Arima Causal Models - An Introduction and an Application to Deterrence Research (From Deterrence Reconsidered, P 135-148, 1982, John Hagan, ed. - See NCJ-88195)

• NCJ Number: 88201
• Author(s): Anonymous
• Date Published: 1982
• Length: 14 pages
• Grant Number(s): T32-MH-14598-05; 78-NI-AX-0021; 79-NI-AX-0094
• Sponsoring Agency: National Institute of Justice (NIJ); National Institute of Mental Health; US Dept of Justice NIJ Pub
• Sale Source: Sage Publications, Inc
• Publication Type: Report (Study/Research)
• Language: English
• Country: United States of America

Annotation

This paper describes an approach to the causal modeling of time series data based on the work of Box and Jenkins as elaborated by their students Pierce and Haugh. The use of the method is illustrated by applying it to a question in deterrence research.

Abstract

The Pierce-Haugh technique is associated with a special definition of causality advanced by Granger. Granger defines causality as predictability across time. Since Granger's definition is expressed in terms of data rather than in terms of theory, it is both more lenient and more restrictive than is the usual definition. The definition can be quite useful in situations in which theory is not well developed. Granger's definition of causality can be implemented in the cross-correlation function between two time series. Once two time series have been cross-correlated and the form of a causal structure has been identified, a model linking the two series can be specified from one of a class of lag models developed by Box and Jenkins. The Pierce-Haugh technique therefore offers a method for discovering and estimating causal relationships from time-series data, although it does have some limitations. For example, it requires a large number of observations, but the number must not be excessive. The Pierce-Haugh technique's application to the relationship between police resources and crime rates used annual time series data on police employees per 100,000 residents and total serious crimes per 100,000 residents in the city of Detroit from 1926 to 1977. In Detroit police and crime were unrelated. This result was reasonable, since the economic theory suggesting a relationship does not take into account the political nature of resource allocation in city government or the effects of police patrol strategies on crime rates. The Pierce-Haugh technique is superior to conventional econometric techniques in situations where relatively less theory exists and where important features of a model's specifications are not known with assurance. The technique may have wide applicability. Notes and 24 references are provided.