Stock markets and their relationship
with the real economy in Latin America
Samuel Brugger *and Edgar Ortiz **
Variance Decomposition Analysis

The decomposition of the variance is an additional study to impulse-response analysis, expressing the percentage volatility a variable registers before the shocks of others at different time horizons. In this way it is possible to measure the volatility generated by the endogenous variable at a specific moment. The results for the first and thirty sixth periods are summarized in Table 8. All the variables exhibit a strong autoregressive tendency, given that after 36 months more than 90% of the variance of each variable is influenced by itself, except in the case of Mexico. Furthermore, all the variables are quickly explained by their own lags. Because the relationship between the real economy and the financial economy is irrelevant, these results are not examined. However, the inverse is relevant. In Argentina, the MERVAL accounts for 1.2% in the first period and rises to 7% in period 36. In Brazil, the BOVESPA accounts for only 0.9% in the first period, and 7.27% of the variance of monthly GDP in period 36. In Chile, the IGPA accounted for 0.01% in the first period and 3.32% of the variance in period 36. Finally, in Mexico, the IPYC accounted for 0.5% of the variance in the first period and 5.8% in period 36.

Another way to balance the correct specification of the model is to examine the extent of the standard error for each equation for the periods in question, that is the level of dispersion of the point estimates obtained for samples of a specific size. The same estimator shows different values for different samples of the same size taken from the same population. A measure of the variability of the estimator must therefore be obtained in relation to the parameter being estimated. The results can be seen in Table 9. Firstly, note that the standard error is greater in the stock market variable than in monthly GDP, which is in accordance with the theory. However, the difference in the standard error between the MERVAL, BOVESPA and IPYC compared to the IGPA in Chile stands out, as there are few disturbances in the IGPA, and a lower standard error (6%) than the other stock markets (Argentina, 12%; Brazil, 13% and Mexico, 10%). The standard error increases the most in the IPYC, whereas in the other stock markets it remains stable.