Fixed effect regressions with AR(1) disturbance. Units of analysis: country-year. Dependent variable: annual per capita growth rate. All predictors lagged one year. Newey-West standard errors in parentheses. (two-tailed tests) Variables and procedures defined in the text. Variables not indicated by source are constructed by the authors. *** p<.01 ** p<.05 *p<.10
Notes for the next iteration: Exclude the following variables: regime durability (which will be dealt with in chapter 14), years independent (which is picked up by country fixed effects), trend (picked up by annual dummies). Substitute the new conflict variables for this conflict variable (drawn from Marshall).
The Democratic Growth Effect We have shown thus far that the relationship between democratic stock and growth is robust in a variety of plausible specifications and operationalizations. (Further tests are relegated to the appendix.) We turn now to the question of its practical significance. Is the democratic growth effect significant in real (policy) terms?
Let us consider the results of model 5 in Table 3.1, in which we control for a range of other possible causal factors. We regard this model as offering a conservative estimate of causal effects since many of the variables introduced as controls in this model may be endogenous to democracy, and hence might be suppressing democracy’s true causal effect on growth. (Note that the coefficient for democracy is virtually unchanged from the reduced-form equation in model 2, so it hardly matters which model one chooses to base this estimate on.)
Within the parameters of this model, a country with no existing stock of democratic capital (for example, Botswana in 1966) experiences the following democratic growth effect: for each full decade of high-quality democracy (Polity2=10), democracy stock increases by approximately 100 points. To estimate the predicted effect of this change on growth, we simply multiply this change by the coefficient on democracy stock, 0.007. So from model 5 in Table 3.1, the predicted growth impact of a decade of high quality democracy is approximately 0.7 percent. Given the well-known cumulative effects of small increases in the growth rate, these changes are significant. For instance, an increase in the annual growth rate from 2 percent to 2.7 percent reduces the time needed to achieve a doubling of incomes from thirty-five to twenty-six years; an increase to 3.4 percent further reduces the doubling period to 20.7 years.7
Methodological Appendix Specification problems pervade all cross-country growth regressions.8 While the fixed-effect format handles the problem of invariant controls, it does nothing to control for factors that might vary over time. To control for convergence effects we include gdp/capita (natural logarithm) as part of the benchmark model. (Thus, we measure the effect of democracy on a country’s growth rate given its current level of economic wealth.)
Other controls are less obvious by virtue of their possibly endogenous relationship to democracy, their lack of robustness, or their theoretical status. At the same time, it is vital that we test as comprehensive a set of alternative controls as possible. These controls must encompass not only those identified by the prodigious literature on economic growth but also those factors that might affect the simultaneity problem discussed above.
However, for a variety of reasons, we do not maintain these controls in most of the tests shown above (Table 3.1) and below (Table 3.2). First, there is a substantial loss in degrees of freedom when the equation is expanded to include the full set of controls. Second, there is serious question about the theoretical justification (not to mention the empirical robustness) of all of these controls. Third, there is the danger of overspecifying causal relationships: note that democracy stock may affect any and all of these control variables. Indeed, the coefficient for democracy stock increases in the full models shown in Table 3.1, a result that seems dubious if one’s principal objective is to measure the independent effect of democracy stock. For all these reasons, it seems safer to work with a smaller benchmark equation, including only gdp per capita. This is the only control that can claim some degree of theoretical consensus, is empirically robust, and is—with respect to the causal question at hand—exogenous. (A recent reevaluation of cross-country growth empirics concludes that the log of gdp per capita is the only variable that is robust across all models [Bleaney & Nishiyama 2002: 45].)
Results shown in Table 3.1 are based on annual data, fixed effects, and an AR1 correction for serial autocorrelation. We now attempt to show that our results are robust even when various elements of this methodology are altered: fixed effects versus random effects, annual versus five-year increments of data, the possible influence of OECD cases (tested this time in a random-effects format), a lagged-dependent-variable approach to modeling serial autocorrelation, the possible peculiarities of the democracy stock variable, and a wide variety of static (time-invariant) control variables, as displayed in Table 3.2.
For each model with annual data we have followed our usual approach of measuring all independent variables in the year prior to the dependent variable. For each model with five-year increments we have maintained the same approach, this time measuring the independent variables in the first year of the period under study. The dependent variable in this case is a five-year average of growth performance during the subsequent period. So in both cases the dependent variable is forward lagged one time-period.
The standard method of correcting for autocorrelation is employed where annual data is used (AR1 error correction), but not when five-year increments are used. (By virtue of the fact that we are dealing with five-year increments, it should be less of a problem.) No correction for serial autocorrelation is usually necessary when a lagged dependent variable is included, as in models 8 and 9, and none is employed.
Model 1 is a fixed-effects model with one control (gdppc) and growth data aggregated across five-year periods. Model 2 is a random-effects model with annual data and the same all-purpose control. Model 3 is a non-fixed-effects model with annual data that includes all large-N controls employed previously (see Table 2), plus some additional static controls, intended to model spatial heterogeneity. These include English legal origin (dummy), Muslims (as percentage of the population), ethnic fractionalization (the likelihood that two persons chosen randomly from a population will share the same ethnicity), East Asia (dummy), Middle East (dummy), Latin America (dummy), and latitude (logarithm of the absolute value of the distance of a country’s capital city from the equator).
Model 4 is a non-fixed-effects model with five-year data increments and the same set of controls. Model 5 is a fixed-effects model with five-year increments and all relevant (varying) controls. Models 6 and 7 replicate models 3 and 4, this time excluding OECD cases. Models 8 and 9 test the lagged-dependent variable approach to tscs analysis, discussed previously. In model 10 we test the benchmark specification in an Arellano-Bond format. This procedure combines first-differencing with a series of lags—equivalent to the total number of prior observations in the dataset—for each variable in the model.9 (Simple first-difference models, without lagged instruments, show results similar to those in model 12.)
In each of these various tests we find that the democracy stock variable retains statistical significance, usually at the .01 level (two-tailed tests).
Alternative Estimators and Models
Country fixed effects:
(lagged dep var)
GDP pc (ln)
English legal origin
Muslims (% pop)
R squared (within)
Prob > F
Sargan test (prob)
All regressions are OLS (Newey-West standard errors in parentheses) except for model 12 which is estimated using the Arellano-Bond estimator. Corrections for autocorrelation in the residual and inclusion of country fixed effects are included as noted. Dependent variable: growth rates, either annually or in five-year increments (mean). All predictors lagged one year. Variables and procedures defined in the text. Where no source is listed, the variable is constructed by the authors. *** p<.01 ** p<.05 *p<.10 (two-tailed tests)
Variable Definitions English legal origin: dummy variable (La Porta et al. 1999).
Ethnic fractionalization: the likelihood that two persons chosen randomly from a population will share the same ethnicity (Alesina et al. 2003).
GDP per capita: from the World Development Indicators (WDI 2003), with a small number of missing cases from the 1950s imputed from the Penn World Tables (pwt 6.1) dataset (Summers & Heston 1991).
Government consumption: government share of real gdp per capita (pwt 6.1).
Growth per capita, trade-weighted: Each country is assigned the mean value of the growth rate of all other countries in the world in that year, weighted by their bilateral trade with the country in question).
Illiteracy: percent of population who cannot read and write a sentence in their native tongue (World Bank 2003), natural logarithm.
Inflation: annual percent change in consumer prices (natural logarithm; World Bank 2003).
Instability: includes assassinations, general strikes, guerilla warfare, government crises, purges, riots, revolutions, and anti-government demonstrations, all from the Banks dataset. Each is added together to form a composite index (construction of index by the authors).
Investment: the share of real gdp comprised by investment (pwt 6.1).
Latitude: logarithm of the absolute value of the distance of a country’s capital city from the equator (calculated by authors).
Life expectancy: life expectancy at birth (World Bank 2003)
4 We employ the World Development Indicators growth variable, measured in constant dollars (WDI 2003). Additional data for the 1950s is imputed using the Penn World Tables (pwt) 6.1 data set (Chain index, constant dollars; Summers & Heston 1991). Our choice of the wdi data set as the primary data source for indicators of country growth is motivated by two concerns. First, wdi country coverage is considerably larger than offered by the pwt data set. Second, for various reasons explored by Nuxoll and Temple, the wdi indicator is probably the best measure of growth performance. See Nuxoll (1994) and Temple (1999: 118–19).
5 We interpolate missing values for illiteracy, life expectancy, and population growth in order to maintain a consistent sample (failing to do so would have significantly reduced the sample size and perhaps biased our results).
6 In additional analyses (not shown), we introduce these control variables seriatim into the benchmark equation to make sure that their individual effects do not impair the performance of the key variable of interest, democracy stock. (They do not.)
7 The number of years that a country growing at rate g takes to double its income is given by ln 2/ln (1+g).