The Engel Curve is a measure that relates income to expenditures on a specific good or service. For this project, I chose to measure how changes in income affect health care expenditures. Conventional wisdom led me to believe that healthcare expenditures should be inelastic in regards to income because people’s level of health should be relatively stable in a developed country like the United States with respect to fluctuations in income. If I was analyzing a developing country, then additional income could mean the difference between consuming the nutrition necessary to stay healthy, having running water, or other factors which could more strongly affect levels of health. However, since the different health outcomes for varying levels of income are less pronounced in the US, I believe that health care expenditures should not depend strongly on income. In order to operationalize the independent variable in this situation, I have decided to use real disposable income per capita. Since the independent variable is measured in per capita terms, it is necessary that the dependent variable is measured in the same way, so I have health care expenditures per capita as my dependent variable during the past 18 years. The health care expenditures were adjusted for inflation based on the CPI during those years.
My initial regression yielded surprising results (Figure 1.) Real disposable income was highly statistically significant (p<.0001,) with a coefficient of 2.93. This implies that a $1 increase in real disposable income was associated with an additional $2.93 spent on health care. This didn’t seem to make much intuitive sense.
Figure 1. The plot unadjusted for health care inflation
Parameter Estimates | ||||||
Variable | Label | DF | Parameter
Estimate |
Standard
Error |
t Value | Pr > |t| |
Intercept | Intercept | 1 | 437.41993 | 119.65909 | 3.66 | 0.0023 |
Real_DI | Real_DI | 1 | 2.92723 | 0.07715 | 37.94 | <.0001 |
Table 1. Results for initial OLS regression where health care expenditures was only adjusted for CPI inflation
I went back to the data to look for any explanation for the odd results, and I realized that, though I had transformed the health care expenditure into real terms, I had done so using general rates of inflation based on the CPI. Health care was notorious for experiencing higher rates of inflation than other goods and services; health care inflation rate was an omitted variable in my regression. The two qualifications of an omitted variable are: it is a determinant of the dependent variable, and it is correlated with x. Clearly, health care inflation is a determinant of health care costs, and health care inflation is highly correlated with real disposable income, so I took this into account with my next regression. I adjusted the health care expenditure variable to account for the increased inflation rate. After performing this transformation, the real disposable income did not have a statistically significant effect on health care expenditures (t value 0.63). This implies that health care expenditures are income inelastic, which makes intuitive sense and follows my earlier prediction.
Parameter Estimates | ||||||
Variable | Label | DF | Parameter
Estimate |
Standard
Error |
t Value | Pr > |t| |
Intercept | Intercept | 1 | 5142.53107 | 254.87614 | 20.18 | <.0001 |
Real_DI | Real_DI | 1 | 0.09607 | 0.15149 | 0.63 | 0.5437 |
Table 2. Results for regression where health care expenditures is adjusted for health care inflation
Unfortunately, autocorrelation seemed highly likely when I looked at the residuals plot (Figure 2.), so I tested for the possibility of first order positive autocorrelation using the durbin-watson statistic.
Figure 2. Possible autocorrelation of residuals
This yielded a durbin watson statistic of 1.3262 and a pr<DW value of 0.0736, which was deemed likely enough to fix for autocorrelation. The following code was used to attempt to fix for autocorrelation:
model healthcare_inflation_adjusted=Real_DI /NLAG=1 dwprob;
After this, real disposable income still yielded statistically insignificant results (Table 3.), further reinforcing the claim that health care expenditures are income inelastic. Given the t-value we are unable to reject the null hypothesis, which states that the coefficient on disposable income is zero, implying that disposable income doesn’t have an effect on health care expenditures. One limitation of this study is the lack of available data for health care inflation rates. Due to this lack of data, only 10 observations were used for the final regressions.
Durbin-Watson Statistics | |||
Order | DW | Pr < DW | Pr > DW |
1 | 1.3262 | 0.0736 | 0.9264 |
NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation.
Parameter Estimates | ||||||
Variable | DF | Estimate | Standard
Error |
t Value | Approx
Pr > |t| |
Variable Label |
Intercept | 1 | 5066 | 293.4165 | 17.27 | <.0001 | |
Real_DI | 1 | 0.1425 | 0.1743 | 0.82 | 0.4404 | Real_DI |
Table 3. Autoreg results for regression