1 The Linear Regression Bivariate Model Specification A Major Distinction Between Economists And Econometricians Is Th 1 (47.32 KiB) Viewed 41 times
1. The Linear Regression Bivariate Model: Specification A major distinction between economists and econometricians is the latter's concern with disturbance terms. (1) Deterministic: C=α+β⋅Y (2) Stochastic: C=α+β⋅Y+ε The word "stochastic" means a target or bull's eye. A stochastic relationship is not always right, just as a dart thrown at a target seldom hits the bull's eye. The disturbance term is used to capture explicitly the size of these "misses" or "errors." The existence of the disturbance term is justified in three main ways. (1) Specification error - the nature of the economic relationship is not correctly specified. (2) Measurement error - the variable being explained cannot be measured accurately, either because of data collection difficulties or because it is unmeasurable. The disturbance term can be thought of as representing this measurement error. Errors in measuring the explaining variable create a serious econometric problem. (3) Human indeterminacy - human behavior is such that actions taken under identical circumstances will differ in a random way. The success of econometricians' methods of estimating parameter values depends on the nature of the disturbance terms. (1) Statistical assumptions concerning the characteristics of the disturbance terms. (2) Means of testing these assumptions. Recall the traditional linear bivariate model:
Estimation of the Model by Least Squares For any set of values of the parameters characterizing a relationship: - The dots - actual observations on the DV (y) and the IV (x) - Estimated values of the DV can be calculated using the values of the IV in the dataset. Predicted Y: - Residuals - estimates of the unknown disturbances Residuals: a) The accuracy of prediction depends on keeping the residuals as small as possible. If corr(x,y)=1.00, the residual =0, - The closer the points on the scatter plot cluster around the regression line, the higher is the resulting correlation between x and y, and the more accurate is the resulting prediction. b) The estimator generating the set of values of the parameters that minimizes the sum of squared residuals (SSE) is called OLS estimator. c) A good estimator generates a set of estimates of the parameters that makes these residuals "small." RSS: Regression Sum of Squares
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