Question

You want to estimate the output produced by a firm as a function of inputs as

?????? = ?0 + ?1??? ????????? + ?2????? + ?3??????? ????? + ?

However, you are concerned that holding inputs constant, firms with better technology will produce more output. Technology is not observable.

A. Which of the following proxy variable/s would you choose to capture the effect of technology on output?

- Location of the firm

-Investment in machines and equipment

-Company bad debts

-Cash in hand

B. Are any of the variables in the model above susceptible to measurement error? Which ones and why?

C. You are now given from a regression of the square of the predicted residuals on the independent variables

?̂^2 = ?0 + ?1??? ????????? + ?2????? + ?3??????? ????? + ?

? 2 = 0.35, ? = 465

Write down your hypothesis and derive an F-statistic from the given information to test for heteroscedasticity of the error term.

Answer 1

A).

Consider the following regression model.

=> Y = b0 + b1*R + b2*L + b3*K + u, where “Y=output”, “R=Raw Materials”, “L=Labor” and “K=Capital”. Now, as we know that firms with better technology will produce more output. So, here we can take “I=Investment in machines and equipment” as a proxy variable to capture the technology on output. Where “I” is related to the better technology .

B).

Now, in the above regression model the variable “Y=output” shows the “Measurement error”. Since a producer will never disclose the true level of production given the level of inputs used. A producer always disclose lower level of production compare to the actual level of production, => the “Reported Y” < “Actual Y”. So, here the dependent variable “Y” shows the “Measurement Error”.

C).

Now, let’s assume that “u^” is the estimated error term, => the 2^nd model is given.

=> u^2 = d0 + d1*R + d2*L + d3*K + e, where “N=465” and “R^2=0.35”. So, given the information the “F statistic” value is given by.

=> F = [R^2/(k-1)]/[(1-R^2)/(N-k)] = [R^2/(1-R^2)]*[(N-k)/ (k-1)].

= [0.35/0.65]*[(465-4)/ (4-1)] = 0.538462*(461/3) = 82.7437, => F = 82.7437.

Now, the null hypothesis is given by “d1=d2=d3=0”, => no problem of “heteroskedasticity” and the alternative hypothesis is “the problem of heteroskedasticity”. So, here the “F- value” is significant at the “5%” level of significance, => here is a problem of “heteroskedasticity”.