Timothy W. McGuire

Some comparisons of tests for a shift in the slopes of a multivariate linear time series model

Abstract Our objective is to find a simple, robust, reasonably powerful test for a shift in one or more of the slopes in a linear time series model at some unknown point of time. Two such tests are ‘Chows test’ (1960) for a shift at the midpoint of the record and the ‘Farley-Hinich test’ (1970b); both can be performed easily with standard regression programs. In section 2, we compare the asymptotic properties of these tests when the disturbance variance is known. As expected, Chows test is superior when the true shift is near the middle of the record; with a single, uniformly-distributed explanatory variable, the Farley-Hinich tests dominates over the remaining eighty-four percent of the record. In section 3, we describe the results of some Monte Carlo experiments with a finite sample, which can be summarized as follows. (i) The asymptotic results of section 2 were appropriate for finite sample power comparisons. (ii) The relative performance of the two tests does not depend appreciably on whether the variance is known. (iii) The likelihood ratio test, which is far more costly to perform than the other two tests, does not dominate either Chows test or the Farley-Hinich test; it has moderately more power at the ends of the record, moderately less in the middle. The conclusion is clear: at low cost (in terms of computer cost and lost power), one can reduce the probability of over- looking a structural shift by routinely performing Chows test or the Farley-Hinich test.

Estimation and Inference for Linear Models in Which Subsets of the Dependent Variable are Constrained

Abstract Subsets of the dependent variable of a linear model often conform to known constraints; for example, this situation arises with Engel curves and with models which estimate transition probabilities, market shares, or other classes of proportions. These models imply a variety of restrictions on the parameters, explanatory variables and residuals which must be treated explicitly in estimating and testing hypotheses about the parameters. This paper discusses these restrictions and develops an estimating procedure which yields consistent estimates which are asymptotically efficient, unbiased and normal.

Measuring and Testing Relative Advertising Effectiveness with Split-Cable TV Panel Data

Abstract Various methods of estimating and testing the relative effectiveness of advertising campaigns using split-cable TV consumer panel data are examined. Sensitivities of the methods to missing observations, serial correlation, and the pattern of the expected advertising campaign impact over time are considered. The maximum likelihood estimators for both the case of no missing observations and the missing-observations case are derived, and a nonlinear model which allows for a gradual diffusion of the relative impact of the campaign is developed. For the data analyzed, the nonlinear model is best for discerning a significant difference between campaigns.

Optimal Skill Mix: An Application of the Maximum Principle for Systems with Retarded Controls

In this paper, we analyze the optimal skill mix in a model with two kinds of imperfectly substitutable labor, skilled and unskilled. The population is characterized by a distribution of innate abilities, and individuals are trained according to optimal rules or market rules (with imperfect expectations); the length of each individuals training period depends upon his innate ability. The market and optimal rules are characterized and compared, and corrective policies are investigated. This model represents a major advance over earlier models, which are based on the following assumptions: (a) either unskilled and skilled labor are perfectly substitutable or training is a necessary condition for employment; (b) individuals are innately identical; (c) in most cases, training occurs either instantaneously or with fixed lag.

More on least squares estimation of the transition matrix in a stationary first-order markov process from sample proportions data

Miller suggested ordinary least squares estimation of a constant transition matrix; Madansky proposed a relatively more efficient weighted least squares estimator which corrects for heteroscedasticity. In this paper an efficient generalized least squares estimator is derived which utilizes the entire covariance matrix of the distrubances. This estimator satisfies the condition that each row of the transition matrix must sum to unity. Madansky noted that estimates of the variances could be negative; a method for obtaining consistent non-negative estimates of the variances is suggested in this paper. The technique is applied to the hypothetical sample data used by Miller and Madansky.

Simultaneous Mode versus Sequential Mode in Real-Time Computer-Mediated Conferencing

A ‘standard’ simultaneous response mode of computer-mediated real-time conferencing was compared to a sequential response mode in order to examine whether deficiences in the former were responsible for earlier observations of arousal and disinhibited behavior of participants towards one another. Twenty four discussions of twelve groups of three and the responses on a postexperimental “preferences-difficulties” questionnaire were analyzed. It was found that both the modes have deficiences which could contribute to arousal and disinhibition. Main deficiences of the simultaneous and sequential modes are identified and discussed. Recommendations for design of conference software based on the analyses are suggested.

Models of Environmental Effects on the Development of IQ

This paper proposes a number of models of the effects of demographic and environmental factors on IQ and its pattern of change over time. The proposed models are concerned with the determinants of an Individual’s true (but unobserved) IQ and the relationship between measured and true IQ’s. Our analyses are based on data from the school records of a panel of 1, 746 students from the Pittsburgh school system and include demographic and environmental measures as well as IQ test scores at kindergarten, fourth, sixth, and eighth grades. The results indicate that the number of parents living in the household has an important positive effect on IQ at kindergarten that persists over the period of analysis. Number of siblings (measuring both birth order and family size) has an important negative influence on cumulative changes in IQ. Females show faster development until fourth grade; the net difference between the sexes almost completely vanishes by eighth grade. However, the predominant influences on the development of IQ are the socioeconomic status of the student’s parents and peers in school, with SES of peers being the more important. We estimate that roughly half of the difference between the measured eighth grade IQ’s of the average white and black student in our sample may be attributed to differences in their peer and parental SES’s. Finally, we caution that our results may be misleading, since our sample is not from a designed experiment and thus some of the explanatory variables could be correlated with unobserved factors that affect IQ.