Density Forecasting: A Survey

A density forecast of the realization of a random variable at some future time is an estimate of the probability distribution of the possible future values of that variable. This article presents a selective survey of applications of density forecasting in macroeconomics and finance, and discusses some issues concerning the production, presentation and evaluation of density forecasts.

The Population Genetic Signature of Polygenic Local Adaptation

Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that may have been influenced by local adaptation. We exploit the fact that GWAS provide an estimate of the additive effect size of many loci to estimate the mean additive genetic value for a given phenotype across many populations as simple weighted sums of allele frequencies. We first describe a general model of neutral genetic value drift for an arbitrary number of populations with an arbitrary relatedness structure. Based on this model we develop methods for detecting unusually strong correlations between genetic values and specific environmental variables, as well as a generalization of $Q_{ST}/F_{ST}$ comparisons to test for over-dispersion of genetic values among populations. Finally we lay out a framework to identify the individual populations or groups of populations that contribute to the signal of overdispersion. These tests have considerably greater power than their single locus equivalents due to the fact that they look for positive covariance between like effect alleles, and also significantly outperform methods that do not account for population structure. We apply our tests to the Human Genome Diversity Panel (HGDP) dataset using GWAS data for height, skin pigmentation, type 2 diabetes, body mass index, and two inflammatory bowel disease datasets. This analysis uncovers a number of putative signals of local adaptation, and we discuss the biological interpretation and caveats of these results.Comment: 42 pages including 8 figures and 3 tables; supplementary figures and tables not included on this upload, but are mostly unchanged from v

Identification of and correction for publication bias

Some empirical results are more likely to be published than others. Such selective publication leads to biased estimates and distorted inference. This paper proposes two approaches for identifying the conditional probability of publication as a function of a study's results, the first based on systematic replication studies and the second based on meta-studies. For known conditional publication probabilities, we propose median-unbiased estimators and associated confidence sets that correct for selective publication. We apply our methods to recent large-scale replication studies in experimental economics and psychology, and to meta-studies of the effects of minimum wages and de-worming programs

Targeted Undersmoothing

This paper proposes a post-model selection inference procedure, called targeted undersmoothing, designed to construct uniformly valid confidence sets for a broad class of functionals of sparse high-dimensional statistical models. These include dense functionals, which may potentially depend on all elements of an unknown high-dimensional parameter. The proposed confidence sets are based on an initially selected model and two additionally selected models, an upper model and a lower model, which enlarge the initially selected model. We illustrate application of the procedure in two empirical examples. The first example considers estimation of heterogeneous treatment effects using data from the Job Training Partnership Act of 1982, and the second example looks at estimating profitability from a mailing strategy based on estimated heterogeneous treatment effects in a direct mail marketing campaign. We also provide evidence on the finite sample performance of the proposed targeted undersmoothing procedure through a series of simulation experiments

Ecological panel inference in repeated cross sections

This paper presents a Markov chain model for the estimation of individual-level binary transitions from a time series of independent repeated cross-sectional (RCS) samples. Although RCS samples lack direct information on individual turnover, it is demonstrated here that it is possible with these data to draw meaningful conclusions on individual state-to-state transitions. We discuss estimation and inference using maximum likelihood, parametric bootstrap and Markov chain Monte Carlo approaches. The model is illustrated by an application to the rise in ownership of computers in Dutch households since 1986, using a 13-wave annual panel data set. These data encompass more information than we need to estimate the model, but this additional information allows us to assess the validity of the parameter estimates. We examine the determinants of the transitions from 'have-not' to 'have' (and back again) using well-known socio-economic and demographic covariates of the digital divide. Parametric bootstrap and Bayesian simulation are used to evaluate the accuracy and the precision of the ML estimates and the results are also compared with those of a first-order dynamic panel model. To mimic genuine repeated cross-sectional data, we additionally analyse samples of independent observations randomly drawn from the panel. Software implementing the model is available.

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1