Spurious Regression and Econometric Trends

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.Spurious regression, trends, unit roots, trend stationarity, structural breaks

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.Federal taxes, long-term revenue elasticity, cointegration, strong exogeneity, forecasts

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

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

A Simple Test for Spurious Regressions

It has been found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of nonstationary data generating processes. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, when there are drifts in the integrated processes generating the data, thus allowing asymptotic inference. This method can be used to distinguish a genuine relationship from a spurious one among integrated (I(1) and I(2)) processes. Simulation experiments show that the test has good properties in small samples. When applying the proposed procedure to real data (including the marriages and mortality data of Yule), we do not find (spurious) significant relationships between the variables.Spurious Regression, Integrated Process, Detrending, Asymptotic Theory, Cointegration, Monte Carlo Experiments.

Spurious Cointegration: The Engle-Granger Test in the Presence of Structural Breaks

This paper analyses the asymptotic behavior of the Engle-Granger t-test for cointegration when the data include structural breaks, instead of being pure I(1) processes. We find that the test does not possess a limiting distribution, but diverges as the sample size tends to infinity. Calculations involving the asymptotic expression of the t-test , as well as Monte Carlo simulations, reveal that the test can diverge in either direction, making it unreliable as a test for cointegration, when there are neglected breaks in the trend function of the data. Using real data on car sales and murders in the US, we present an empirical illustration of the theoretical results.Spurious cointegration, structural breaks, integrated processes

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 analysed by Nelson and Plosser (1982) are characterized by their containing both a deterministic and a stochastic trend

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 analysed by Nelson and Plosser (1982) are characterized by their containing both a deterministic and a stochastic trend

Trade liberalization and regional income convergence in Mexico: a time-series analysis

We study the hypothesis of convergence amongst Mexican regions since 1940 with special interest in the post-trade liberalization period. A standard time-series convergence test shows that per capita income levels between the capital and the rest of the regions tend to narrow over time. Using the concept of deterministic and stochastic convergence, we describe the specific characteristics of the growth pattern for each of the regions. We find evidence that supports the hypothesis that trade reforms reversed the convergence process of some regions, especially those less developed. Results further suggest that trade liberalization did not contribute to per capita income convergence between the U.S. and Mexico border regions

Income convergence: the Dickey-Fuller test under the simultaneous presence of stochastic and deterministic trends

We investigate the efficiency of the Dickey-Fuller (DF) test as a tool to examine the convergence hypothesis. In doing so, we first describe two possible outcomes, overlooked in previous studies, namely Loose Catching-up and Loose Lagging-behind. Results suggest that this test is useful when the intention is to discriminate between a unit root process and a trend stationary process, though unreliable when used to differentiate between a unit root process and a process with both deterministic and stochastic trends. This issue may explain the lack of support for the convergence hypothesis in the aforementioned literature