A Time-Series Analysis of the Medical Care Price Index: Implications for Appraising Economic Losses
Bowles, Tyler J., Lewis, W. Cris, Journal of Forensic Economics
The time-series properties of wage growth rates, discount rates, and net discount rates have been a subject of significant forensic economics research. Payne, Ewing, and Piette (1999) provides the most recent example of this type of study; others include Pelaez (1991); Bonham and La Croix (1992); Gamber and Sorenson (1993, 1994); Pelaez (1996); and Payne, Ewing, and Piette (1998). Surprisingly, the time-series techniques used in this research (i.e., unit root and cointegration tests) have not been applied to other variables that often are part of economic loss appraisals. This paper fills part of this void by applying appropriate time-series analysis to the medical care price index, which is an important variable in valuing life care plans. The time-series properties of a second variable, the net discount rate defined approximately as the difference between the discount rate and medical care inflation, will be the subject of a subsequent paper.(1)
The assumptions about the time path of the medical care price index is an important determinant of the present value of a life care plan. The experience of the authors is that some economists and/or life care planners assume a medical care inflation rate that is inconsistent with their assumptions concerning overall inflation, nonmedical care inflation, and the discount rate. For example, it is not unusual to see some historic average medical care inflation rate used together with a current interest rate for discounting. As the latter reflects expected not historic inflation, the two parameters are not consistent.
Furthermore, it also is not unusual for the projected medical care inflation rate to be significantly higher (sometimes more than twice as high) than the projected overall rate of inflation. In cases involving long projection periods--70 years or more for an infant injured at birth--these assumptions often result in extremely large damage calculations.(2) More fundamentally, these inconsistent assumptions can lead to results that are economic nonsense. This will be demonstrated below.
This paper (a) reviews the general mathematical relationship among price indexes and demonstrates the long-run consequences of unreasonable and/or inconsistent assumptions regarding the time paths of the several price indexes used; and (b) applies modern econometric time-series analysis to provide insight into the time-series properties of the medical care price index. The remainder of the paper is divided into three parts. Section II discusses the relationship among the medical care, nonmedical care, and overall price indexes and illustrates the long-run implications of inconsistent assumptions about the time path of each of these indexes. Given the implications of this analysis, it follows that the relevant time-series properties of the medical care price index be evaluated. Thus, Section III reviews relevant time-series principles and applies tests of stationarity to the medical care inflation rate. Finally, Section IV summarizes the analysis.
II. Price Index Time Paths
Let [Y.sub.t] = real GDP for period t; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = real medical care output; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = real nonmedical care output; and, [P.sub.t], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = the price of GDP, medical care, and nonmedical care, respectively. Although each of these variables is a vector, there is no loss of generality by treating them as scalars. By definition
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
That is, the overall price of GDP is an average of the prices of medical care and nonmedical care weighted by the shares of output in each sector. Equation (2) also can be written as
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = labor inputs in sector i, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = labor productivity in sector i, and the superscripts m, n, and e refer to medical care, nonmedical care, and overall output, respectively. …