Stock markets and their relationship

with the real economy in Latin America

with the real economy in Latin America

DATA AND METHODOLOGY

Econometric Modeling ( ...continuation )

Econometric Modeling ( ...continuation )

the *y*_{t} and *x*_{t} lags show endogeneity in the specifications. It is also assumed that ε_{t} is a column vector of random or innovation errors that are considered correlated at the same time but not self-correlated. As a result they do not have a diagonal covariance matrix (Charemza and Blangiewicz, 2001). As the VAR models only have lagged variables on the right and these are not correlated with the error term, each equation is estimated with ordinary least squares. To explain changes to GDP as a consequence of GDP lagged values and changes to stock market yields, the present study applies the following regression for each country:

**( 9 )**

**( 10 )**

A determining factor is the number of lags that should be applied so each lag must be evaluated one by one until the optimal number is found. For this it is important to compare the statistical information criteria with the results generated for each specification.

The impulse response equations are obtained estimating a VAR model. The model examines the dynamic interrelations and causality relations between stock market activity and GDP identifying shocks in the cointegrating system. The VAR estimate is a multivariate generalization of Granger causality. The dynamic behavior of the VAR model can be characterized plotting the impulse response functions, which determine how each endogenous variable responds in time in this variable and in other endogenous variables. However, the impulse response can only be calculated if the model is stable and in equilibrium long term. Here, shocks in the period of the endogenous variable affect the other endogenous variables. Plotting the impulse response function synthesizes the dynamic structure of the system. To carry out empirical analyses of changes in Latin America’s emerging markets and the GDPS of their respective countries, this study applies a bivariate VAR model for each case:

**( 11 )**

**( 12 )**

Impulse response analysis is a useful tool for evaluating the congruence and dynamic sensibility of the variables specified in the model. However care must be taken not to have covariances different from 0, that is correlated errors, as this would make it impossible to specify the response to the variables before specific variable impulses (Pindyck and Rubinfeld, 2001). The analysis indicates the dynamic response of the dependent variable in the VAR system to shocks in the error terms or innovations in all the endogenous variables, excluding the effects of exogenous variables. It is important that the response to the impulse be calculated if the VAR is in long term equilibrium. The length of the shock must also be taken into account, for if this is very short, the evolution of the shocks cannot be examined precisely nor the dynamic stability of the VAR. If the VAR is stable, a disturbance would mean the system deviating from equilibrium, although it would stabilize again after a few periods. A characteristic of this analysis is that if Cholesky’s original methodology is applied, the order of the assignment of variables is very important, given that this bears directly on the results. That is to say the model is solved following the causality line assigned in the specification. However, in the present case this can be left out as the analysis is only based on two variables.