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"Magnus, Jan R."
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Matrix differential calculus with applications in statistics and econometrics
A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have.
eBook
Natural Resources, Institutional Quality, and Economic Growth in China
The resource curse has been mainly studied using cross-country samples. In this paper we analyze a cross-province sample from one country: China. We focus on the interplay between resource abundance, institutional quality, and economic growth, using two different measures of resource abundance (a stock: resource reserves; and a flow: resource revenues), and employing various econometric approaches including varying coefficient models. We find that resource abundance has a positive effect on economic growth at the provincial level in China between 1990 and 2008, an effect that depends nonlinearly on institutional quality (1995 confidence in courts). The ‘West China Development Drive’ policy, initiated in 2000, caused substantial changes, which we investigate through a comparative panel-data analysis.
Journal Article
Statistics and Common Sense
Common sense is a dynamic concept and it is natural that our (statistical) common sense lags behind the development of statistical science. What is not so easy to understand is why common sense lags behind as much as it does. We conduct a survey among Japanese students and provide examples and tentative explanations of a number of statistical questions where common sense and statistical science diverge.
Supplementary materials
for this article are available online.
Journal Article
effect of health benefits on climate change mitigation policies
This paper studies the interplay between climate, health, and the economy in a stylized world with eleven heterogeneous regions, with special emphasis on USA, Europe, China, India, and Africa. We introduce health impacts into a simple economic integrated assessment model where both the local cooling effect of SO ₂ and the global warming effect of CO ₂ are endogenous, and investigate how these factors affect the equilibrium path. Regions do not respond in the same way to climate change. In particular, emission abatement rates and health costs depend on the economic and geographical characteristics of each region. Two policy scenarios are considered, Nash and Optimal, for which we present both global and regional results. Results for Africa and China are highlighted.
Journal Article
On using the t-ratio as a diagnostic
The t-ratio has not one but two uses in econometrics, which should be carefully distinguished. It is used as a test and also as a diagnostic. I emphasize that the commonly-used estimators are in fact pretest estimators, and argue in favor of an improved (continuous) version of pretesting, called model averaging.
Journal Article
Records in Athletics Through Extreme-Value Theory
We are interested in two questions on extremes relating to world records in athletics. The first question is: What is the ultimate world record in a specific athletic event (such as the 100-m race for men or the high jump for women), given today's state of the art? Our second question is: How \"good\" is a current athletic world record? An answer to the second question also enables us to compare the quality of world records in different athletic events. We consider these questions for each of 28 events (14 for both men and women).
We approach the two questions with the probability theory of extreme values and the corresponding statistical techniques. The statistical model is of a nonparametric nature; only some \"weak regularity\" of the tail of the distribution function is assumed. We derive the limiting distribution of the estimated quality of a world record.
While almost all attempts to predict an ultimate world record are based on the development of world records over time, this is not our method. Instead, we use all top performances. Our estimated ultimate world record tells us what, in principle, is possible in the near future, given the present knowledge, material (shoes, suits, equipment), and drug laws.
Journal Article
Global Warming and Local Dimming: The Statistical Evidence
Two effects largely determine global warming: the well-known greenhouse effect and the less well-known solar radiation effect. An increase in concentrations of carbon dioxide and other greenhouse gases contributes to global warming: the greenhouse effect. In addition, small particles, called aerosols, reflect and absorb sunlight in the atmosphere. More pollution causes an increase in aerosols, so that less sunlight reaches the Earth (global dimming). Despite its name, global dimming is primarily a local (or regional) effect. Because of the dimming the Earth becomes cooler: the solar radiation effect. Global warming thus consists of two components: the (global) greenhouse effect and the (local) solar radiation effect, which work in opposite directions. Only the sum of the greenhouse effect and the solar radiation effect is observed, not the two effects separately. Our purpose is to identify the two effects. This is important, because the existence of the solar radiation effect obscures the magnitude of the greenhouse effect. We propose a simple climate model with a small number of parameters. We gather data from a large number of weather stations around the world for the period 1959-2002. We then estimate the parameters using dynamic panel data methods, and quantify the parameter uncertainty. Next, we decompose the estimated temperature change of 0.73°C (averaged over the weather stations) into a greenhouse effect of 1.87°C, a solar radiation effect of—1.09°C, and a small remainder term. Finally, we subject our findings to extensive sensitivity analyses.
Journal Article
Maximum Likelihood Estimation of the Multivariate Normal Mixture Model
The Hessian of the multivariate normal mixture model is derived, and estimators of the information matrix are obtained, thus enabling consistent estimation of all parameters and their precisions. The usefulness of the new theory is illustrated with two examples and some simulation experiments. The newly proposed estimators appear to be superior to the existing ones.
Journal Article
Weighted-Average Least Squares (WALS): Confidence and Prediction Intervals
We consider inference for linear regression models estimated by weighted-average least squares (WALS), a frequentist model averaging approach with a Bayesian flavor. We propose a new simulation method that yields re-centered confidence and prediction intervals by exploiting the bias-corrected posterior mean as a frequentist estimator of a normal location parameter. We investigate the performance of WALS and several alternative estimators in an extensive set of Monte Carlo experiments that allow for increasing complexity of the model space and heteroskedastic, skewed, and thick-tailed regression errors. In addition to WALS, we include unrestricted and fully restricted least squares, two post-selection estimators based on classical information criteria, a penalization estimator, and Mallows and jackknife model averaging estimators. We show that, compared to the other approaches, WALS performs well in terms of the mean squared error of point estimates, and also in terms of coverage errors and lengths of confidence and prediction intervals.
Journal Article