I gathered data on “Disposable Personal Income” and “Personal consumption expenditures: Laundry and dry cleaning services” from the Saint Louis Fed’s online database, FRED. Both data series were annual data from 1959 to 2015 and were in nominal terms ($B), which allowed consumption and income data points to match on an “apples-to-apples” basis. I chose to use disposable personal income because that is the figure the aggregate “U.S. household” has to decide where to spend; as opposed to GDP, which would be multiple translations removed from the household income figure that consumers decide to spend on laundry or elsewhere.

By creating an Engel Curve through OLS, my model’s independent variable was Disposable Personal Income and my model’s dependent variable was Consumption expenditures on laundry and dry cleaning services. I decided to take a time series approach to creating an Engel Curve as I believed that the regression output on roughly 50 years of data would better substantiate a potential relationship between income and laundry-related expenditures than a cross-section approach, which would only evaluate the relationship at one point in time. At the expense of more accurate regression coefficients – which would have resulted from a cross-sectional approach – the time series method will capture this relationship through most of its existence (while admittedly bringing in additional noise).

 

Model 1 yields the following regression coefficients:

These results suggest that for every $1.00 increase in disposable personal income, household expenditures on laundry and dry cleaning services increased by $0.0009. It can also be extrapolated that laundry-related expenses make up 0.09% of consumers’ total expenditures. Given the large t-Value and small p-value, disposable personal income is a significant predictor of laundry expenditures. The coefficient on income suggests that laundry expenditures are a normal good (expenditures increase as income increases). However, the chart below – which is the Engel curve – reveals that although the coefficient suggests the service is a normal service, there are certain years in which outliers exist. Nevertheless, the general trend, quantified by the coefficient on income, holds strong.

Because of the irregularities found in the trends (especially at the extreme income levels), I suspected that the OLS regression was subject to heteroscedastic errors, meaning that the variance in each error isn’t constant across all observations. The lack of homoscedastic errors violates one of the Gauss-Markov assumptions and means that although the estimated coefficient is unbiased, the standard errors are biased, leading to unreliable hypothesis tests and standard errors. A visual representation of the heteroscedastic errors is below, as well as the white test results, confirming my suspicions.

 

The lack of white noise errors led me to question that I had an omitted variables problem – there must be some factor other than income that predicts expenditures on laundry and dry cleaning services. The below chart led me to hypothesize that the data was competing with itself, meaning that an increase in income increased the expenditures on dry cleaning but decreased expenditures on coin-operated Laundromats (and vice versa).

Because the FRED website wasn’t specific as to what was and wasn’t included in Laundry and dry cleaning services, I needed to control for one of two competing forces in my data set. Therefore, in an effort to isolate income’s affect on dry cleaning expenditures, I found data from Statista detailing U.S. Laundromat revenue from 2002 to 2015. Adding this series as an independent variable in my model (along with Disposable Personal Income), I re-ran the model.

These results suggest that a $1.00 increase in disposable personal income will increase laundry and dry cleaning service expenditures by $0.0003, holding Laundromat revenue constant. This effectively suggests that for every $1.00 increase in disposable income, a consumer will spend $0.0003 more on dry cleaning (p-value 0.0015). The inclusion of the Laundromat revenue variable clearly helps explain how income affects dry cleaning expenditures, as evidenced by the now homoscedastic errors:

 

 

Relationship between Income and Dry Cleaning Expenditures