The EM principle implies the moments underlying the information matrix test for switching regressions are the expectation given the data of the moments one would test if one knew the subpopulation each observation originated from. Thus, we identify components related to conditional heteroskedasticity, conditional and unconditional skewness, and unconditional kurtosis of regression residuals within each regime. Simulations indicate analytical expressions for the asymptotic covariance matrix of those moments adjusted for sampling variability in parameter estimators provide reliable finite sample sizes and good power against various alternatives, especially combined with the parametric bootstrap. We apply the test to cross-country convergence regressions.

This paper examines how parental consent requirements and access frictions jointly shape teenage reproductive decisions. Exploiting the Spanish 2015 reform that mandated parental consent for 16–17-year-olds, together with Spanish administrative microdata on all registered abortions and births, I find that the reform led to declines in both abortions and pregnancies among affected teenagers. Consistent with a two-stage decision framework, most of the reduction in abortions operates through a decrease in pregnancies, indicating behavioral responses before pregnancy. A simple model of teenage abortion decisions is used to interpret these findings and to clarify how legal and access barriers interact. Using data on proximity to abortion centers and local religiosity, I show how these access frictions operate in the context of parental consent requirements. Where travel costs are high, parental involvement is effectively required even in the absence of formal consent laws, limiting the impact of the reform. When parental consent does bind, local norms shape the margin of adjustment: in more traditional municipalities, the reform primarily affects abortion decisions conditional on pregnancy.

We show that the Laubach and Williams (2003) model and its variants in Holston, Laubach and Williams (2017, 2023) cannot estimate the natural rate with finite precision when either the IS curve or the Phillips curve are flat. To solve this unobservability, we propose a simple augmented model with a mean-reverting interest rate gap that considerably narrows the natural rate’s confidence bands in those empirically relevant situations. We also assess the ability of the corporate risk premium and the share of working age population to explain movements in the natural rate, but they generate filtered estimates that fluctuate too much.

This paper investigates whether Germany’s historical confessional divides continue to influence contemporary political behavior by exploiting persistent geographic variation between historically Catholic and Protestant areas through a Geographic Regression Discontinuity Design. Integrating historical and geospatial data with modern electoral and census sources, I find that historically Catholic municipalities show systematically higher support for the center-right Union parties than their counterparts in every federal election from 1990 to 2025, while historically Protestant areas are more likely to support parties on the center-left and left of the political spectrum. Individual-level survey data covering all Federal Elections since 1953 and the German General Social Survey provide suggestive evidence that voting behavior is shaped by confessional affiliation.