Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. We establish instead that a suitable transformation of the forecast error- known as the generalized forecast error- possesses an equivalent set of properties. The paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts.

In this chapter, I review the main methods and techniques of complex systems science. As a

This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approach of Pearl. The settable system framework nests these prior approaches, while affording significant improvements to each. For example, the settable system approach permits identification and estimation of causal effects without requiring exogenous instruments, generalizing the classical structural equations approach; it relaxes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates; and it accommodates mutual causality, generalizing the DAG approach. We provide necessary and sufficient conditions for identification of covariate-conditioned average causal effects, parametric and nonparametric estimation results, and new tests for unconfoundedness.

Abstract This paper demonstrates the extensive scope of an alternative to standard instrumental variables methods, namely covariate-based methods, for identifying and estimating e¤ects of interest in general structural systems. As we show, commonly used econometric methods, speci…cally parametric, semi-parametric, and nonparametric extremum or moment-based methods, can all exploit covariates to estimate well-identi…ed structural e¤ects. The systems we consider are general, in that they need not impose linearity, separability, or monotonicity restrictions on the structural relations. We consider e¤ects of multiple causes; these may be binary, categorical, or continuous. For continuous causes, we examine both marginal and non-marginal e¤ects. We analyze e¤ects on aspects of the response distribution generally, de…ned by explicit or implicit moments or as optimizers (e.g., quantiles). Key for identi…cation is a speci…c conditional exogeneity relation. We examine what happens in its absence and …nd that identi…cation generally fails. Nevertheless, local and near identi…cation results hold in its absence, as we show.

The Enron Corporation went from a $65 billion dollar market capitalization to bankruptcy in just 16 months. Using statistical techniques for extracting the implied probability distributions built into option prices, I examine the market’s expectation of Enron’s risk of collapse. I find that the options market remained far too optimistic about the stock until just weeks before their bankruptcy filing.

This paper demonstrates the extensive scope of an alternative to standard instrumental variables methods, namely covariate-based methods, for identifying and estimating effects of interest in general structural systems. As we show, commonly used econometric methods, specifically parametric, semi-parametric, and nonparametric extremum or moment-based methods, can all exploit covariates to estimate well-identified structural effects. The systems we consider are general, in that they need not impose linearity, separability, or monotonicity restrictions on the structural relations. We consider e¤ects of multiple causes; these may be binary, categorical, or continuous. For continuous causes, we examine both marginal and non-marginal effects. We analyze effects on aspects of the response distribution generally, defined by explicit or implicit moments or as optimizers (e.g., quantiles). Key for identification is a specific conditional exogeneity relation. We examine what happens in its absence and find that identification generally fails. Nevertheless, local and near identification results hold in its absence, as we show.

Abstract not found

In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools employed, and the foundational science of complex systems. The focus of this chapter is overwhelmingly on the third heading, that of tools.