In Bayesian theory, the data together with the prior produce a posterior. We show that it is also possible to follow the opposite route, that is, to use data and posterior information (both of which are observable) to reveal the prior (which is not observable). We then apply the theory to...

We consider the question whether top tennis players in a top tournament (Wimbledon) employ an optimal (efficient) service strategy. We show that top players do not, in general, follow an optimal strategy, and we provide a lower bound of the inefficiency. The inefficiency regarding winning a...

We specify a stochastic economy-climate model, adapting Nordhaus' deterministic economy-climate model by allowing for Weitzman-type stochasticity. We show that, under expected power utility, the model is fragile to heavy-tailed distributional assumptions and we derive necessary and sufficient...

This paper studies the interplay between climate, health, and the economy in a stylized world with four heterogeneous regions, labeled 'West' (cold and rich), 'China' (cold and poor), 'India' (warm and poor), and 'Africa' (warm and very poor). We introduce health impacts into a simple integrated...

This paper develops a dynamic model consisting of two regions (North and South), in which the accumulation of human capital is negatively influenced by the global stock of pollution. By characterizing the equilibrium strategy of each region, we show that the regions' best responses can be...

Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these...

We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuous-time macro model and the parametrization of rotation matrices governing...

A linear structure is a family of matrices that satisfy a given set of linear restrictions, such as symmetry or diagonality. We add to the literature on linear structures by studying the family of matrices where all diagonal elements are zero, and discuss two econometric examples where these...

A Bayesian typically uses data and a prior to produce a posterior. In practice, the data and the posterior are often observed but not the prior. We shall follow the opposite route, using data and the posterior information to reveal the prior. We then apply this theory to (equilibrium) climate...

We consider the estimation of the mean of a multivariate normal distribution with known variance. Most studies consider the risk of competing estimators, that is the trace of the mean squared error matrix. In contrast we consider the whole mean squared error matrix, in particular its...