Empirical evidence suggests that the expansion o f the financial sector is associated with higher rates o f growth. Most notably the work by Barro and Sala-i-Martin (1995) and King and Levine (1993) find evidence in this direction. It is not clear, however, whether these empirical measurements o f the relationship have succeeded in isolating the effect, on growth, o f the exogenous improvements in the financial system. The natural feedback from econom ic growth to the activity o f the financial sector is likely to overshadow the purely financial innovations. For this reason it is difficult to assess empirically the extent o f this effect.
Much o f the empirical work on endogenous growth has used an approach where the data is averaged over time to estimate subsequently cross-section regressions. Variations o f this approach consider two, three or four periods o f time; it averages the data over these periods and it estimates the parameters from this shrinking panel o f data. W e call this process phase-averaging as these periods define particular data phases. Campos, Ericsson
and Hendry (1990) have shown that phase averaging is more likely to produce more problems than benefits, as aggregation from annual data entails loss o f information and does not reduce other data problems such as serial-correlation.
In our case, when the process generating the financial activity variable has some dynamic components, the use o f phase averaging can introduce additional bias in the estimates o f the model. Depending on the dynamic structure o f the process generating the error term, problems related to serial-correlation, in the error term can be increased by phase
averaging. In summary, when using phase averages, the degree o f exogeneity on the
explanatory variable has to be much higher in order to obtain reasonable estimates compared to using annual frequencies in the estimation.
We find that the length o f the phase average produces increased distortions on the value o f the estimated parameter in a regression, where the regressor is not strictly exogenous.
Creating the phase-averaged series entails losing information from the original data. First, it is necessary to decide where to start with the phase-averaged series and forfeit the previous observations; it is also probable that observations will be lost at the end o f the time period. Second, the data in interior o f the averaged periods are dropped. It is clear from our examination that these observations should be considered and that w e do not need to evaluate only the period averages or to consider only the rate o f growth between the two end-periods.
Likewise, we study the use o f instrumental-variables to overcome the simultaneity and counteract biases as in Atje and Jovanovic (1993) and Harris (1997). We find that this is 194
inferior to som e more direct specification o f the model. Instrumental variables estimation is also increasingly inefficient with the size o f the phase average.
We do not find reasons to average the explanatory variables over periods o f time in the growth model under study. We show that the most convenient procedure to test the effect o f financial size on growth in a time series entails using the data in the most disaggregate form possible.
Pesaran and Smith (1995) study the properties o f time aggregation when the regressors are stationary and when they are integrated. In the stationary case, and using a slightly different averaged model than ours, they study the between-regression and find this produces inconsistent estimators. They also study a long-run version o f the model and find that the corresponding OLS estimates converge to their population counterparts for long time series, but they are biased in a short time series even when the cross-section is large. In another work Lee, Pesaran and Smith (1998) also identify inconsistent estimators, in dynamic panels, when there is country heterogeneity in growth effects and in speeds o f convergence.
Arestis et al. (2001) find that the growth-enhancing effect provided by stock markets may have been exaggerated by empirical studies using cross-country growth regressions.
Bergstrom (1984) studies continuous-time stochastic models and the properties o f aggregation over time. In his work he is concerned about the use o f quarterly or yearly measurements when more time disaggregate data is not available. He advocates for the study o f continuous-time structural models rather than discrete versions o f the m odels. If 195
one is considering the discrete versions o f the models this should be based on the
continuous specification. From his observation that aggregation over time is an
inconvenience, created by the frequency in which the data can be collected, he considers it unrealistic "to assume that the econom y m oves in discrete jumps between successive positions o f temporary equilibrium at intervals whose interval coincides with the observation period." (op.cit. p. 1147). He demonstrates that the actual form taken by the discrete model is not invariant with the level o f time aggregation: "The simultaneity in the unlagged endogenous variables [...] is necessary in order to avoid the unrealistic assumption that the minimum lag in any causal dependency is nor less than the observation period." (ibid.). He shows that a discrete model can be drawn for the observation period and that this "is [...] o f no importance except for the fact that the shorter the observation period the more observations there will be and the more efficient w ill be the estimates o f the structural parameters." (op.cit. p. 1149) We acknowledge two o f Bergstrom's findings: first, long term relationships do not necessarily have the same form as short term ones and second, estimating parameters from a more time-disaggregated model is more efficient i f this model is the known structural relationship.
The rest o f this chapter is organised as follows. We study in Section 2 the effects o f phase averaging in the OLS and IV estimation o f a simple dynamic system; w e look at the effect in the size and bias over the parameters and efficiency o f the estimation method. In section 3 we disaggregate over time and estimate parameters for the models in Barro and Sala-i- Martin (1995) and King and Levine (1993). We identify some positive but weak effects o f finance on growth. In section 4 we study the effect o f different phase average length
applied to a Latin-American database on finance and growth. A frequently used
measurement o f financial activity in empirical analysis is the liquid-liabilities-to-output 196
ratio. It has been successfully used in Atje and Jovanovic (1993), King and Levine (1993) and Barro and Sala-i-Martin (1995). We analyse extensively the effect o f this financial characteristic on growth. Section 5 contains some concluding remarks and identifies new areas for future research.