The Incidental Parameters Problem in Testing for Remaining Cross-section Correlation

In this paper we consider the properties of the Pesaran (2004, 2015a) CD test for cross-section correlation when applied to residuals obtained from panel data models with many estimated parameters. We show that the presence of period-specific parameters leads the CD test statistic to diverge as length of the time dimension of the sample grows. This result holds even if cross-section dependence is correctly accounted for and hence constitutes an example of the Incidental Parameters Problem. The relevance of this problem is investigated both for the classical Time Fixed Effects estimator as well as the Common Correlated Effects estimator of Pesaran (2006). We suggest a weighted CD test statistic which re-establishes standard normal inference under the null hypothesis. Given the widespread use of the CD test statistic to test for remaining cross-section correlation, our results have far reaching implications for empirical researchers.Comment: 84 pages, 11 table

Semiparametric Bayesian inference in multiple equation models

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We develop an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent normal-Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two-equation structural model drawn from the labour and returns to schooling literatures

A New Materials and Design Approach for Roads, Bridges, Pavement, and Concrete

Increased understanding of demand for transport energy and how to improve road pavement materials would enable decision makers to make environmental, financial, and other positive changes in future planning and design of roads, bridges, and other important transportation structures. This research comprises three studies focused on pavement materials and a fourth study that examines energy demand within the road transportation sector. These studies are as follows: 1. A techno-economic study of ground tire rubber as an asphalt modifier; 2. A computational fluid dynamics analysis comparing the urban heat island effect of two different pavement materials – asphalt and Portland Cement Concrete; 3. A new approach that modifies the surface of ground tire rubber using low-cost chemicals and treatment methods to be used in asphalt applications; and 4. Analysis of road transport energy demand in California and the United States. The findings of these studies include that 1. GTR is an effective and economically suitable additive for modified asphalt, 2. the suitability of PCC pavements in urban settings should be reexamined, 3. Surface modification of GTR materials can improve compatibilization of particles for the manufacture of asphalt materials, and 4. gasoline sales are generally price inelastic in both the U.S. and California. Ultimately, these four studies improve understanding of road pavement materials and transport energy demand. They lay out important information about the future of the relationship between materials and design in the transportation industry. These findings may be used by engineers, policymakers, and others in the industry to better consider implications of decisions involved in design, creation, and modification of structures using pavement and concrete, including roads, bridges, etc

Smooth Transition Regression Models in UK Stock Returns

This paper models UK stock market returns in a smooth transition regression (STR) framework. We employ a variety of financial and macroeconomic series that are assumed to influence UK stock returns, namely GDP, interest rates, inflation, money supply and US stock prices. We estimate STR models where the linearity hypothesis is strongly rejected for at least one transition variable. These non-linear models describe the in-sample movements of the stock returns series better than the corresponding linear model. Moreover, the US stock market appears to play an important role in determining the UK stock market returns regime.

Projected principal component analysis in factor models

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are related to the projected linear space. When the dimensionality is large, the factors can be estimated accurately even when the sample size is finite. We propose a flexible semiparametric factor model, which decomposes the factor loading matrix into the component that can be explained by subject-specific covariates and the orthogonal residual component. The covariates' effects on the factor loadings are further modeled by the additive model via sieve approximations. By using the newly proposed Projected-PCA, the rates of convergence of the smooth factor loading matrices are obtained, which are much faster than those of the conventional factor analysis. The convergence is achieved even when the sample size is finite and is particularly appealing in the high-dimension-low-sample-size situation. This leads us to developing nonparametric tests on whether observed covariates have explaining powers on the loadings and whether they fully explain the loadings. The proposed method is illustrated by both simulated data and the returns of the components of the S&P 500 index.Comment: Published at http://dx.doi.org/10.1214/15-AOS1364 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Focused information criterion and model averaging for generalized additive partial linear models

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.Comment: Published in at http://dx.doi.org/10.1214/10-AOS832 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Investigating uncertainty in macroeconomic forecasts by stochastic simulation

We investigate four sources of uncertainty with CPB’s macroeconomic model SAFFIER: provisional data, exogenous variables, model parameters and residuals of behavioural equations. Uncertainty is an inherent attribute of any forecast. We apply a Monte Carlo simulation technique to calculate standard errors for the short-term and medium-term horizon for GDP and eight other macroeconomic variables. The results demonstrate that the main contribution to the total variance of a medium-term forecast emanates from the uncertainty in the exogenous variables. For the short-term forecast both exogenous variables and provisional data are most relevant.

Bayesian Semiparametric Inference in Multiple Equation Models

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We derive an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent Normal-Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two-equation structural model drawn from the labor and returns to schooling literatures.nonparametric regression; nonparametric instrumental variables; SUR model; endogeneity; nonlinear simultaneous equations

What is the best risk measure in practice? A comparison of standard measures

Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticised for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straightforward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. As a consequence, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications. For backtesting ES, we propose an empirical approach that consists in replacing ES by a set of four quantiles, which should allow to make use of backtesting methods for VaR. Keywords: Backtesting; capital allocation; coherence; diversification; elicitability; expected shortfall; expectile; forecasts; probability integral transform (PIT); risk measure; risk management; robustness; value-at-riskComment: 27 pages, 1 tabl