Estimator Choice and Fisher's Paradox: A Monte Carlo Study

Abstract

This paper argues that Fisher's paradox can be explained away in terms of estimator choice. We analyse by means of Monte Carlo experiments the small sample properties of a large set of estimators (including virtually all available single-equation estimators), and compute the critical values based on the empirical distributions of the t-statistics, for a variety of Data Generation Processes (DGPs), allowing for structural breaks, ARCH effects etc. We show that precisely the estimators most commonly used in the literature, namely OLS, Dynamic OLS (DOLS) and non-prewhitened FMLS, have the worst performance in small samples, and produce rejections of the Fisher hypothesis. If one employs the estimators with the most desirable properties (i.e., the smallest downward bias and the minimum shift in the distribution of the associated t-statistics), or if one uses the empirical critical values, the evidence based on US data is strongly supportive of the Fisher relation, consistently with many theoretical models.Fisher's paradox, Cointegration, Single-equation estimators, Monte Carlo analysis,

Panel cointegration tests of the Fisher effect

“…Hence, based on the p-values from the asymptotic normal distribution, the full Fisher effect must be rejected at the 1% level for eight of the 20 countries, for Belgium, Canada, Switzerland, Germany, the United Kingdom, Ireland, Japan and Portugal. As argued by Crowder and Hoffman (1996) and Caporale and Pittis (2004), however, a less than unit slope may not reflect the actual data-generating process but rather a downward endogeneity bias on the part of the estimators employed. If this is the case, inference based on the normal distribution could be misleading.…”

“…This time, however, we make the assumption that the vector v it , w it 0 has a joint distribution, which will enable us to model the endogeneity through the correlation between v it and w it . In particular, following Caporale and Pittis (2004), we shall assume that v it , w it 0 follows the first-order vector autoregression normally distributed innovations. For simplicity, we assume that inflation is strictly nonstationary and that there are no common factors.…”

Structural Breaks, Inflation and Interest Rates: Evidence from the G7 Countries

“…In this regard, and as Chadha and Dimsdale (1999) [28] point out, demographic change, technological progress, fiscal incentives, changes in the taxation of profits, the size of the public 1 Recently, Caporale and Pittis (2004) [2], and Panopoulou (2005) [3] emphasized that this is a key issue in the empirical evidence supporting the Fisher relationship. debt, investors' perception of risk and the degree of regulation or deregulation of capital markets could alter the constant and inflation parameters.…”

What Fisher knew about his relation, we sometimes forget

“…The standard cointegration techniques by Crowder and Hoffman (1996), Ng and Perron (1997), Dotsey et al (2003), Caporale and Pittis (2004), and Sun and Phillips (2004) do not fit the purposes of our study since the consumption growth component is found to be stationary, 3 and is used to explain the short run fluctuations around the long-run Fisher relation. We follow Mehra (1993) who uses an error correction method to tackle a similar problem for the joint estimation of the long-and shortrun money demand function.…”

“…Recent empirical studies (Crowder and Hoffman, 1996;Caporale and Pittis, 2004;Sun and Phillips, 2004;Phillips, 2005;Christopoulos and Leon-Ledesma, 2007;Westerlund, 2008) have addressed problems around the estimation of this relation, such as the existence of procyclical fluctuations in the real interest rate and the coefficient of inflation not being equal to 1. While they focus solely on finding methodological solutions for the empirical failures of this relation, we suggest that theory can lend a hand.…”