1. Download the data PIOdUCtiOE-dta from Moodle. This data set contains data on output (value added) and inputs at the industry level for 459 industries in 1958 and 1993- Suppose the relationship between output and inputs is described by a Cobb- Douglas production function Y.- = AKEL? where 3'; is a measure of output, K, is the dapital stock, and L,- is employment. Answer questions (a) to (f) for the year 1958 only; part (g) will also use the 1993 data. (a) Transform the production function to a linear equation by taking logs. Estimate the parameters 0- and )6 by an OLS regression using total value added as your measure of output. (b) Test whether your estimates are consistent with the production function exhibiting constant returns to scale, i.e. H:a+=1 against the alternative H1 : al = 1. Do you reject the hypothesis at the 5% level? What is the Pvalue of your test? (c) An alternative way to test the hypothesis of constant returns to scale is to impose this restriction on the parameters and transform your regression model. De- rive the necessary transformation, and show how the constant returns hypothesis amounts to a t-test in this transformed model. Carry out this test. Verify that your result matches what you found in (b) (d) An alternative way of specifying the production function is to dene K, as the total value of shipments and to add materials as a factor of production. Test whether this three factor production function exhibit constant returns to scale. (e) Finally, also add energy as a fourth factor of production to the model in (d). 1. Is energy a signicant factor of production? 2. Does this model exhibt constant returns to scale? (f) Explain for which Specication of the production function the test for constant returns to scale makes the most sense (i.e. think about the economic content of the idea of constant returns). (g) Return to the three factor production function from part (d). Repeat the regres- sion for the year 1993. Does the production function exhibit constant returns in 1993? How have the production fimction parameters changed over time? Test whether the production function parameters other than A are the same in 1958 and 1993