When economic theory is not enough... : identification through heteroskedasticity in a likelihood-based approach

Since the seminal contribution by Rigobon (2003, The Review of Economics and Statistics 85, 777-792) some authors have proposed identification conditions in heteroskedastic bivariate systems of equations. None of them, however, can be generalized lo larger systems and, especially for macroeconomic applications, this represents a strong limitation. This paper shows how the analysis of identification of simultaneous equations systems with different volatility regimes can be reconciled with the conventional likelihood-based setup. We propose a new specification that explicitly models the heteroskedasticity in the residuals, and study the conditions for identification when both heteroskedasticity and traditional restrictions on the parameters are jointly considered. A Full Information Maximum Likelihood (FIML) algorithm is discussed and the small sample performances of estimators and tests on the parameters are studied through Monte Carlo simulations. Finally, this methodology is used to investigate the relationships between sovereign bond yields for some highly indebted EU countries.