Позитивные изменения. Том 2, № 2 (2022). Positive changes. Volume 2, Issue 2 (2022)

WHY DOES THE RANDOMIZED ASSIGNMENT METHOD WORK WELL?

As discussed, the ideal comparison group should be as similar as possible to the treatment group in all respects, except with respect to its participation in the program that is being evaluated. When we randomly assign units to treatment and comparison groups, that randomized assignment process in itself will produce two groups with a high probability of being statistically identical — as long as the number of potential units to which we apply the randomized assignment process is sufficiently large.

Figure 3 illustrates why randomized assignment produces a comparison group that is statistically equivalent to the treatment group.

To estimate the impact of a program using randomized assignment, we simply take the difference between the outcome under treatment (the mean outcome of the randomly assigned treatment group) and our estimate of the counterfactual (the mean outcome of the randomly assigned comparison group). We can be confident that our estimated impact constitutes the true impact of the program, since we have eliminated all observed and unobserved factors that might otherwise plausibly explain the difference in outcomes.

Inserts 2 and 3 give real-world applications of randomized assignment to evaluate the impact of a number of different interventions around the world.

Insert 2: RANDOMIZED ASSIGNMENT AS A PROGRAM ALLOCATION RULE: CONDITIONAL CASH TRANSFERS AND EDUCATION IN MEXICO

The Progresa program, now called "Prospera," provides cash transfers to poor mothers in rural Mexico conditional on their children's enrollment in school and regular health checkups. The cash transfers, for children in grades 3 through 9, amount to about 50 percent to 75 percent of the private cost of schooling and are guaranteed for three years. The communities and households eligible for the program were determined based on a poverty index created from census data and baseline data collection. Because of a need to phase in the large-scale social program, about two-thirds of the localities (314 out of 495) were randomly selected to receive the program in the first two years, and the remaining 181 served as a comparison group before entering the program in the third year. Based on the randomized assignment, Schultz (2004) found an average increase in enrollment of 3.4 percent for all students in grades 1–8, with the largest increase among girls who had completed grade 6, at 14.8 percent. The likely reason is that girls tend to drop out of school at greater rates as they get older, so they were given a slightly larger transfer to stay in school past the primary grade levels. These short-term impacts were then extrapolated to predict the longer-term impact of the Progresa program on schooling lifetime and earnings.

Source: Schultz, Paul. "School Subsidies for the Poor: Evaluating the Mexican Progresa Poverty Program." Journal of Development Economics 74 (1): 199–250. 2004