Medical Net Discount Rates:

Transcription

1 Medical Net Discount Rates: An Investigation into the Total Offset Approach Andrew G. Kraynak Fall 2011 COLLEGE OF THE HOLY CROSS ECONOMICS DEPARTMENT HONORS PROGRAM

2 Motivation When estimating the cost of future medical care, forensic economists (FEs) use a medical cost net discount rate (MNDR), constructed with a growth rate and a discount rate, to adjust for inflation and investment rates. A discount rate allows a court to award compensation for damages to a victim in a lump sum, instead of drawing out the award by requiring the liable party to pay for the victim s medical costs year after year. The medical component of the Consumer Price Index (MCPI) is used as the growth rate when calculating the net discount rate for court awards that involve compensation for future medical care. The MCPI is used in conjunction with an interest rate in order to calculate the MNDR. There is, however, no consensus among FEs on which interest should be used for MNDRs. An argument in favor of the use of shorter-term interest rates comes from a frequently cited US Supreme Court ruling on lost future earnings. It dictates the use of an interest rate that is both the best and safest (Jones and Laughlin v. Pfeifer pg. 537). Although these terms are somewhat contradictory, the ruling later describes the interest rate that should be used in discounting as simply the safest. This emphasis on safety provides a basis for using securities of shorter duration with lower returns. While the Pfeifer ruling was made in regards to lost earnings, the case can be extended to provide a principle for discounting awards for future medical costs. Ireland and Tucek (2011) have assembled tables with historical averages of discount rates constructed with five different interest rates (3-Month, 1-Year, and 10-Year US Treasury securities, corporate AAA bonds, and municipal bonds). The broad spectrum of interest rates included in their tables attests to the diversity in opinion of FEs on which interest rate is proper for MNDRs. The historical averages of MNDRs constructed with 3-Month and 1-Year US 2

3 Treasury securities are approximately within one half of one percent of zero for their thirty year averages, which use data from 1981 to Historical averages, however, may not be the best predictor of future MNDRs. Ewing, Payne, and Piette (2001) use time series analysis to look at the MNDR during the period from January 1981 to May 2000, using monthly data for both the growth rate (MCPI) and the interest rate (Treasury notes and bonds with 1-, 2-, 3-, and 10-year maturities). They reject the total offset approach, which states that the growth rate and interest are equal over time: Regardless of the discount rate used to compute the MNDR, we found evidence against the use of the total offset method (Ewing, Payne, and Piette 2001). Their study also uses the Augmented Dickey- Fuller (ADF) test to establish the stationarity of the MNDR. Gelles and Johnson (1996) describe a regime change in the Federal Reserve s monetary policy that structurally shifted post-1980 interest rates. Ewing, Payne, and Piette (2001) begin their data series after the regime change in order to avoid the Federal Reserve s policy shift. Furthering the time series analysis, Sen and Gelles (2006) use a Crash Model (following Zivot and Andrews, 1992) and find the MNDR to be trend-break stationary over the period from January 1980 to January Using the MCPI and a 1-year Treasury note, Sen and Gelles find that the MNDR has a break-point in January When looking at historical averages of MNDRs, a break-point date has the same effect as a regime change in the Federal Reserve: forensic practitioners should use the estimated trend function in the post-break period to forecast the medical net discount rates (Sen and Gelles 2006). 1 Only the 1-year Treasury bill was used by Sen and Gelles (2006) to establish break-dates for MNDRs that were constructed with various medical Consumer Price Subindexes. This study employs the MNDR constructed with the medical care CPI, and uses its break-date of January 1994 for tests on the 3-month MNDR, 6-month MNDR, and 1-year MNDR. Ideally, break-dates would be estimated using the Crash Model for each variation of the MNDR in this study, but a Crash Model was beyond the scope of this paper. 3

4 Since the study by Ewing, Payne, and Piette (2001), a full decade s worth of MCPI and interest rate data has become available. This new decade of data contains MNDRs that are, on average, lower in value than MNDRs in previous years. Additionally, the 3-Month and 6-Month US Treasury securities, which have lower rates of return than the 1-Year US Treasury security, were not included in the study by Ewing, Payne, and Piette (2001). In light of these facts, the question of total offset seems to require further examination. This study seeks to build upon the framework of Ewing, Payne, and Piette (2001) by first replicating their results using data from January 1980 to May 2000 (referred to henceforth as the period). I will then add to their work by extending their data set to include MNDRs into 2011 (henceforth the Extended period). Additionally, this study will employ the 3-Month and 6-Month Treasury bills to inquire into the question of whether the total offset approach can be justified with the MNDR based on Treasury securities of shorter duration (i.e. the safest ). Finally, I will use the January 1994 break-date established by Sen and Gelles (2006) to compare the analysis of the period to the period (Early Split period) and the period (Late Split Period). Figure 1 shows the 3-Month, 6-Month, and 1-Year MNDR series over the Extended period. In order to replicate a part of the study by Ewing, Payne, and Piette (2001), MNDRs were constructed using the percent change in the medical component of the Consumer Price Index (MCPI) and the rate of return on the 1-Year Treasury Security. The data were collected on a monthly basis beginning in January 1980 and ending in August Data for the percent change in the MCPI were calculated based on the percent change of one month from the same month in the previous year. Data for rates of the constant maturity 1-Year Treasury Securities were obtained from the St. Louis Federal Reserve s FRED series (Federal Reserve Economic 4

5 Data) and converted to a bond yield basis. 2 The simple MNDR calculation was used by Ewing, Payne, and Piette (2001), and this study employs the same formula for only the 1-Year MNDR in an effort to make the results directly comparable to several of the findings by Ewing, Payne and Piette (2001). Simple MNDR = r g Figure 1 * All MNDRs were constructed using the Complex MNDR calculation and are expressed in terms of percent. MNDR using the 1-Year Constant Maturity Treasury Security The rate of return on the constant maturity 1-Year Treasury security is used as the interest rate (r), and the percent change in the MCPI is used as the growth rate (g). When these two rates 2 The Treasury Department reports that CMT yields are read directly from the Treasury s daily yield curve and represent bond equivalent yields for securities that pay semiannual interest, which are expressed on a simple annualized basis. I converted these interest rates to a bond-yield basis. 5

6 are equal over time, the MNDR will be zero and the total offset approach could be justified. To test for the Total Offset approach, a t-test was performed separately on the, Extended, and Split periods. By simply regressing the MNDR on a constant, the null hypothesis that the MNDR is zero was tested against the alternative hypothesis that the MNDR is not equal to zero. If the null hypothesis is rejected then the total offset approach cannot be justified for the MNDR constructed with the 1-Year Treasury Security. Table 1 shows the results of the t-test for the different periods. Table 1 Test for Total Offset of 1-Year MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) Constant T-Statistic P-Value The t-statistic for the period matches the results of Ewing, Payne, and Piette (2001), and I was similarly able to reject the null hypothesis of total offset for all time periods except the Late Split, from February 1994 to August The Late Split period produced a negative constant and an insubstantial t-statistic, meaning that MNDR is not statistically different from zero. The use of total offset approach could, therefore, be justified based on the Late Split period. These results were found to be robust with the more complex formula (described below) 3 Ewing, Payne, and Piette (2001) report a t-statistic of , and the small difference between the t- statistics is thought to be because of data revisions in the MCPI subsequent to publication of their article. 6

7 for MNDR and can be found in the appendix. As suggested by Sen and Gelles (2006), the Late Split period is most relevant in terms of usefulness for FEs because it does not include inappropriate MNDRs. A simple test for the total offset approach, however, does not justify the use of zero as the MNDR. Historical MNDR series are only relevant to the projection of a future MNDR if the series exhibits some type of stationarity over time. Stationarity in time-series analysis means that a series exhibits mean-reversion after exogenous shocks. A series that does not revert back to its mean over time but rather seems to experience random upward and downward movement is referred to as a random walk or nonstationary series. Historical MNDRs are only useful if the series is stationary around zero, an historical mean, or a trend function. Otherwise, future MNDRs would be independent of previous MNDRs, making professional forecasts and current values for the interest and growth rates perhaps more accurate predictors in determining future MNDRs. An ADF test was conducted on the 1-Year MNDR series to determine if there is a unit root. The presence of a unit root indicates that the series is nonstationary and exhibits a random walk. The test was separately conducted on each of the following periods:, Extended, Early Split, and Late Split. The null hypothesis of the ADF test is that the series has a unit root (i.e. is not stationary). Subsequently, rejection of the null hypothesis implies stationarity and that the historical series of MNDRs are relevant for future MNDR estimations. The ADF test produces a τ-statistic (tau-statistic) that has a different distribution than an ordinary t-statistic, and the one-sided P-values for the ADF statistic must be used as provided by MacKinnon (1996). Table 2 reports the τ-statistic and the P-value for the ADF test. 7

8 Table 2 Test for Stationarity (Augmented Dickey-Fuller*) of 1-Year MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) τ-statistic P-Value * A time trend was not included because of the a priori hypothesis of Total Offset. The number of lagged differences included in the ADF test was determined by the Modified Aikaike s Information Criterion with a maximum number of lags set at three. The appendix shows the number of lags used for each test. The Extended period is stationary with a P-value below five percent, but for the, Early Split, and Late Split periods the null hypothesis of nonstationarity cannot be rejected. The result of stationarity in Ewing, Payne, and Piette (2001) was not upheld for the 1- Year MNDR because a different number of lagged variables was used in this study s ADF test. 4 MNDR using the 6-Month Constant Maturity Treasury Security MNDRs were constructed using the percent change in the MCPI and the rate of return on the 6-Month Constant Maturity Treasury Security. The data series was collected on a monthly basis from January 1980 to August 2011 and converted in the same way as the MCPI and 1-Year Constant Maturity Treasury Security in the previous section. The MNDR based on the 6-Month Treasury Security was constructed with the more complex and accurate formula for the MNDR. 4 The results from Ewing, Payne, and Piette (2001) were replicated using their specification of three laggeddifference variables. This ADF test yielded a τ-statistic of with a P-value of , making the MDNR series marginally (10% level) significant. 8

9 Ewing, Payne, and Piette (2001) did not look at MNDRs using interest rates with durations of less than one year, and this study will construct these MNDRs using the complex MNDR calculation. Complex MNDR = (r g)/(1+g) The interest rate (r) is the rate of return on the constant maturity 6-Month Treasury Security, and the growth rate (g) is the percent change in the MCPI. The more complex MNDR formula does not change the conclusion that when r and g are equal over time, the MNDR will be zero and the total offset approach could be justified. Again, a simple t-test was performed to test for the total offset approach by regressing the MNDR on a constant with the null hypothesis that the MNDR is zero. The t-test was performed separately on each of the periods in Table 3. Table 3 Test for Total Offset of 6-Month MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) Constant T-Statistic P-Value The total offset approach is rejected for the and Late Split periods. However, the Late Split period has a negative constant, suggesting the use of negative discounting (i.e. more than offset). The constant for the Early Split period is only marginally (10% level) significantly different from zero, and the MNDR for the Extended period has a constant that is not statistically different from zero. Therefore, total offset approach could be justified for the MNDR based on the Extended and the Early Split periods. 9

10 Sen and Gelles (2006) find evidence to suggest that their post-break period is the most relevant period for FEs, and Table 3 indicates a negative MNDR for the Late Split period (i.e. more than total offset). With the 6-Month Treasury Security, the result of a negative MNDR makes intuitive sense because the MNDR using the 1-Year Treasury Security, constructed with a larger interest rate, was found to be zero in the previous section for the Late Split period. In order to justify the use of the total offset (or more than total offset) approach, the series must exhibit stationarity over time. An ADF test was conducted on the 6-Month MNDR series with the customary null hypothesis of nonstationarity. The test was conducted on each of the periods separately, and the resulting τ-statistics and MacKinnon (1996) P-values appear in Table 4. Table 4 Test for Stationarity (Augmented Dickey-Fuller*) of 6-Month MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) τ-statistic P-Value * A time trend was not included because of the a priori hypothesis of Total Offset. The number of lagged differences included in the ADF test was determined by the Modified Aikaike s Information Criterion with a maximum number of lags set at three. The appendix shows the number of lags used for each test. The MNDR for the Extended period is stationary with a P-value below five percent. Nonstationarity cannot be rejected for the, Early Split, and Late Split periods. Therefore, the MNDR for these three periods are not mean-reverting around a constant, and historical data do not help predict their future values. 10

11 For the Extended series, the MNDR based on the 6-Month Treasury Security is not statistically different from zero and is stationary. Therefore, this finding justifies the use of the total offset approach based on the MNDRs over the Extended period. MNDR using the 3-Month Constant Maturity Treasury Security MNDRs were constructed using the percent change in the MCPI and the rate of return on the 3-Month Constant Maturity Treasury Security. The data series was collected over the same dates and converted as described in the previous sections. Performing a simple t-test, the total offset approach was tested with a regression of the MNDR on a constant with the null hypothesis that the MNDR is zero. Table 5 shows the results of the test for each series. Table 5 Test for Total Offset of 3-Month MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) Constant T-Statistic P-Value The total offset approach is rejected for the MNDR over the and Late Split periods. However, the MNDR for the Late Split period has a negative constant which suggests the use of negative discounting (i.e. more than offset). The Extended and Early Split MNDRs have constants that are not statistically different from zero, and as a result, the total offset approach could be justified based on both of the series. Sen and Gelles (2006) find evidence to suggest that their post-break period is the most relevant period for FEs, and the results in Table 5 indicate the use of a negative MNDR 11

12 and imply more than total offset. The constant for Late Split series of the 3-Month MNDR is smaller (i.e. more negative) than both the results from the 1-Year and 6-Month MNDRs, which makes intuitive sense. An ADF test was performed on the 3-Month MNDR with a null hypothesis of nonstationarity. Table 6 displays the results of the ADF tests for each of the periods. Based on the P-values in Table 6, the MNDRs for the, Early Split, and Late Split periods are found to be nonstationary around their means. Historical MNDRs for those three periods do not help predict future MNDRs. Nonstationarity can be rejected for the MNDR over the Extended period with a P-value below five percent. The Extended MNDR is found to be both not statistically different from zero and stationary around its mean. These findings justify the use of total offset based on the 3-Month MNDR over the Extended period. Table 6 Test for Stationarity (Augmented Dickey-Fuller*) of 3-Month MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) τ-statistic P-Value * A time trend was not included because of the a priori hypothesis of Total Offset. The number of lagged differences included in the ADF test was determined by the Modified Aikaike s Information Criterion with a maximum number of lags set at three. The appendix shows the number of lags used for each test. Final Remarks 12

13 This paper addresses whether the use of the total offset approach is appropriate for FEs. I added to the work of Ewing, Payne, and Piette (2001) by testing MNDRs constructed with the 3- Month and 6-Month Treasury Security and extending the data set to August 2011 for all three MNDRs. Additionally, I took into consideration a study by Sen and Gelles (2006) that found a break-point for the 1-Year Treasury Security in January By regressing MNDRs on a constant and performing ADF tests, the, Extended, Early Split, and Late Split periods were tested to determine whether the MNDR was equal to zero and stationary. The results were mixed and certainly did not provide concrete evidence for either the justification or condemnation of total offset. Despite the lack of uniform results, this study differs from earlier studies in that it shows a sweeping rejection of total offset is no longer warranted. A summary of this study s findings shows the lack of uniform results with regard to total offset. The 1-Year MNDR was found to be not statistically different from zero for the Late Split period but was only stationary for the Extended period. The 6-Month MNDR was not statistically different from zero for the Extended and Early Split periods but was only stationary for the Extended period. Results from the 3-Month MNDR also showed that the Extended and Early Split MNDRs have a constant not statistically different from zero, but only the Extended series exhibited stationarity. Additionally, the 6-Month and 3-Month MNDRs had negative constants in the simple regression over the Late Split period; despite the implication of more than total offset, these Late Split series were found to be nonstationary, implying the historical mean is unsuitable for forecasting by FEs. References 13

14 Ewing, Bradley T., James E. Payne, and Michael J. Piette, The Time Series Behavior of the Medical Cost Net Discount Rate: Implications for Total Offset and Forecasting, Journal of Forensic Economics, 2001, 14(1), Ewing, Bradley T., James E. Payne, and Michael J. Piette, An Inquiry Into the Time Series Properties of Net Discount Rates, Journal of Forensic Economics, 1999, 12(3), Gelles, Gregory M., and Walter D. Johnson, Comment: Justifying Utilization of the Total Offset Method: An Opposing Comment, Journal of Legal Economics, 1996, 6, Ireland, Thomas R., and David Tucek, Historical Net Discount Rates-An Update Through 2010, Journal of Legal Economics, 2011, 18(1), MacKinnon, James G., Numerical Distribution Functions for Unit Root and Cointegration Tests, Journal of Applied Econometrics, 1996, 11(6), Sen, Amit and Gregory Gelles, On the Time Series Properties of the Medical Net Discount Rates, Journal of Business Valuation and Economic Loss Analysis, 2006, 1(1), Article 4. U.S. Department of the Treasury, "Are the CMT Yields Annual Yields?" Resource Center, 12 Mar. 2011, Web, 20 Jan Jones & Laughlin Steel Co. v. Pfeifer, 462 US 523 (1983) 14

15 Total Offset Tests 1-Year Treasury Security Dependent Variable: MNDR_1YR_SIMP Sample: 1981M M05 Included observations: 233 Extension C Dependent Variable: MNDR_1YR_SIMP Sample: 1981M M08 Included observations: 368 C Split: Early Dependent Variable: MNDR_1YR_SIMP Sample: 1981M M01 Included observations: 157 C Split: Late Dependent Variable: MNDR_1YR_SIMP Sample: 1994M M08 Included observations: 211 C

16 6-Month Treasury Security Dependent Variable: MNDR_6MO_COMP Sample: 1981M M05 Included observations: 233 Extension C Dependent Variable: MNDR_6MO_COMP Sample: 1981M M08 Included observations: 368 Split: Early C Dependent Variable: MNDR_6MO_COMP Sample: 1981M M01 Included observations: 157 C Split: Late Dependent Variable: MNDR_6MO_COMP Sample: 1994M M08 Included observations: 211 C Month Treasury Security 16

17 Dependent Variable: MNDR_3_MO_COMP Sample: 1981M M05 Included observations: 233 Extension C Dependent Variable: MNDR_3_MO_COMP Sample: 1981M M08 Included observations: 368 Split: Early C Dependent Variable: MNDR_3_MO_COMP Sample: 1981M M01 Included observations: 157 C Split: Late Dependent Variable: MNDR_3_MO_COMP Date: 01/18/12 Time: 03:06 Sample: 1994M M08 Included observations: 211 C Unit Root Tests (Augmented Dickey-Fuller Test) 17

18 1-Year Treasury Security (No Trend) Null Hypothesis: MNDR_1_YR has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Extension Null Hypothesis: MNDR_1_YR has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Split: Early Null Hypothesis: MNDR_1YR_SIMP has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Split: Late Null Hypothesis: MNDR_1YR_SIMP has a unit root 18

19 Exogenous: Constant Lag Length: 3 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Month Treasury Security (No Trend) Null Hypothesis: MNDR_6MO_COMP has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Extension Null Hypothesis: MNDR_6MO_COMP has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Split: Early Null Hypothesis: MNDR_6MO_COMP has a unit root 19

20 Exogenous: Constant Lag Length: 2 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Split: Late Null Hypothesis: MNDR_6MO_COMP has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Month Treasury Security (No Trend) Null Hypothesis: MNDR_3_MO_COMP has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Extension 20

21 Null Hypothesis: MNDR_3_MO_COMP has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Split: Early Null Hypothesis: MNDR_3_MO_COMP has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Split: Late Null Hypothesis: MNDR_3_MO_COMP has a unit root Exogenous: Constant Lag Length: 3 (Automatic based on Modified AIC, MAXLAG=3) Augmented Dickey-Fuller test statistic Test critical values: 1% level % level % level Year Treasury Security Complex MNDR Total Offset Test 21

22 Table 1A Test for Total Offset of 1-Year MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) Constant T-Statistic P-Value Unit Root Test (Augmented Dickey-Fuller Test) Table 2A Test for Stationarity (Augmented Dickey-Fuller 1 ) of 1-Year MNDR (Jan May 2000) Extended (Jan Aug. 2011) Early Split (Jan Jan.1994) Late Split (Feb Aug. 2011) τ-statistic P-Value A time trend was not included because of the a priori hypothesis of Total Offset. The number of lagged differences included in the ADF test was determined by the Modified Aikaike s Information Criterion with a maximum number of lags set at three. 22