Academic journal article Journal of Forensic Economics

# The Time Series Behavior of the Medical Cost Net Discount Rate: Implications for Total Offset and Forecasting

Academic journal article Journal of Forensic Economics

# The Time Series Behavior of the Medical Cost Net Discount Rate: Implications for Total Offset and Forecasting

## Article excerpt

I. Introduction

An important issue in forensic economics is the appropriate valuation of future medical needs. When faced with a party that requires ongoing medical care or treatment, it is intuitively appealing to calculate the economic damages using the total offset method. In this context, total offset refers to a complete offset between increases in medical costs and the discount rate. However, this method is only accurate for the special case in which the growth rate in medical costs just equals the discount rate. Thus, the economist must often forecast medical cost inflation, the discount rate, or both. A task of this type requires knowledge of how these variables behave over time as well as how they are likely to behave in the future. This paper examines the growth rate of the composite consumer price index (CPI) medical care index in relation to several discount rates.

Our analysis begins by constructing several versions of the medical cost net discount rate (MNDR). The first task of this paper is to determine if the total offset method is appropriate. Specifically, we perform a simple t-test to see if the mean of the MNDR equals zero. If the MNDR equals zero, then the total offset method would seem appropriate. However, our results strongly suggest that none of the MNDRs equal zero and thus we proceed to examine the times series properties of each MNDR by conducting stationarity tests. (1)

The second task of this paper is to determine if the MNDR can be characterized as a stationary process or a nonstationary process. If the MNDR is nonstationary, due to deterministic trend or a unit root, then the use of historical averages for forecasting purposes is inappropriate. On the other hand, if the MNDR is stationary around its mean, then the use of historical averages of the MNDR may be used for forecasting. Regardless of the discount rate chosen, we find evidence that the MNDR is a stationary process. This implies that the historical average of the MNDR may be used in applied work. However, the issue of what constitutes an appropriate horizon, both in terms of calculating the historical average and in projecting into the future, is not answered by the stationarity tests.

The third task of the paper is to determine the time required for the MNDR to revert back to its long-run mean value following a shock. In order to answer this question we estimate an autoregressive model for each of the MNDRs and simulate a one-standard deviation shock to the series and trace out the effect on the MNDR over time. The results of these simulations suggest that it takes almost two and one-half years for the impact of a shock to the MNDR to fully dissipate. Our findings indicate that one may use the historical average of the medical net discount rate computed from the medical care component of the CPI. However, caution should be used whenever the horizon under investigation or the number of observations used to compute the historical average is less than 27 months. The following sections of the paper describe the data and the methodology used in our analysis as well as comments and suggestions for additional research.

II. Data, Methodology and Results

Monthly data covering the period January 1980 to May 2000 were collected for the CPI medical care index and several interest rates. (2) The annual growth rate in the cost index (g) was computed on a year-over-year basis that provides a usable starting point of 1981:01. (3) Rates on constant maturity 1-, 2-, 3-, and 10-year Treasury securities were obtained and converted to a bond yield basis (r). The medical net discount rate was computed as: (4)

(1) MNDR = r - g

We denote the medical care cost net discount rate constructed using the 1-, 2-, 3-, and 10-year interest rates by MNDR1, MNDR2, MNDR3, and MNDR10, respectively. Figure 1 presents plots of the medical net discount rates. Note that the medical net discount rates follow a similar pattern over time. …

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