We derive a new family of probability densities that have the property of closed-form integrability. This flexible family finds a variety of applications, of which we illustrate density forecasting from models of the AR-ARCH class for U.S. inflation. We find that the hypernormal distribution for...

We argue that the current framework for predictive ability testing (e.g.,West, 1996) is not necessarily useful for real-time forecast selection, i.e., for assessing which of two competing forecasting methods will perform better in the future. We propose an alternative framework for out-of-sample...

This paper proposes a method for comparing and combining conditional quantile forecasts in an out-of-sample framework. We construct a Conditional Quantile Forecast Encompassing (CQFE) test as a Wald-type test of superior predictive ability. Rejection of CQFE provides a basis for combination of...

In this paper we compare the relative efficiency of different methods of forecasting the aggregate of spatially correlated variables. Small sample simulations confirm the asymptotic result that improved forecasting performance can be obtained by imposing a priori constraints on the amount of...

This paper proposes tests for comparing the accuracy of density forecasts. The evaluation makes use of scoring rules, which are loss functions defined over the density forecast and the realizations of the variable. In particular, a logarithmic scoring rule leads to the development of asymptotic...

This paper demonstrates the extensive scope of an alternative to standardinstrumental variables methods, namely covariate-based methods, for identifying and es-timating effects of interest in general structural systems. As we show, commonly usedeconometric methods, speci…cally parametric,...

We give two new approaches to testing a conditional form of exogeneity. This conditionensures unconfoundedness and identication of eects of interest in structural systems. Asthese approaches do not rely on the absence of causal eects of treatment under the null,they complement earlier methods of...

We study the scope of local indirect least squares (LILS) methods for nonparametrically estimating average marginal effects of an endogenous cause X on a response Y in triangular structural systems that need not exhibit linearity, separability, or monotonicity in scalar unobservables. One main...

We study the interrelations between (conditional) independence and causal relations in settable systems. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide...

This paper examines the ways in which structural systems can yield observed variables, other than the cause or treatment of interest, that can play an instrumental role in identifying and estimating causal effects. We focus speciÖcally on the ways in which structures determine exclusion...