La situación del sector agrario durante el siglo XX

Interestingly, we have discussed the average treatment effect at a local level before, under IV. This was the LATE parameter or, when taking the limits using a continuous

instrument, the MTE. To understand the similarities and differences between DD and local IV we consider the fuzzy design case and notice that both methods will identify the same

parameter in a sharp design framework, namely the mean effect of treatment on a randomly selected individual among the treated close to the eligibility cutoff point.

The fuzzy design case is slightly more complex. DD relies on continuity and the local independence assumption in equation (54). The latter determines the parameter

identified by DD as being the average impact of treatment on a randomly selected individual with a value of z at the threshold.

In turn, LATE relies on the independence assumptions (43)-(44) and on the

monotonicity assumption (46). Under these conditions, LATE identifies the average impact of treatment on a randomly selected individual from the group of agents that change

participation status as the value of the instrument changes from z^*− to z^*+.

The empirical estimates of LATE and DD when applied to the same neighborhood of z coincide exactly, what differs is the interpretation. The preferred interpretation should ^* be justified on the grounds of the specific application and policy design. If individuals are believed to have no decision power at the local level, then estimates may represent local effects on randomly selected individuals (DD interpretation). Alternatively, if the policy

provides clear participation incentives on one side of the threshold and individuals are expected to make informed participation decisions, then a local impact on the movers becomes a more credible interpretation (LATE).²⁵

VII.C. Weaknesses of DD

An obvious drawback of DD is its dependence on discontinuous changes in the odds of participation. In general this implies that only a local average parameter is identifiable. As in the binary instrument case of local IV, the DD analysis is restricted to the discontinuity point dictated by the design of the policy. As discussed before under LATE with continuous instruments, the interpretation of the identified parameter can be a problem whenever the treatment effect, α , changes with z.

To illustrate these issues, consider the context of our educational example. Suppose a subsidy is available for individuals willing to enroll in high education for as long as they score above a certain threshold s in a given test. The subsidy creates a discontinuity in the cost of education at the threshold and, therefore, a discontinuity in the participation rates. On the other hand, the test score, s, and the returns to education, α , are expected to be

(positively) correlated if both depend on, say, ability. But then, the local analysis will only consider a specific subpopulation with a particular distribution of ability which is not that of the whole population or of the treated population. That is, at best the returns to education are estimated at a certain margin and other more general parameters cannot be inferred.

However, we could also suspect that neither the DD nor the LATE assumptions hold in this example. The former requires local independence of the participation decision from the potential gains conditional on the test score. But at any given level of the test score there is a non-degenerate distribution of ability levels. If higher ability individuals expect to gain more from treatment and are, for this reason, more likely to participate, then the local independence

assumption of DD (54) cannot be supported. The latter requires exogeneity of the instrument (test score) in the decision rule. But again, if both the test score and the gains from treatment depend on ability and individuals use information on expected gains to decide about

participation, then the instrument will not be exogenous in the selection rule. However, while this may be a serious problem to the use of LATE more generally, the infinitesimal changes considered here will reduce its severity when applied in the context of DD.

Related with the previous comment, there is also the possibility that individuals manipulate z in order to avoid/boost the chances of participation. Such behavior would in general invalidate the DD and LATE identification strategies by rendering the two

comparison groups incomparable with respect to the distribution of unobservables. In a recent paper, Lee (2008) notices that this is only a problem if the individuals can perfectly control z, thus positioning themselves at one or the other side of the threshold at will. But even with imperfect control over z, the interpretation of the identified parameter may change, particularly when a change in policy is being explored. This is because an endogenous reaction to the eligibility rule by manipulating z will affect the composition of the group on the neighborhood of the threshold. Thus, the estimated effects may correspond to a margin very different from what would be expected in the absence of such behavior.

In the context of the education illustration being recurrently used in this paper, notice that agents will certainly react to the existence of an education subsidy and to the eligibility rules. If eligibility is based on a test-score they may put extra effort on preparing for it if willing to continue investing in education. Thus, for sure the group of individuals scoring above the eligibility threshold will differ from that of individuals scoring below not only due to ability but also because preparation effort is endogenously selected. However, the ex-ante random nature of the test-score implies that any two groups scoring just

nfinitesimally differently will be compositionally identical as such small differences in test

scores are random. Thus, the local DD/LATE will still identify the treatment effect at the threshold margin. However, the introduction of a subsidy policy will affect effort in

preparation for the test and thus change the distribution of test-scores and the composition of students in the neighborhood of the threshold. Thus, the post-policy marginal student in terms of eligibility will not be the same as the pre-policy one, particularly perhaps with respect to ability, and this will determine the estimated impact.

A final downside of DD, which is also common with local IV relates to the implementation stage. By restricting analysis to the local level, the sample size may be insufficient to produce precise estimates of the treatment effect parameters.