DiNardo, Fortin, and Lemieux (1996). In what follows we briefly review” the approach in this setting, and describe the necessary modifications. Additional detail can be found in DiNardo, Fortin, and Lemieux (1996) read more.

One way to begin would be to postulate two different wage equations, one for 1970 recent immigrants and another for 1990 recent immigrants:

where j390 and в70 are the OLS estimates from equation (3) and (2) respectively, and .Y90 and X70 are the means of X variables in 1990 and 1970 for recent immigrants. У 70 is the mean salary of 1970 recent immigrant workers had they been paid with the wage function of recent immigrants in 1990. V^(°} is the mean salary of 1990 recent immigrants if they had been paid according to the wage function of 1970 recent immigrants.

In practical applications, the Oaxaca,/Blinder approach is generally restricted to a comparison of means. In fact, when the distributions one is comparing are uni modal, symmetric and have similar variances, the Oaxaca approach comes quite close to being a “sufficient statistic” for the effect of changes in the structure of wages.

As has been well documented, however, changes in the shape of the distribution of wages over the time period we consider have been quite dramatic. With a simple modification of noil-parametric density estimation, however, it. is easy to analyze such changes. One goal is to estimate the density that would have prevailed in 1990, had the distribution of wage determining characteristics been as it was among 1970 recent immigrants.