The impact of literacy on earnings

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A simple theoretical framework
Estimation results

A simple theoretical framework

We now turn to examining the instrumental importance of literacy in terms of its impact on earnings. We saw in the previous section that literacy is primarily determined by schooling. This immediately raises the possibility that commonly estimated returns to schooling are in fact capturing the returns to literacy. To both represent this point and provide a framework for interpreting the earnings regressions that follow, we begin by presenting a simple hedonic model of earnings generation. The discussion that follows is based on Green and Riddell (2003).

Assume that each worker potentially possesses a range of skills and can possess each of them in varying amounts (including zero). To make the exposition simpler, we will couch our discussion in terms of three skills. Individual earnings are determined according to some function of the skills an individual possesses and puts into use, as follows:

where E_i are earnings for individual i in our sample year, G_i^k is the amount of skill k that person i sells in the market, and ε_i is a disturbance term that is independent of the skills. We think of the disturbance term as capturing either individual idiosyncratic events that are independent of the skill levels or measurement error in earnings. We interpret the f(.) function as an earnings generation function derived ultimately from an overall production function that is separable in other (non-skill) inputs. Thus, by characterizing the f(.) function, we can learn about the importance of the various skills and how they interact in production. To help in focussing ideas, we will think of G¹ as cognitive skills of the type measured in literacy tests, G² as other (perhaps manual) skills that are not captured in such tests and might be acquired through work experience, and G³ as non-cognitive characteristics such as persistence that might be partly acquired through schooling.

Based on 1), we can construct a set of skill price functions given by,

Note that the prices can vary according to the complete bundle of attributes the individual sells. We are interested in characterizing this set of skill price functions. Once we have done that, we will know the relative importance of the various skills in production and also whether the different skills are complements or substitutes in production.

Characterizing either 1) or 2) would be a relatively straightforward exercise if we observed the skills, G_i^k. Typically, of course, we do not observe them. What we do observe is some of the inputs used in generating the skills. To see how they enter our framework, consider a set of production functions for generating the skills:

where h indexes the attribute type, yrs corresponds to years of formal schooling, exp is years of experience in the work force and θ is a vector of innate abilities. Note that we differentiate between abilities (which are innate) and skills (which may be acquired and are directly useful in production). The vector of abilities, θ, may include both cognitive and non-cognitive elements. That is, non-cognitive abilities such as persistence could be useful in generating both non-cognitive and cognitive skills.

If we do not observe the G_i^k's directly, we can obtain an estimating equation by substituting the equations given by 3) into 1). This then yields a quasi-reduced form specification for annual earnings given by,

Thus, we are considering an hierarchical model in which covariates standardly used in wage regressions are inputs into skill production and these skills (plus an independent error term) completely determine wages.

Now, let us examine the partial derivatives of earnings with respect to each of the skill production inputs (e.g., schooling, experience or an element of the ability vector). The partial derivative associated with one of the inputs, x, can be expressed as,

where we suppress the i subscript for simplicity. Thus, if x corresponds to years of schooling, yrs, then equation 5) says that the observed effect of an additional year of schooling reflects the effects of an extra year of education on the production of each attribute times the price paid for that attribute. It is apparent from equation 5) that with measures only of earnings and observable inputs used in producing attributes, we cannot make any statements about skill production or how skills combine in production apart from statements that either a critical combination of the derivatives on the right hand side of 5) are zero (and, hence, δE/δx = 0) or some of them are not. If we have individual observations on a skill, e.g., G¹, however, we can potentially say much more.

With G¹ observed, our quasi-reduced form earnings function becomes:

The derivative of this function with respect to G1 corresponds to the attribute price function, r₁ - though, now we need to express the price as a function of yrs_i, exp_i, and θ_i:

With the price function given in 7), we cannot fully specify the interactions of G¹, G² and G³ in production but we can learn more about them. In particular, the derivatives of r₁ with respect to the skill production input, x, is equal to (again suppressing the i subscript):

Further, we can consider the derivative of g* in equation 6) with respect to x:

With observed values for the derivatives, δr₁/δx and δg*/δx, we may be able to place restrictions on the f function. Thus, the fact that δh₂/δx and δh₃/δx appear in all these functions raises the possibility of putting restrictions on the production functions for the non-observed skills based on sign and significance patterns in the observed derivatives. With these restrictions in hand, we may further be able to place restrictions on the δr₁/δG^k terms. In our framework, these latter terms reflect interactions in production of the non-observed skills with G¹.

We can also learn something about the production of G¹ from the differences between the derivatives, 5) and 9). These derivatives (e.g., the derivative of earnings with respect to schooling first not conditioning and then conditioning on G¹) differ by the term δf/δG¹ * δh₁/δx. Thus, the difference between these observed derivatives reflect the extent to which the coefficient on, for example, schooling in a standard earnings regression reflects the channel of added schooling generating added earnings through added cognitive skill creation. Given that we observe G¹ directly, we can go further and derive insights into the production of G¹ (as reflected in the δh₁/δx terms) through direct estimation. That is essentially what we did in the previous section, where our main conclusions were that literacy is primarily produced through formal schooling and deteriorates with time after the person leaves school. The latter effect may be offset to some (likely relatively minor) extent by having a job that uses literacy skills.

Note that, as expressed in equation 7), the skill price facing an individual will be a function of the ability vector, θ_i. In terms of our framework, this implies that the impacts of elements of the θ_i vector on r₁ can be written as in equation 8) with x replaced by the relevant element of θ_i. That is, if we could observe θ_i, we could learn more about the interactions of the various skills in production. In terms of empirical implementation, the fact that r₁ = δE/δG¹ could vary with unobservables points to the use of quantile regressions since they effectively allow us to observe derivatives of earnings with respect to observable variables at the different values of the unobservables that generate the various conditional quantiles. Moreover, if θ_i were a scalar rather than a vector, the h() functions were monotonic in θ_i and the f function were monotonically increasing in skills then increasing quantiles of the earnings distribution, conditional on G¹, yrs and exp, would be associated with increasing values of θ_i and we could sign δr₁/δθ based on how δE/δG¹ varies across increasing conditional earnings quantiles.

Estimation results

We present estimation results from mean regressions using the log of weekly wages in Table 7. We run the regressions on a restricted sample that includes only individuals with weekly wages that are over $50 and below $20,000 per week to eliminate a few extreme outliers. We also cut out the self-employed because their earnings will not fit in a model of the type outlined above without making further extensions to include returns to capital. The OLS 1 column shows the results from a standard regression with a female dummy, years of schooling, experience and experience squared as covariates. The results are extremely standard in terms of their magnitudes and sign patterns (see Card (1999) for a review of the very large relevant literature). In the OLS 2 column, we add our average literacy variable. This variable is the simple average of the 4 literacy scores. We take this approach because this is what is suggested by our factor analysis of the scores. Essentially, that analysis indicates the scores are highly collinear. We have estimated specifications in which we include all 4 scores separately. In those estimations, Document literacy enters statistically significantly with a coefficient of 0.0021, Numeracy enters statistically significantly with a coefficient of 0.0011 and Problem Solving and Prose literacy have smaller, not statistically significant and offsetting coefficients. Note that these significant separate effects essentially add up to the estimated coefficient on average literacy presented in Table 7. This suggests that Numeracy may have separate effects from the other three types of literacy and that its effects are smaller than whatever is being captured (primarily) in the document score.

Adding average literacy to our standard earnings regression leads to a reduction in the derivative of log earnings with respect to education from 0.087 without the literacy variable to 0.069 when it is included. This is a reduction of about 20%, suggesting both that literacy skills play an important role in the returns to education and that education has a substantial impact on earnings over and above the impact related to production of literacy skills. This effect, however, is noticeably smaller than observed in the IALS 1994 (Green and Riddell (2003)). This may reflect a more flawed earnings measure in the earlier dataset.

In contrast to the effect on the schooling coefficient, the coefficients on the experience variables are unchanged when we introduce the literacy variable. This is a direct reflection of the fact that literacy generation is not related to age or experience in the cross-section. In terms of the framework set out above, experience does not enter the literacy skill production function and so the first term on the right hand side of equation 5 is zero. The implication is then that the derivative with respect to experience is the same whether or not we condition on literacy. In fact, however, we have seen that age does enter the literacy production function in a negative way but it is offset by cohort effects that are declining across recent generations. If the IALS 1994 had a comparable earnings measure and we could estimate a pooled cohort regression of the type we estimated for literacy in the previous section then we would see that literacy does have an impact on those estimated coefficients. In particular, a standard finding that earnings increase with age for a given cohort estimated without the inclusion of the literacy variable would be converted to an even steeper slope with the inclusion of the literacy variable.¹ The implication is that any increase in earnings with age must be due to an even more substantial increase in returns to non-literacy skills of a type that are acquired through working since literacy skills themselves are actually declining.

Finally, the direct impact of literacy skills on earnings is substantial. A 25 point increase in the average literacy score (the equivalent of about 1/2 of a standard deviation in the literacy score distribution) has an impact equivalent to an extra year of schooling.

As mentioned in our theoretical discussion, our estimation may be affected by standard omitted variables bias. In particular, the error term in the regression may include various types of ability which are correlated with the included variables. Typically, ability is assumed to affect both schooling choices and earnings, leading to biased estimates. Given our specified model, if we assume that unobserved cognitive abilities only affect the generation of cognitive skills and other, non-cognitive abilities do not affect the generation of cognitive skills then literacy will not be correlated with the error term and does not, itself, represent an endogeneity problem. However, we still need to address the potential endogeneity of schooling. We do this using province in which the individual resided and interactions of it with age as our instrument as we did in the literacy estimation. As before, we control for province of current of residence at the same time. In fact, all of the specifications include controls for current province whose effects are not reported in the table for the sake of brevity.

The results from instrumenting for schooling when the literacy variable is not included are reported in the IV 1 column of Table 7. Instrumenting reduces the coefficient on schooling slightly, which is suggestive of endogeneity problems with the simple OLS estimation. In the IV 2 column, we repeat this exercise but also include the average literacy effect. The instrumenting yields a somewhat smaller schooling coefficient than in the simple OLS results in the OLS 2 column. As in the simple OLS estimates, introducing the average literacy score reduces the schooling coefficient by approximately 20%. The literacy score coefficient itself rises somewhat but is of roughly the same order of magnitude as in the OLS 2 column. Thus, our main conclusions are not altered by instrumenting.

As discussed earlier, our theoretical framework points to advantages from using a quantile regression framework. We present the results of quantile regression estimation for the 10^th, 25^th, 50^th, 75^th and 90^th quantiles in Table 8. The key implications from the estimation are as follows. First, returns to both schooling and experience decline across quantiles. The finding of heterogeneity in returns to education across the earnings distribution has been observed by previous authors. Buchinsky (1997) finds returns to education that rise across quantiles for all experience groups. Arias et al. (2001) estimate similar quantile regressions using US twins data and incorporating approaches to address endogeneity. With non-IV estimation, they find that the coefficient on education rises from the 10^th to the 50^th percentile but does not change across the upper portion of the distribution. When using instruments to address measurement error and twins status to address ability bias, their estimated schooling coefficients appear relatively similar across the distribution but are not very precisely estimated in the tails.

Perhaps the most interesting result in Table 8 is the relative lack of variation in the coefficient on the literacy score variable across the quantiles. While the coefficient for the 10th quantile appears substantively smaller than those at the other quantiles it is not actually statistically significantly so. Moreover, if we run quantile regressions at the quantiles directly surrounding the 10^th quantile (e.g., the 5^th and 15^th quantiles), we obtain estimated literacy effects that are almost exactly the same as those reported for the upper quantiles – the 10^th quantile appears to be a bit of a statistical outlier. In the context of our theoretical model this implies that cognitive skills do not interact with other attributes in earnings generation. Thus, other attributes such as beauty (Hamermesh and Biddle (1994)) and leadership skills (Kuhn and Weinberger (2005)) may contribute to individual earnings but their contributions are not enhanced by having more literacy skills. Literacy skills are not a silver bullet that both contributes directly to earnings and increases returns to other attributes. Put another way, to the extent that leadership skills contribute to earnings and perhaps productivity, these results do not suggest that firms should target leadership training by cognitive skill level: workers with various cognitive skill levels will receive the same benefit from the training.

Finally, our estimates of the effects of literacy presented here are identical to those we found with the IALS 1994 data (Green and Riddell (2003)). In both cases, with standard specifications, the coefficient on average literacy in a median earnings regression is 0.0029. We regard this as something of a fluke, since the earnings measures in the two studies are not the same and other variables have different estimated effects in the two studies. However, the key patterns estimated using the IALS 1994 hold up, including the size of the literacy effect and the fact that the literacy effect does not vary across quantiles. As in that study, we conclude that literacy is an important determinant of earnings but that there is a great deal of earnings variation that is accounted for by other factors.

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Note

1. We cannot prove this result but it is strongly suggested by the relationship between literacy and age combined with standard omitted variable bias derivations.