Ling Hu Publications

This paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices. The theory extends recent work by Park and Phillips (2000) on binary choice models. As in this earlier work, the maximum likelihood (ML) estimator is consistent and has a limit theory with multiple rates of convergence (n3/4 and n1/4) and mixture normal distributions where the mixing variates depend on Brownian local time as well as Brownian motion. An extended arc sine limit law is given for the sample proportions of the various choices. The new limit law exhibits a wider range of potential behavior that depends on the values taken by the threshold parameters.

Keywords: Brownian motion, Brownian local time, Discrete choice model, Dual convergence rates, Extended arc sine laws, Integrated time series, Maximum likelihood estimation, Threshold parameters

JEL Classification: C22, C25

We apply a discrete choice approach to model the empirical behavior of the Federal Reserve in changing the federal funds target rate, the benchmark of short term market interest rates in the US. Our methods allow the explanatory variables to be nonstationary as well as stationary. This feature is particularly useful in the present application as many economic fundamentals that are monitored by the Fed and are believed to affect decisions to adjust interest rate targets display some nonstationarity over time. The empirical model is determined using the PIC criterion (Phillips and Ploberger, 1996; Phillips, 1996) as a model selection device. The chosen model successfully predicts the majority of the target rate changes during the time period considered (1985-2001) and helps to explain strings of similar intervention decisions by the Fed. Based on the model-implied optimal interest rate, our findings suggest that there a lag in the Fed’s reaction to economic shocks and that the Fed is more conservative in raising interest rates than in lowering rates.

Keywords: Extended arc sine laws, Federal funds target rate, Interest rate, Monetary policy, Nonstationary discrete choice

JEL Classification: C22, C25, E43, E52