APEC 3003, Spring 2023 Homework 1
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APEC 3003, Spring 2023
Homework 1
Simple linear regression: Price transmission along the supply chain
In this homework, you will take a publicly available data set from the U.S. Department of Agriculture’s Economic Research Service and use it to examine how much of price changes at the farm level of an agricultural product are passed along to consumers. For instance, how much does a 10 cent increase in price at the farm gate increase the price that a consumer pays at retail? We’ll look at this question for beef. The questions will take theoretical knowledge of ordinary least squares (OLS) regression and apply it to this data.
One model to answer this question would be to estimate a simple linear regression of price changes at retail on price changes at the farm gate. A change in price at retail for month t would be PriceChange
while a change in farm gate price for month t would be PriceChange
The regression specification here is:
PriceChanget(r)etail = β0 + β1 PriceChanget(f)arm + et (1)
Theory questions
Question 1 (20 points)
For the regression equation above, what is the dependent variable? What is the independent variable? Write out the equation for the estimate of βˆ1 and explain the meaning of the components in this context.
Question 2 (15 points)
What does it mean for βˆ1 to be consistent? Include some formal definition as well as intuition. Describe informally the difference between unbiasedness and consistency. For bonus points: come up with an example of a biased but consistent estimator and an unbiased but inconsistent estimator.
Question 3 (15 points)
What are some unobserved or unmeasured factors that could be in the error term et in equation (1) above? Do you believe the assumption that PriceChanget(f)arm is uncorrelated with all of these factors? Why or why not?
Applied questions
In the Simple Linear Regression module on Canvas, you will find a file called “meat price history.xls.”1 Column A shows the month for which the values are measured. Columns B through D of this sheet show price values, in cents per pound of retail weight equivalent, for beef products measured at different stages of the supply chain, from before it leaves the farm to retail. Columns E-G are my own calculations of month-to-month changes in price for net farm price, wholesale price, and retail price.
Load this data in to R. You can use the read_excel() command from package readxl that we covered in lab . I’d suggest including options to skip the first 2 rows (skip = 2), since they contain variable description information
1 Hahn, William. January 12, 2023.“Meat Price Spreads.”US Department of Agriculture Economic Research Service Data Products. https://www.ers.usda.gov/data-products/meat-price-spreads/
Data sources: All the data in the sheets are USDA, Economic Research Service (ERS) calculations based on USDA, Agricultural Marketing Service data for the farm, wholesale, and byproduct values. The retail values are based on Bureau of Labor Statistics retail price data.
rather than data.
Now the data is clean and in R, ready to go.
Question 4 (15 points)
Check on the data. Are there missing values? Are you concerned about the missing values? Report a table of summary statistics - including number of observations, mean, standard deviation, maximum, and minimum - for the change in farm price and change in retail price variables.
Question 5 (15 points)
Make a plot of historical changes in retail prices and another plot of changes in farm prices. The R command ggplot() (included in the package tidyverse) that we covered in lab can make a plot for you. What do you notice about these two plots relative to each other?
Question 6 (20 points)
In R, using bivariate OLS with the command lm(), estimate the regression specification in equation (1). Report βˆ0 and βˆ1 . Give an interpretation of the estimated parameter βˆ1 .
2023-02-06