In this paper we present a "routine activity approach" for analyzing crime rate trends and cycles. Rather than emphasizing the characteristics of offenders, with this approach we concentrate upon the circumstances in which they carry out predatory criminal acts. Most criminal acts require convergence in space and time of likely offenders, suitable targets and the absence of capable guardians against crime. Human ecological theory facilitates an investigation into the way in which social structure produces this convergence, hence allowing illegal activities to feed upon the legal activities of everyday life. In particular, we hypothesize that the dispersion of activities away from households and families increases the opportunity for crime and thus generates higher crime rates. A variety of data is presented in support of the hypothesis, which helps explain crime rate trends in the United States 1947-1974 as a byproduct of changes in such variables as labor force participation and single-adult households.

Social Change and Crime Rate Trends: A Routine Activity Approach

Many econometric models are susceptible to analysis only by asymptotic techniques and there are three principles, based on asymptotic theory, for the construction of tests of parametric hypotheses. These are: (i) the Wald (W) test which relies on the asymptotic normality of parameter estimators, (ii) the maximum likelihood ratio (LR) procedure and (iii) the Lagrange multiplier (LM) method which tests the effect on the first order conditions for a maximum of the likelihood of imposing the hypothesis. In the econometric literature, most attention seems to have been centred on the first two principles. Familiar " t-tests " usually rely on the W principle for their validity while there have been a number of papers advocating and illustrating the use of the LR procedure. However, all three are equivalent in well-behaved problems in the sense that they give statistics with the same asymptotic distribution when the null hypothesis is true and have the same asymptotic power characteristics. Choice of any one principle must therefore be made by reference to other criteria such as small sample properties or computational convenience. In many situations the W test is attractive for this latter reason because it is constructed from the unrestricted estimates of the parameters and their estimated covariance matrix. The LM test is based on estimation with the hypothesis imposed as parametric restrictions so it seems reasonable that a choice between W or LM be based on the relative ease of estimation under the null and alternative hypotheses. Whenever it is easier to estimate the restricted model, the LM test will generally be more useful. It then provides applied researchers with a simple technique for assessing the adequacy of their particular specification. This paper has two aims. The first is to exposit the various forms of the LM statistic and to collect together some of the relevant research reported in the mathematical statistics literature. The second is to illustrate the construction of LM tests by considering a number of particular econometric specifications as examples. It will be found that in many instances the LM statistic can be computed by a regression using the residuals of the fitted model which, because of its simplicity, is itself estimated by OLS. The paper contains five sections. In Section 2, the LM statistic is outlined and some alternative versions of it are discussed. Section 3 gives the derivation of the statistic for

https://www.jstor.org/stable/pdfplus/2297111.pdf

The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics

A great deal of use has undoubtedly been made of least squares regression methods in circumstances in which they are known to be inapplicable. In particular, they have often been employed for the analysis of time series and similar data in which successive observations are serially correlated. The resulting complications are well known and have recently been studied from the standpoint of the econometrician by Cochrane & Orcutt (1949). A basic assumption underlying the application of the least squares method is that the error terms in the regression model are independent. When this assumption—among others—is satisfied the procedure is valid whether or not the observations themselves are serially correlated. The problem of testing the errors for independence forms the subject of this paper and its successor. The present paper deals mainly with the theory on which the test is based, while the second paper describes the test procedures in detail and gives tables of bounds to the significance points of the test criterion adopted. We shall not be concerned in either paper with the question of what should be done if the test gives an unfavourable result.

Testing for serial correlation in least squares regression. II.

Efficient tests for normality, homoscedasticity and serial independence of regression residuals

This bestselling and thoroughly classroom-tested textbook is a complete resource for finance students. A comprehensive and illustrated discussion of the most common empirical approaches in finance prepares students for using econometrics in practice, while detailed case studies help them understand how the techniques are used in relevant financial contexts. Worked examples from the latest version of the popular statistical software EViews guide students to implement their own models and interpret results. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Building on the successful data- and problem-driven approach of previous editions, this third edition has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time. A companion website, with numerous student and instructor resources, completes the learning package.

Introductory Econometrics for Finance

For testing the hypothesis that successive members of a series of observations are independent J. von Neumann [5] (see also B. I. Hart [4]) and R. L. Anderson [1] have proposed test statistics and tabulated their significance points. von Neumann's criterion seems well designed to detect deviations from the null hypothesis which might be encountered in practice but its exact distribution is unknown. On the other hand Anderson's statistic, while it has a known distribution, is based on a circular conception of the population which is rarely plausible in practice. In the present note certain noncircular statistics are proposed for which exact distributions can be obtained from Anderson's results. The statistics are derived from the usual noncircular statistics by sacrificing a small amount of relevant information. Their application is noted to certain regression problems for which no satisfactory tests are at present available. Finally, some general remarks are made about the choice of best statistics for the problems discussed.

/pdf/exact-tests-of-serial-correlation-using-noncircular-2x8cv6q5kr.pdf

G. S. Watson

Papers

Testing for serial correlation in least squares regression. II.

Exact Tests of Serial Correlation using Noncircular Statistics