Weak Theories and Parameter Instability: Using Flexible Least Squares to Take Time Varying Relationships Seriously

A common assumption by time-series analysts is that the estimated coefficients remain fixed through time. Yet this strong assumption often has little grounds in substantive theory or empirical tests. If the true coefficients change over time, but are estimated with fixed-coefficient methods such as Ordinary Least Squares (OLS) or its many offshoots, then this can lead to significant information loss, as well as errors of inference. This article demonstrates a method, Flexible Least Squares (FLS), for exploring the relative stability of time-series coefficients. FLS is superior to other such methods in that it enables the analyst to diagnose the magnitude of coefficient variation and detect which particular coefficients are changing. FLS also provides an estimated vector of time-varying coefficients for exploratory or descriptive purposes. FLS properties are demonstrated through simulation analysis and an evaluation of the time-varying characteristics of explanations of presidential approval from 1978 to 1997.