Nonlinear regression models have been widely used in practice for a variety of time series and
cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular,
Smooth Transition Regression (STR) models have been shown to be very useful for representing and capturing
asymmetric behavior. Most STR models have been applied to univariate processes, and have made a
variety of assumptions, including stationary or cointegrated processes, uncorrelated, homoskedastic or conditionally
heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity,
the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax
the assumption of weakly exogenous regressors and to discuss moment based methods for estimating STR
models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic
test of linearity of the underlying process under endogeneity, developing an estimation procedure
and a misspecification test for the STR model, presenting the results of Monte Carlo simulations to show
the usefulness of the model and estimation method, and providing an empirical application for inflation rate
targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated
by a straightforward application of existing results in the literature.
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