Robustness

A couple of additional analyses serve to test the robustness of the results; see Table 4.5, column (2).

Table 4.5 - Robustness Tests

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

(1) (2) (3) (4)

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

First, the period length is set to 50 years resulting in a potential maximum number of 480 observations. Robust findings regard the coefficients of population size and executive constraints. They remain nearly the same. The stock of innovation events, however, has as slightly negative effect now, and the interaction term is non-significant. The coefficient of

human capital, on the other side, turns positive. Even though the coefficient is significant, its size is still small and of little economic relevance. The insight of rising complexity of ideas remains unaffected. Note that, with halfcenturies, the number of subsequent periods for a country is 10 at the maximum; very few, given that only time variability is exploited by the estimation technique.

Next, subsample estimates ought to ensure that the results are not due to distortions in the database. The first subsample excludes Germany from the regression (column (3)), the second is additionally based only on periods prior to 1900 (column (4)). This is because of a potential discontinuity in documentation behavior as well as a potential bias in favour of German innovation events. Excluding Germany does not alter the general insights in comparison to the original sample. Human capital has no effect, the impact of institutions is reduced, and all other statements made above remain valid. Prior to 1900, however, the returns to the stock of existing knowledge are higher than in the full sample. The coefficient points at constant returns and suggests that - at the prevailing level of technology- ideas had not yet started to get more complex. The interaction term suggests that a gap to the technological frontier was not detrimental during times of generally lower technological levels. Also, according to column (4), population size did not matter prior to 1900. Note, however, that the low number of observations may not provide enough variability to bring out some effects in the presence of highly collinear covariates.

Detailed results of all further robustness checks are documented in Appendix B.3. None of them, however, calls the principle findings into question. Hence, at this point, a brief summary of the performed tests should suffice. A negative binomial regression has been fitted to the data to account for potential violation of the Poisson assumption due to overdispersion.

Further, a lagged dependent variable was included in the Poisson regression to eliminate serial

Innovation and Growth on a Macro Level, 1500-1990 129

correlation.⁹⁸ As would be expected, the coefficients are reduced in size, but all statements remain generally true. Next, endogeneity is likely to be an objection against the analysis.

Especially population size is under suspicion. In the complete specification of Table 4.4, its coefficient exceeds the value 1. This may be due to spillover effects on the one hand, or due to reversed causality on the other. Imposing the restriction ψ =1, however, does not change the regression results drastically. Moreover, reversed causality should not affect the coefficients of the knowledge stock, which is insignificant, and human capital, which is negative. Also, the coefficient of the interaction term is argued to be intact, because national innovations are not important for economic growth as demonstrated in section 4.4.

Admittedly, institutional change might be an outcome of innovative activities rather than the driving force behind them. This is especially true in light of the broad notion of innovation events. The database encompasses events, which rather express institutional than technological improvements. For example, regulations related to technological development may in fact be an outcome of the latter. Including those in the left-hand side variable might lead to an upward bias in the right-hand side measure of institutions. Hence, the regression was performed for an alternative dependent variable adjusted to reflect only actual

98 If the dependent variable did contain a unit root or a time trend, first differencing might be necessary. Time trends owing to the rise in the international stock of knowledge or population are controlled for explicitly. A potential trend due to changes in the documentation behavior of innovation events, on the other hand, is eliminated by including times dummies in the regressions. Also, apart from trends, it appears from Figure 1 that the individual series do not contain that much dependency. Given the difficulty of unit root testing in unbalanced panels, this graphical evidence must suffice at this point. That is, differencing does not seem necessary.

Including a lagged dependent variable, however, actually requires dynamic estimation techniques, because it is correlated with the individual effects by construction. Such methods have been applied in a count data context by Crepon and Duguet (1997) or Blundell, Griffith and van Reenen (1999). The respective procedures, however, are not implemented in standard econometric software packages. A new user-written Gauss-program by Windmeijer (2006) is capable of performing such analyses. Applying this program would be a way to further substantiate the robustness of my findings. So far, potential bias from including an LDV is ignored. Anyhow, there is little economic reason to think that innovation frequency in one period depends that strongly on the number of innovations in the previous period, given that period length is 10 years, and that the stock of international knowledge already contains the innovations of all preceding periods. Much of what may cause serial correlation can most likely be captured by the individual effects in the model., because the latter reflects the entry level innovation knowledge stock, i.e. the stock of past innovations of each country (also see Blundell, Griffith and van Reenen, 1999, p. 534).

technological improvements, such as discoveries, inventions, constructions etc. Once again, the findings are not changed fundamentally. Nevertheless, this adjustment does not abandon the possibility of institutions being endogenous. Finding an instrument, which captures the exogenous variation in institutions over time, however, is a challenge that could not be mastered in this work. In consequence, not being able to disprove this criticism calls for caution in interpreting the results. Last, in some cases, the place of an event deviates from the country, where the person(s) associated with it received their education. A final check makes sure that the coefficients are stable, when the dependent variable is based on the place of education instead of the place of innovation.