Econometrics:model of crime
Econometrics:model of crime ECO 5100
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This 2 page Class Notes was uploaded by Rahul Bose on Wednesday June 22, 2016. The Class Notes belongs to ECO 5100 at Wayne State University taught by Arjun in Summer 2016. Since its upload, it has received 12 views. For similar materials see Econometrics in Economcs at Wayne State University.
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Date Created: 06/22/16
Chapter one : Introduction Econometrics is based upon the development of statistical methods for estimating economic relationships, testing economic theories, and evaluating and implementing government and business policy An empirical analysis uses data to test a theory or to estimate a relationship. How to proceed? The first step is the careful formulation of the question of interest. The question might deal with testing an economic theory, or testing the effects of a government policy. In some cases, a formal economic model is constructed. An economic model consists of mathematical equations that describe various relationship. Nobel Prize winner Gary Becker postulated a utility maximization framework to describe an individual’s participation in crime. Certain crimes have clear economic rewards, but most criminal behaviors have costs. The opportunity costs of crime prevent the criminal from participating in other activities such as legal employment. And there are costs associated with the possibility of being caught and then, if convicted, the costs associated with incarceration. From Becker’s perspective, the decision to undertake illegal activity is one of resource allocation, with the benefits and costs of competing activities taken into account. Under general assumptions, we can derive an equation describing the amount of time spent in criminal activity as a function of various factors: y = f(x1, x2, x3, x4, x5, x6, x7) (1) where y =hours spent on criminal activities, x1 ="wage" for an hour spent in criminal activity, x2 =hourly wage in legal employment, x3 =income other than from crime or employment, x4 =probability of getting caught, x5 =probability of being convicted if caught, x6 =expected sentence if convicted, and x7 =age. Other factors generally affect the crime decision, but the list above is representative of what might result from a formal economic analysis. As common in economic theory, we have not been specific about the function f(.). This function depends on an underlying utility function. Formal economic modeling is sometimes the starting point for empirical analysis, but it is more common to use economic theory less formally, or even to rely entirely on intuition. A labor economist would like to study the effects of job training on worker productivity. It is obvious that factors such as education, experience, and training affect worker productivity. And workers are paid commensurate with their productivity. This simple reasoning leads to a model such as: wage = f(educ, exper , training), (2) where wage = hourly wage, educ = years of formal education, exper = years of workforce experience, and training = weeks spent in job training. First, the form of the function f(.) must be specified. Second, some variables cannot be observed. e.g. the wage for criminal activity, the probability of being caught,etc. These are solved by specifying a particular econometric model: crime = β0 + β1wagem + β2othinc + β3freqarr + β4freqconv +β5avgsen + β6age + u, (3) where crime =some measure of the frequency of criminal activity, wagem =the wage can be earned in legal employment, othinc =the income from other sources (e.g. assets, inheritance, etc.), freqarr =the frequency of arrests for prior infractions (to approximate the probability of arrest), freqconv =the frequency of conviction, and avgsen =the average sentence length after conviction. The choice of these variables is determined by the economic theory as well as data considerations. The term u contains unobserved factors, e.g. the wage for criminal activity, moral character, family background, and errors in measuring things like criminal activity and the probability of arrest. We could add family background variables to the model, such as number of siblings, parents’ education, and so on, but we can never eliminate u entirely. In fact, dealing with this error term or disturbance term is perhaps the most important component of any econometric analysis. The constants β0, β1, ..., β6 are the parameters of the econometric model, and they describe the directions and strengths of the relationship between crime and the factors used to determine crime in the model.
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