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This chapter summarises the recent approaches to optimal forecast combination from a frequentist perspective. The availability of big data leads to the development of many different models of the same macroeconomic variables. The challenge is to seek the best way to combine all relevant information from big data to create optimal forecast. Forecast combination provides one plausible approach. This chapter discusses the practical aspects of combining forecasts optimally and theoretical properties of the combination both for point forecasts and density forecasts. Specifically, the chapter derives the asymptotic distributions of the estimated optimal weight under two of the most popular forecasting criteria: Mean Squared Forecast Error and Mean Absolute Deviation. This chapter also revisits the insights of the so-called forecast combination puzzle, which shows that in practice a simple average of forecasts outperforms more complex weighting strategies. These theoretical results help address the puzzle by providing a mean to test statistically the difference between the estimated optimal weight and the simple average. The optimal weights obtained from minimising the Kullback–Leibler Information Criterion (KLIC) are discussed in the context of density forecast combination. This chapter also proposes a novel Generalized Method of Moments approach for density forecast combination. The connection between the proposed approach and the conventional approach by minimising KLIC is also investigated in some details.

This paper proposes a framework for the analysis of the theoretical properties of forecast combination, with the forecast performance being measured in terms of mean squared forecast errors (MSFE). Such a framework is useful for deriving all existing results with ease. In addition, it also provides insights into two forecast combination puzzles. Specifically, it investigates why a simple average of forecasts often outperforms forecasts from single models in terms of MSFEs, and why a more complicated weighting scheme does not always perform better than a simple average. In addition, this paper presents two new findings that are particularly relevant in practice. First, the MSFE of a forecast combination decreases as the number of models increases. Second, the conventional approach to the selection of optimal models, based on a simple comparison of MSFEs without further statistical testing, leads to a biased selection.

Item does not contain fulltext, OBJECTIVE: To describe social differences in postponing a general practitioner visit in 31 European countries and to explore whether primary care strength is associated with postponement rates. DATA SOURCES: Between October 2011 and December 2013, the multicountry QUALICOPC study collected data on 61,931 patients and 7,183 general practitioners throughout Europe. STUDY DESIGN: Access to primary care was measured by asking the patients whether they postponed a general practitioner visit in the past year. Social differences were described according to patients' self-rated household income, education, ethnicity, and gender. DATA COLLECTION/EXTRACTION METHODS: Data were analyzed using multivariable and multilevel binomial logistic regression analyses. PRINCIPAL FINDINGS: According to the variance-decomposition in the multilevel analysis, most of the variance can be explained by patient characteristics. Postponement of general practitioner care is higher for patients with a low self-rated household income, a low education level, and a migration background. In addition, although the point estimates are consistent with a substantial effect, no statistically significant association between primary care strength and postponement in the 31 countries is determined. CONCLUSIONS: Despite the universal and egalitarian goals of health care systems, access to general practitioner care in Europe is still determined by patients' socioeconomic status (self-rated household income and education) and migration background.

© 2020 Proceedings - 21st International Congress on Modelling and Simulation, MODSIM 2015. All rights reserved. This paper proposes a unified framework to study the theoretical properties of forecast combination. By setting up the forecast combination problem as a panel data model, the paper obtains the necessary and sufficient conditions for optimal weight as well as the necessary and sufficient conditions for the simple average to be the optimal weight under Mean Squared Forecast Errors (MSFE). These conditions are consistent with existing results in the literature but the derivations are much simpler due to the proposed framework. In addition to existing results, this paper also establishes two useful theoretical results. First, it derives the necessary and sufficient conditions for a single model to outperform simple average of forecasts. As argued in the paper, it is unlikely that any individual model would satisfy these conditions in practice and therefore, it explains the empirical observation that simple average of forecasts often outperforms any single model. More importantly, it provided a theoretical explanation on the superiority of forecast combinations, at least in the MSFE sense. Second, the paper also shows that the MSFE of simple average of forecast decreases as the number of model increases. This implies that a single model is unlikely to be superior over simple average of forecasts if the number of models increases in the combination. This paper shows that the proposed framework is also useful in studying the forecast combination puzzle. The paper verifies the existing view that the puzzle may be a result of estimation error in the optimal weight but more importantly, it identifies an additional cause of the puzzle. Specifically, the MSFE may be an inconsistent estimator of the forecast variance and thus, it may produce inconsistent results on the forecast performance of different models with different weighting schemes. A series of Monte Carlo ex

This paper examines the finite sample properties of structural change tests with an unknown breakpoint for the probit model in the presence of serial correlation. The combination of structural change and serial correlation renders model estimation challenging, affecting the consistency of coefficient estimates. Although there is vast literature concerning structural change tests for linear time series models, the literature for such tests in the context of binary choice models is somewhat sparse. More importantly, the empirical literature has applied the standard tests of structural change on the discrete choice model, despite the fact that most of these tests were developed specifically for the linear regression model. Subsequently, the theoretical properties of these tests in the context of non-linear models are unknown. This includes the class of discrete choice models, such as probit and logit. The issue becomes even more complicated in the presence of serial correlation, since typical tests for structural change often require the assumption of independence in the error terms. Even when the tests allow for a weakly dependent structure in the data, their finite sample performance remains unknown.This paper conducts simulation analysis on the size of ‘supremum’ Wald, LR and LM tests for structural change in the context of the probit model with varying levels of serial correlation. It is found that the shortcomings of the tests in linear models are magnified in probit models. In particular, the tests exhibit greater size distortion for the probit model than the linear model with the same level of serial correlation. Bootstrapping is also considered as an alternative approach to obtaining critical values, and though it reduces the size distortion in finite samples, it is unable to accommodate the distortion associated with a high level of serial correlation.

This paper presents a structural change test for panel data models in which the break (or the change) affects some, but not all, cross-section units in the panel. The test is robust to non-normal, heteroskedastic and autocorrelated errors, as well as end-of-sample structural change. The test amounts to computing and comparing pre- and post-break sample statistics as Chow (1960) type F statistics averaged over cross-section units. The cases of known and unknown break date are both considered. Under mild assumptions, the test has a limiting standard normal distribution as the number of cross-sections tends to infinity. Monte Carlo experiments show that the test has good size and power under a wide range of circumstances, including when the break date is unknown and differs across individual units, and when errors exhibit cross-section dependence. Finally, the test is illustrated by seeking a break in the dynamics of trade among euro area countries following the introduction of the euro.

Although the impact of structural breaks on testing for unit root has been studied extensively for univariate time-series, such impact on panel data unit root tests is still relatively unknown. A major issue is the choice of model in accommodating different types of break prior to testing for unit root. Model misspecification has been known to affect unit root tests performance in the univariate case but the effect of misspecification on panel tests is still unknown. This paper has two objectives: (i) it proposes a new test for unit root in the presence of structural break for panel data. The test allows the intercepts, the trend coefficients or both to change at different date for different individuals. Moreover, the test allows for the possibility that only some, but not all, of the individuals experienced structural breaks. Under some mild assumptions, the test statistics is shown to be asymptotically normal which greatly facilitates valid inferences. (ii) This paper provides a systematic study on the impact of structural instability on testing for unit root using Monte Carlo Simulation. The results show that correct specification is crucial for unit root testing in the presence of structural instability. In addition, the proportion of individuals experienced structural instability can also affect the performance of the test substantially.

This paper introduces a new test for structural instability among only some individuals at the end of a sample in a panel regression model. Most tests for structural breaks in the literature are appropriate when the break is relatively long lasting and happens in the middle of a sample. The distribution of the corresponding test statistic is suitably found using asymptotics in which the number of observations before and after the break point go to infinity. However, it is often at the end of a sample that researchers and policy-makers alike are interested in testing for instability. Andrews (2003) proposes a test for structural break which was shown to be particularly useful when the number of post-break observations is small. Unlike the well known Predictive Failure test of Chow (1960), the critical values of Andrews’s (1993) test statistic are calculated using parametric sub-sampling methods making the test robust to non-normal, heteroskedastic and serially correlated errors. The extension of the test to panel data, under the assumption of cross sectional independence, is relatively straightforward as shown in Mancini-Griffoli and Pauwels (2006). This extension assumes an alternative hypothesis that all individuals exhibit a break, as in other tests for structural breaks in the panel literature. Yet, these tests do not allow the interesting alternative that only some - and not all - individuals are affected by a break. This paper addresses such question by introducing a standardized Z statistic built from Andrews (2003) statistics averaged across individuals.Methodologically, the proposed procedure is similar to the approach in Im et al. (2003) which, while focussing on the different question of unit root tests, also considers an average of separate statistics. The test statistic is shown to follow a normal distribution as the number of individuals goes to infinity by using the Lindeberg-Feller Central Limit Theorem (LFCLT). This greatly simplifies the computation