Question 1.

Step1: First we need to create a new variable "output value", which is the total value of the rice produced. To construct a variable in excel for all the households, simply use the formula "=variable1*variable2" in the cell corresponding to the first household, then drag the lower right corner of that cell to fill in the entire column. Make sure to label you variables as you go along to avoid confusion.

Step2: Now that we have our dependent variable, we need to put everything in natural log. For each of the variables we need to estimate the production function:

output_i = A * Land^x1 * Labor^x2

create the logged version of this variable for all the households. I recommend keeping your independent variable in one column and your dependent variables in a block of adjacent columns to facilitate easier use of the regression function in excel.

Step3: Finally, we are ready to perform our regression. Use the "Data Analysis" tab, select "regression" then press "ok". You will see an "Input Y range" selector, use the selector to drag across the entire column of your dependent variable. Note that if you choose to include the top cell with variable labels the "Labels" box must be checked. Next use the "Input X Range" selector to highlight ALL of your independent variables (keeping the columns side by side helps make this easier). Then press the "Ok" button to perform the regression.

a. What are the values of X₁ and X₂? At what level are the two coefficients significant?

b. Interpret the coefficients, in the context of what they mean for the relationship between output, land and labor.

c. What is the sum of the two coefficients? What's the scale of production in this setting?

Question 2. 

As an extension of the previous problem. We may not believe that land and labor are the only inputs used in producing rice. Let's not forget that rice production is very irrigation intensive, we should probably include that variable into the equation. This would change our production function to:

output_i = A * Land^X1 * Labor^X2 * Irrigation^X3

Apply what you have learned in question 1 to re-estimate your model.

a. What are the values of the coefficients now? At what levels are the coefficients significant?

b. Interpret the coefficient on irrigation. What does it mean for rice production?

c. Now sum up your coefficients and obtain the scale of production.