The Band Pass Filter*

We develop optimal finite‐sample approximations for the band pass filter. These approximations include one‐sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for U.S. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money–inflation relationship before and after 1960.     

Minsky Goes to Buffalo—and Takes on the Economics Establishment

This essay is based on remarks presented by the author at The Fourth Bi-Annual Cross-Border Post Keynesian Conference, Buffalo State College, on October 9, 2009. It addresses the economic challenges facing Buffalo, New York, and countless other American cities, especially in the Northeast and Midwest; draws on the writings of Hyman Minsky to offer an interpretation of what many now call the Great Recession, which began in late 2007; and challenges the image of Minsky presented by mainstream economists and journalists, with special attention to a recent lecture by Paul Krugman. The essay closes by returning to Buffalo, where—as Minsky anticipated in the 1990s—the economic fate of working families depends largely on the outcome of a national struggle over the shape of future U.S. economic transformation.     

An analysis of asymmetric demand response to price changes: The case of local telephone calls

Asymmetric demand responses to price changes are not an observable implication of classical demand theory, which predicts that consumers will react to a small price increase in much the same way as they do to a small price decrease. Yet applied researchers have long speculated that consumers are more sensitive to price increases than they are to price decreases. In addition, recent empirical studies generally support the theory of asymmetric demand responses. We construct a dynamic model based on data gathered from monthly telephone bills for 128 New York Telephone customers over a five-year period. Our results support the conclusion that customers react more quickly and strongly when prices go up than they do when prices go down.We would like to thank Manny Haas and Bernie Reddy for their comments and suggestions.     

Robustness issues in multilevel regression analysis

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.     

Longitudinal Meta-analysis

The goal of meta-analysis is to integrate the research results of a number of studies on a specific topic. Characteristic for meta-analysis is that in general only the summary statistics of the studies are used and not the original data. When the published research results to be integrated are longitudinal, multilevel analysis can be used for the meta-analysis. We will demonstrate this with an example of longitudinal data on the mental development of infants. We distinguish four levels in the data. The highest level (4) is the publication, in which the results of one or more studies are published. The third level consists of the separate studies. At this level we have knowledge about the degree of prematurity of the group of infants in the specific study. The second level are the repeated measures. We have data about the test age, the mental development, the corresponding standard deviations, and the sample sizes. The lowest level is needed for the specification of the meta-analysis model. Both the way in which the multilevel model has to be specified (the Mln-program is used) as the results will be presented and interpreted.