General Equilibrium Approaches

A more clearly interpretable approach to the problem of measuring indirect e¤ects of pro-grams is to construct equilibrium models of the labor market in which both direct and indirect e¤ects are modeled. One recent example is Davidson and Woodbury (1993) who consider these issues in the context of evaluating a bonus scheme to encourage unemployed workers to …nd jobs more quickly using a Mortensen-Pissarides search model in which prices are …xed. A second recent example is the analysis of Heckman, Lochner and Taber (1998b), who consider the evaluation of tuition subsidy programs in a general equilibrium model of human capital accumulation with both schooling and on the job training and with hetero-geneous skills in which prices are ‡exible. The …rst is a model of displacement with …xed prices; the second is a model of substitution.

Both studies demonstrate the problems with, and possibilities for, general equilibrium analysis of the impacts of active labor market programs. They both …nd important indirect e¤ects of the programs they evaluate. At the same time, both studies demonstrate that the task of …nding credible parameters for general equilibrium models is a challenging one.

We …rst consider the analysis of Davidson and Woodbury.

9.2.1 Davidson and Woodbury

The reemployment bonus scheme analyzed by Davidson and Woodbury (1993) accelerates the rate at which unemployed persons o¤ered the bonus …nd jobs. The bonus is paid to currently unemployed eligible persons with spells below a threshold level who …nd jobs within a speci…ed time frame. By stimulating aggregate search activity, the bonus may also have macro e¤ects on output and on the search behavior of unsubsidized participants.

The higher taxes raised to …nance the program may reduce aggregate search activity by the unsubsidized as their return to market activity declines. The higher level of search by the subsidized may discourage search by their unsubsidized competitors in the labor market.

Davidson and Woodbury (1993) consider four classes of workers: (a) Unemployment insurance (UI) recipients who are eligible for the bonus if they get hired; (b) UI recipients who are ineligible for a bonus because of the length of their current unemployment spell (the bonus is only paid to persons with an unemployment spell below a certain length); (c)

UI recipients who have exhausted their bene…ts; and (d) jobless workers who were never eligible to receive UI bene…ts and cannot receive a bonus. They develop an equilibrium model of search assuming that workers are income maximizing and the bonus is o¤ered in the steady state.

Workers with a bonus have an incentive to accelerate their search. Those ineligible for a bonus in the current spell experience two o¤setting e¤ects: (a) the competition for jobs increases, making search less pro…table and (b) the bene…ts of being unemployed rise in the next spell because of the bonus. The second e¤ect promotes search because of the eligibility for the program conferred on persons when they eventually secure a job and are at risk for future unemployment. In their simulations these e¤ects cancel out, leaving the search activity of this group una¤ected. However, because of enhanced search by those with the subsidy, the rate of job acquisition declines for those currently ineligible for the bonus.

For those who are permanently ineligible, only the …rst e¤ect operates; as a result they reduce their search activity. This generates displacement. During recessions, the existence of a bonus leads to displacement of non-bonus workers (those permanently ineligible and those whose bene…ts are exhausted or whose eligibility has expired). Permanently ineligible workers always experience displacement. Davidson and Woodbury estimate that 30-60 percent of the gross employment e¤ect of the bonus program is o¤set by displacement of UI-ineligible workers. Microeconomic treatment analyses of program participant employment experiences provide a substantially misleading picture of the e¤ect of the program on society at large. We next turn to a general equililbrium model of an economy with wage ‡exibility and indirect e¤ects.

9.2.2 Heckman, Lochner and Taber

The typical microeconomic evaluation of tuition policy estimates the response of college enrollment to tuition variation using geographically dispersed cross-sections of individuals facing di¤erent tuition rates. These estimates are then used to determine how subsidies to tuition will raise college enrollment. The impact of tuition policies on earnings are evaluated using a schooling-earnings relationship …t on pre-intervention data and do not account for the enrollment e¤ects of the taxes raised to …nance the tuition subsidy. Kane (1994) and Cameron and Heckman (1998) exemplify this approach.

The danger in this widely used practice is that what is true for policies a¤ecting a small number of individuals, as studied by social experiments or as studied in the microeconomic

“treatment e¤ect” literature, need not be true for policies that a¤ect the economy at large.

A national tuition-reduction policy may stimulate substantial college enrollment and will also likely reduce skill prices. However, agents who account for these changes will not enroll in school at the levels calculated from conventional procedures which ignore the impact of

the induced enrollment on skill prices. As a result, standard policy evaluation practices are likely to be misleading about the e¤ects of tuition policy on schooling attainment and wage inequality. The empirical question is: how misleading? Heckman, Lochner and Taber (1998b) show that conventional practices in the educational evaluation literature lead to estimates of enrollment responses that are ten times larger than the long-run general equilibrium e¤ects. They improve on current practice in the “treatment e¤ects” literature by considering both the gross bene…ts of the program and the tax costs of …nancing the treatment as borne by di¤erent groups.

Evaluating the general equilibrium e¤ects of a national tuition policy requires more information than the tuition-enrollment parameter that is the centerpiece of partial equi-librium policy analysis. Policy proposals of all sorts typically extrapolate well outside the range of known experience and ignore the e¤ects of induced changes in skill quantities on skill prices. To improve on current practice, Heckman, Lochner and Taber (1998b) develop an empirically justi…ed rational expectations, perfect foresight overlapping-generations gen-eral equilibrium framework for the pricing of heterogeneous skills. It is based on an em-pirically grounded theory of the supply of schooling and post-school human capital, where di¤erent schooling levels represent di¤erent skills. Individuals di¤er in learning ability and in initial endowments of human capital. Household saving behavior generates the aggregate capital stock, and output is produced by combining the stocks of di¤erent human capitals with physical capital. Factor markets are competitive and there is price ‡exibility. The framework explains the pattern of rising wage inequality experienced in the United States in the past 30 years. They apply their framework to evaluate tuition policies that attempt to increase college enrollment.

For two reasons, the “treatment e¤ect” framework that ignores the general equilibrium e¤ects of tuition policy is inadequate. First, the parameters of interest depend on who in the economy is “treated” and who is not. Second, these parameters do not measure the full impact of the program. For example, increasing tuition subsidies may increase the earnings of uneducated individuals who do not take advantage of the subsidy. To pay for the subsidy, the highly educated would be taxed and this may a¤ect their investment behavior. In addition, more competitors for educated workers enter the market as a result of the policy, and their earnings are depressed. Conventional methods ignore the e¤ect of the policy on nonparticipants operating through changes in equilibrium skill prices as well as Calmfors’ tax e¤ect. In order to account for these e¤ects, it is necessary to conduct a general equilibrium analysis.

The analysis of Heckman, Lochner and Taber (1998) has major implications for the widely-used di¤erence-in-di¤erences estimator. If the tuition subsidy changes the aggre-gate skill prices, the decisions of nonparticipants will be a¤ected. The “no treatment”

benchmark group is a¤ected by the policy and the di¤erence-in-di¤erences estimator does

not identify the e¤ect of the policy for anyone compared to a no treatment state.⁹¹

Using their model, Heckman, Lochner and Taber (1998b) simulate the e¤ects of a revenue-neutral $500 increase in college tuition subsidy on top of existing programs that is

…nanced by a proportional tax, on enrollment in college and wage inequality. They start from a baseline economy that describes the U.S. in the mid 1980s and that produces wage growth pro…les and schooling enrollment and capital stock data that match micro and macro evidence. The partial equilibrium increase in college attendance is 5.3 percent in the new steady state. This analysis holds skill prices, and therefore college and high school wage rates, …xed – a typical assumption in microeconomic “treatment e¤ect” analyses.

When the policy is evaluated in a general equilibrium setting, the estimated e¤ect falls to 0.46 percent. Because the college-high school wage ratio falls as more individuals attend college, the returns to college are less than when the wage ratio is held …xed. Rational agents understand this e¤ect of the tuition policy on skill prices and adjust their college-going behavior accordingly. Policy analysis of the type o¤ered in the “treatment e¤ect”

literature ignores the responses of rational agents to the policies being evaluated. There is substantial attenuation of the e¤ects of tuition policy on capital and on the stocks of the di¤erent skills in their model compared to a partial equilibrium treatment e¤ect model.

They demonstrate that their results are robust to a variety of speci…cations of the economic model.

They also analyze short run e¤ects. When they simulate the model with rational ex-pectations, the short-run college enrollment e¤ects are also very small, as agents anticipate the e¤ects of the policy on skill prices and calculate that there is little gain from attend-ing college at higher rates. Under myopic expectations, the short-run enrollment e¤ects are much closer to the estimated partial equilibrium e¤ects. With learning on the part of agents, but not perfect foresight, there is still a substantial gap between partial equilibrium and general equilibrium estimates.

Heckman, Lochner and Taber (1998b) also consider the impact of a policy change on discounted earnings and utility and decompose the total e¤ects into bene…ts and costs, including tax costs for each group, thus isolating Calmfors’ tax e¤ect. Table 9.1 compares outcomes in two steady states: (a) the benchmark steady state and (b) the steady state associated with the new tuition policy. Given that the estimated schooling response to a $500 subsidy is small, they instead use a $5000 subsidy for the purpose of exploring general equilibrium e¤ects on earnings. (Current college tuition subsidy levels are this high or higher at many colleges in the U.S.) The row “High School - High School” reports the change in a variety of outcome measures for those persons who would be in high school

91This problem of spillover e¤ects was …rst studied by Lewis (1963) who pointed out its implications for estimating the union-nonunion wage di¤erential from cross section and repeated cross section comparisons.

under either the benchmark or new policy regime; the “High School - College” row reports the change in the same measures for high school students in the benchmark state who are induced to attend college by the new policy; the “College - High School” outcomes refer to those persons in college in the benchmark economy who only attend high school after the policy; and so forth.

By the measure of the present value of earnings, some of those induced to change are worse o¤. Contrary to the monotonicity assumption built into the LATE parameter discussed in Section 7, and de…ned in this context as the e¤ect of the tuition subsidy on the earnings of those induced by it to go to college, they …nd that the tuition policy produces a two-way ‡ow. Some people who would have attended college in the benchmark regime no longer do so. The rest of society also is a¤ected by the policy—again, contrary to the implicit assumption built into LATE that only those who change status are a¤ected by the policy. People who would have gone to college without the policy and continue to do so after the policy are …nancially worse o¤ for two reasons: (a) the price of their skill is depressed and (b) they must pay higher taxes to …nance the policy. However, they now receive a tuition subsidy and for this reason, on net, they are better o¤ both …nancially and in terms of utility. Those who abstain from attending college in both steady states are better o¤ in the second. They pay higher taxes, but their skill becomes more scarce and their wages rise. Those induced to attend college by the policy are better o¤ in terms of utility but are not necessarily better o¤ in terms of income. Note that neither category of non-changers is a natural benchmark for a di¤erence-in-di¤erences estimator. The movement in their wages before and after the policy is due to the policy and cannot be attributed to a benchmark

“trend” that is independent of the policy.

Table 9.2 presents the impact of the $5,000 tuition policy on the log earnings of indi-viduals with ten years of work experience for di¤erent de…nitions of treatment e¤ects. The partial equilibrium version given in the …rst column holds skill prices constant at initial steady state values. The general equilibrium version given in the second column allows prices to adjust when college enrollment varies. Consider four parameters initially de…ned in a partial equilibrium context. The average treatment e¤ect is de…ned for a randomly selected person in the population in the benchmark economy and asks how that person would gain in wages by moving from high school to college. The parameter treatment on the treated is de…ned as the average gain over their non-college alternative of those who attend college in the benchmark state. The parameter treatment on the untreated is de…ned as the average gain over their college wage received by individuals who did not attend college. The marginal treatment e¤ect is de…ned for individuals who are indi¤erent between going to college or not. This parameter is a limit version of the LATE parameter under conventional assumptions made in discrete choice theory (Heckman, 1997). Column 2 presents the general equilibrium version of treatment on the treated. It compares the

earnings of college graduates in the benchmark economy with what they would earn if no one went to college.⁹² The treatment on the untreated is de…ned analogously by compar-ing what high school graduates in the benchmark economy would earn if everyone in the population were forced to go to college. The average treatment e¤ect compares the average earnings in a world in which everyone attends college versus the earnings in a world in which nobody attends college. Such dramatic policy shifts produce large estimated e¤ects.

In contrast, the general equilibrium marginal treatment e¤ect parameter considers the gain to attending college for people on the margin of indi¤erence between attending college and only attending high school. In this case, as long as the mass of people in the indi¤erence set is negligible, partial and general equilibrium parameters are the same.

The …nal set of parameters Heckman, Lochner and Taber (1998b) consider are versions of the LATE parameter. This parameter depends on the particular intervention being studied and its magnitude. The partial equilibrium version of LATE is de…ned on the outcomes of individuals induced to attend college, assuming that skill prices do not change.

The general equilibrium version is de…ned for the individuals induced to attend college when prices adjust in response to the policy. The two LATE parameters are quite close to each other and are also close to the marginal treatment e¤ect.⁹³ General equilibrium e¤ects change the group over which the parameter is de…ned compared to the partial equilibrium case. For the $5,000 subsidy, there are substantial price e¤ects and the partial equilibrium parameter di¤ers substantially from the general equilibrium parameter.

Heckman, Lochner and Taber (1998b) also present partial and general equilibrium es-timates for two extensions of the LATE concept: LATER (the e¤ect of the policy on those induced to attend only high school rather than do to college)—Reverse LATE—and TLATE (the e¤ect of the policy on all of those induced to change whichever direction they ‡ow).

LATER is larger than LATE, indicating that those induced to drop out of college have larger gains from dropping out than those induced to enter college have from entering.

TLATE is a weighted average of LATE and LATER with weights given by the relative proportion of people who switch in each direction.

The general equilibrium impacts of tuition on college enrollment are an order of magni-tude smaller than those reported in the literature on microeconometric treatment e¤ects.

The assumptions used to justify the LATE parameter in a microeconomic setting do not carry over to a general equilibrium framework. Policy changes, in general, induce two-way

92In the empirical general equilibrium model of Heckman, Lochner and Taber (1998b), the Inada condi-tions for college and high school are not satis…ed in the aggregate production function and the marginal product of each skill group when none of it is utilized is a bounded number. If the Inada conditions were satis…ed, this counterfactual and the counterfactual treatment on the untreated would not be de…ned.

93The latter is a consequence of the discrete choice framework for schooling choices analyzed in the Heckman, Lochner and Taber (1998b) model. Recall our discussion in Section 3.4.

‡ows and violate the monotonicity—or one-way ‡ow—assumption of LATE. Heckman, Lochner and Taber (1998b) extend the LATE concept to allow for the two-way ‡ows in-duced by the policies. They present a more comprehensive approach to program evaluation by considering both the tax and bene…t consequences of the program being evaluated and placing the analysis in a market setting. Their analysis demonstrates the possibilities of the general equilibrium approach and the limitations of the microeconomic “treatment e¤ect”

approach to policy evaluation.