tailieunhanh - Lecture Undergraduate econometrics, 2nd edition - Chapter 3: The simple linear regression model: Specification and estimation

Chapter 3 - The simple linear regression model: Specification and estimationIn this chapter, students will be able to understand: An economic model, an econometric model, estimating the parameters for the expenditure relationship. | Chapter 3 The Simple Linear Regression Model Specification and Estimation An Economic Model Suppose that we are interested in studying the relationship between household income and expenditure on food. We ask the question How much did your household spend on food last week Suppose that the continuous random variable y has a probability density function fy that describes the probabilities of obtaining various food expenditure values. The probability density function in this case describes how expenditures are distributed over the population and it might look like one of those in Figure . Slide Undergraduate Econometrics 2nd Edition -Chapter 3 The probability distribution in Figure is actually a conditional probability density function since it is conditional upon household income. If x weekly household income then the conditional probability density function is f y x 480 . The conditional mean or expected value of y is E y x 480 py x and is our population s average weekly food expenditure. The conditional variance of y is var y x 480 Ơ2 which measures the dispersion of household expenditures y about their mean py x. The parameters py x and Ơ2 if they were known would give us some valuable information about the population we are considering. If we knew these parameters and if we knew that the conditional distribution f y x 480 was normal N py x Ơ2 then we could calculate probabilities that y falls in specific intervals using properties of the normal distribution. In order to investigate the relationship between expenditure and income we must build an economic model and then an econometric model that forms the basis for a Slide Undergraduate Econometrics 2nd Edition -Chapter 3 quantitative economic analysis. If we consider households with different levels of income we expect the average expenditure on food to change. In Figure we show the probability density functions of food expenditure for two different levels of weekly income 480 and 800. .