Dynamic GMM

Our second step involves estimating the dynamic growth regression by GMM using the method proposed by Arellano and Bond (1991). The panel unit root tests gener-ally suggest that growth of real GDP per worker is stationary. To obtain consistent estimators, the lagged levels (or di¤erences) of the proposed explanatory variables may be used as long as they are correlated with the variable they are supposed to instrument. Evaluating the correlation with x_t and x_{t p} (or x_t and x_{t p} for system-GMM) for p= 1;2;3 shows that all the …rst di¤erences of explanatory variables correlate up to at least their third-level lag.

The following instruments were used. Lags two and three are included for growth, and, following Roodman (2009), collapsed. For other variables, which are likely predetermined rather than strongly exogenous, only third lags are included.

The instrument list is also collapsed. Standard errors, which should be consistent in the presence of any pattern of heteroskedasticity and autocorrelation within panels, are corrected for the small sample bias in line with Windmeijer (2005).

Table 2 presents the estimation results for the economic growth with di¤erent model speci…cations. The results vary considerably depending on the model spec-i…cation used. The Sargan, and in particular, Hansen test-statistics are generally

insigni…cant, i.e. the instruments are valid. Moreover, the models seem to pass the Arellano-Bond test for second-order serial correlation and the Wald test for joint signi…cance for coe¢ cients.

The results of the baseline model, where growth is explained by its own lag, investment, government consumption, and economic freedom, show that previous growth rate and economic freedom are statistically signi…cant while investment and government consumption are not. This …nding is in line with similar earlier studies. The coe¢ cient for lagged growth is 0.287 and highly signi…cant (1% level of signi…cance), while the measure of the economic freedom also obtains a statistically signi…cant coe¢ cient 0.01. The Wald test for joint signi…cance for coe¢ cients is 214.68, indicating the model is valid.

Following Minier (2007), we test several interaction terms. In particular, we introduce the interactions of economic freedom with other variables into our model.⁹ The second model brings the interaction between economic freedom and investment to the estimated model, which changes the results compared to our baseline model.

The coe¢ cient of growth is reduced, but remains signi…cant. Both investment and government consumption now seem to have an impact on growth. The impact of investment is positive, while the impact of government consumption is negative, possibly an indication of wasteful spending. The most interesting result is that the interaction term is negative and signi…cant: i.e. in the presence of greater economic freedom, previous investment tends to have a negative e¤ect. We next test the interaction between economic freedom and government consumption in the third model. There are again notable changes. The baseline results reappear, but investment is now also statistically signi…cant. Lastly, introducing the interaction between economic freedom and growth into the model makes a notable change compared to previous models as lag of growth is no longer signi…cant.

Since all the models seem to pass the tests for measuring the performance of instruments and/or the model, it is di¢ cult to judge which one is preferable. If the fourth model represents the full (general) model, then the last interaction terms which are statistically insigni…cant do not seem to bring any value-added to the

9Other interactions were tested, but only those that seemed to have an impact are presented here.

model or the results. Therefore, model two with one interaction term would seem to specify a correct model. These results also have an intuitive appeal.

In order to ease the interpretation of the results, we re-estimate model two using standardized variables. First, increases in investment have a higher impact than that of any other variable with the exception of interaction. This runs counter to some previous …ndings. As the interaction is signi…cant, the entire marginal e¤ect should be considered. For the sake of simplicity, we assume we are one standard deviation above the expected level of economic freedom. Increasing investment by one standard deviation slightlydecreases growth (1.6-1.7=-0.1). Moreover, assum-ing we are one standard deviation above the expected level of investment, we …nd that increasing economic freedom by one standard deviationdecreases growth quite substantially (0.7-1.7=-1.0). If we are below the expected levels, the impact is the opposite: the presence of interaction increases the total marginal e¤ect and the impact on growth is magni…ed.

In summary, economic freedom and investment initially impact positively on growth, whereas the size of government seems to have an negative impact on growth.

However, in the presence of high level of economic freedom (investment), the impact of investment (economic freedom) seems to have a detrimental e¤ect on growth. If we have economic freedom (investment) below or close to its expected value, then increases in investment (economic freedom) surely increase growth. There appears to be a “too much of a good thing” phenomenon at work at their joint presence.¹⁰ Increases in investment and economic freedom are good as long as they are not overdone.

10We also tested this idea by including the square of size of government, investments and economic freedom instead of their interactions, which all turned out to be insigni…cant. While the interpretation of interactions term as an indicator of a "too much of a good thing" phenomenon might seem unconventional, it is in fact what happens here. Since the total marginal e¤ect of either one of variables becomes negative if we increase the other beyond its mean value, taken together these positive forces become detrimental.

Variables Growth of real GDP per worker 1998-2005, N=25, T=8

Model (1) (2a) (2b) (3) (4)

(…rst lags) Coe¤. Coe¤. z-values Coe¤. Coe¤.

Growth .287*** .191** .174*** .261*** .035

(.110) (.098) (.071) (.087) (.579)

Investment .001 .011*** 1.595*** .010** .013***

(.001) (.003) (.431) (.005) (.004)

Gov’t Cons. -.001 -.004*** -.752*** -.003 -.005*

(.001) (.001) (.162) (.003) (.003)

EFI .001** .003*** .730*** .002** .003**

(-6.5e ⁴) (.001) (.255) (8.9e ⁴) (.001) EFI*Investment - -1.8e ⁴*** -1.718*** -1.6e ⁴ -2.3e ⁴**

(5.6e ⁵) (.542) (1.1e ⁴) (9.7e ⁵)

EFI*Gov’t Cons. - - - -7.6e ⁶ 3.4e ⁵

(7.2e ⁵) (6.1e ⁵)

EFI*Growth - - - .004

.010

Instruments 9 11 11 13 15

Observations 232 232 232 232 232

Sargan J-test 7.50 5.00 5.02 5.56 7.81

p-value 0.19 0.54 0.54 0.59 0.45

Hansen J-test 4.66 2.50 2.18 4.78 6.92

p-value 0.46 0.87 0.90 0.69 0.54

m₂ -0.80 -0.96 -0.79 -0.91 -0.62

p-value 0.43 0.338 0.43 0.365 0.53

Wald test 214.68*** 113.4*** 74.44*** 346.31*** 387.85***

p-value 0.00 0.00 0.00 0.00 0.00

Table 2: Estimation results with Arellano and Bond two-step GMM. (***) and (**) and (*) indicate that the coe¢ cient is signi…cant at 1, 5 and 10 % level of signi…cance. Robust standard errors are reported below the coe¢ cients.