## Archive for July 31, 2014

### EVALUATING THE WELFARE STATE: Repeated Cross Section Data 4

July 31, 2014The first term arises from the change in the number of participants induced by the policy change. The second and third terms arise from changes in output among participants and nonparticipants induced by the policy change. The fourth term is the marginal direct output cost of the change in the intensity of policy t^-.

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### EVALUATING THE WELFARE STATE: Repeated Cross Section Data 3

July 29, 2014

For policy j let and Ybe individual output for person i in the direct participation (Dj = 1) and direct non-participation (Dj ~ 0) state, respectively. The vector of program intensity variables j) as the social cost of j. The value c^0 defines another benchmark policy, “0”, in which there is no program and therefore no participants. This policy has associated cost function co(^o).

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### EVALUATING THE WELFARE STATE: Repeated Cross Section Data 2

July 27, 2014The Relationship Between Traditional Cost-Benefit Analysis and The Parameters Widely Used In The Econometric Evaluation Literature

In this section we relate the parameters estimated in the micro-econometric evaluation literature to the parameters needed to perform cost-benefit analysis. We present empirical evidence on the importance of accounting for the direct costs of a program and the marginal welfare costs of taxation in assessing the net benefits of a policy. We follow the literature in cost-benefit analysis and assume that the policy being evaluated has a voluntary component and that valid evaluations of a policy can be derived from looking at the impact of the policy on self-selected participants and nonparticipants.

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### EVALUATING THE WELFARE STATE: Repeated Cross Section Data

July 25, 2014

Heckman and Robb (1985) demonstrate that all panel data identification assumptions about means, variances and covariances have counterparts in repeated cross section data. Conditional mean versions of all of the identification assumptions presented in Section С have counterparts in repeated cross sections of unrelated persons sampled from the same populations. We first consider the reversible case.

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### EVALUATING THE WELFARE STATE: The Irreversible Case

July 23, 2014

In the irreversible case, there are no counterparts for (I-lib)’, (I-llb)”, (I-12b) or (I-12b V because there are no observations on treated persons in the preprogram period t’. First consider the case where program enrollment date r is fixed and common for all persons. The probability space is restricted so Рг(1)г/ = 1 | X) — 0 and no value of Yt} is defined. F(yy]\Dt — 1, X) can be identified from F(yy1 \ Dt = 1, X) if the preprogram outcomes of participants have the same relationship to program outcomes in t as their nonprogram outcomes in period t. (This is just assumption (I-12a).) We cannot use (I-12b) to construct F(yfi,y\ | Dt = О, X) because no value of Yt} is defined. In the irreversible case, we have a truncated sample.

If we invoke a conditional independence assumption and assume a counterpart to (1-12) defined for the reversible case:

we can identify the full joint distribution.19 Otherwise, we can only identify the criteria for the population conditional on Dt = 1. Since we know (Y®,Ytl) conditional on Dt = 1 and X, we can use a vector generalization of Theorem A-2, presented in Appendix A as Theorem A-3, to identify F(y®,y] | X) and F(y®,y},Dt\X). What is required is a set of X values where Pv(Dt = 1 | X) = 0. Under the assumptions made in Theorem A-3, it is possible to recover the full distribution of outcomes even in the reversible case.

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### EVALUATING THE WELFARE STATE: Reversible Programs 2

July 21, 2014

These are strong implicit behavioral assumptions. Assumption (I-12a) and (I-12a)’ require that persons who participate in t but not in tf have the same no-treatment mean outcome in tf as persons who take treatment in period t would have in t. It rules out that the switch from Dt> = 0 to Dt = 1 is caused by differences in Y° between t* and t. More precisely, it excludes Yfi as a determinant of Dt>. Assumptions (I-12b) and (I-12b)’ are comparable assumptions about the lack of influence of in determining participation in t’.

One way to justify these identifying assumptions is to postulate a strengthened form of the conditional independence assumption used to justify matching:

This condition rules out any dependence between Dt and Dti and the components of YtDt) that cannot be predicted by X. This assumption rules out selection on any unobserved components of potential outcomes. It is inconsistent with the Roy model. A weaker version of (1-13) is that conditional on Dt and X, (Y^*’, YtDt) are independent of

This condition rules out any dependence between the components of ( Yt?], YtDt) that cannot be predicted by Dt and X and the random variable Dti. (I-12a)’ and (I- 12b)’ can be justified by these assumptions.

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### EVALUATING THE WELFARE STATE: Reversible Programs

July 19, 2014

Nonstationarity in the external environment, the effects of aging and life cycle investment, and idiosyncratic period-specific shocks render assumptions (I-lla) and (I-1 lb) suspect. To circumvent these problems, the identifying assumptions are usually reformulated at the population level and conditioning variables X are assumed that “adjust” Yt? and Y]° and Ytj and Y^ to equality in distribution or conditional mean and allow for idiosyncratic fluctuations. For simplicity, we only conduct a two-period analysis, but to estimate the necessary adjustments may require more data. The modified identification conditions become

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### EVALUATING THE WELFARE STATE: Panel Data 1

July 17, 2014If randomization is performed on eligibility for the program, we recover F(y°\X), F(yl \D = 1 ,X) and F(y°\D = 1 , X). (See Heckman 1992 and Heckman and Smith, 1993). In addition, we recover Pr(D = 1 |X), at least for those values of X possessed by eligible persons. Many would regard F(y° |X) as a better approximation to the no-policy outcome distribution than the approximation embodied in assumption (A-l). Although both approximations ignore general equilibrium effects, F(y° |JV) avoids self-select ion bias. Randomization at eligibility does not recover the full joint distribution of outcomes unless additional assumptions of the type previously discussed are invoked. Table 3 summarizes the information obtained from the two types of experiments.

### EVALUATING THE WELFARE STATE: Social Experiments 2

July 15, 2014

With these assumptions, we can construct or bound all of evaluation criteria presented in Section 1 for the conditional (on D = 1) distribution. Under conditional independence assumption (1-3), it is possible to recover the complete marginal distributions F(yl \D = 1, X) = F(yx \X) and F(y°\D = 1,X) = F(y° \X) and bound F{y°, yl \X) using the Frechet bounds; or to identify F(y°, y1 \X) by (a) making an assumption connecting the quantiles of the two marginal distributions or (b) assuming as in (1-5) that gains A are unrelated to the base state Y°.

If decision rule (18) is postulated, we may use the Roy model (under the conditions specified in Theorem A-l) to identify F(y°,t/1 |X) from the conditional distributions F(y° \D = 1 ,X) and F(yl |D = 1,X). Under assumptions (A-l) and (A-2), we can answer the evaluation questions comparing policy j with policy u0” that were posed in Section 1 for the entire population and the conditional population.

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### EVALUATING THE WELFARE STATE: Social Experiments 1

July 13, 2014

Thus in place of (1-3), which is defined solely in terms of variables X in the outcome equations, we may assume that access to a variable Z produces conditional independence:

Under these assumptions we may recover the marginal and joint distributions as discussed in the subsection on conditional independence. Interpreted in this way the instrumental variables method generalizes the matching method and extends the identification analysis based on conditional independence in terms of variables in the outcome equation to utilize a larger conditioning set beyond those variables.