THE IMMIGRANTS: Native Wages Distributions

General Considerations

Until this point, our focus has been on simple summaries of the data. Such approaches have many advantages, not least of which is a considerable amount of “data reduction”: summarizing vast quantities of information compactly. On the other hand, some aspects of wrage structure changes can be obscured by a focus on simple summary statistics other.

In this section, we again compare immigrant wages to native wages from our four Census samples except that wTe now focus on the entire distribution of wages. It might be interesting to consider the effect of supply and demand, minimum wages and their possible employment effects, and de-unionization, on the wage outcomes of immigrants and natives as in DiNardo, Fortin, and Lemieux (1996). Similarly, it would be interesting to incorporate the possible interaction between changes in the level of immigration and the wage structure of natives as in Card (1990), Butcher and Card (1991), Borjas, Freeman, and Katz (1992) and Borjas, Freeman, and Katz (1996). Inter alia, limitations of the necessary time-consistent information from the four samples lead us instead to limit our focus to the distribution of observed wages.

Methodological Concerns

The non-parametric density estimates we consider in this paper use the kernel density estimator introduced by Rosenblatt (1956) and Parzen (1962). The kernel density estimate Д of a univariate density / based on a random sample
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where h is the bandwidth and /\(-) is the kernel function.

A potentially important issue in kernel density estimation is choice of bandwidth. Put simply, larger bandwidths result in more bias and less variance (over-smoothing), while smaller bandwidths result in less bias and more variance (under-smoothing). Although there are a number of different methods for automatically choosing the bandwidth ranging from cross -validation10 to “plug-in” methods11, there is no consensus on what is “optimal.’’ Instead we apply the simple dictum: since it is generally easier to smooth with the eye than “unsmoothe” with the eye, we choose bandwidths that err on the side of being “too small.” Furthermore, when wre consider more than one density estimate at a time, we apply the same bandwidth to each. The estimates in this section use bandwidths from 0.0477 to 0.0988, using smaller bandwidths for larger samples. As the general shape of the densities remain the same for a for a fairly large range of bandwidths, the issue of bandwidth seems to have little practical importance in our exercise.

Less important is the issue of kernel choice, and for all our estimates we use a Gaussian kernel.