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EF3450L1 - EF3450 SECTION I An overview of the classical...

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‘Principles of Econometrics’ 1 EF3450 SECTION I An overview of the classical linear regression model
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‘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.
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‘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.
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‘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
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‘Principles of Econometrics’ 5 Graph (Scatter Diagram) 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 Excess return on market portfolio Excess return on IBM
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‘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 = α + β x t + u t where t = 1,2,3,4,5
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‘Principles of Econometrics’ 7 { α ∆Χ E(Y|X) E(Y|X) Average Expenditure X (income) E(Y|X)= α + β X β = E(Y|X) X The Economic Model: a linear relationship between average expenditure on food and income.
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‘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. - Random outside influences on y t which we cannot model
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‘Principles of Econometrics’ 9 Determining the Regression Coefficients So how do we determine what α and β are?
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