This chapter examines the properties o f causality tests in the context o f econom ic growth and development using small-sample data. In particular, we perform such causality tests for the relationship between econom ic growth and a number o f different measures o f financial deepening.
Performing individual country tests, using time series, allows us drawing conclusions about the significance o f the causality relationship in that particular country. Given the specific policies that have been implemented in that region during the time period it would be possible to draw conclusions about the usefulness o f these policies to stimulate the variables o f interest. However, when using yearly data for an individual country the problem o f small sample usually arises, in particular when using data from developing countries. Kendall (1954) first identified the problem where statistical inference from dynamic models, using short time series, presents significant biases due to the finite size o f the sample. These biases are likely to affect the conclusions based on single time series 31
and yearly data. Subsequently, White (1961) provided approximations and Sawa (1978) identified an exact formula for the bias in the auto-regressive model.
The use o f panels o f data rather than individual country time series opens the possibility o f increasing the degrees o f freedom to measure the average effect across regions or countries. In the case o f causality tests, when using panels that combine data from several countries, it becom es possible to draw conclusions that go beyond particular policies that have been implemented in each country. However, differences in parameter size in the cross section are likely to produce problems with the estimation method. Robertson and Symons (1992) study the properties o f long and short time series and long and short panels. They find that even for small parameter variation, biases can be severe. They also find that allowing for fixed effects to control for panel heterogeneity, an Anderson and Hsiao-type estimator, does not reduce the problems in practice. The problem with the false imposition o f parameter equality among panels is that it induces serial correlation o f the residuals. This, in turn, increases the problem o f bias in the auto-regressive model.
Country specific-fixed or random effects can produce problems with the estimation, in the presence o f non-independent or correlated error terms. These estimation problems are similar to those arising in time series when a serially correlated error term is not independent from the explanatory variables; for example lagged values o f the dependent variable. The use o f instruments as earlier values o f the dependent variable is not always possible, as for most dynamic structures o f the model, they are still correlated with the error term. Therefore, individual country time-series regression has the advantage over
panel estimation, o f not having this country fixed or random effect problem.
Pesaran and Smith (1995) study the properties o f stationary regressors and, pooling time series and cross section data, they find that this produces inconsistent estimates. They also identify a tendency o f fixed effects to underestimate short run effects and overestimate long run effects. In work related to endogenous growth estimation Lee, Pesaran and Smith (1998) identify inconsistent estimators, when there is county heterogeneity in growth effects and in speeds o f convergence.
Caselli, Esquivel and Lefort (1996) study this problem in the context o f endogenous- growth regressions. In their panel estimation they identify two problems: first, countries' fixed effects are correlated with the right-hand-side variables and second, som e regressors are endogenous. These two problems w ill induce to biased estimates in m ost cases. Furthermore, estimating the within model or performing quasi-demeaning will not solve the problem. Taking away the mean, or a fraction o f it, from the explanatory variables produces variables that are correlated with all past and futures observations o f the error term. When quasi-demeaning, unless the theta 'effect' is very small, the correlation between the regressors and the error term will be important. The addition o f endogenous regressors to non-independent error term increases the problems with the estimates. Caselli et. ai. propose an Arellano-Bond-type estimation method to account for this problem. They identify strikingly faster convergence rates, o f a country to its ow n steady state, than was previously believed to be the case.
Finally, Attanasio, Picci and Scouru (1998) study causality test using panel data techniques and applying the Arellano-Bond method and coefficient heterogeneity. Under these assumptions, they find significant differences in the causal relationships substantiated by each technique.
The rest o f this chapter is organised as follows. In Section 2 w e study the asymptotic properties o f causality tests in relation to different stochastic representations o f the process. W e identify different conditions that allow for OLS consistency under A R (1) regressors. This is necessary as the short sample formulas rely on consistency o f the estimators. In this section we also set out the main specification o f the test that w ill be used to establish the size o f bias. In Section 3 w e use the specification from section 2 and identify formulas for the bias on the lagged dependent variable and other regressors. This section makes extensive use o f recursive formulas for expectation o f stochastic matrices. In Section 4 w e study the biases over the usual Wald F-statistics, using simulation techniques, under different lengths o f the dynamic structure. In Section 5 w e use these findings to analyse causality tests on a Latin-American and Caribbean financial, banking oriented, database. Finally, Section 6 concludes the chapter.