The empirical model

If - for a specific country - the number of innovation events per period as given by the IAB data, I&_jt, mirrors its actual contribution to the change in knowledge, A&_jt, and likewise,

Innovation and Growth on a Macro Level, 1500-1990 121

the international stock of technological knowledge, A , may be proxied by the cumulated _t^* number of worldwide innovation events, I , then the mean function of the respective count _t^* data regression model can be written as

(

)

jt C N I u

I^& =explog +ψ log +φlog ^*+βZjt + ^(4.9)

where u are country-specific unobserved effects._j ⁹¹ The dependent variable gives the number of events within a period, whereas all of the right-hand side variables are measured at the beginning of a period. N , the size of the population, is the scale factor in the model. It is _jt constructed as a combination of population figures from McEvedy and Jones (1978) and Maddison (1995).⁹² Note that the constant, logC , is different from logδ . It merely reflects exogenous technological progress, which would take place even if the covariates were all zero, because the right-hand side of the equation controls for unobserved country effects and the vector Z. The latter includes a couple of variables, which serve to revisit the debates sketched briefly in section 4.2. They will be discussed subsequently.

First, inst is a proxy for the institutional setting. It measures constraints on the _jt executive. It is a combination of the variable used by Acemoglu, Johnson and Robinson (2005), and the respective Polity IV variable by Marshall and Jaggers (2002). Constraints on executives may be crude. But it is the only measure capable of proxying for the institutional environment in a broad sense for a diverse set of countries over a long time period. Most likely, a society that controls the power of executives and representatives also ensures a relatively high degree of liberty. On the one hand, liberal trade regulations etc. enhance access to international knowledge and thereby facilitate its adoption. Also, they may affect the

91 See Cameron and Trivedi (1998) for a comprehensive textbook treatment of count data regression models.

92 Details on the construction of all explanatory variables are provided by Appendix B.2.

perception of potential entrepreneurs regarding whether or not investments in new techniques are worthwhile or not. Beyond that, however, institutions like the protection and enforcement of property rights may affect innovativeness immediately by creating incentives or facilitating the innovation process.

Similarly, geography may have an immediate impact on innovativeness, which goes beyond its role as a facilitator of technology adoption. Even if a country cannot adopt technologies because of a lack of human capital or an unfavorable institutional setting, researchers may be able to get access to the respective knowledge. This seems more likely the closer a country is located to the technological leaders, especially during the prerailroad and -telegraph era. Geography is modeled by a set of five dummy variables, geo1 through geo5, which reflect the distance of a country to the innovative center of Europe. geo1=1 for the UK, France, Germany, Netherlands, or Belgium. Those constitute the center of Europe. geo5=1, if the respective country is located outside of Europe. Turkey is classified in this category. geo2 through geo4 reflect intermediate states. Distance is measured in terms of the number of borders that need to be crossed in order to reach one of the geo1 countries. This indicator seems to reflect more accurately than pure distance the potential for technology diffusion.⁹³

Eventually, h is a measure of human capital. Because the stock of human capital, _jt rather than its flow, is relevant to produce innovations, years of schooling are chosen as its basis. A direct measure of school years exists only during 1960-1990 (Barro and Lee, 2001).

For years prior to 1960, literacy rates are available for few countries. Also, numeracy can be measured based on age-heaping data for a variety of countries (Crayen and Baten, 2008). And as of 1830, primary and secondary school enrollment figures do exist (Lindert, 2004). In order to obtain a human capital variable that is consistent over time, those diverse inputs have to be

93 Apart from geographical proximity, cultural proximity may facilitate knowledge diffusion. It correlates highly with geographical proximity, though.

Innovation and Growth on a Macro Level, 1500-1990 123

transformed into years of schooling. From enrollment rates, for instance, a rough measure of school years may be inferred by making a few simplifying assumptions about the average length of primary and secondary schooling. In the case of literacy and numeracy data, regression analyses are needed to estimate the general relationship between literacy - or numeracy respectively - and years of schooling. Then, years of schooling can be predicted.

Eventually, common observations may be used to merge the resulting series such that consistent time series without breaks are obtained for each country. Finally, actual years of schooling are related to the potential maximum number of school years. The absolute maximum is assumed to be equal across countries. Reasoning that total primary and secondary education lasts 12 years and tertiary education 5 years, it was set to 17 years.⁹⁴

Eventually, Z contains an interaction term, which is the product of logged _jt international knowledge stock and efficiency, eff . The latter proxies for the distance of an _jt economy from the technological frontier. It is defined as eff_jt =Y_jt Y_t^{max, where} Yt^maxis the maximum income per capita across countries in every period. This measure is based on Maddison (1995); some missing values were filled by interpolation. The intention behind including this term is to control for the potential indirect effect of the other covariates in Z . _jt Apart from how much knowledge is available in the world, it may also matter for a country's innovativeness, whether researchers in the country actually have access to it. Access may be restricted by the capability of an economy to exploit or adopt the respective techniques and implement them in the economy's production sector. The degree to which a country is able to adopt foreign technology, in turn, may depend primarily on its human capital stock, the institutional framework, as well as its proximity to innovative countries. In other words: if the

94 Changing this fictitious upper bound would not affect the analysis as it translates into the same percentage change for all observations. Its application simply serves to point out that the adopted notion of human capital does not allow boundless growth.

interaction is excluded, the covariates in Z may just capture the fact that access to _jt knowledge is enhanced.

4.5.2 Results

The results are based on a fixed effects Poisson regression model. It has been proposed by Hausman, Hall and Griliches (1984) and - together with the fixed effects negative binomial regression model – has today become the standard estimation technique for count dependent variables in the presence of unobserved heterogeneity.⁹⁵ The Poisson regression analysis employs a panel of 48 countries and 6 decades from 1500-1800 (these are 1500-1509, 1550-1559, 1600-1609, 1650-1659, 1700-1709, and 1750-1759) plus 20 decades from 1800-1990;

i.e. a theoretical maximum number of 1248 observations.⁹⁶ Because the explanatory variables are not available throughout, the panel is unbalanced. Country dummies were included to control for unobserved heterogeneity, and time dummies are supposed to filter out potential trends. The model has been estimated with and without the vector of control variables. Table 4.4 presents the results.

When the control variables are excluded from the model, population has a positive effect. It is close to one as would be expected; doubling population size leads to twice the number of ideas. Depending on the specification it varies between 1.4 and 0.8.

The stock of worldwide ideas is important, but the coefficient size of roughly 0.6 implies that a country’s contribution to international knowledge growth can be kept constant only in the presence of population growth, because the generation of ideas gets more

95 In Stata, these are implemented in the commands -xtpoisson- and -xtnbreg-.

96 In principle, observations could be created for any country in the world. For most countries, however, the dependent variable would take on the value zero. Thus, only countries, which actually turn up in the database - i.e. for which at least one innovation event is reported - are considered; that is 48. Further, periods prior to 1500 cannot be considered because of a lack of GDP data.

Innovation and Growth on a Macro Level, 1500-1990 125

difficult.⁹⁷ The interaction term (column (3)) indicates that in an economy, which operates close to the frontier (i.e. eff =1), a further shift affects its innovative potential stronger, the coefficient being closer to one than before. Further, it suggests that the state of efficiency (i.e.

the extent to which internationally available technology is actually being applied) within the economy is extremely relevant for its innovativeness. Given the location of the technological frontier in the 1990ies (logI^* ≈10), a catch-up of ∆eff =0.5 would lead to roughly 90%

more innovation events per period, respectively 70% when human capital and democracy are controlled for.

Table 4.4 - Poisson estimates of equation (4.9)

Dependent Variable: Number of innovation events per decade (Metz, 2003), 1500-1990

log(N) 0.978*** 0.793*** 1.421*** 1.421***

Notes: Standard errors in parentheses. Time/country dummies are not reported. *** p<0.01, ** p<0.05, * p<0.1.

97 Note that with Poisson estimation, the dependent variable is the absolute number of innovations per period, not the log of it. The interpretation of the coefficients, however, is the same.

Apparently, the stock of previous innovations picks up the effect of institutions. It is no longer significant, when executive constraints are included in the regression (see column (3)).

The latter exert a vigorous effect on a country’s innovativeness. A one-point increase on the 7-point scale causes an 18% rise in the number of innovations per period. Running the whole scale roughly doubles the number of innovation events.

Surprisingly, the effect of human capital turns out negative. Obviously, an increase in human capital, which leaves the economy's efficiency unaffected, reduces the number of innovations the latter is able to generate. At first glance, this is a totally counterintuitive result. But consider for a moment the idea that schooling duration is altogether irrelevant for innovativeness. Because additional education is time-consuming, it would be consequent to think of it as actually being detrimental to innovativeness, if many potential innovators decide to waste time in the educational system. Alternatively, one might reason that public education impairs the unrestricted flourishing of a creative mind. To judge the size of the effect, consider a one-year increase in average years of schooling. If the average length of academic education is 5 years, such a gain could be reached by inducing an additional 20% of the population to complete this type of program. In an industrialized country with h≈0.6, this is roughly equivalent to a 10%-change in h. The coefficient implies a reduction of innovation events by about 4%, respectively 3% in the complete specification. This is a rather small and hardly economically relevant effect. But in spite of a high degree of collinearity between the explanatory variables, it turns out significant and should not be ignored.

The geography dummies indicate that countries which do not belong to the innovative center of Europe produce fewer innovations. Nevertheless, it would be hard to make the case that distance aggravates the effect. Three borders separating a country from the most innovative ones seem to be worse than two borders. Then, again, the periphery dummy is

non-Innovation and Growth on a Macro Level, 1500-1990 127

significant; merely being located outside of Europe is of greater disadvantage. The size of the effects is an average over time, hence further interpretation would be meaningless.