Reconsidering the evidence: Are Eurozone business cycles converging

This paper, using 40 years of monthly industrial production data, examines the relationship between the business cycles of the 12 Eurozone countries. Since estimates of the business cycle have been found to be sensitive to how the cycle is measured, a range of alternative measures are considered. We focus on both parametric and nonparametric univariate measures of the ‘classical’ and ‘growth’ cycles. We then investigate whether Eurozone business cycles have converged. This is based on an analysis of the distribution of bivariate correlation coefficients between the 12 countries’ business cycles. This extends previous work that has tested for convergence, in a similar manner by focusing on correlation, but has not considered the entire distribution, instead focusing on the mean correlation coefficient or particular bivariate correlation coefficients. Although empirical inference about individual Eurozone business cycles is found to be sensitive to the measure of the business cycle considered, our measure of convergence between the Eurozone business cycles exhibits common features across the alternative measures of the business cycle. Interestingly, we find that there have been periods of convergence, identified by the distribution tending to unity, and periods of divergence. Although further data are required to corroborate the story, there is evidence to suggest that the Euro-zone has entered a period of convergence after the clear period of divergence in the early 1990s in the aftermath of German unification and at the time of the currency crises in Europe. This is encouraging for the successful operation of a common monetary policy in the Eurozone. --

Least squares estimation in nonlinear cohort panels with learning from experience

We discuss techniques of estimation and inference for nonlinear cohort panels with learning from experience, showing, inter alia, the consistency and asymptotic normality of the nonlinear least squares estimator employed in the seminal paper by Malmendier and Nagel (2016). Potential pitfalls for hypothesis testing are identified and solutions proposed. Monte Carlo simulations verify the properties of the estimator and corresponding test statistics in finite samples, while an application to a panel of survey expectations demonstrates the usefulness of the theory developed

Co-breaking : representation, estimation and testing

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Least squares estimation in nonlinear cohort panels with learning from experience

We discuss techniques of estimation and inference for nonlinear cohort panels with learning from experience, showing, inter alia, the consistency and asymptotic normality of the nonlinear least squares estimator employed in the seminal paper by Malmendier and Nagel (2016). Potential pitfalls for hypothesis testing are identified and solutions proposed. Monte Carlo simulations verify the properties of the estimator and corresponding test statistics in finite samples, while an application to a panel of survey expectations demonstrates the usefulness of the theory developed

Strong consistency of the least squares estimator in regression models with adaptive learning

This paper looks at the strong consistency of the ordinary least squares (OLS) estimator in linear regression models with adaptive learning. It is a companion to Christopeit & Massmann (2018) which considers the estimator’s convergence in distribution and its weak consistency in the same setting. Under constant gain learning, the model is closely related to stationary, (alternating) unit root or explosive autoregressive processes. Under decreasing gain learning, the regressors in the model are asymptotically collinear. The paper examines, first, the issue of strong convergence of the learning recursion: It is argued that, under constant gain learning, the recursion does not converge in any probabilistic sense, while for decreasing gain learning rates are derived at which the recursion converges almost surely to the rational expectations equilibrium. Secondly, the paper establishes the strong consistency of the OLS estimators, under both constant and decreasing gain learning, as well as rates at which the estimators converge almost surely. In the constant gain model, separate estimators for the intercept and slope parameters are juxtaposed to the joint estimator, drawing on the recent literature on explosive autoregressive models. Thirdly, it is emphasised that strong consistency is obtained in all models although the near-optimal condition for the strong consistency of OLS in linear regression models with stochastic regressors, established by Lai & Wei (1982a), is not always met