Keele (2010, Political Analysis 18:189–205) emphasizes that the incumbent test for detecting proportional hazard (PH) violations in Cox duration models can be adversely affected by misspecified covariate functional form(s). In this note, I reevaluate Keele’s evidence by running a full set of Monte Carlo simulations using the original article’s illustrative data-generating processes (DGPs). I make use of the updated PH test calculation available in R’s survival package starting with v3.0-10. Importantly, I find the updated PH test calculation performs better for Keele’s DGPs, suggesting its scope conditions are distinct and worth further investigating. I also uncover some evidence for the traditional calculation suggesting it, too, may have additional scope conditions that could impact practitioners’ interpretation of Keele (2010). On the whole, while we should always be attentive to model misspecification, my results suggest we should also become more attentive to how frequently the PH test’s performance is affected in practice, and that the answer may depend on the calculation’s implementation.

Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and redshift. As key results are increasingly derived using Bayesian inference, there is increasing scrutiny on Bayesian methods. In this review, we discuss the phenomenon of model misspecification, in which results obtained with Bayesian inference are misleading because of deficiencies in the assumed model(s). Such deficiencies can impede our inferences of the true parameters describing physical systems. They can also reduce our ability to distinguish the ‘best fitting’ model: it can be misleading to say that Model A is preferred over Model B if both models are manifestly poor descriptions of reality. Broadly speaking, there are two ways in which models fail. Firstly, models that fail to adequately describe the data (either the signal or the noise) have misspecified likelihoods. Secondly, population models—designed, for example, to describe the distribution of black hole masses—may fail to adequately describe the true population due to a misspecified prior. We recommend tests and checks that are useful for spotting misspecified models using examples inspired by gravitational-wave astronomy. We include companion python notebooks to illustrate essential concepts.

The classical credibility theory is a cornerstone of experience rating, especially in the field of property and casualty insurance. An obstacle to putting the credibility theory into practice is the conversion of available prior information into a precise choice of crucial hyperparameters. In most real-world applications, the information necessary to justify a precise choice is lacking, so we propose an imprecise credibility estimator that honestly acknowledges the imprecision in the hyperparameter specification. This results in an interval estimator that is doubly robust in the sense that it retains the credibility estimator’s freedom from model specification and fast asymptotic concentration, while simultaneously being insensitive to prior hyperparameter specification.

Models testing interactive and quadratic hypotheses are common in Political Science but control strategies for these models have received little attention. Common practice is to simply include additive control variables, without relevant product terms, into models with interaction or quadratic terms. In this paper, we show in Monte Carlos that interaction terms can absorb the effects of other un-modeled interaction and non-linear effects and analogously, that included quadratic terms can reflect omitted interactions and non-linearities. This problem even occurs when included and omitted product terms do not share any constitutive terms. We show with Monte Carlo experiments that regularized estimators, the adaptive Lasso, Kernel Regularized Least Squares (KRLS), and Bayesian Additive Regression Trees (BART) can prevent the misattribution of interactive/quadratic effects, minimize the problems of efficiency loss and overfitting, and have low false-positive rates. We illustrate how inferences drawn can change when relevant product terms are used in the control strategy using a recent paper. Implementing the recommendations of this paper would increase the reliability of conditional and non-linear relationships estimated in many papers in the literature.

This paper tests the ability of New Keynesian models to match the data regarding a key channel for monetary transmission: the dynamic interactions between macroeconomic variables and their corresponding expectations. We exploit survey expectations data and adopt a dynamic stochastic general equilibrium (DSGE)-VAR approach to assess the extent and sources of model misspecification. The results point to serious misspecification in the expectations-formation side of the DSGE model. The rational expectations hypothesis is primarily responsible for the model's failure to capture the co-movements between observed macroeconomic expectations and realizations. Alternative models of expectations formation help partially reconcile the New Keynesian model with the data.

The classical twin design uses data on the variation of and covariation between monozygotic and dizygotic twins to infer underlying genetic and environmental causes of phenotypic variation in the population. By using data from additional relative classes, such as parents, extended twin family designs more comprehensively describe the causes of phenotypic variation. This article introduces an extension of previous extended twin family models, the Cascade model, which uses information on twins as well as their siblings, spouses, parents, and children to differentiate two genetic and six environmental sources of phenotypic variation. The Cascade also relaxes assumptions regarding mating and cultural transmission that existed in previous extended twin family designs. The estimation of additional parameters and relaxation of assumptions is potentially important, not only because it allows more fine-grained descriptions of the causes of phenotypic variation, but more importantly, because it can reduce the biases in parameter estimates that exist in earlier designs.

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.

The rational expectations hypothesis swept through macroeconomics during the 1970s and permanently altered the landscape. It remains the prevailing paradigm in macroeconomics, and rational expectations is routinely used as the standard solution concept in both theoretical and applied macroeconomic modelling. The rational expectations hypothesis was initially formulated by John F. Muth Jr. in the early 1960s. Together with Robert Lucas Jr., Thomas (Tom) Sargent pioneered the rational expectations revolution in macroeconomics in the 1970s.

In their landmark paper, Bray and Savin note that the constant-parameters model used by their agents to form expectations is misspecified and that, using standard econometric techniques, agents may be able to determine the time-varying nature of the model's parameters. Here, we consider the same type of model as employed by Bray and Savin except that our agents form expectations using a perceived model with parameters that vary with time. We assume agents use the Kalman filter to form estimates of these time-varying parameters. We find that, under certain restrictions on the structure of the stochastic process and on the value of the stability parameter, the model will converge to its rational expectations equilibrium. Further, the restrictions on the stability parameter required for convergence are identical to those found by Bray and Savin.