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.IV Estimator, Spurious Regression, Broken-Trend stationarity, Unit Root

Testing for an irrelevant regressor in a simple cointegration analysis

This paper investigates the asymptotic behavior of the t-ratio associated to an irrelevant variable in a three-variable cointegration analysis. It is proved that the t-ratio converges to a non-standard distribution suitable for statistical inference. Although the test-statistic is not pivotal when the innovations are serially correlated, Monte Carlo evidence suggests that the size distortion can be considerably mitigated by means of HAC standard errors.Irrelevant variables, cointegration, t-ratio, statistical inference

Inflation and breaks: the validity of the Dickey-Fuller test

This article proves the asymptotic efficiency of the Dickey Fuller (DF) test when the Data Generating Process of the variable under consideration is in fact mean stationary with breaks. Monte Carlo simulations show that asymptotic properties remain valid for sample sizes of practical interest. We illustrate its performance by studying inflation rate series, a variable that should be stationary if the monetary authority follows an effective inflation targeting regime: shocks are short-lived, therefore, inflation fluctuates randomly around pre-specified targets.Dickey-Fuller test, Mean Stationary Process, Structural Breaks

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.Catching-up, Convergence, Deterministic Trend, Unit Root

Non Linear Moving-Average Conditional Heteroskedasticity

Ever since the appearance of the ARCH model (Engle 1982a), an impressive array of variance specifications belonging to the same class of models has emerged. Despite numerous successful developments, several empirical studies seem to show that their performance is not always appropriate. In this paper a new conditional heteroskedastic variance model is proposed: the Non-Linear Moving Average Conditional Heteroskedasticity (NLMACH). Its properties are similar to those of the ARCH-class specifications although it does not belong to this class and represents an alternative for modeling conditional volatility through a non-linear moving average specification. Pseudo Maximum likelihood allows for ease of estimation.Conditional Heteroskedastic Models, NLMACH(q), Volatility.

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.Divergence, Loose Catching-up/Lagging-behind, Convergence, Deterministic and Stochastic trends

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.Unit Root, Deterministic Trend, Trend Regression, R2

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

Spurious regression under broken trend stationarity

We study the phenomenon of spurious regression between two random variables when the generating mechanism for individual series follows a stationary process around a trend with (possibly) multiple breaks in its level and slope. We develop relevant asymptotic theory and show that spurious regression occurs independently of the structure assumed for the errors. In contrast to previous findings, the spurious relationship is less severe when breaks are present, whether or not the regression model includes a linear trend. Simulations confirm our asymptotic results and reveal that, in finite samples, the spurious regression is sensitive to the presence of a linear trend and to the relative locations of the breaks within the sampleSpurious regression, Structural breaks, Stationarity

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