La “conciencia purificada” del Husserl trascendental y los “problemas funcionales

The aim of this section is to investigate the properties of alternative estimation methods for each of the model specifications considered above.

It is useful to start by considering a naive estimator in the general framework (3) of the returns to educational level j (relative to level 0) for individuals reaching this level: the simple difference between the observed average earnings of indi­ viduals with Sji=l and the observed average earnings of individuals with 5'o,=l.

This observed difference in conditional means can be rewritten in terms of the average treatment on the treated parameter ATT (what we are after) and the bias potentially arising when the earnings of the observed group with Soi=l (yo | Soi=l)

are used to represent the counterfactual (yo \ Sji=l):

Naive estimator = E(y,-1 Sji=l) - E(y, | 5o,=l)

= E(yji - y0 115yf= 1 ) - { E(yo, 15;,-= 1 ) - E(yo/1 Soi- 1 )}

ATT - { bias }

The key issue is that when estimating the return to a particular educational choice we are likely to observe only optimal decisions, resulting in the sample of individuals who make each choice being not random. If this is ignored and indi­ viduals for whom the choice was optimal are simply compared to those for whom it was not, the estimates will suffer from bias. Using experimental data, Heckman, Ichimura, Smith and Todd (1998) provide a very useful breakdown of this bias term:

bias = E(yo/1 5/,=l) - E(yoi | 5o,-=l) = 8 1 + 82 + 83 (9) The first two components arise from differences in the distribution of observed characteristics X between the two groups: 8 1 represents the bias component due to non-overlapping support of the observables and 8 2 is the error part due to mis- weighting on the common support, as the resulting empirical distributions of ob­ servables are not necessarily the same even when restricted to the same support. The last component, 8 3, is the true econometric selection bias resulting from “se­ lection on unobservables”, in our notation bji and £{.

Of course, a properly designed and ideally implemented randomized experi­ ment would eliminate the bias discussed above. Pure education or schooling ex­ periments are however very rare. It is difficult to persuade parents or the students themselves of the virtues of being randomised out of an education programme - except for rather minor programmes. Our application will be to the main stages of educational level in the UK and randomised assignment is unavailable.

Instead, our focus will be on non-experimental approaches. Many alternative methods are available and all have been widely used. Each of these methods uses observed data together with some appropriate identifying assumptions to recover the missing counterfactual. Depending on the richness and nature of the available data and the postulated model for the outcome and selection processes, the re­ searcher can thus choose among the alternative methods the one most likely to avoid or correct the sources of bias outlined above.

More common than randomised experiments are the socalled “natural” experi­ ments. The idea is to find real-world events which assign individuals to different levels of schooling in a random way, that is independently of any characteristics that affect earnings. This is for instance the case where some educational rule or qualification level (say minimum schooling leaving age) is exogenously changed for one group but not another. Provided the groups are representative samples from the population, then this simple comparison can recover a parameter of in­ terest like the average treatment effect. Where the samples differ in their ability levels or other characteristics it may still be possible to recover an average effect for those who experience the change in rules.

proximation to a randomized trial by exploiting an exogenous change in schooling that only affects a subsample of the target group. This relates to instrumental vari­ able methods more generally, where some variable (or transformation of the data) has to be found that can vary schooling independently of the heterogeneity terms.

The control function approach too takes advantage of the existence of a deter­ minant of schooling which can legitimately be omitted from the earnings equa­ tion. This variable is exploited to estimate an additional equation that determines which educational choice is made, which is then used to augment the earnings re­ gression with selectivity variables reflecting the selection bias.

An alternative to using instruments to control for correlation between individ­ ual factors and schooling choices is the matching method. This method attempts to measure all individual factors that may be the cause of such dependence and then purge the relationship between schooling and earnings of any important ob­ served heterogeneity that would lead to bias.

The initial setting for the discussion of the three broad classes of alternative methods we consider - instrumental variable, control function and matching - will be based on the biases that occur from the simple application of ordinary least squares to the estimation of each of the model specifications described in the pre­ vious section. As mentioned, the primary model specification will be the single discrete treatment heterogeneous returns model (6), but the extension to the multi­ ple treatment model (7) will also be considered and so will the specific issues that occur in the one factor-years of schooling specification (8). In each of these, the complications that are engendered by allowing the return parameter P to be het­ erogeneous - and acted upon by individuals - will be central to the discussion.