Estimating an Engel Curve for US Dairy Consumption
Using OLS, this model estimates an Engel Curve examining the relationship between US dairy consumption and income. The data involved includes real disposable personal income per capita (RDPI) in the United States from 1995 – 2015 provided by Federal Reserve Economic Data and per capita dairy consumption (DCPC) measured in average pounds per person in the United States from 1995 to 2015 provided by the United States Department of Agriculture (USDA). DCPC is modeled as the dependent variable with RDPI and RDPI squared as independent variables.
The descriptive statistics indicate a mean RDPI of $33,627.38 and range from $27,180.00 – $38,431.00. DCPC for this dataset has a mean of 595.8 pounds per person and a range from 561.9 – 627.2 pounds per person.
The OLS results for this sample indicate that as real disposable personal income (RDPI) increases by one thousand dollars, average dairy consumption per person (DCPC) increases by 0.001 pounds per person, holding income squared (RDPI2) constant. The coefficient on RDPI is not statistically significant at a 5% level (p= 0.8749). As income squared increases by one thousand dollars, average dairy consumption per person increases by 6.247242E-8 pounds. The coefficient on RDPI2 is not statistically significant at a 5% level (p= 0.5597). The model fit the data well with an R2 of 0.9400 and an adjusted R2 of 0.9334. The results indicate that there is a weak relationship between income and dairy consumption but the model fit the data well.
Autocorrelation is expected for time series of this nature. The results from the Durbin Watson test indicate a high D value (D = 1.4232) where a value of 2 indicates there is no autocorrelation present in the sample.
Correcting for autocorrelation, the new results indicate that a one-thousand-dollar increase in income decreases dairy consumption by 0.002 pounds per person, holding income squared constant. A one-thousand-dollar increase in income squared increases dairy consumption by 1.0884E-7 pounds per person, holding income constant. The new R2 from the Yule Walker estimates (0.9433) and regress R2 (0.9208) indicate that the corrected model fit the data well.
There are several limitations to this model:
- There is an extremely weak relationship between income and dairy consumption, as shown by small coefficients on income and income squared. Small coefficients could be due to a lack of additional observation years.
- There are most likely other explanatory factors that influence dairy consumption such as individual preferences and allergies.
- There is a small amount of autocorrelation present, and correcting for autocorrelation gives changes the relationship between income and dairy consumption from a very small positive number to a very small negative number and the relationship between income squared and dairy consumption remains infinitesimally positive. Other model misspecifications could be present.
- Including more specific variables such as milk, icecream, and yogurt consumption could further differentiate between the data and offer insight into individual dairy components in relation to income. This could also eliminate multicollinearity if present.
United States Department of Agriculture, Dairy Products: per capita consumption, United States (Annual). Retrieved from https://www.ers.usda.gov/data-products/dairy- data/, February 14, 2017.
U.S. Bureau of Economic Analysis, Real Disposable Personal Income: Per Capita [A229RX0], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/A229RX0, February 14, 2017.