On the Power of GLS-Type Unit Root Tests

Elliott, Rothenberg and Stock (1996), (ERS), present a 'GLS' variant of the Dickey-Fuller (DF) unit root test. Their statistic is approximately point-optimal invariant at a chosen local alternative, and usually displays better finite sample power than the DF test. Following the usual efficiency motive for GLS estimation, the higher finite sample power of the ERS test has often been attributed to the greater accuracy of the estimate of the series' non-stochastic component under stationary alternatives close to the null. This paper shows that the GLS estimates of the non-stochastic component are not, in general, more accurate. The power gain arises from the fact that the GLS statistic's null distribution has a greater positive shift relative to the DF test, than its distribution under relevant alternatives, and this persists even when the GLS estimates of the non stochastics have higher variance than the OLS estimates.     

Het vergelijken van twee verschillende schatters voor een percentiel P van een normale verdeling

A comparison is made between two different methods to estimate the probability that a normally distributed observation is less than a certain value. One method is based on the binomial distribution, the other one on HALD'S maximum likelihood estimates of the parameters of a censored normal distribution. For large sample sizes a graph of the relative efficiency of these two estimates is constructed. A sampling experiment was performed in order to investigate for one particular situation the possible bias of HALD'S maximum likelihood estimate, which is only asymptotically unbiassed.     

A Coincident Index,Common Factors,and Monthly Real GDP*

The Stock–Watson coincident index and its subsequent extensions assume a static linear one‐factor model for the component indicators. This restrictive assumption is unnecessary if one defines a coincident index as an estimate of monthly real gross domestic products (GDP). This paper estimates Gaussian vector autoregression (VAR) and factor models for latent monthly real GDP and other coincident indicators using the observable mixed‐frequency series. For maximum likelihood estimation of a VAR model, the expectation‐maximization (EM) algorithm helps in finding a good starting value for a quasi‐Newton method. The smoothed estimate of latent monthly real GDP is a natural extension of the Stock–Watson coincident index.     

Logit based parameter estimation in the Rasch model

The similarities between the logistic regression model and the Rasch model (used in psychometric item response theory) are used to derive several methods based on logits that produce parameter estimates for the Rasch model. A result from LeCam and Dzhaparidze is used by which an initial consistent estimate is transformed by one scoring method iteration into an estimate that has the same asymptotic efficiency as the (in this case conditional) maximum likelihood estimate of the item parameters. Indirect evidence about the bias of this CML estimator is produced by studying the (more easily derived) bias of the estimator based on the unweighted logits. Finally, some simple weighted least squares logit-based estimates are presented, and their performance is assessed. On the whole, the computationally simpler logit-based estimates give a fairly good approximation to the CML estimates.     

The relationship between wage growth and wage levels

We estimate the covariance between the permanent component of wages and a random coefficient on experience in models both with potential experience and with actual experience. Actual experience is allowed to be arbitrarily correlated with both the permanent component of wages and the random component on experience. We find no evidence that workers of higher ability experience faster wage growth. Our point estimates suggest that a worker with a one standard deviation higher level of permanent ability would have a return to annual potential experience that is 0.61 of a percentage point lower. The analogous point estimate for actual experience is 0.87 of a point lower. Contrary to the popular perception, wage growth among low‐skill workers appears to be at least as high as that for a medium‐skilled worker. Copyright © 2009 John Wiley & Sons, Ltd.     

Wages,non-wage characteristics,and predominantly male jobs

This paper estimates the wage premium associated with working in predominantly male jobs. It also examines whether this wage premium is greater than the compensation workers demand for the less desirable non-wage characteristics of such jobs. The coefficients of the change in the proportion of men in an occupation on the change in wages for quits and layoffs provide opposing biased estimates of the wage premium; because workers who voluntarily quit move to better matches, but those that are laid off accept jobs from the representative distribution of job offers. Specifically, when the premium paid over- (under-)compensates for undesirable work characteristics, the quit estimate is a downward (upward) biased estimate of the wage premium, while the layoff estimate is biased upward (downward). Results from the U.S. National Longitudinal Survey of Youth (NLSY) and the U.S. Panel Study of Income Dynamics (PSID) indicate that: (1) the estimated bounds of the wage premium are large; and (2) the wage premium overcompensates for the non-wage characteristics of male jobs.     

Using weather ensemble predictions in electricity demand forecasting

Weather forecasts are an important input to many electricity demand forecasting models. This study investigates the use of weather ensemble predictions in electricity demand forecasting for lead times from 1 to 10 days ahead. A weather ensemble prediction consists of 51 scenarios for a weather variable. We use these scenarios to produce 51 scenarios for the weather-related component of electricity demand. The results show that the average of the demand scenarios is a more accurate demand forecast than that produced using traditional weather forecasts. We use the distribution of the demand scenarios to estimate the demand forecast uncertainty. This compares favourably with estimates produced using univariate volatility forecasting methods.     

The informativeness of estimation moments

This paper introduces measures for how each moment contributes to the precision of parameter estimates in generalized method of moments settings. For example, one of the measures asks what would happen to the variance of the parameter estimates if a particular moment was dropped from the estimation. The measures are all easy to compute. We illustrate the usefulness of the measures through two simple examples as well as an application to a model of joint retirement planning of couples. We estimate the model using the British Household Panel Survey, and we find evidence of complementarities in leisure. Our sensitivity measures illustrate that the estimate of the complementarity is primarily informed by the distribution of differences in planned retirement dates. The estimated econometric model can be interpreted as a bivariate ordered-choice model that allows for simultaneity. This makes the model potentially useful in other applications.     

Maximum entropy measurement error estimates of singular covariance matrices in undersized samples

Theil and Laitinen (1980) proposed a maximum entropy (ME) technique to estimate singular moment matrices arising from undersized samples. They fitted a continuous ME distribution to the values of a variable arranged in an ascending order of magnitude. In this paper we relax their continuity assumption and simplify matters from a practical viewpoint. Our continuity is restricted to a range around each observation arising from measurement errors. We propose measurement error maximum entropy (MEME or ME2) distribution yielding a positive definite estimate of the dispersion matrix for undersized samples. Some desirable properties of ME2 distribution are mentioned. An example illustrates the simplicity of our ME2 estimation and shows that our estimates can be closer to the true values.     

The shape of hiring and separation costs in France

In this article, we estimate the structure of costs of hiring, terminating, and retiring employees in France. We use a representative panel data set of French establishments that contains direct measures of these various costs as well as measures of entries and exits for the years 1992 and 1996.First, we show that our panel data source is able to reproduce results obtained by Abowd and Kramarz (2003) when we use the cross-section dimension. Our estimates show that collective terminations are much more expensive than individual terminations: legislation, namely the requirement to set up a “social plan” in case of collective terminations, magnifies firing costs. Collective terminations entail very large fixed costs. Termination costs are essentially linear in the number of terminated workers, with collective terminations being much more expensive. The costs of retirement are concave in the number of retired workers with a fixed cost component which is smaller than the one estimated for terminations, and quite smaller than that obtained by Abowd and Kramarz (2003). Finally, we find that hiring costs are small and seem only present when hiring on CDI; costs of hiring on short-term contracts are almost zero. Finally, the fixed (firm-specific) component of hiring costs is very small.     

Assessment of cell number for a multinomial distribution with application to genomic data

We consider inference procedures for cell number assessment of a multinomial distribution using the least square principle and quadratic programming. We establish the consistency of the estimators under regularity conditions. Simulation results show that our approach yields a more accurate estimate than the often-used naive estimator. We also demonstrate the proposed methodology via two genomic data sets.     

Estimating the Demand for Housing, Land, and Neighbourhood Characteristics

This paper provides estimates of the structure of demand for individual housing and neighbourhood characteristics and for land in two British cities. We estimate a hedonic price function, and from this obtain the implicit prices of house attributes. These prices are used to estimate a demand system for each city. These perform well, and enable us to calculate price and income elasticities for each of the non-dichotomous characteristics and for land. To counteract criticisms of demand estimates derived within the hedonic framework a method is developed for selecting an appropriate set of instrumental variables. Estimates derived from this method, however, differ only slightly from those obtained using the conventional techniques. Several features of these estimates provide insights into the unusual characteristics of the British housing market, the effects of constraints imposed by land use planning, and the effects of changing income distribution on the structure of demand.     

Quantile models and estimators for data analysis

Quantile regression is used to estimate the cross sectional relationship between high school characteristics and student achievement as measured by ACT scores. The importance of school characteristics on student achievement has been traditionally framed in terms of the effect on the expected value. With quantile regression the impact of school characteristics is allowed to be different at the mean and quantiles of the conditional distribution. Like robust estimation, the quantile approach detects relationships missed by traditional data analysis. Robust estimates detect the influence of the bulk of the data, whereas quantile estimates detect the influence of co-variates on alternate parts of the conditional distribution. Since our design consists of multiple responses (individual student ACT scores) at fixed explanatory variables (school characteristics) the quantile model can be estimated by the usual regression quantiles, but additionally by a regression on the empirical quantile at each school. This is similar to least squares where the estimate based on the entire data is identical to weighted least squares on the school averages. Unlike least squares however, the regression through the quantiles produces a different estimate than the regression quantiles.     

TECHNOLOGICAL INNOVATION AND EMPLOYMENT IN DERIVED LABOUR DEMAND MODELS: A HIERARCHICAL META‐REGRESSION ANALYSIS

The effect of technological innovation on employment is of major concern for workers and their unions, policy makers and academic researchers. We meta‐analyse 570 estimates from 35 primary studies that estimate a derived labour demand model. We contribute to existing attempts at evidence synthesis by addressing the risks of selection bias and that of data dependence in observational studies. Our findings indicate that: (i) hierarchical meta‐regression models are sufficiently versatile for addressing both selection bias and data dependence in observational data; (ii) innovation's effect on employment is positive but small and highly heterogeneous; (iii) only a small part of residual heterogeneity is explained by moderating factors; (iv) selection bias tends to reflect preference for upholding prevalent hypotheses on the employment effects of process and product innovations; (v) country‐specific effect‐size estimates are related to labour market and product market regulation in six OECD countries in a U‐shaped fashion; and (vi) OLS estimates reflect upward bias whereas those based on time‐differenced or within estimators reflect a downward bias. Our findings point out to a range of data quality and modelling issues that should be addressed in future research.     

Production Technology Estimates and Balanced Growth

Capital‐labour substitution and total factor productivity (TFP) estimates are essential features of many economic models. Such models typically embody a balanced growth path. This often leads researchers to estimate models imposing stringent prior choices on technical change. We demonstrate that estimation of the substitution elasticity and TFP growth can be substantially biased if technical progress is thereby mis‐specified. We obtain analytical and simulation results in the context of a model consistent with balanced and near‐balanced growth (i.e. departures from balanced growth but broadly stable factor shares). Given this evidence, a constant elasticity of substitution production function system is then estimated for the US economy. Results show that the estimated substitution elasticity tends to be significantly lower using a factor‐augmenting specification (well below one). We are also able to reject conventional neutrality forms in favour of general factor augmentation with a non‐negligible capital‐augmenting component. Our work thus provides insights into production and supply‐side estimation in balanced‐growth frameworks.     

Identifying relevant and irrelevant variables in sparse factor models

This paper considers factor estimation from heterogeneous data, where some of the variables—the relevant ones—are informative for estimating the factors, and others—the irrelevant ones—are not. We estimate the factor model within a Bayesian framework, specifying a sparse prior distribution for the factor loadings. Based on identified posterior factor loading estimates, we provide alternative methods to identify relevant and irrelevant variables. Simulations show that both types of variables are identified quite accurately. Empirical estimates for a large multi‐country GDP dataset and a disaggregated inflation dataset for the USA show that a considerable share of variables is irrelevant for factor estimation.     

Estimating non-simultaneous changes in the mean of vectors

A sequence of independent vectors with correlated components is considered. It is supposed that there is one change point in the mean of each component and changes need not occur simultaneously. The asymptotic distribution of the change point estimators is studied. If the true change points are well separated, the explicit asymptotic distribution of the change point estimators is presented. In the case the true change points coincide, it is shown that the limit distribution of properly standardized change points estimates exists. It depends not only on the underlying time series dependence structure, but also on the ratio of the sizes of the changes. The asymptotic distribution function is not known, but due to the invariance principle it can be obtained by simulations.     

Poverty and crime in 19th century Germany

We estimate the impact of poverty on crime in 19th century Bavaria, Germany. Rainfall is used as an instrumental variable for grain (rye) prices to address econometric identification problems in the existing literature. The rye price was a major determinant of living standards during this period. The rye price has a positive effect on property crime: a one standard deviation increased property crime by 8%. OLS estimates are twice as large as instrumental variable estimates, highlighting the value of our empirical approach. Higher rye prices lead to significantly less violent crime, though, and we argue that higher beer prices, caused by the higher rye prices, are a likely explanation.     

Corrections for coarsely categorized measures: LISREL's polyserial and polychoric correlations

Versions 5 and 6 of LISREL (Joreskog and Sorbom, 1981) contain procedures that estimate the underlying correlation between continuous variables on the basis of crude rank category measures. The procedures assume that the distribution of the measured variables would have been bivariate normal if they had not been categorized. Using survey data and simulations, the accuracy of these polyserial/polychoric (P/P) based estimates of the underlying correlations are compared with those based on simple equal distance scoring of the categories. The results indicate that under some conditions, e.g., nearly normally distributed variables and moderate to high correlations, the polyserial/polychoric based estimates are better. Under other conditions, e.g., a moderate to high degree of skew and kurtosis and low correlations, the equal distance score based estimates are better. Under all conditions, the amount of error decreases fairly rapidly as the number of categories is increased from two to five.     

Fitting Regional Income Distributions in the European Union*

Cross‐sectional distribution of per capita (log) GDP across the European Union regions from 1977 to 1996 is analysed. Kernel density estimates reveal a multimodal structure of the distribution during the 1970s and early 1980s, and a tendency towards unimodality since the mid‐1980s. The distribution is further analysed by a mixture of normal densities. A two well‐separated component mixture fits the distributions in the 1970s and early 1980s. These two clusters tend to converge, supporting the idea of a process of catching up. In the mid‐1990s, a small group of very rich regions is generated by a separated component.