Panel Data Tests Of PPP: A Critical Overview

This paper reviews recent developments in the analysis of non-stationary panels, focusing on empirical applications of panel unit root and cointegration tests in the context of PPP. It highlights various drawbacks of existing methods. First, unit root tests suffer from severe size distortions in the presence of negative moving average errors. Second, the common demeaning procedure to correct for the bias resulting from homogeneous cross-sectional dependence is not effective; more worryingly, it introduces cross-correlation when it is not already present. Third, standard corrections for the case of heterogeneous cross-sectional dependence do not generally produce consistent estimators. Fourth, if there is between-group correlation in the innovations, the SURE estimator is affected by similar problems to FGLS methods, and does not necessarily outperform OLS. Finally, cointegration between different groups in the panel could also be a source of size distortions. We offer some empirical guidelines to deal with these problems, but conclude that panel methods are unlikely to solve the PPP puzzl

A panel model for predicting the diversity of internal temperatures from English dwellings

Using panel methods, a model for predicting daily mean internal temperature demand across a heterogeneous domestic building stock is developed. The model offers an important link that connects building stock models to human behaviour. It represents the first time a panel model has been used to estimate the dynamics of internal temperature demand from the natural daily fluctuations of external temperature combined with important behavioural, socio-demographic and building efficiency variables. The model is able to predict internal temperatures across a heterogeneous building stock to within ~0.71°C at 95% confidence and explain 45% of the variance of internal temperature between dwellings. The model confirms hypothesis from sociology and psychology that habitual behaviours are important drivers of home energy consumption. In addition, the model offers the possibility to quantify take-back (direct rebound effect) owing to increased internal temperatures from the installation of energy efficiency measures. The presence of thermostats or thermostatic radiator valves (TRV) are shown to reduce average internal temperatures, however, the use of an automatic timer is statistically insignificant. The number of occupants, household income and occupant age are all important factors that explain a proportion of internal temperature demand. Households with children or retired occupants are shown to have higher average internal temperatures than households who do not. As expected, building typology, building age, roof insulation thickness, wall U-value and the proportion of double glazing all have positive and statistically significant effects on daily mean internal temperature. In summary, the model can be used as a tool to predict internal temperatures or for making statistical inferences. However, its primary contribution offers the ability to calibrate existing building stock models to account for behaviour and socio-demographic effects making it possible to back-out more accurate predictions of domestic energy demand

Panel Data Tests of PPP. A Critical Overview

This paper reviews panel unit root and cointegration tests in the context of PPP. It highlights various drawbacks of existing methods. First, unit root tests suffer from severe size distortions in the presence of negative moving average errors. Second, the common demeaning procedure to correct for the bias resulting from homogeneous cross-sectional dependence is not effective; more worryingly, it introduces cross-correlation when it is not already present. Third, standard corrections for the case of heterogeneous cross-sectional dependence do not generally produce consistent estimators. Fourth, if there is between-group correlation in the innovations, the SURE estimator is affected by similar problems to FGLS methods, and does not necessarily outperform OLS. Finally, cointegration between different groups in the panel could also be a source of size distortions. We offer some empirical guidelines to deal with these problems, but conclude that panel methods are unlikely to solve the PPP puzzle.Purchasing Power Parity (PPP), Panel unit root and cointegration tests, Cross-sectional dependence

The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective

Several market and macro-level variables influence the evolution of equity risk in addition to the well-known volatility persistence. However, the impact of those covariates might change depending on the risk level, being different between low and high volatility states. By combining equity risk estimates, obtained from the Realized Range Volatility, corrected for microstructure noise and jumps, and quantile regression methods, we evaluate the forecasting implications of the equity risk determinants in different volatility states and, without distributional assumptions on the realized range innovations, we recover both the points and the conditional distribution forecasts. In addition, we analyse how the the relationships among the involved variables evolve over time, through a rolling window procedure. The results show evidence of the selected variables\u2019 relevant impacts and, particularly during periods of market stress, highlight heterogeneous effects across quantiles

Group Inference in High Dimensions with Applications to Hierarchical Testing

High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local heritability. Group inference in regression models can be measured with respect to a weighted quadratic functional of the regression sub-vector corresponding to the group. Asymptotically unbiased estimators of these weighted quadratic functionals are constructed and a novel procedure using these estimators for inference is proposed. We derive its asymptotic Gaussian distribution which enables the construction of asymptotically valid confidence intervals and tests which perform well in terms of length or power. The proposed test is computationally efficient even for a large group, statistically valid for any group size and achieving good power performance for testing large groups with many small regression coefficients. We apply the methodology to several interesting statistical problems and demonstrate its strength and usefulness on simulated and real data

The causality between energy consumption and economic growth: A multi-sectoral analysis using non-stationary cointegrated panel data

The increasing attention given to global energy issues and the international policies needed to reduce greenhouse gas emissions have given a renewed stimulus to research interest in the linkages between the energy sector and economic performance at country level. In this paper, we analyse the causal relationship between economy and energy by adopting a Vector Error Correction Model for non-stationary and cointegrated panel data with a large sample of developed and developing countries and four distinct energy sectors. The results show that alternative country samples hardly affect the causality relations, particularly in a multivariate multi-sector frameworkEnergy Sector, Panel Unit Roots, Panel Cointegration, Vector Error Correction Models, Granger Causality

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field