Most of the time, there is no shortage of econometric methods that may be used in empirical economics projects for the purposes of estimation or inference. Occasionally, however, a researcher may run into a gap in econometric theory when looking for the most suitable technique for a specific purpose. The discussion here focuses on two such gaps that hindered the interpretion of certain types of empirical results, but whose bridging seemed conceptually feasible.
The first was a pseudo R squared for use with probit and other dichotomous dependent variable equations. The literature was full of alternative proposals, but they all seemed to be flawed as intuitive indicators of the fit of equations such as the probit models used to forecast recessions using the yield curve spread. Initially, Estrella and Hardouvelis (1991) used an alternative that had been proposed by McFadden, but its construction seemed ad hoc and there was no guarantee that it provided an accurate intuitive assessment of the fit. In response, Estrella (1998) constructed a pseudo R squared that satisfies several desirable properties that other measures lack, and in the process showed that the McFadden measure is misleading except under very restrictive data-dependent conditions, which fortuitously the data for the 1991 article approximately met. The Estrella R squared has been included in several commercial econometrics packages and is the default measure for DDV models in the econometrics package RATS. It has been adopted in much of the subsequent yield curve research.
The second gap was the need for exact p values for use in tests of unknown structural breakpoints in econometric models. These tests have been performed in applications that include the forecasting models using the yield curve, as well as the evaluation of certain competing macroeconomic models. An algorithm to compute exact p values of break tests where the breakpoint is unknown was developed and applied in joint work with Fuhrer (2003). Estrella (2003) presented an efficient algorithm for computing exact p values and gave a table of exact critical values for a range of models and testing strategies.
Estrella, Arturo and Gikas Hardouvelis (1991) “The term structure as a predictor of real economic activity.” Journal of Finance 46: 555-576.
Estrella, Arturo (1998) “A new measure of fit for equations with dichotomous dependent variables.” Journal of Business and Economic Statistics. Working Paper.
Estrella, Arturo and Jeffrey C. Fuhrer (2003) “Monetary policy shifts and the stability of monetary policy models.” Review of Economics and Statistics.
Estrella, Arturo (2003) “Critical values and p values of Bessel process distributions: Computation and application to structural break tests.” Econometric Theory.