EF3450L1 - Principles of Econometrics 1 EF3450 SECTION I An...

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Unformatted text preview: Principles of Econometrics 1 EF3450 SECTION I An overview of the classical linear regression model Principles of Econometrics 2 Some Notation Denote the dependent variable by y and the independent variable(s) by x 1 , x 2 , ... , x k where there are k independent variables. Some alternative names for the y and x variables: y x dependent variable independent variables regressand regressors effect variable causal variables explained variable explanatory variable Note that there can be many x variables but we will limit ourselves to the case where there is only one x variable to start with. In our set-up, there is only one y variable. Principles of Econometrics 3 Regression is different from Correlation If we say y and x are correlated, it means that we are treating y and x in a completely symmetrical way. In regression, we treat the dependent variable ( y ) and the independent variable(s) ( x s) very differently. The y variable is assumed to be random or stochastic in some way, i.e. to have a probability distribution. The x variables are, however, assumed to have fixed (non-stochastic) values in repeated samples. Principles of Econometrics 4 Simple Regression: An Example Suppose that we have the following data on the excess returns on IBM stock (IBM) together with the excess returns on a market index: We have some intuition that the beta on this fund is positive, and we therefore want to find whether there appears to be a relationship between x and y given the data that we have. The first stage would be to form a scatter plot of the two variables. Year, t Excess return = r IBM, t rf t Excess return on market index = rm t- rf t 1 17.8 13.7 2 39.0 23.2 3 12.8 6.9 4 24.2 16.8 5 17.2 12.3 Principles of Econometrics 5 Graph (Scatter Diagram) 5 10 15 20 25 30 35 40 45 5 10 15 20 25 Excess return on market portfolio Excess return on IBM Principles of Econometrics 6 Finding a Line of Best Fit We can use the general equation for a straight line, y = a + bx to get the line that best fits the data. However, this equation (y = a + bx ) is completely deterministic. Is this realistic? No. So what we do is to add a random disturbance term, u into the equation. y t = + x t + u t where t = 1,2,3,4,5 Principles of Econometrics 7 { E(Y|X) E(Y|X) Average Expenditure X (income) E(Y|X)= + X = E(Y|X) X The Economic Model: a linear relationship between average expenditure on food and income. Principles of Econometrics 8 Why do we include a Disturbance term? The disturbance term can capture a number of features:- We always leave out some determinants of y t- There may be errors in the measurement of y t that cannot be modelled....
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This note was uploaded on 02/22/2009 for the course ECONOMICS 4313 taught by Professor Tsui during the Spring '09 term at HKU.

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EF3450L1 - Principles of Econometrics 1 EF3450 SECTION I An...

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