Naturally, econometricians have borrowed from mathematical statisticians whenever possible. In addition, new techniques have developed in order to deal with the complexities of economic data and the test of the predictions of economic theories. Thus, econometrics and mathematical statistics are highly overlapped, but they each have their own focuses. For example, linear regression analysis is the mainstay in both fields, but its focus and interpretation differ markedly. 3 Steps in empirical analysis in economics I will give you a general overview, and may use the terms that you might be unfamiliar (but you should find out all of the terminology soon). An empirical analysis is to use data to test a theory or to estimate a relationship. How does one to carry out this type of analysis? Step 1: carefully formulate the question of interest When the question you want to investigate involves the testing of economic theories, a formal mathematical equations that describe various relationships should be constructed to make an economic model. For example, utility maximization, individual consumption decisions, s.t. budget constraint. The assumption that individuals make choices to maximize their well-being, s.t. to resource constraints, provides a very powerful approach to create tractable models. The demand equations are one example of the deductions from utility maximization. Quantity demanded of each commodity depends on various factors including its own price, price of other related goods, income, preferences. On the other hand, forming a model is not always relying on economic theory (is it good news?), it is more common to use economic theory less formally, and even entirely on intuition and common sense. This view has some merit, although there are cases in which formal derivations provide insights that intuition can overlook. Example 1: Economic model of crime In a seminar talk, Nobel Prize winner Gary Becker postulated a utility maximization framework to describe an individual’s participation in crime. He considers the decision to undertake illegal activity is one of resource allocation, with the benefits and costs of competing activities taken into account. Benefits: certain crimes have clear economic rewards Costs: prevent the criminal from participating in other activities such as legal employment, the cost of incarceration. Now we consider an equation describing the amount of time spent in criminal activity as a function of many factors.

3 ? = ?(?1, ?2,?3,?4,?5,?6,?7)(1.1) Where y=hours spent in 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 Example 2: New car sales in UK ? = ?(?

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- Fall '19