Daniel Ventosa-Santaulària

Spurious Regression and Trending Variables

This paper analyses the asymptotic and finite sample implications of different types of nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study cases when the nonstationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t−statistic in a linear regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases considered, when at least one of the variables behaves in a nonstationary way. Simulation experiments confirm our asymptotic results.

Testing for a Deterministic Trend when there is Evidence of Unit-Root

Whilst the existence of a unit root implies that current shocks have permanent effects, in the long run, the simultaneous presence of a deterministic trend obliterates that consequence. As such, the long-run level of macroeconomic series depends upon the existence of a deterministic trend. This paper proposes a formal statistical procedure to distinguish between the null hypothesis of unit root and that of unit root with drift. Our procedure is asymptotically robust with regard to autocorrelation and takes into account a potential single structural break. Empirical results show that most of the macroeconomic time series originally analyzed by Nelson and Plosser (1982) are characterized by their containing both a deterministic and a stochastic trend.

REVENUE ELASTICITY OF THE MAIN FEDERAL TAXES IN MEXICO

An inelastic tax system increases the uncertainty associated with tax revenue collection. This results in continuous short-term adjustments to maintain the stability of tax collection. In this paper, we estimate the revenue elasticity of the principal taxes in Mexico, finding a much greater elasticity than that found in previous studies. A cointegration model between the revenue and taxes is used which satisfies strong exogeneity, providing a basis for congruent and reliable projections. Using this model, the tax revenue projected for 2011 is much lower than the estimates prepared by Mexico’s federal government.

Spurious Instrumental Variables

Spurious regression phenomenon has been recognized for a wide range of Data Generating Processes: driftless unit roots, unit roots with drift, long memory, trend and broken-trend stationarity, etc. The usual framework is Ordinary Least Squares. We show that the spurious phenomenon also occurs in Instrumental Variables estimation when using non stationary variables, whether the non stationarity component is stochastic or deterministic. Finite sample evidence supports the asymptotic results.