Dave Hansen and Drs. Bret Mackay and Norm Thurston, Economics
Introduction
My study aimed at settling an unresolved issue in contemporary health economic literature: Can doctors target their annual income levels, or are these levels subject to business cycle trends? Answering this question proved to be complex because in so doing it would have to fill a void in economists’ understanding of physician behavior.
Literature Review
Permanent Income hypothesis is the theory of consumption according to which people choose consumption based on their permanent income, and use saving and borrowing to smooth consumption in response to transitory variations in income. In contrast, the Target Income hypothesis of physician pricing suggests that with an increase in the number of physicians, physicians will increase both their prices and their demand to provide themselves with a target income. The prediction of the target-income hypothesis—namely, that an increase in the supply of physicians will result in higher prices and/or greater demand—is contrary to traditional economic theory, which suggests that increased supplies will lead to lower prices. Contemporary literature does not solve this debate of physician income behavior. In my study, I aim to discover if doctors use increased work hours or higher fees during upward trended business cycles and the converse during downward trended business cycles.
Data Description and Methodology
In this study, I am testing the cyclicality of physician income related to changes in GDP. Physician income is mean net physician income after expenses before taxes as collected by the American Medical Association, and GDP is in current and real (1992) dollars as collected by the Federal Reserve Board. My null hypothesis is that GDP shares a cyclical relationship with each type of physician income. If I fail to reject this hypothesis, the statistical analysis supports the Permanent Income Hypothesis; rejecting the null lends support to the Target Income Hypothesis.
In speaking with various professors in the Economic Department regarding typical properties time series data tends to have, I concluded that there existed a real possibility of the presence of autocorrelation and unit roots in each series. Additionally, taking the natural log of each element in the data set provides more intuition relative to the actual numbers. The above two premises represent the starting point in my research and analysis.
The initial step was to find a Q-statistic, formed by Box and Pierce (1970) to test for autocorrelation and partial autocorrelation. Q-statistic can be used to determine whether all autocorrelation coefficients are zero; approximately distributed as a Chi-distribution with K degrees of freedom. The presence of autocorrelation and partial autocorrelation implies that random shocks to the data decay slowly in following periods instead of affecting only the original period. The Q-statistic will be useful in testing for autocorrelations of the original data set and also of the residuals of various regressions later in the analysis.
In testing for autocorrelation and partial autocorrelation, I found that each series rejected the null hypothesis of no correlation; however, first differencing each series, with the exception of GDP, yielded stationary processes.
Once I have determined the presence of a unit root, I can pools the series, allowing for different intercepts, followed by the utilization of a seemingly unrelated regression (SUR). This will allow me to capitalize on the correlations between various series. This, however, might result in a spurious regression (Robinson, 368), which despite a high R-squared, renders results without any economic meaning.
Because studies in empirical macroeconomics almost always involve nonstationary and trending variables, such as income, I have reason to assume that in fact the data is nonstationary. As a result, I can look at unobserved components, and decompose into regular and irregular components. Since all of the series except GDP become stationary by first differencing, we can assume they are I(1). This result allows the use of cointegration techniques to test whether the partial difference between two series might be stable around a fixed mean, or I(0).
A principal feature of cointegrated variables is that their time paths are influenced by the extent of any deviation from long-run equilibrium. After all, if the system is to return to the long-run equilibrium, the movements of at least some of the variables must respond to the magnitude of the disequilibrium.
By definition, cointegration necessitates that the variables be integrated of the same order; thus, the initial step is to determine each variable’s order of integration. I used both the Augmented Dickey-Fuller test and the Phillips-Perron test to infer the number of unit roots (if any) in each of the variables. If the variables are integrated of different orders, it is possible to conclude that they are not cointegrated. It is important to note that GDP may have 2 or more unit roots, while all physician incomes, except that of Pediatricians, only have one. This would imply only Pediatricians’ income my exhibit cointegration with GDP; however, following the model, and using the Johansen test results implies that cointegration may actually exist. For this reason, I have decided to include results from cointegration tests.
Results
In performing tests to determine the existence of cointegration, I found the residuals of • êt = a1êt-1 + • t were not generated by a white-noise process, and hence used the ADF test to check for unit roots. These diagnostic checks yielded that no unit root exists in these residuals. Hence, the error terms are indeed stationary, and cointegration does exist.
Cointegration existing between GDP and each of the physician income series infers that physician income behaves according to the Permanent Income Hypothesis. If this truly is the case, then the validity of explanations using the Targeted Income Hypothesis do not hold, which in turn imply that physicians do not induce demand. However, many more tests need to be run to verify these initial findings. Because my data is limited, my initial analysis of nonstationary series may be wrong. If so, I will approach the next step in two possible ways. First, I can employ a filter to control for the fixed effect of physician specialty. One example is the Hodrick- Prescott decomposition (1984), which decomposes a series into a trend and stationary component. This will enable me to extract the same trend from a set of variables, such as a business cycle trend. Unfortunately, however, I do not have the necessary software to run this filter, hence further analysis in this area is required.
The major “leap of faith” I made was to overlook the differing unit root processes with GDP and all types of physicians, save pediatrics. I question the validity of my approach, but given my limited access to software, I performed all the tests possible. If invalid, then the Targeted Income Hypothesis holds; if not, the Permanent Income Hypothesis is more valid.
It does, however, seem that the residuals of the cointegration for all physician income variables are stationary. If so, then my next step is to run Vector Error Correction tests (VEC), which are regretfully beyond my software capabilities. VEC tests will delineate the relationships between shocks to GDP and a specific income series. If positively related, then shocks to the former would induce an increase to the former; if negatively related, shocks to the former induce decreases to the other. The VEC test, if appropriate, holds the relationship between GDP and physician incomes.
Reference
- Robinson, Enders A., Time Series Analysis and Applications, Houston: Goose Pond Press, 1981.