Autocorrelation Consistent Standard Error Research Articles

On robust inference in time-series regression

Summary Least squares regression with heteroskedasticity consistent standard errors (‘OLS-HC regression’) has proved very useful in cross-section environments. However, several major difficulties, which are generally overlooked, must be confronted when transferring the HC technology to time-series environments via heteroskedasticity and autocorrelation consistent standard errors (‘OLS-HAC regression’). First, in plausible time-series environments, OLS parameter estimates can be inconsistent, so that OLS-HAC inference fails even asymptotically. Second, most economic time series have autocorrelation, which renders OLS parameter estimates inefficient. Third, autocorrelation similarly renders conditional predictions based on OLS parameter estimates inefficient. Finally, the structure of popular HAC covariance matrix estimators is ill-suited for capturing the autoregressive autocorrelation typically present in economic time series, which produces large size distortions and reduced power in HAC-based hypothesis testing, in all but the largest samples. We show that all four problems are largely avoided by the use of a simple and easily implemented dynamic regression procedure, which we call DURBIN. We demonstrate the advantages of DURBIN with detailed simulations covering a range of practical issues.

The association between beverage-specific alcohol consumption and mortality among road users in Russia, 1965–2019

A vast body of literature suggests a relationship between alcohol consumption and road traffic fatalities. Despite an impressive downward trend in road traffic fatalities in Russia, the death rate is still unacceptably high. Far fewer studies have differentiated the association by road users and types of alcoholic beverages. This population-based study aims to estimate the associations of total and beverage-specific alcohol per capita (15+) consumption (APC) based on official alcohol sales statistics and road traffic mortality using police data on the number of deaths by road users. The study covers the period 1965–2019. We employed a first-order difference linear regression model with robust and autocorrelation consistent standard errors, controlling for a level of motorisation. To examine the possible evolution of the phenomenon, we repeated models separately for three consecutive periods (1965–1984, 1985–2002, 2003–2019). The findings suggest that an annual 1-litre increase in APC (in litres of pure alcohol) associated with a corresponding increase in the death rates (per 100,000 inhabitants) of both unprotected road users and motor vehicle occupants by about 0.3 (p < 0.01) and 0.4 (p < 0.05), respectively. A beverage-specific analysis for 1965–2019 revealed a positive and significant association between mortality of pedestrians and cyclists and the consumption of strong alcoholic beverages (p < 0.05) as well as mortality of drivers and passengers and the consumption of weaker alcoholic beverages, primarily beer (p < 0.01). Various road safety strategies should be applied to prevent road traffic fatalities of road users.

WHO AVOID TAXES? AN EMPIRICAL STUDY FROM THE CASE OF INDONESIA

This paper investigated the propensity and the magnitude of tax avoidance risk exposure among different taxpayers by analyzing both enterprise-related and government-related variables. Providing far-reaching analysis and examining a relatively unexplored area of conforming tax avoidance, this study employs two measurements of tax avoidance including non-conforming and conforming tax avoidance. In the brain area of empirical analysis, this paper combined a fixed-effect model to control omitted variable bias together with adoption of heteroskedasticity and autocorrelation-consistent standard errors (HAC/clustered SE). The results depict that the magnitude of tax avoidance risks varies depending on the characteristics of taxpayers. Higher risks were found in so-called foreign-controlled enterprises and foreign invested enterprises. With respect to entities’ sector, this study also demonstrates that the propensity of higher risk exposure was depicted in financial and mining sector relative to full sample taxpayers.

Effects of Climate Change on the Yield and Cropping Area of Major Food Crops: A Case of Bangladesh

The crops that we grow for food need specific climatic conditions to show better performance in view of economic yield. A changing climate could have both beneficial and harmful effects on crops. Keeping the above view in mind, this study is undertaken to investigate the impacts of climate change (viz. changes in maximum temperature, minimum temperature, rainfall, humidity and sunshine) on the yield and cropping area of four major food crops (viz. Aus rice, Aman rice, Boro rice and wheat) in Bangladesh. Heteroskedasticity and autocorrelation consistent standard error (HAC) and feasible generalized least square (FGLS) methods were used to determine the climate-crop interrelations using national level time series data for the period of 1972–2010. Findings revealed that the effects of all the climate variables have had significant contributions to the yield and cropping area of major food crops with distinct variation among them. Maximum temperature statistically significantly affected all the food crops’ yield except Aus rice. Maximum temperature also insignificantly affected cropping area of all the crops. Minimum temperature insignificantly affected Aman rice but benefited other three crops’ yield and cropping area. Rainfall significantly benefitted cropping area of Aus rice, but significantly affected both yield and cropping area of Aman rice. Humidity statistically positively contributed to the yield of Aus and Aman rice but, statistically, negatively influenced the cropping area of Aus rice. Sunshine statistically significantly benefitted only Boro rice yield. Overall, maximum temperature adversely affected yield and cropping area of all the major food crops and rainfall severely affected Aman rice only. Concerning the issue of climate change and ensuring food security, the respective authorities thus should give considerable attention to the generation, development and extension of drought (all major food crops) and flood (particularly Aman rice) tolerant varieties.

Long-Run Covariance and its Applications in Cointegration Regression

Long-run covariance plays a major role in much of time-series inference, such as heteroskedasticity- and autocorrelation-consistent standard errors, generalized method of moments estimation, and cointegration regression. We propose a Stata command, lrcov, to compute long-run covariance with a prewhitening strategy and various kernel functions. We illustrate how long-run covariance matrix estimation can be used to obtain heteroskedasticity- and autocorrelation-consistent standard errors via the new hacreg command; we also illustrate cointegration regression with the new cointreg command. hacreg has several improvements compared with the official newey command, such as more kernel functions, automatic determination of the lag order, and prewhitening of the data. cointreg enables the estimation of cointegration regression using fully modified ordinary least squares, dynamic ordinary least squares, and canonical cointegration regression methods. We use several classical examples to demonstrate the use of these commands.

Enhanced Routines for Instrumental Variables/Generalized Method of Moments Estimation and Testing

We extend our 2003 paper on instrumental variables and generalized method of moments estimation, and we test and describe enhanced routines that address heteroskedasticity- and autocorrelation-consistent standard errors, weak instruments, limited-information maximum likelihood and k-class estimation, tests for endogeneity and Ramsey's regression specification-error test, and autocorrelation tests for instrumental variable estimates and panel-data instrumental variable estimates.