You are planning to estimate a short-run production function for your firm, and you have collected the following data on labor usage and output.
Labor usage output
3 1
7 2
9 3
11 5
17 8
17 10
20 15
24 18
26 22
28 21
30 23
(a) Does a cubic equation appear to be a suitable specification, given this data? You may wish to construct a scatter diagram to help you answer this question.
(b) using a computer and software for regression analysis, estimate your firm's short-run production function using the data given here. Do the parameter estimate have the appropriate alegebraic signs? Are they statistically significant at the 5 percent level?
(c) At what point do you estimate marginal product begins to fall?
(d) Calculate estimates of total, average, and marginal products when the firm employs 23 workers.
(e) When the firm employs 23 workers, is short-run marginal cost (SMC) rising or falling? How can you tell?
a) do a scatter plot as suggested.
b) estimate several equations, be sure to do an OLS as well as a cubic.
c,d,e) repost if you are having trouble interpreting your results.
What is a OLS?
Sorry bout that.
Ordinary Least Squares
which is your standard linear regression methodology.
I did a polynomial curve using excel, do I need to also do a OLS as well, or could I come up with the same answers either way. What is the difference between the two?
Sorry bout that.
Ordinary Least Squares
which is your standard linear regression methodology.
When conducting a regression analysis, there are different methods that can be used to estimate the relationship between variables. OLS, or Ordinary Least Squares, is one of the most commonly used methods for linear regression. It is specifically used to estimate the parameters of a linear equation.
In your case, if you have used Excel to create a polynomial curve, you have already estimated a non-linear relationship between labor usage and output using a cubic equation. This is different from OLS, which assumes a linear relationship between the variables.
While both methods can provide estimates for the relationship between variables, they differ in the assumptions and interpretation. OLS assumes a linear relationship and estimates the coefficients that best fit the line to the data points. On the other hand, a polynomial curve such as a cubic equation allows for a non-linear relationship and estimates the coefficients specific to that equation.
To determine whether you need to perform an OLS regression analysis in addition to the polynomial curve, it depends on what you want to understand from your data. If you are primarily interested in estimating a cubic relationship and overall fit of the non-linear curve, then the polynomial curve may be sufficient. However, if you want to compare the fit and statistical significance of a linear relationship using OLS, you would need to perform that additional analysis.
It's worth noting that OLS can be easier to interpret and provides statistical measures (such as p-values) to assess the significance of the estimated coefficients. Polynomial curves, on the other hand, can provide a more flexible fit to the data but may be harder to interpret in terms of statistical significance.