Building on the time-varying-coefficient (TVC) model, we propose a generalization of the concept of cointegration, allowing for the possibility that a set of variables measured with error entails a nonlinear relationship with unknown functional form. Both the dependent and explanatory variables of this relationship may be nonstationary (not necessarily of unit-root type), but there exists a nonlinear combination of all these explanatory variables that completely explains all the variation in the dependent variable. The TVC model allows us to test for the presence of this generalized cointegration in the absence of knowledge of the true nonlinear functional form and the full set of explanatory variables. We present the basic stages of the technique and discuss in detail how the issues of nonstationarity and cointegration affect each stage of the TVC estimation procedure.

Estimated microproduction functions confront two major problems—those of (1) unknown functional forms and (2) the measurement of capital independent of the distribution of output among the factors of production. The latter problem has emerged unresolved from the earlier Cambridge capital controversy. In the presence of these two problems, all specifications of microproduction functions have involved nonunique coefficients and error terms. We provide a method of deriving time-varying coefficients that produces unique coefficients and error terms. Specifically, we respecify the microproduction function in such a way that its coefficients are the sums of (i) the appropriate partial derivatives and (ii) exact representations of excluded-variable biases. By decomposing the total coefficients, we obtain the unique coefficients and a unique error term. Our treatment of heterogeneous capital is not subject to the criticisms of that concept that emerged during the Cambridge controversy.

We examine whether the importance of lagged inflation in the New Keynesian Phillips Curve (NKPC) may be a result of specification biases. NKPCs are estimated for four countries: France, Germany, Italy, and the United Kingdom. Using time-varying coefficient (TVC) estimation, a procedure that can deal with possible specification biases, we find support for the NKPC model that excludes lagged inflation. Our results indicate a Phillips-curve relationship for the countries considered that does not contain an inertial element.

Under certain interpretations of its coefficients, a specified econometric model is an exact representation of the “true” model, defining the “objective” probability distribution. This note enumerates these interpretations. In the absence of the conditions implied by these interpretations, the econometric model is misspecified. The note shows that model misspecifications prevent the satisfaction of a necessary and sufficient condition for individual expectations to be rational in Muth's sense. Whereas restrictive forms of econometric models can give very inaccurate predictions, this note describes the conditions under which the predictions generated from time-varying coefficient models coincide with the predictions generated from the relevant economic theory.