the results it will be possible to tell how this affects the well-being of people and the society as a whole
The second dogma that Card debunked in his research is the impact of the migrants influx on the employment of the indigenous population. This was indicated by the classical model of the balance of supply and demand in the market. In this model any increase in population (including due to migration) leads to an increase in the number of workers in the market, and if the number of jobs is fixed, it gives a decrease in wages and an increase in unemployment. David Card published two major papers on this topic. The first was the result of a study of how the inflow of more than 120,00 °Cuban migrants in the 80s affected the Miami labor market. It was impossible to simply compare unemployment and wages in Miami “before and after” the migrants influx. The US economy experienced growth in 1979 and decline in 1981 for reasons that had nothing to do with these migrants. But Card analyzed average changes in wages and unemployment from the late 1970s to the 1980s in Atlanta, Houston, Los Angeles, Tampa and St. Petersburg. Then he subtracted these changes from the change in the results of the labor market in Miami and got the impact of the influx of immigrants on wages and unemployment in the city. Card found that this influx had virtually no effect on the wages of unskilled non-Cubans in Miami, nor did it increase unemployment among blacks or non-Cubans.
The methodological basis of the Card’s research was the “difference in differences” method. This method can be widely used to study the factors of influence in natural experiments. The essence of the method in its simplest implementation looks like the following: some outcomes are observed for two groups and two time periods. One of the groups is exposed, or participates in a program in one of the periods, and the second group is not affected in any of the periods. In the case when the same objects within the groups are observed in each period, the average change in outcome in the second (control) group is subtracted from the average change in outcome in the first (experimental) group. This eliminates the bias when comparing outcomes in the experimental and control groups only in the second period, which may be a consequence of constant differences between the groups, as well as the bias when comparing over time, which may be caused by time trends unrelated to the program.
The possibilities and potential of this methodology can be considered in more detail using the example given by Jeffrey Wooldridge in the paper “Evaluation by the method of “Difference of differences”: suppose that one of the US states implements a healthcare program for the elderly aged 65 years and older, and a certain health indicator is the dependent variable. One possibility is to use data only of residents of the state in which the program is implemented, both before and after its implementation, and take residents under the age of 65 (or between the ages of 55 and 64) as a control group, and residents aged 65 and older as an experimental group. A potential problem with an analysis of this kind is that other factors unrelated to the new state program may affect the health of older people compared to younger ones, for example, changes in health policy at the federal level. A different analysis strategy is to form a control group in another state where there is no such a health program. Thus, a constant change is imposed between the two groups, and later on the influence of the program itself on the studied indicator is measured.
So, let's return to the mathematical formula of this method.
If there are repeated samples over two time periods, the model tested using this method is written as follows:
y = B0 + BldB + 0d2 + 1d2dB + u (1)
where y is the outcome of interest,
d2 is a dummy variable for the second period, dB is a dummy variable for the experimental group.
The dummy variable d2 captures factors that would cause changes in y even in the absence of an impact or a program. The dummy variable dB captures possible differences between the experimental and control groups, respectively. The coefficient of interest 1 is found with the interaction variable d2dB, which coincides with the dummy variable equal to one for observations in the experimental group in the second period. Estimation 1 by the "difference of differences" method (PP-estimation) is the usual estimation of the least squares method for equation (1) based on a random sample of the studied groups. It can be written as
1 = (yB,2 — yB,1) — (yA,2 — yA,1), (2)
where A denotes the control group.
If there are repeated samples over two time periods, the model tested using this method is written as follows: y = B0 + e1dB + 0d2 + 1d2dB + u, where y is the outcome of interest, d2 is a dummy variable for the second period, dB is a dummy variable for the experimental group.
Thus, the sample in our study will also represent two groups, which will be expressed in the two groups of companies, one of which was a violator of the law (experimental) in one of the two periods, and the other did not carry out such actions in any of the periods (control). Thus, the variable d2 in our equation characterizes the period corresponding to a particular observation, and the variable dB will represent the difference between the experimental and control groups. As a result, this method gives us the opportunity to identify the net impact of the program on any individual social or economic component.
The second major work of David Card was the study of the impact of the minimum wage on employment. The hypothesis was tested that
