Theoretical Problem

Theoretical Problem

The short-run production function for a firm in the business of calculator assembly is given by , where “q” is finished calculator output and “l” represents hours of labor input. The firm is a price taker for both calculators (which sell for “p”) and workers (which can be hired at a wage rate of “w” per hour).
1. What is the short-run supply function for assembled calculators ?
2. What is the effect of a change in the wage on the quantity supplied?
3. What is the own-price elasticity of supply for calculators?
Supply Estimation Assignment
You are a junior economist for the Economic Research Service at the USDA whose job is to figure out certain characteristics of the supply of chicken broilers in the U.S. Not only must you correctly perform the statistical analysis, but your presentation of the results is vitally important. You need to be able to effectively communicate your findings with those who are not as well versed as you in economic theory and econometrics. Make it look sharp!
You may work in groups on this assignment but every individual must turn in his/her own assignment that represents his/her own work.
Part I: Data Collection
1. Lucky for you as the lead economist you now have a junior economist working for you. You assign him to go find the raw data that you need. Specifically you ask him to collect:
From the ERS Database:
a. Annual data on the total production of young chickens (also known as broilers) in the U.S. from 1950 – 2001
From the Bureau of Labor Statistics:
a. A price index that represents the prices farmers received for broilers
b. A price index for corn as a major input of production (feed)
c. The consumer price index

2. The data this junior economist collected is available for you as a .csv file in Angel. Download it and read it into STATA.
Part II: Data Estimation
1. Convert all price indexes into $2001 using the cpi variable (whenever I refer to prices after this, I will mean real prices).
2. Create a per capita supply variable (“percapq”) that is “q” divided by “pop” (population).
3. Model the supply of broilers (per capita) as a function of the concurrent price of broilers and the price of corn:

What do you expect the signs of and to be? Display the table in your write-up. Are the signs as expected?
4. Why might the specification listed above suffer from omitted variable bias?
5. Oftentimes researchers approximate technological change in an industry by including some sort of time trend in the model. Create a variable called “time” (use the command, gen time = _n). This will create a linear time trend numbered 1-52 (the number of years of data we have). Now estimate the model:

Display the table in your write-up. Now are the signs of and consistent with our theory? Calculate the own-price elasticity of supply for broilers. Is supply elastic or inelastic?
6. Including a linear time trend as a way to proxy for technological change imposes some assumptions on how such changes take place. What is the assumption about how much technological improvement there is from one year to the next (in percentage terms—a discussion of this can be found in Ch. 2 of the textbook)?
7. How would you account for non-linear technological change in your regression specification? Include a “time squared” term in your regression. Display the results in your write-up. What happens to the coefficient on broiler price? Why might this be the case given the source of variation in prices in this data?
To test whether multicollinearity might be a problem, regress broiler price on the other covariates in the model (as discussed in class). What do the results tell you?
8. Suppose you were aware that a major technological innovation in broiler production occurred in 1984. How would you account for this in your model? Change your model accordingly as display the results in your write-up. Do you reject or fail to reject the hypothesis that production changed substantially in 1984 (at the 5% level), holding other factors constant?
9. As you know, the dataset you are using is a time series. Get Stata to formally recognize this by typing “tsset time.” In time series data, serial correlation (or autocorrelation) can be a problem. This will not affect your point estimates, but it will affect your standard errors. To examine whether your data exhibits serial correlation:
a. Calculate the residuals from your regression in #5 (you will need to run this regression again first). The command is “predict resid, residuals.” “Resid” is the name of the variable that contains the residuals from this regression.
b. Graph these residuals against time (use Stata’s “graph twoway” feature, but you will need to fill in the details). What kind of serial correlation (positive or negative), if any, do you think exists?
c. A common type of serial correlation occurs when the error from this period is correlated with the error from last period. To test for this kind of serial correlation, regress “resid” on its 1-period lag (type “help tsvarlist” to figure out how to include a 1-period lag in your model). Display the results in your write-up.
d. Does this regression indicate positive or negative serial correlation? A test for this kind of serial correlation is a t-test associated with the coefficient on the lagged residuals. Do you reject or fail to reject the null hypothesis of no serial correlation?
10. As a smart economist, you realize that broiler production decisions are likely not a function of the concurrent price, but what price suppliers expect to receive when their chickens have matured (some time in the future). A simple model of expectations suggests that people expect prices tomorrow to be exactly what they are today (you could do worse!). If it takes 1 year to harvest broilers, then the price that matters explaining the quantity of broilers supplied in year X is the price in year X-1.
a. Perform the same regression as you did in #5 but add the 1-period lagged value of the chicken price and corn price to your specification. Display the results in your write-up. What do the results tell you about which year’s prices are more important for explaining production in a given year?
b. Test the hypothesis (look into Stata’s “test” command) that the effect of this year’s chicken price is the same as the effect of last year’s chicken price. Do you reject or fail to reject the null hypothesis that the effects are the same?

 
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