“A Bias Recognized Is a Bias Sterilized”: The Effects of a Bias in Forecast Evaluation

Are traditional tests of forecast evaluation well behaved when the competing (nested) model is biased? No, they are not. In this paper, we show analytically and via simulations that, under the null hypothesis of no encompassing, a bias in the nested model may severely distort the size properties of traditional out-of-sample tests in economic forecasting. Not surprisingly, these size distortions depend on the magnitude of the bias and the persistency of the additional predictors. We consider two different cases: (i) There is both in-sample and out-of-sample bias in the nested model. (ii) The bias is present exclusively out-of-sample. To address the former case, we propose a modified encompassing test (MENC-NEW) robust to a bias in the null model. Akin to the ENC-NEW statistic, the asymptotic distribution of our test is a functional of stochastic integrals of quadratic Brownian motions. While this distribution is not pivotal, we can easily estimate the nuisance parameters. To address the second case, we derive the new asymptotic distribution of the ENC-NEW, showing that critical values may differ remarkably. Our Monte Carlo simulations reveal that the MENC-NEW (and the ENC-NEW with adjusted critical values) is reasonably well-sized even when the ENC-NEW (with standard critical values) exhibits rejections rates three times higher than the nominal size.

Social Ills in Rich Countries: New Evidence on Levels, Causes, and Mediators

The income inequality hypothesis claims that in rich societies inequality causes a range of health and social problems (henceforth: social ills), e.g. because economic inequality induces feelings of status anxiety and corrodes social cohesion. This paper provides an encompassing test of the income inequality hypothesis by exploring levels and breeding conditions of social ills in 40 affluent countries worldwide, as well as pathways for a subsample of wealthy European countries. Our aggregate-level research is based on a revised and updated Index of Social Ills inspired by Wilkinson and Pickett’s book The Spirit Level, which we compile for both more countries (40) and more years (2000–2015) and combine with survey information about experienced quality-of-life as potential mediators. We get three major results: First, cross-sectionally income inequality is indeed strongly and consistently related to social ills, but so is economic prosperity. Second, while longitudinally changes in inequality do not result in changing levels of social ills, rising prosperity effectively reduces the amount of social ills, at least in Europe. Finally, whereas the cross-sectional analysis indicates that aspects of social cohesion most consistently mediate between economic conditions and social ills, the longitudinal mediation analyses could not ultimately clarify through which pathway rising prosperity reduces social ills. Overall we conclude that the income inequality hypothesis is, at best, too narrow to fully understand health and social problems in rich countries.

A Simple Encompassing Test for the Deterministic and Bilinear Unit Root Models

A new parameters’ encompassing test is proposed for deciding between the deterministic unit root processes with a structural break and the bilinear unit root model without such break. The test consists in testing three sets of hypotheses regarding parameters in a simple regression model. The test uses the t-ratio and F-statistics, of non-trivial distributions under the null hypothesis. The finite sample distributions for the relevant statistics are tabulated and the asymptotic distribution of the F-test is derived. The test has been applied for the daily stock price indices for 66 countries, for the period 1992-2001. The results support the conjecture that the bilinear model dominates the structural break model more often than the other way around. Also, it is likely that in practical applications the bilinear unit root process might be mistaken for the deterministic unit root process with a structural break.Financial support of INTAS project No. 03-51-3714 Nonstationary multivariate and nonlinear econometric models: theory and applications is gratefully acknowledged.

Selecting Single Model in Combination Forecasting Based on Cointegration Test and Encompassing Test

Combination forecasting takes all characters of each single forecasting method into consideration, and combines them to form a composite, which increases forecasting accuracy. The existing researches on combination forecasting select single model randomly, neglecting the internal characters of the forecasting object. After discussing the function of cointegration test and encompassing test in the selection of single model, supplemented by empirical analysis, the paper gives the single model selection guidance: no more than five suitable single models can be selected from many alternative single models for a certain forecasting target, which increases accuracy and stability.