14 KPP reconsider VAR analysis around two facts: a) shocks to different variable are not independent b) shocks are correlated across time'<sup>3</sup> . These two issues led them to examine system-wide shocks (as opposed to variable-specific) and to deal in some manner with future shocks given their autocorrelation. The way they did this was by means of the expectations operator conditional on history and/or shock. The constructed response averages out future shocks, hence it is an average of what might happen in the future given the past and present.

The key features of the Generalized Impulse Response analysis are: a) Impulse response functions and variance decompositions are independent of the ordering of the variables (compositional problem) or any other a-priori restrictions on the variance-covariance matrix of the reduced form residuals b). The analysis describes how the system behaves after a specific historical shock, taking into consideration the correlation among shocks. Since historical shocks are not orthogonal, they do not add up to 1 00%.

# D. **Results for 1992-1998: Generalized Variance Decomposition of Output and Impulse-Response Functions**

The country-specific GVAR models were estimated using monthly data for the same set of five variables (industrial output growth, real interest rates, real exchange rates, sovereign spreads and terms of trade<sup>14</sup> ) during the period 1992-1998. To capture international capital markets dynamics we used the Brady Bonds sovereign spread and if the country did not have one the regional average was used. Appendix 3 contains a detailed description and source of each variable).

The lag-selection process was done with different information criteria. The Akaike criterion yielded almost always twelve lags, while the Schwarz criterion pointed at lag one. The likelihood ratio test between the two orders indicated that the longer lag length was preferable'<sup>5</sup> . (Appendix 3 presents a summary of the VAR estimates for each country and the coefficient of variation of each of the variables during the sample period.

The generalized variance decomposition of output in the eight countries shows (Table 3) that these variables explain fairly well the forecast error variance of output during this

> " They consider a third issue which is the state of the system prior to the shock and afterwards, but we do not examine this complication here since it applies only to non-linear systems.

> 14 Many variables are excluded mainly because of sample size limitations. One of the most obvious exclusions is US output growth, that in the first section tumed out to be statistically insignificant. In Mexico's case there is a very close relationship between industrial production in both countries. However, when you include US industrial output in Mexico's VAR very undesirable results emerge: after shocking the TOT, output diverges from stationary levels: the same thing happens when the spreads are shocked. More work is needed in this topic. Another omitted variable is the quantity variable, or the capital flows, but the last section of the paper discusses this issue in more detail.

'5 The only exception was Argentina where 8 lags were used because of data limitations. The variables were differenced to achieve stationarity, hence our analysis does not incorporate potential restrictions imposed by long-run relationships among the non-stationary variables. Again, the main obstacle was the sample size to perform the type of cointegrated VAR analysis done by Ahmed (1999).