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A multilevel problem concerns a population with a hierarchical structure. A sample from such a population can be described as a multistage sample. First, a sample of higher level units is drawn (e.g. schools or organizations), and next a sample of the sub‐units from the available units (e.g. pupils in schools or employees in organizations). In such samples, the individual observations are in general not completely independent. Multilevel analysis software accounts for this dependence and in recent years these programs have been widely accepted. Two problems that occur in the practice of multilevel modeling will be discussed. The first problem is the choice of the sample sizes at the different levels. What are sufficient sample sizes for accurate estimation? The second problem is the normality assumption of the level‐2 error distribution. When one wants to conduct tests of significance, the errors need to be normally distributed. What happens when this is not the case? In this paper, simulation studies are used to answer both questions. With respect to the first question, the results show that a small sample size at level two (meaning a sample of 50 or less) leads to biased estimates of the second‐level standard errors. The answer to the second question is that only the standard errors for the random effects at the second level are highly inaccurate if the distributional assumptions concerning the level‐2 errors are not fulfilled. Robust standard errors turn out to be more reliable than the asymptotic standard errors based on maximum likelihood.

Since the fiscal expansion during the Great Recession 2008-2009 and the current European consolidation and austerity measures, the analysis of fiscal multiplier effects is back on the scientific agenda. The number of empirical studies is growing fast, tackling the issue with manifold model classes, identification strategies, and specifications. While plurality of methods seems to be a good idea to address a complicated issue, the results are far off consensus. We apply meta regression analysis to a set of 89 studies on multiplier effects in order to provide a systematic overview of the different approaches, to derive stylized facts and to separate structural from method-specific effects. We classify studies with respect to type of fiscal impulse, model class, multiplier calculation method and further control variables. Moreover, we analyse subsamples of the model classes in order to evaluate the effects of model-class-specific properties, currently discussed in the literature, such as the influence of central bank reaction functions and liquidity constrained households. As a major result, we find that the reported size of the fiscal multiplier crucially depends on the setting and method chosen. Thus, economic policy consulting based on a certain multiplier study should lay open by how much specification affects the results. Our meta analysis may provide guidance concerning influential factors.

ABSTRACTAsymmetric loss functions often arise where regression estimates are used in management decision making. However, regression analysis has traditionally made use of a symmetric loss function in which the cost of underestimating equals the cost of overestimating. If the loss function is linear and the degree of asymmetry can be determined, the asymmetric regression method presented in this paper can be employed to find appropriate regression estimates. Asymmetric regression analysis requires no unusual data inputs other than an estimate of the cost asymmetry and can be performed efficiently using standard linear programming techniques.

Linkage errors can occur when probability‐based methods are used to link records from two distinct data sets corresponding to the same target population. Current approaches to modifying standard methods of regression analysis to allow for these errors only deal with the case of two linked data sets and assume that the linkage process is complete, that is, all records on the two data sets are linked. This study extends these ideas to accommodate the situation when more than two data sets are probabilistically linked and the linkage is incomplete.

Two-step estimators for hierarchical models can be constructed even when neither stage is a conventional linear regression model. For example, the first stage might consist of probit models, or duration models, or event count models. The second stage might be a nonlinear regression specification. This note sketches some of the considerations that arise in ensuring that two-step estimators are consistent in such cases.

Provides graduate students in the social sciences with the basic skills they need to estimate, interpret, present, and publish basic regression models using contemporary standards. Key features of the book include:interweaving the teaching of statistical concepts with examples developed for the course from publicly-available social science data or drawn from the literature. thorough integration of teaching statistical theory with teaching data processing and analysis.teaching of Stata and use of chapter exercises in which students practice programming and interpretation on the same data set. A