A replication of ‘Education and catch-up in the Industrial Revolution’ (American Economic Journal: Macroeconomics, 2011)

Although European economic history provides essentially no support for the view that education of the general population has a positive causal effect on economic growth, a recent paper by Becker, Hornung and Woessmann (Education and catch-up in the Industrial Revolution, 2011) claims that such education had a significant impact on Prussian industrialisation. The author shows that the instrumental variable they use to identify the causal effect of education is correlated with variables that influenced industrialisation but were omitted from their regression models. Once this specification error is corrected, the evidence shows that education of the general population had, if anything, a negative causal impact on industrialisation in Prussia. (Submitted as Replication Study) JEL I25 N13 N63 O14


Introduction
Many theories of economic growth emphasise the role of education as a causal factor in the growth process. 1 In this context, education is often interpreted as meaning education of the general population, and this is the sense in which the term 'education' will be understood throughout the present paper. However, cross-country data for the second half of the twentieth century provide no clear evidence that such education leads to faster economic growth (Pritchett 2006). European economic history also provides little support for the view that education of the general population has an important causal influence on economic growth. Although both education levels and income per capita increased in most European economies between 1550 and 1900, no study has so far been able to show that this association reflects a causal effect of education on growth rather than rising incomes enabling people to consume more education. This lack of evidence of a role for education of the general population in historical economic growth has led the recent literature to focus on the contribution of the knowledge and skills of particular groups to pretwentieth century economic growth (Kelly et al. 2014, Squicciarini and Voigtländer 2015, Dittmar and Meisenzahl 2016. One study does, however, claim to provide evidence that education of the general population had an important causal influence on industrialisation in the nineteenth century. Becker, Hornung and Woessmann (henceforth BHW) argue that such education made an important contribution to the industrialisation of Prussia. 2 The Prussian experience, they contend, is consistent with models of technological diffusion in which education contributes to growth by facilitating adoption of new 1 See, for example, Lucas (1988), Romer (1990) and Mankiw et al. (1992). 2 BHW (2011) technologies. 3 In BHW's view, education played an important role in enabling Prussia, as an industrial follower, to catch up with Britain, the technological leader, during the nineteenth century. If correct, BHW's analysis of education and industrialisation in Prussia would be very significant, as it would provide, for the first time, evidence that education of the general population had a causal effect on economic growth before 1900.
To deal with potential two-way causation and identify the causal effect of education on growth, BHW use pre-industrial education as an instrumental variable for education during the period of Prussian industrialisation. However, as this paper will show, a number of variables that influenced industrialisation and were correlated with pre-industrial education are omitted from the cross-section regression specifications on the basis of which BHW conclude that education contributed to industrialisation. Pre-industrial education is therefore not a valid instrument in these regressions, and hence the estimated effects of education in these regressions do not correspond to the causal influence of education on industrialisation. When these omitted variables are included in the regression models, the estimated effects of education change dramatically. In the first half of the nineteenth century, the causal effect of education on overall industrialisation turns out to be negative and both economically and statistically significant. In the second half of the century this causal effect is negative, of modest economic significance, and not statistically significant.
When the regression models are specified in such a way that pre-industrial education is a valid instrument, therefore, there is no evidence that education had a positive causal influence on overall industrialisation in Prussia: if anything, the causal effect was negative. Prussian experience in the nineteenth century cannot be used to support the view that education of the general population plays an important positive role in the growth process, whether by facilitating the adoption of new technologies or by any other causal mechanism.
2. The BHW analysis BHW analyse the contribution of education to Prussian industrialisation using a dataset for the 334 Prussian counties that existed in 1849. 4 The major institutional reforms which took place in Prussia after military defeat by France in 1806 made it possible, by about 1820, for Prussia to benefit from the technological advances that had occurred in Britain. Prussia's own industrial revolution began in the mid-1830s.
BHW argue that the change in Prussian institutions which made this possible can be treated as exogenous from the point of view of their econometric analysis. After this exogenous change, different Prussian counties industrialised to differing extents, and the causal effect of education can be identified, they argue, by analysing the relationship between these differences and differences in the counties' educational levels.
BHW recognise that any causal relationship between education and industrialisation may go in both directions. The growth of factory production could have created new occupations with lower educational requirements, decreasing the general level of education; or it could have increased the demand for human capital, increasing educational levels. Conversely, if industrialisation raised living standards, these higher incomes might have increased the demand for education. Any attempt to identify the causal effect of education on industrialisation must take account of this 4 County is BHW's translation of the German word Kreis. A Kreis is an administrative unit which is closer to the American than to the British sense of county. possible reverse causality. BHW do so by carrying out an instrumental variables (henceforth IV) analysis of the cross-section effect of education on industrialisation in 1849 and 1882. They use the level of education in 1816, measured by enrolment in elementary and middle schools as a share of the population aged from six to 14, as an instrument for later education. Their argument is that education in 1816 can be used to isolate the component of subsequent education which did not depend on subsequent industrialisation, and thus to identify the causal effect of education. BHW further argue that differences in education levels among Prussian counties in 1816 reflected exogenous historical idiosyncracies and therefore had no direct effect on subsequent industrialisation. Based on these considerations, they argue that education in 1816 is a valid instrument for subsequent education.
Pre-industrial education is more likely to satisfy the requirement for a valid instrument -that it has no direct effect on subsequent industrialisation -if the crosssection regression models include other measures of the pre-industrial characteristics of each county. This reduces the likelihood that pre-industrial education is correlated with the error term in the regression models because of being correlated with other pre-industrial features of counties which have been incorrectly omitted from these models. BHW therefore include several such measures in their preferred specifications. As indicators of pre-industrial development, the share of the population living in cities in 1816 and the number of looms per capita in 1819 are included as regressors. To proxy for mineral resource availability, the number of steam engines used in mining in 1849 is included. The number of sheep in 1816 is used as a proxy for the availability of wool for the textile industry. The share of farm labourers in the population in 1819 is included as an indicator of whether a county was less likely to industrialise because of its more agricultural orientation. Various measures of pre-industrial public infrastructure which might have influenced subsequent industrialisation are also included as regressors: the number of public buildings per capita in 1821, a dummy variable registering the presence of paved inter-regional roads in 1815, and a measure of the capacity of river transport ships in 1819.
Prussian industrialisation occurred, BHW argue, in two phases: the first from approximately 1835 to 1850, the second during the latter half of the nineteenth century. 5 Consequently they estimate separate cross-section regression models of Prussian industrialisation in 1849 and 1882. The definitions of the variables used for their main analysis differ somewhat between the two periods. Total industrialisation in each county in 1849 is measured as the share of factory employment in total population, and BHW also disaggregate this measure of total industrialisation into three industrial sectors -metal, textile, and all other branches. Total industrialisation in 1882 is measured as the share of manufacturing employment in total county population, again distinguishing between the same three sectoral components.
Education in 1849 is measured by the average number of years of primary schooling in the 1849 working population in each county, which is constructed from school enrolment data available for 1816 and 1849 and population data for 1849. 6 For the 1882 regression, education is measured by the literacy rate in 1871, defined as the share of those able to read and write in the total population aged 10 or over at this date.
The regression models also include measures of basic demographic and BHW find that pre-industrial education is strongly correlated with education in both 1849 and 1871 and thus satisfies the requirement of being a relevant instrument for IV estimation of the causal effect of education on industrialisation. The crosssection regression models for both periods yield estimates of this effect for total industrialisation and non-textile industrialisation that are both economically and statistically significant. However, BHW find no evidence that education contributed to textile industrialisation, which, they suggest, may be because in the textile sector technological developments were more incremental and child labour was more important. BHW conclude from their cross-section results that, except in textiles, education was an important causal influence on Prussian industrialisation in both its phases.
The BHW results for their preferred cross-section regression models of total industrialisation in the first and second phases of Prussian industrialisation are shown in Table 1, together with the results that I obtained by re-estimating their models. As Table 1 shows, I was able to reproduce the BHW results exactly. The estimated effects of education on total industrialisation correspond to elasticities of 0.53 in the first phase of industrialisation and 0.73 in the second phase. 7 As an alternative to cross-section regression models, BHW also combine their observations for 1816, 1849 and 1882 into a panel dataset which they use to estimate fixed-effect models. These models control for any time-invariant unobserved heterogeneity which might be present in the cross-section models. BHW conclude that the results from their fixed-effect panel regressions confirm those from their crosssection regressions: education had an important causal effect on Prussian industrialisation.
BHW's conclusion that education played an important role in Prussian industrialisation is based on a particular econometric strategy. But is this strategy justified? The remainder of this paper argues that it is not. BHW's preferred regression models omit a number of variables that measure regional effects, which the historical literature has found were important influences on Prussian industrialisation.
BHW's instrumental variable -education in 1816 -is correlated with variables that measure regional effects, and thus it is likely that, in their preferred models, BHW's instrument is not valid. Furthermore, BHW do not use a systematic model selection procedure to choose, from the large number of variables that might have influenced Prussian industrialisation, a regression model with which to conduct inference about the effects of education on industrialisation. When these problems are addressed, it 7 Here and throughout the paper all reported elasticities are calculated at sample mean values. turns out that the data available for nineteenth century Prussia fail to yield empirical support for the view that education played a positive causal role -rather the contrary.

Regional effects and regression models of Prussian industrialisation
Any satisfactory analysis of the relationship between education and industrialisation in Prussia must take into account regional effects (Tipton 1976  Prussia thus provides another reason why regional effects need to be taken into account in analysing Prussian industrialisation.
To some extent, BHW acknowledge these institutional and legal differences across Prussia in their tests of the robustness of their preferred regression specifications. One of these involves the addition of a dummy variable for the western parts of Prussia, which indicates whether a county was in the Rhineland or Westphalia. However, this only allows for limited provincial differences, whereas, as the discussion above shows, there are reasons to expect differences both between the  and 7 not included as regressors are the latitude and longitude of counties, because these are very strongly correlated with the provincial dummy variables and the measures of distance to Berlin, London, and nearest provincial capital.
The results for year of annexation and province reported in Table 2   Before investigating the implications of this finding for estimates of the causal effect of education on Prussian industrialisation, I consider some issues in the specification of appropriate regression models of Prussian industrialisation.

Specification of regression models of Prussian industrialisation
Adding the year of a county's annexation by Prussia, province dummies, and interactions between these variables as regressors to BHW's preferred models yields very strong evidence that these variables should be included. The null hypothesis that the coefficients of year of annexation, the province dummies, and their interactions are all zero is strongly rejected both for overall industrialisation and its three sectoral components. Furthermore, the addition of these variables to BHW's preferred models changes the estimated effect of education on industrialisation: there is no evidence at all that education had a positive effect in the first phase of Prussian industrialisation, and only limited evidence of a positive effect in the second phase.
However, selecting models by adding variables to a basic specification is not a satisfactory approach. The limitations of the specific-to-general procedure have been known at least since Anderson (1962) showed that the optimal procedure for the choice of degree of a polynomial regression was a general-to-specific approach.
Correct inference about the effects of education on Prussian industrialisation requires an empirical model of industrialisation that can be justified by a convincing model In outline, the general-to-specific procedure involves starting with a very general regression model that is subjected to various tests of adequacy as a representation of the data-generating process. guarantee that just one model will be selected.
A criticism that is often levelled against this model selection procedure is that it involves data-mining -"the data-dependent process of selecting a statistical model" (Leamer 1978, 1). In much empirical economics, and certainly in the case of the determinants of Prussian industrialisation, some data-mining is unavoidable, because there are many plausible explanatory variables and no theoretical guidance as to which should be included in the regression model. The case for using the general-tospecific procedure is that it is a systematic method of model selection which has good properties, as Hendry and Krolzig (2005) and Campos et al. (2005) show. In particular, the two most serious concerns about this procedure -that selection of variables by significance tests will lead to biased coefficient estimates and that treating a selected model as if it were certain will result in under-estimates of coefficient standard errors -do not appear to be important in practice.
In order to provide more satisfactory empirical models of Prussian industrialisation with which to make inferences about the causal effect of education, I use the following version of the general-to-specific procedure. I begin with an over-  Table 2.
The general regression model was estimated by IV with the instrument for the education variable being education in 1816. The test of adequacy applied to the general regression model was whether the null hypothesis that the estimated coefficients did not differ between two subsamples could be rejected at the 0.05 level.
These subsamples were obtained by randomly dividing the full sample of 334 counties into two groups of equal size. This null hypothesis was always rejectedperhaps unsurprisingly, given that there were at least 30 variables whose estimated coefficients might differ between the two subsamples -and so the general model was expanded by allowing some variables to have different effects in the two subsamples. The general-to-specific model selection procedure used here is very different from the approach used by BHW to investigate the robustness of their preferred regression models, even though it uses most of the variables considered by BHW in their robustness checks. In Tables 6 and 7 of their paper, BHW report the results of adding 11 variables to their preferred specifications, but they do so in eight separate steps. Hence BHW's conclusion that their estimates of the effect of education on industrialisation are robust to the addition of the these variables is not justifiable, because piecemeal addition of possible regressors provides no information about whether the estimates are robust to the simultaneous inclusion of all these variables.

Cross-section estimates of the effect of education on Prussian industrialisation
What are the estimated effects of education on Prussian industrialisation that emerge from the model selection procedure discussed in the previous section? Table 3 presents the results for the first phase of Prussian industrialisation, in which the dependent variable is a measure of industrialisation in 1849, while Table 5 presents the results for the second phase, in which the dependent variable is a measure of industrialisation in 1882 while industrialisation in 1849 is included as a regressor. 19 Table 3 shows IV and OLS estimates of the terminal regression model for Prussian industrialisation in 1849 obtained using the general-to-specific procedure.

The first phase of industrialisation
The first-stage F statistic for the IV estimates in Table 3 Table 3 the respective IV and OLS estimates are similar, so it can be concluded that IV estimation is not required.
In contrast to the positive estimates of the effect of education on industrialisation reported by BHW in their Table 3, both the IV and OLS estimates of the effect of education on overall industrialisation in Table 3 Table 4. Dropping these 11 observations dramatically changes the estimated effect of education on industrialisation in the metal sector: neither the IV nor the OLS estimate is statistically significant, and these point estimates correspond to elasticities that are only about one-quarter of the size of those obtained using the full sample. However, the estimated effect of education on overall industrialisation remains negative and statistically significant, though it corresponds to a smaller elasticity than that obtained from the full sample. When the influential observations are dropped, the negative effect of education on industrialisation is primarily driven by the negative effect in textile industrialisation. 24 Following the approach of Belsley et al. (1980), an observation was identified as influential if the absolute value of the difference between the estimated regression coefficient for education with all observations included and with one observation excluded, scaled by its standard error in the latter case, was greater than 2/sqrt(334). The dramatic change in the estimated effect of education on industrialisation in the metal sector when 11 observations are dropped from the sample casts some doubt on the robustness of the estimates in Table 3. However, the only reason for dropping these observations is that they are identified as influential by a mechanical procedure, and it can be argued that this is not a compelling basis for so doing: the sample is what it is, and it should not be altered in the absence of clear evidence that particular observations are outliers because of mismeasurement or other anomalies.
Thus it is unclear whether the negative effect of education on Prussian industrialisation in the first phase is driven by the effects of education in the metal or in the textile sector. However, it is clear that the effect of education on overall industrialisation was negative.
A possible explanation of the negative causal effect of education on industrialisation is that greater education reduced the supply of child labour to factories, thus increasing the cost of labour and lowering the profitability of industrial activity. Some support for this interpretation comes from the debates preceding the enactment of the Prussian child labour law in 1839: many opponents of this new legislation were concerned that removing children from their jobs in order to send them to school would be damaging to industry (Anderson 2013). The negative effects in Table 3 are thus consistent with contemporary evidence on the Prussian economy.
The general-to-specific selection procedure yields a terminal model which includes several regressors that did not appear in BHW's preferred specification:  Table 3 the estimated effect of the Rhineland dummy is negative, in contrast to what might have been expected given the institutional advantages that the Rhineland is supposed to have had. The distance to London was smaller on average for counties in the Rhineland than for any other Prussian province: once this is taken into account, the effect on industrialisation in 1849 of being located in the Rhineland appears to be negative. 25 The fact that a number of province dummies and the share of Protestants appear as regressors in the terminal model of first-phase Prussian industrialisation selected by the general-to-specific procedure suggests that inference about the causal effect of education on industrialisation based on models that do not include these variables is likely to be misleading. As Table 2  included as a regressor. 26 By controlling for the level of industrialisation in 1849, these estimates show the effect of education on industrialisation in Prussia specifically during the period 1849-82. In these regressions, education is measured by the literacy rate rather than by years of schooling.
The first-stage F statistics for the IV estimates are all about 20 and the weakinstrument-robust confidence intervals are somewhat different from the standard one based on the asymptotic distribution of the IV estimator. Table 5 therefore reports both forms of 95 per cent confidence interval for the estimate of the coefficient of literacy.
The p values of the C statistic reported in Table 5    corresponding to an elasticity of 0.673. Table 3, the IV estimate of the effect of education on metal industrialisation in Table 5 is large and negative, though not statistically significant. Is this finding robust to the exclusion of influential observations? Table 6 shows the results of re-estimating the second-phase terminal model after dropping 18 observations that were identified as influential using the same procedure as described in footnote 24. Although the IV point estimate of the effect of education on industrialisation in the metal sector is still not statistically significant, it corresponds  Table 5 to some extent, but not enough to change the main finding.

As in
The negative though statistically insignificant IV estimate of the effect of education on overall industrialisation in Prussia during the period 1849-82 shown in Table 5 is very different from the positive and both statistically and economically significant estimate reported by BHW in equation (2) of their Table 5. However, BHW's preferred regression specification for the second phase of Prussian industrialisation omits several variables which the general-to-specific procedure selects as relevant regressors in Table 5: the distance to London, the share of Protestants, landownership inequality, and a number of province dummies, both on their own and interacted with year of annexation. Some of these variables are correlated with the instrument for education in 1871, as Table 2 shows, and thus inference about the effect of education cannot be based on the BHW specification.
The results in Tables 3 and 5  is what BHW use. The need for IV estimation arises because, as a consequence of reverse causation, current education is expected to be correlated with the error term in the equation explaining current industrialisation. But this implies that lagged education will be correlated with the lagged error term, and this lagged error term is a component of the time-demeaned error term that is used in fixed-effect estimation. If current education is an endogenous regressor, lagged education will inevitably be correlated with the error term in the fixed-effect regression model and hence cannot be a valid instrument for current education in such a panel model. Lagged education simply cannot be used as an instrument in order to test whether any association between education and industrialisation in panel regression models reflects a causal influence of the former on the latter. Unfortunately, BHW's data do not contain any alternative instruments for education in panel regression models, and thus it is not possible to analyse the causal effect of education on industrialisation in such models.
This leads to an ineluctable conclusion: panel analysis of the BHW dataset cannot throw any light on whether education had a causal influence on Prussian industrialisation.

Conclusion
The conclusion of this paper is simple: there is no evidence that education had a positive causal effect on overall Prussian industrialisation. Rather, in the first phase of Prussian industrialisation, education had an unambiguous negative influence on overall industrialisation, while in the second phase it had an effect that was negative but poorly determined. To be sure, in the period 1849-82 there is evidence that education had a positive causal effect on industrialisation in the non-metal non-textile sector, but in terms of the influence on overall industrialisation this was outweighed by negative effects in other industrial sectors. An important question for future research is why education had a clear negative effect on Prussian industrialisation in the first phase. The conjecture that greater education lowered industrialisation by reducing the supply of child labour to factories needs more thorough investigation. If increased education did cause industrialisation to fall by reducing child labour, the overall assessment of this negative effect becomes a much more complicated matter.
Another question that requires further research is whether the negative effect of education on industrialisation was more pronounced in the metal or the textile sector.
BHW reached very different conclusions about the causal effect of education on Prussian industrialisation because their preferred regression models excluded regressors that were correlated with pre-industrial education, the instrumental variable they used in an attempt to identify the causal influence of education. Thus pre-industrial education is an invalid instrument in BHW's preferred regression models and the estimates of the causal effects of education obtained from these models are inconsistent. This key point emerged from the use in this paper of a systematic procedure to select regression models of Prussian industrialisation.
By including a number of variables that were excluded from BHW's preferred specifications, the regression models that were selected by the procedure used in this paper not only increased the plausibility of the claim the pre-industrial education is a valid instrumental variable, but also yielded a number of new findings about the determinants of Prussian industrialisation. The most striking of these is the importance of the distance from London, which had a substantial negative effect in both phases of Prussian industrialisation, particularly the first one. Here, too, further research is needed to establish in what precise way proximity to the industrial leader in the nineteenth century contributed to Prussian industrialisation.
The more general conclusion to be drawn from this paper is that there is still no evidence that education of the population in general had an important causal effect on economic development before 1900. The absence of such evidence remains a major puzzle for economists and historians. Until it is possible either to find evidence of such a causal influence of education of the general population before the twentieth century, or to provide an explanation of why the causal role of such education became important only after 1900, the emphasis placed on the role of education of the general population in the growth process will remain unconvincing.