chapter9

chapter9 - CHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS...

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CHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS QUESTIONS 9.1. ( a ) In a log-log model the dependent and all explanatory variables are in the logarithmic form. ( b ) In the log-lin model the dependent variable is in the logarithmic form but the explanatory variables are in the linear form. ( c ) In the lin-log model the dependent variable is in the linear form, whereas the explanatory variables are in the logarithmic form. ( d ) It is the percentage change in the value of one variable for a (small) percentage change in the value of another variable. For the log-log model, the slope coefficient of an explanatory variable gives a direct estimate of the elasticity coefficient of the dependent variable with respect to the given explanatory variable. ( e ) For the lin-lin model, elasticity = slope Y X . Therefore the elasticity will depend on the values of X and Y . But if we choose X and Y , the mean values of X and Y , at which to measure the elasticity, the elasticity at mean values will be: slope Y X . 9.2. The slope coefficient gives the rate of change in (mean) Y with respect to X , whereas the elasticity coefficient is the percentage change in (mean) Y for a (small) percentage change in X . The relationship between two is: Elasticity = slope Y X . For the log-linear, or log-log, model only, the elasticity and slope coefficients are identical. 66
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9.3. Model 1 : i i X B B Y ln ln 2 1 + = : If the scattergram of ln Y on ln X shows a linear relationship, then this model is appropriate. In practice, such models are used to estimate the elasticities, for the slope coefficient gives a direct estimate of the elasticity coefficient. Model 2 : i i X B B Y ln 2 1 + = : Such a model is generally used if the objective of the study is to measure the rate of growth of Y with respect to X . Often, the X variable represents time in such models. Model 3 : i i X B B Y ln 2 1 + = : If the objective is to find out the absolute change in Y for a relative or percentage change in X , this model is often chosen. Model 4 : ) (1/ 2 1 i i X B B Y + = : If the relationship between Y and X is curvilinear, as in the case of the Phillips curve, this model generally gives a good fit. 9.4. ( a ) Elasticity. ( b ) The absolute change in the mean value of the dependent variable for a proportional change in the explanatory variable. ( c ) The growth rate. ( d ) Y X dX dY ( e ) The percentage change in the quantity demanded for a (small) percentage change in the price. ( f ) Greater than 1; less than 1. 9.5. ( a ) True . X d Y d ln ln = Y X dX dY , which, by definition, is elasticity. ( b
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chapter9 - CHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS...

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