13 statistically significant, although, converting to an annual growth rate, it does appear, dividing the estimated coefficient of 13 by the 27 years of the period, that one extra year of education in 1960 raises the growth rate of a developing country by 0.48% p.a. over the period 1960-87. This term can be regarded as representing a pure externality effect, with a higher level of education raising the rate at which technical progress is possible. It compares with a statistically significant figure of 0.14% p.a. found by Weale (1992) for the developed countries. The coefficients on increased availability of education have no counterpart in Barro's study. Nevertheless, the _World Development Report_ study suffers from the presence of a number of poorly determined coefficients, and the imposition of some theoretical restrictions, similar to those applied to the study discussed next, would help in the interpretation of the results.

Mankiw, Romer and Weil (1992) present the results of an exercise similar to those of Baumol and _World Development Report, 1991,_ but with fewer explanatory variables, and using what is probably a less satisfactory measure of educational attainment. They explain the increase in output per person of working age between 1960 and 1985 by means of 1960 output per person of worldng age, the average investment ratio, the increase in population and the average fraction of the workforce attending secondary school (SCHOOL), with all variables being expressed in logarithms. Dividing their coefficients by 25 to convert them to explain growth at an annual rate, the coefficient on SCHOOL falls to 0.011 and that on the log investment rate to 0.020. However one must also divide Mankiw, Romer and Weil's coefficients by the sample means in order to make them comparable with those figures estimated in levels rather than logs. With an average of around 20% of the product invested, Mankiw, Romer and Weil's coefficient on investment would be comparable to a figure of 0.1 in Barro's equatioti.

It is still not possible to make a direct comparison of the education effects because Mankiw, Romer and Weil look at the fraction of the working-age population attending secondary school and not at the fraction of the school-age population attending secondary school. However, if we assume that 38% of the relevant age group attended secondary school over the period (being the mean of the 1960 and 1985 figures quoted by Barro), then the coefficient of 0.011 must be divided by 0.38 to make it comparable with Barro's. The resulting figure, of 0.027 is higher than Barro's estimate of 0.018, but it must be remembered that Mankiw, Romer and Weil omit any effect from expansion of primary education. If expansion of primary education is correlated with that of secondary education, then their regression would be expected to overstate the effects of secondary education. One might also be concemed that they use average school attendance during the sample period, and there is a risk of simultaneity bias arising from interaction between this and output growth. Furthermore, the analysis of section 4 implies that there is also a risk of simultaneity between education and population growth, suggests the desirability of using instrumental variables.