TEMATICA TRABAJOS DE GRADO PERIODO 2005-

We build our estimation procedure on the identi…cation results developed in Section 3.2.2 although we adopt two parametric assumptions. First, the distribution of random preferences is assumed to be a normal distribution when both schools yield positive utility to students. Second, the probabilities that only one school has positive utility are described by logistic functions which depend on a smaller set of covariates. Following the notation of Section 3.2.2, we write the probability measure of the regions in Figure 1, for instance the north-east quadrant (that is VS _{> 0; V}F _{> 0) as:}

SF_{(X) =} 1

1 + exp(X SF): The choice probability is thus derived from equation (13):

Pr(D = S _{j (Z); X) =} S(X) + SF(X) (log(PS) log(PF) + X )

in which (:) is the zero mean unit normal distribution15 _{and the success probabilities P}d _are

to be replaced by their simulated predictions using grade equations (column 1 of Table 5 and column 2 of Table 6) as developed in the previous Section 4.2.3. In the …rst part of Table 9, we report the estimated preference coe¢ cients and in the second part we present more readable summary statistics of the estimated probabilities of each region, SF(X). There are three di¤erent speci…cations included in this table. The key di¤erence is how explanatory variables enter the speci…cation of S and SF. We chose to use two main variables, ability m0 and Living in Fortaleza

as the main drivers of these probabilities and the three columns of Table 9 include one or both of these variables.

The results are very stable across speci…cations. As far as parameters are concerned, ability signi…cantly a¤ects the probability of the region of jointly positive values, (S; F ) (and as a conse- quence of adding up, also the preference for F alone). Living in Fortaleza decreases preferences for Sobral alone ( S) or jointly with Fortaleza ( SF). The second part of Table 9 shows that the average probability of preferring Sobral alone (resp. Fortaleza alone) to the outside option is

15_{As the range of the log probability di¤erence is not the whole real line as in Section 3.2.2, the scale of the error}

around 0.06 (respetively 0.55). These frequencies stay almost invariant across speci…cations. This shows that students heavily favor Fortaleza over Sobral and this con…rms that Fortaleza is the most popular medicine school in the state of Cearà. The ratio of those probabilities is 10 which is approximately the ratio between the populations of the two cities albeit much larger than the ratio of …nal seats in the two schools (150/40). Nonetheless, there is a substantial fraction of students whose utilities for both schools are positive (more than 40%)

We now turn to parameters that a¤ect preferences of students who prefer both schools to the outside option in the north-east quadrant of Figure 1. The variables, "Living in Fortaleza", Age, Gender (female) and ability, m0;have a negative impact on the preference for Sobral, the smaller

school. In contrast, the number of repetitions have a positive impact on choosing the medical school in Sobral. A well educated father a¤ects positively preferences for the bigger school in Fortaleza while mother’s education does not have any signi…cant in‡uence on preferences. This is probably because of the colinearity between parents’educations.

Finally, we tested the maintained hypothesis that performance shocks and preference shocks are independent by introducing the residual ^u1 in this preference equation. The hypothesis cannot

be rejected at the 10% level (the p-value is equal to 0.184).

5

Evaluation of the Impact of Changes of Mechanisms

We now turn to the normative implications of our results and we investigate the impact of various changes of the existing mechanism.

The …rst counterfactual experiment that we implement is to cut seats at the second-stage exam and o¤ering twice instead of four times, the number of …nal seats. The University would incur lower costs in exchange with a possibly degraded selection if good students perform poorly at the …rst-stage exam.

Second, we experiment with enlarging the choice set of students before taking exams. They now can list two ordered choices at most. This means that even if students fail the …rst stage quali…cation in one of the two schools they may still get the other major. This implies that the average skill level of passing students increases although the di¤erence between the two majors is attenuated.

more in-depth selection at the second-stage. Another natural change to experiment is therefore to change the timing of choice-making and allow students to choose their …nal major after taking the …rst-exam and learning their grades. This would generate more opportunistic behavior.

Before entering the details of these new mechanisms, we …rst analyze the identi…cation of utilities from estimated preferences and success probabilities that are key in these evaluations. We show that expected utilities are underidenti…ed and suggest how we can construct plausible bounds for the counterfactual estimates. Second, we explain how we compute counterfactual estimates conditional on observed choices.