Appendix

Comment on issues in the interpretation of empirical evidence on human capital

Cross-country growth regressions

Brock and Durlauf (2000) raise three main “questions” about current empirical practice in the study of the determinants of growth. These are relevant to deciding how much weight to place on the available evidence – particularly that presented in OECD (2000b).

Model uncertainty due to theory uncertainty

Cross-country growth regressions are limited by data availability and low degrees of freedom in the variables that can be included. Due to multicollinearity and missing variable bias, estimated co-efficients can vary widely in different specifications. Growth theory is “open ended” as to which variables should be included[81]. Brock & Durlauf consider that previous strategies (e.g. extreme bounds analysis) to address model uncertainty are insufficiently systematic, (and in some respects misguided), to yield useful predictions for policy purposes[82].

The most recent OECD study (OECD, 2000a) appears to take considerable care in testing the robustness of the co-efficient estimates across a range of different specifications, including: introduction of country-specific time dummies; sample variations across countries and over time; estimation of standard cross-country regressions and panel data regressions based on five-year averages; identification of and controls for outliers; exclusion and inclusion of various countries. However only a limited range of variables (guided by theoretical considerations about their influence on growth) are included in alternative specifications. The order of magnitude of the co-efficient on human capital is robust to all these specifications.

Nevertheless, the study probably falls considerably short of the sort of policy focused systematic testing and summarising of the results of alternative models recommended by Brock and Durlauf. The OECD (2000a) authors themselves note that the human capital variable may be picking up the effects of omitted variables.

Model uncertainty due to heterogeneity uncertainty

According to Brock and Durlauf (2000): “The vast majority of empirical growth studies assume that the parameters which describe growth are identical across countries… the assumption of parameter homogeneity seems particularly inappropriate when one is studying complex heterogeneous objects such as countries”. Moreover, a number of studies have shown this assumption to be incorrect.

OECD (2000b) addresses this issue reasonably well, in two ways:

• The sample is restricted to a number of countries where an assumption of homogeneity is more plausible.
• The assumption of homogeneity across countries is limited to a small number of variables that are, on theoretical grounds, believed to influence the long-run steady state output path. The assumption is tested in the data.

Direction of causality

Brock and Durlauf (2000) note: “Many of the standard variables which are used to explain growth patterns – democracy, trade openness, rule of law, social capital, etc. are as much outcomes of socioeconomic relationships as growth itself”. Hence simple regressions should not be interpreted as structural. Even the use of instrumental variables is likely to be flawed, given model uncertainty (it is difficult to eliminate the possibility that an instrumental variable is correlated with omitted growth factors in the regression).

Commenting on a similar study to OECD (2000b), de la Fuente[83] argues that this is less likely to be an issue where human capital is measured as a stock rather than through enrolment rates – because the stock changes only slowly over time. This argument is not conclusive, because investment rates may be correlated with (anticipated) growth rates – faster growing countries may invest more resources in increasing the stock of human capital – and it is variation in the latter across countries and across time that is identifying effects in the regression analysis in OECD (2000b). For instance, a recent study, Bils and Klenow (2000), concludes that much of the association runs from growth to schooling.

Measurement error

Recent studies (e.g. Krueger and Lindahl, 2000; de la Fuente and Domenech, 2000) show that earlier work on the relationship between the stock of human capital and economic growth was subject to significant measurement error in the human capital variable. This appears to explain the failure of many earlier studies to find a significant relationship, particularly when change in the human capital stock was used as the dependent variable (thus magnifying the effect of mis-measurement). OECD (2000b) uses a much-improved dataset constructed by de la Fuente and Domenech for OECD countries, and this undoubtedly contributes to the much stronger relationship found.

On the other hand, as David (2001) points out, even the best measurement of average years of schooling remains a very crude proxy for the diverse theoretically relevant concepts of human capital. Relevant dimensions not captured include the quality of education (in some studies proxied by results in internationally comparable achievement tests; in others, by resource inputs), and how education is distributed among the employed workforce, as opposed to the working age population. Other models (see Romer, 2000) suggest that it is the numbers of scientists and engineers that is relevant, through effects on research and development, and technology creation and adoption.

Microeconomic evidence

As Temple (2000) notes: “The evidence that earnings are positively associated with schooling is robust and uncontroversial; the obvious difficulty lies in giving this association a causal interpretation”.

An important empirical problem is the omission (through lack of data) of variables that are correlated with both schooling and earnings – such as family background, and ability. If more able individuals have higher earnings regardless of education, then the effects of education on productivity are likely to be overstated. Another related problem is that the costs and benefits of education are likely to differ across individuals, and may be thus correlated with the explanatory variables (such as years of schooling), thus also leading to biased estimates.

Econometricians have attempted to overcome these problems using a range of techniques. They have mainly used situations – so-called “natural experiments” – where variations in schooling occur for reasons likely to be independent of the unobserved characteristics (e.g. ability) of the individuals studied. These techniques tend to find that labour market returns to schooling are similar to those found in conventional studies.

Nevertheless, even these studies are not conclusive. A further set of models suggest reasons why earnings may be correlated with schooling even if schooling has no effect on productivity. High-ability individuals, who find schooling less difficult, may stay in school for longer because this decision signals their ability to employers. The results from “natural experiment” studies can be interpreted in a way consistent with these studies.

Signalling models predict that the social returns to education (in terms of earnings) will be lower than the private returns. Acemoglu and Angrist (2000) use historical variations in compulsory schooling laws across states in the United States as a way to test this, and find that social and private returns to additional years of schooling are very similar. Acemoglu (2001b) concludes from this that signalling effects are likely to be weak (at least at this level of schooling)[84].

More generally, the problems in inferring a causal relationship between education and labour earnings are likely to apply a fortiori to the relationship with other outcomes that influence or constitute well-being. Available data sets and research effort focussed on these issues are many times weaker than in the case of education and earnings.

Similar issues apply in understanding the determinants of educational achievement and attainment[85]. Consequently, considerable care is needed in interpreting the empirical evidence to select suitable human capital policies to improve outcomes. Uncertainties in the evidence need to be identified, and factored into policy design, taking account of the risks inherent in the nature of the proposed policy. Experimental design and evaluation may sometimes be the best means to provide sufficient confidence to justify large-scale implementation of new policies.