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A variable Y depends upon some explanatory variables X2…..Xk in the following manner: Y = β1 + β2 X2 + β3X3 +…+ βk Xk + u.If for some reason, there is no data available on a certain variable, say X3, and a proxy variable Z that is linearly related to X3 is used instead, then X3 = µ + αZ.The regression model is now rewritten as:Y = β1 + β2 X2 + β3(µ+αZ)β4 X4 +…+ βk Xk + u = (β1 + β3µ) + β2 X2 + β3αZ + β4X4+…+ βk Xk + uWhat are the consequences of including a proxy variable as shown above?

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MCQs on Econometrics, which is the use of statistical methods to develop theories or test existing hypotheses in economics or finance. 
 


A variable Y depends upon some explanatory variables X<sub>2</sub>…..X<sub>k</sub> in the following manner: Y = β<sub>1</sub> + β<sub>2</sub> X<sub>2</sub> + β<sub>3</sub>X<sub>3</sub> +…+ β<sub>k</sub> X<sub>k</sub> + u.<br/>If for some reason, there is no data available on a certain variable, say X<sub>3</sub>, and a proxy variable Z that is linearly related to X<sub>3</sub> is used instead, then X<sub>3</sub> = µ + αZ.<br/>The regression model is now rewritten as:<br/>Y = β<sub>1</sub> + β<sub>2</sub> X<sub>2</sub> + β<sub>3</sub>(µ+αZ)β<sub>4</sub> X<sub>4</sub> +…+ β<sub>k</sub> X<sub>k</sub> + u<br/> = (β<sub>1</sub> + β<sub>3</sub>µ) + β<sub>2</sub> X<sub>2</sub> + β<sub>3</sub>αZ + β<sub>4</sub>X<sub>4</sub>+…+ β<sub>k</sub> X<sub>k</sub> + u<br/>What are the consequences of including a proxy variable as shown above?





 
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