IDENTIFYING THE ROLE OF COGNITIVE ABILITY IN EXPLAINING THE LEVEL OF AND CHANGE IN THE RETURN TO SCHOOLING.(Statistical Data Included)

I. Introduction

This paper examines the contribution of ability to the rise in the economic return to education. A common view in both the popular and professional literature is that much of the increase in the return to education can be attributed to an increase in the return to ability. Herrnstein and Murray (1994) make this a cornerstone of their analysis, referring to the research of Blackburn and Neumark (1993) who report that the rise in the economic return to education is concentrated among those with high ability. This is a different proposition from the one stated by Herrnstein and Murray, but it is not necessarily inconsistent with it. In a similar vein, Murnane, Willett, and Levy (1995) conclude that a substantial fraction of the rise in the return to education between 1978 and 1986 for young workers can be attributed to a rise in the return to ability. When they condition on ability, the rise in the economic return to education is diminished.

The implicit assumptions that govern much of this literature are

* that ability is valued in the market (or is a proxy for characteristics that are valued),

* that the price of ability (or the proxied characteristics) is rising in the new market for skills, and

* that ability is correlated with education.

As a consequence of these assumptions, failure to control for ability leads to an upward bias in the estimated economic return to education, and the bias is greater in periods when the return to ability is greater. This is one possible explanation for a positive interaction of education, time and ability. Other explanations are

* that the correlation between ability and schooling is increasing over time, due to increasing application of the meritocratic principle in educational enrollment, even if the return to ability remains constant (Herrnstein & Murray, 1994) and

* that ability-education bundles produce skills that are more valued in the new economy, that the skills are superadditive functions of ability and education (Rubinstein & Tsiddon, 1999), and that the demand for the highest skills has increased disproportionately.

The small ability bias reported by Chamberlain and Griliches (1975) may be a consequence of the low economic return to ability in the time period of their samples. Ability bias is greater in an era with greater return to ability or with a more meritocratic relationship between schooling and ability. Herrnstein and Murray (1994) argue that both of these factors are at work in the modern economy.

Ability bias is usually discussed as a problem of omitted variables. (See, for example, Griliches (1977) or Chamberlain and Griliches (1975).) Include the missing ability variable and--except for problems of measurement error--there will be no bias. The conventional formulation of the ability-bias problem ignores the strong dependence between education and ability that Herrnstein and Murray (1994) argue has become stronger in recent years. If the dependence between ability and education becomes too strong, it is impossible to isolate the effect of education from ability even when the latter is perfectly observed. This gives rise to the logically prior problem of sorting bias, which this paper discusses.

Table 1 shows that there are very few white male college graduates with low ability in the NLSY. Further, there are no white men with postgraduate education in the lowest-ability quartile; so, for that ability quartile, no estimate of the wage gain of such education is possible. For many schooling-ability pairs, the cells are empty (or nearly so), which makes it difficult to isolate separate ability effects and schooling effects and difficult, if not impossible, to identify main effects of ability and education. In the limit, if ability and education are perfectly stratified, returns to education cannot be isolated from returns to ability, even if ability is perfectly measured. Empirically, the two are indistinguishable.(1)

TABLE 1.--PERCENT OF HIGHEST GRADE COMPLETED BY ABILITY QUARTILE AGE 30, WHITE MALES NUMBER OF OBSERVATIONS: 1621

 
Highest Grade 
Completed       Quartile   Quartile   Quartile   Quartile 
                   1          2          3          4 
 
     7            2.0        0.0        0.0        0.0 
     8            6.7        0.5        0.0        0.0 
     9           10.4        1.7        0.2        0.0 
    10            7.9        3.2        0.0        0.0 
    11            9.6        2.7        1.0        0.0 
    12           54.0       63.2       46.9       22.5 
    13            3.9        7.2       11.1        4.4 
    14            3.0        7.9       10.1       10.6 
    15            0.5        1.7        3.9        4.9 
    16            2.2        9.6       19.4       33.6 
    17            0.0        1.0        1.7        5.2 
    18            0.0        0.5        3.0        8.4 
    19            0.0        0.5        1.2        5.4 
    20            0.0        0.2        1.0        4.9 

Notes: 1) Here, ability is defined as general intelligence, or g. We compute g as the ASVAB test score vector times the eigenvector associated with the largest eigenvalue in the test score covariance matrix.

2) Sample includes all respondents who were employed, out of school, and had valid observations each year from age 24 to age 30. Anyone receiving more schooling after age 30 was excluded.

Missing data also complicate attempts to separate the effects of age and time. Estimates of the role of ability in explaining the increasing return to schooling that are reported in the recent literature follow the same people or repeated cross-section samples of the same cohorts over time. To follow the same people or cohort over time is also to follow them as they age, and the econometric problem created by such samples is more severe than the usual age-period-cohort effect problem.(2) Figure 1 is a Lexis diagram for a single cohort of a specified initial age followed over time. Shaded cells indicate the data that exist for each age and time period. If panel data or repeated cross-section data consist of only a single age cohort, age and time are hopelessly confounded, and it is impossible to identify separate age and time effects. Even with multiple age cohorts (see, for example, figure 2 for the data structure of the NLSY panel), there are many empty cells. The "main effects" for time or age--defined as averages over entire rows and columns--cannot be computed. (In the age-period-cohort problem, these averages can be identified if cohort effects are suppressed.) Some of the components that are required to form these means are missing. It is also impossible to identify interactions associated with the empty cells without imposing parametric structure (for example, that age and time effects are linear so that trends fit …