A comparison of two model averaging techniques with an application to growth empirics

Parameter estimation under model uncertainty is a difficult and fundamental issue in econometrics. This paper compares the performance of various model averaging techniques. In particular, it contrasts Bayesian model averaging (BMA) — currently one of the standard methods used in growth empirics — with a new method called weighted-average least squares (WALS). The new method has two major advantages over BMA: its computational burden is trivial and it is based on a transparent definition of prior ignorance. The theory is applied to and sheds new light on growth empirics where a high degree of model uncertainty is typically present.     

Central bank’s forecasts and lack of transparency: An assessment of the effect on private expectations in a large emerging economy

We analyze whether the Central Bank of Brazil’s Inflation Reports projections influences the private’s inflation expectations. Specifically, we investigate how the central bank’s inflation forecasts affect the private sector’s inflation expectations through a qualitative and quantitative examination of the disagreement measure between them. Furthermore, we appraise if the lack of transparency resulting from the difference between the central bank’s inflation forecasts and the realized inflation affects the private’s inflation expectations. Although the findings confirm the previous studies that point out that the central bank transparency can affect the readjustment of market expectations, the results do not rule out the possibility of the central bank’s forecast and private’s inflation expectations being affected reciprocally.     

Bayesian prediction with cointegrated vector autoregressions

A complete procedure for calculating the joint predictive distribution of future observations based on the cointegrated vector autoregression is presented. The large degree of uncertainty in the choice of cointegration vectors is incorporated into the analysis via the prior distribution. This prior has the effect of weighing the predictive distributions based on the models with different cointegration vectors into an overall predictive distribution. The ideas of Litterman [Mimeo, Massachusetts Institute of Technology, 1980] are adopted for the prior on the short run dynamics of the process resulting in a prior which only depends on a few hyperparameters. A straightforward numerical evaluation of the predictive distribution based on Gibbs sampling is proposed. The prediction procedure is applied to a seven-variable system with a focus on forecasting Swedish inflation.     

Combining exponential smoothing forecasts using Akaike weights

Simple forecast combinations such as medians and trimmed or winsorized means are known to improve the accuracy of point forecasts, and Akaike’s Information Criterion (AIC) has given rise to so-called Akaike weights, which have been used successfully to combine statistical models for inference and prediction in specialist fields, e.g., ecology and medicine. We examine combining exponential smoothing point and interval forecasts using weights derived from AIC, small-sample-corrected AIC and BIC on the M1 and M3 Competition datasets. Weighted forecast combinations perform better than forecasts selected using information criteria, in terms of both point forecast accuracy and prediction interval coverage. Simple combinations and weighted combinations do not consistently outperform one another, while simple combinations sometimes perform worse than single forecasts selected by information criteria. We find a tendency for a longer history to be associated with a better prediction interval coverage.     

Judgmental adjustment of forecasts: A comparison of methods

Attention has recently been given to combinations of subjective and objective forecasts to improve forecast accuracy. This research offers an extension on this theme by comparing two methods that can be used to adjust an objective forecast. Wolfe and Flores (1990) show that forecasts can be judgmentally adjusted by analysts using a structured approach based on Saaty's analytic hierarchy process (AHP). In this study, the centroid method is introduced as a vehicle for forecast adjustment and is compared to the AHP. While the AHP allows for finer tuning in reflecting decision maker judgement, the centroid method produces very similar results and is much simpler to use in the forecast adjustment process.     

MODEL AVERAGING IN ECONOMICS: AN OVERVIEW

Standard practice in empirical research is based on two steps: first, researchers select a model from the space of all possible models; second, they proceed as if the selected model had generated the data. Therefore, uncertainty in the model selection step is typically ignored. Alternatively, model averaging accounts for this model uncertainty. In this paper, I review the literature on model averaging with special emphasis on its applications to economics. Finally, as an empirical illustration, I consider model averaging to examine the deterrent effect of capital punishment across states in the USA.     

Spatial Growth Regressions: Model Specification,Estimation and Interpretation

Abstract

We attempt to clarify a number of points regarding use of spatial regression models for regional growth analysis. We show that as in the case of non-spatial growth regressions, the effect of initial regional income levels wears off over time. Unlike the non-spatial case, long-run regional income levels depend on: own region as well as neighbouring region characteristics, the spatial connectivity structure of the regions, and the strength of spatial dependence. Given this, the search for regional characteristics that exert important influences on income levels or growth rates should take place using spatial econometric methods that account for spatial dependence as well as own and neighbouring region characteristics, the type of spatial regression model specification, and weight matrix. The framework adopted here illustrates a unified approach for dealing with these issues.     

Forecast encompassing tests for the expected shortfall

We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES has received much attention since its introduction into the Basel III Accords, which stipulate its use as the primary market risk measure for international banking regulation. We utilize joint loss functions for the pair ES and Value at Risk to set up three ES encompassing test variants. The tests are built on an asymptotic theory that is robust to misspecifications. We investigate the finite sample properties of the tests in an extensive simulation study. Finally, we use the encompassing tests to illustrate the potential of forecast combination methods for different financial assets.     

Probability distributions or point predictions? Survey forecasts of US output growth and inflation

We consider whether survey respondents’ probability distributions, reported as histograms, provide reliable and coherent point predictions, when viewed through the lens of a Bayesian learning model. We argue that a role remains for eliciting directly-reported point predictions in surveys of professional forecasters.     

Judgmental aggregation strategies depend on whether the self is involved

We report the results of a novel experiment that addresses two unresolved questions in the judgmental forecasting literature. First, how does combining the estimates of others differ from revising one’s own estimate based on the judgment of another? The experiment found that participants often ignored advice when revising an estimate but averaged estimates when combining. This was true despite receiving identical feedback about the accuracy of past judgments. Second, why do people consistently tend to overweight their own opinions at the expense of profitable advice? We compared two prominent explanations for this, differential access to reasons and egocentric beliefs, and found that neither adequately accounts for the overweighting of the self. Finally, echoing past research, we find that averaging opinions is often advantageous, but that choosing a single judge can perform well in certain predictable situations.     

Decomposing the effects of crowd-wisdom aggregators: The bias–information–noise (BIN) model

Aggregating predictions from multiple judges often yields more accurate predictions than relying on a single judge, which is known as the wisdom-of-the-crowd effect. However, a wide range of aggregation methods are available, which range from one-size-fits-all techniques, such as simple averaging, prediction markets, and Bayesian aggregators, to customized (supervised) techniques that require past performance data, such as weighted averaging. In this study, we applied a wide range of aggregation methods to subjective probability estimates from geopolitical forecasting tournaments. We used the bias–information–noise (BIN) model to disentangle three mechanisms that allow aggregators to improve the accuracy of predictions: reducing bias and noise, and extracting valid information across forecasters. Simple averaging operates almost entirely by reducing noise, whereas more complex techniques such as prediction markets and Bayesian aggregators exploit all three pathways to allow better signal extraction as well as greater noise and bias reduction. Finally, we explored the utility of a BIN approach for the modular construction of aggregators.     

三层供应链协同预测博弈研究

运用纳什均衡和贝叶斯更新模型,得到了在一个三层供应链中联合预测的实现条件。模型中,供应商、运输商、零售商均需决定在预测技术上的投资水平,三方的需求预测将会被汇总成一个统一的预测。结果表明,各方预测能力越接近中等水平,会有更多成员倾向于在预测上进行投资。预测能力偏离中等水平越远,越容易出现搭便车行为,即至少有一方不进行预测。