A simplified formula, unavailable elsewhere, for making rapid calculations in the courtroom. By Gerald D. Martin

Excerpted from Exposing Deceptive Defense Doctors

The difficulty with making a quick calculation of the value of a case is that the textbooks on finance and economics do not offer a formula leading to an easy calculation of a loss in present value when the growth rate in earnings is not the same as the interest rate being used to discount those earnings to their present value. In two of the more recent texts on forensic economics, one provides a full page worksheet that refers to a 51 page appendix of tables to be used to find an answer. While correct, the limitation in their use is that the appendix values offer growth rates in earnings in 1% increments from 0% to 10%, the interest rate choices are again in 1% increments from 0% to 18%, and the period of the loss must be in whole years. The second is similar, but offers a bit more detail. In it, after setting up the worksheet, the 50 page appendix provides tables using 1% increments in growth rates from 0% to 6%, 1% increments in the interest rate from 0% to 15 %, and whole year loss periods. This text also gives the correct answer, but only if everything is in convenient whole numbers.

Unfortunately, most cases, when handled on an individual client basis, fail to cooperate and the numbers are nearly always something other than nice, neat whole numbers. Consider, for instance, a forecast that must be made when the future period of loss is 31.4 years, the first year loss is \$21,295, the growth rate in earnings is 5.4% and the discount rate is 8.3%. These data do not fit into the appendix values created, and to use them will give only an approximation of the loss.

Rather than a greatly expanded set of tables to cover all possible fractional numbers, it would be much easier to learn a single formula that can be solved on any financial calculator and would handle these fractional numbers. Such a formula exists, has been published by this author at least three times since 1978, and has been used by at least two other researchers as the basis for commer­cial computer programs. The formula is not available in standard present value texts, but was derived from actuarial statistical formulas. It has been used to verify the accuracy of the textbook work­sheets mentioned above and gives the same answer calculated for sample problems in those texts.

This is a guide, rather than a statistical text, so the tedious proofs of the formula will be omitted. The formula is:

Where:

PV = the present value of the future loss

E = the current annual earnings with first payment made immediately

d = the discount rate

g = the earnings growth rate

n = the time period of the loss

In the example created above,

E = \$21,295

d = 8.3 %

g = 5.4%

n = 31.4 years

By substituting the values for the symbols, the formula becomes:

PV = \$21,295        [(1.054)31.4– 1]

[(1.083)          ]

[(1.054) – 1    ]

[(1.083)          ]

and the solution in present value is \$456,125.

In this example, it was assumed that the first payment would be made at the start of the first year. If you wish to assume that the first payment will be made at the end of the first year, then in the formula, where the value of E appears, just divide E by 1 + d, or \$21,295 divided by 1.083. The solution now becomes \$421,168. Mid-year payments would be calculated by dividing E by 1 + .5d to get a solution of \$437,950.

Perhaps a more realistic estimate would be to assume that the payments would coincide with the receipt of a paycheck at the end of each month rather than each year. The same formula would be used with the following adjustments to our original example:

E of \$21,295 is divided by 12 months to equal \$1,774.58 and then \$1,774.58 is divided by 1 + (d/12), or 1.0069, to get \$1762.42

d of .083 is divided by 12 months to equal .0069

g of .054 is divided by 12 months to equal .0045

n of 31.4 is multiplied by 12 month to equal 376.8

and the solution is \$438,545.

The beauty of this formula is its versatility and the ease with which the economist can make rapid calculations in the courtroom when given hypothetical situations or a new set of facts. Further, it is not constrained to just a set of existing tables that may not fit the existing problem, but can handle fractional value in all of the variables. In addition, it can easily be used to calculate the present value of a stream of earnings that do not begin as a loss for several years in the future by simply calculating the loss as of the time in the future of the first loss and then applying a standard lump sum reduction over the remaining time to the current time.

If you plan to ask your economist at trial to make calculations using varying assumptions of time, growth rates, and interest rates, be sure to ask him before trial if he can do it. Or, you may want to ask your opponent’s economist to make the calculations, hoping, of course, that he cannot do them quickly. You also may catch him resorting to an offset method where he is not making the calculations as shown here but is assuming the growth rate to be 0% and solving for an annuity present value with a discount rate/growth rate differential.

#### §1211      A Simplified Calculation to Find Delayed Payment Case Value

The previous section dealt with finding the present value of a stream of payments that begin immediately, but many cases involve a stream of payments that may not begin for many years in the future. The lost earnings of an injured child normally would not begin until the child reaches an age somewhere between 18 and 22, and the earnings of a female/mother may not begin for several years if she planned to raise her children before returning to the workforce. In these cases, there is a lag period from the trial date to the start of the earnings loss that must be incorporated. During this period, any money awarded will be invested and no withdrawals will be made. In addition, earnings will have continued to increase during the fallow period of non-work.

Consider the following example: Joe Matterhorn has been injured in a fire and will not be able to return to work for an extended period as he must undergo multiple skin grafts over the next 5 to 6 years. When he does return, he will be able to work only half time. His full time job pays \$20,000, but at half time Joe will only be able to earn \$10,000 per year in today’s dollars when he does return. Assume that earnings are expected to increase at an annual rate of 4.40% and the discount rate is 6.50% based on long term Treasury bond yields. Total remaining worklife from the date of trial is 22.5 years. This takes Joe to the end of his statistical worklife, and you need to know the present value of Joe’s mitigating earnings as of the trial date, which is 5.5 years prior to the date the doctor’s expect Joe to return to work. (It is assumed that what Joe is able to earn upon return to work in 5.5 years will be a deduction against his total earnings loss.) The problem for you is that there is a 5.5 year fallow period in which Joe will not have any earnings. What he has lost in that period is easy to calculate, as you learned in section 1210. The following example is a different formula that can be easily stored in a hand held programmable calculator, such as the HP17BII or the HP19BII, or stored on a computer spreadsheet program. Once stored, all that is needed for you to do is input variables and out comes your answer in present value.

In our example, the annual mitigation in today’s dollars is \$10,000, the discount rate will be 6.5%, the earnings increase rate will be 4.4%, the period before the earnings mitigation begins is 5.5 years, and the total time period is 22.5 years from the trial date to the end of worklife. The following worksheet shows the data with the formula for the value “PV” at the bottom of the worksheet.

Formula for use with programmable calculators such as the HP17BII or 19BII

PV=(V/((D-G)/(1+G)))*(1+((D-G)/(1+G)))^0.5*(1-(1+((D-G)/(1+G)))^(-T))

-(V/((D-G)/(1+G)))*(1+((D-G)/(1+G)))^0.5*(1-(1+((D-G)/(1+G)))^(-L)

PV = Present Value

V = Starting Value (wages, medical expenses, household services, etc.)

D = Discount rate entered as a decimal (6.5% entered as .065)

G = Growth rate entered as a decimal (4.40% entered as .044)

T = Total time from PV date to end of loss period; enter zero if loss starts immediately

To check the formula, enter:

V = \$10000

D = .065 (6.5%)

G = .044 (4.4%)

T = 22.5 Years

L = 5.5 Years

The Present Value (PV) will be: \$129,249

Then change L to zero and PV will become \$181,343. This is the result if mitigation of earnings loss begins at the trial date rather than 5.5 years later. The formula assumes pay increases occur at the start of each year and discounting is done at the middle of each year.

Be sure to enter the formula for “PV” into your calculator exactly as it is shown (except that in the calculator it will all be on one continuous line). Time periods and dollar amounts are entered directly, but you must enter the increase rate and the discount rate as decimal equivalents. The 4.4% wage increase rate is entered as .044 and the 6.5% discount rate is entered as .065. With a formula such as this you can easily make your own estimates of the loss and if your economist has the formula programmed into a handheld calculator at trial or deposition, he or she can easily answer hypothetical questions or make changes indicated by other testimony.

Please note that when the value for G (wage growth) is exactly equal to the value for D (Discount Rate), the formula will return an answer of “Solution Not Found.” This is not of great concern as it simply means that with D = G the formula will generate “zero” values and one cannot multiply or divide by “zero” and get a meaningful answer. Fortunately, the solution is so simple it requires but a quick multiplication to find the present value (PV). With D = G, regardless of how large or small they are, then just multiply the starting value (V) by the time period (T) and you have your answer in present value. Using the example given above and changing only the values of D and G so that they are equal, we get an answer for the full time period (T) by multiplying T * V. Thus, 22.5 years times \$10,000 equals \$225,000. For the shorter period where earnings do not begin for 5.5 years, then subtract L from T and multiply the answer by V. Or, (22.5 – 5.5) * \$10,000 = 17.0 * \$10,000 = \$170,000. (Note that when D = G we have what economists call a total offset, or a net discount rate of zero.)

#### §1220  The Nominal Rates Method v. the Offset Methods

The Alaska Method, the Partial Offset Method, and the Real Rates Method are all variations of an offset calculation where the difference in some earnings and growth rates are taken, while the Standard Method uses the nominal rates. What many economists will not tell you is that any of the offset methods result in a larger loss estimate than will the nominal rates method. The reason for this discrepancy is hidden in the calculations. On the surface, it may seem that a calculation using a 9% discount rate and a 7% growth rate, just to pick two numbers for illustration, will yield the same result as using the difference between the two, where the growth rate is set at 0% and the discount rate at 2%, maintaining the 2% differential. The problem arises because in the nominal rates method, both the growth rate and the discount rate are functions that, if graphed over time, yield a curved line. But if one of the values, in this case, the growth rate, is set at 0%, it becomes a straight line function while the 2% discount rate remains a curved line. Consequently, the gap between earnings and discounting increases more rapidly in an offset method.

To illustrate with the rates mentioned, and assuming that the payment due at the end of the first year is \$10,000 and the loss will occur for 4 years, the following losses are found:

1st year payment    \$10,000     \$10,000     \$10,000

Growth rate              7%             1%              0%

Discount rate           9%             3%              2%

Present Value           \$35,700    \$37,718     \$38,077

The first column of numbers would represent the nominal rates method, the second set would be a real rates method, and the third set would be a partial offset. A total offset would, of course, result in a loss of \$40,000. Clearly, then, any type of offset method will lead to a claim for a larger loss than is necessary to compensate the plaintiff. While the differences may seem small, remember that most cases involve larger annual dollar amounts as well as longer time periods. With the formula described in this chapter in mind, an economist can quickly demonstrate the differences in the methods.

Additional refinements can be made using the same basic formula. To add in the loss of fringe benefits, simply take the answer to the lost earnings problem and multiply it by 1 plus the fringe benefit rate. For instance, with a benefit package of 23.5670, just multiply your answer by 1.235. Then, personal consumption can also be included if you multiply the earnings loss by 1 minus the personal consumption rate. For example, if personal consumption is 27%, then multiply your earnings solution by .73. What the formula will not do is adjust for the reinvestment rate, but most economists do not use one. An example of how the reinvestment rate can be incorporated is included in the complete appraisal presented in the following chapter.

#### §1221      Current, Historical, and Forecast Interest Rates

Some economists discount losses to their present value using the interest rates currently available in the market, while others prefer to use an average of historical interest rates. Yet another group prefers to use forecasts of interest rates, which are available from a number of credible sources. This is an issue that is unresolved and likely to remain that way in jurisdictions where there is no clear guidance given to the economist either through pattern jury instructions or appeal opinions. There is justification for each method and none can be dismissed out of hand.

Those using current rates maintain that the plaintiff can only invest in securities available to him when he has the award in hand, and he then can only receive the current rates available. Recall, however, that there are two components needed to calculate the present value of an award, and the interest (discount) rate is but one. The other is the rate of growth in the item being analyzed, which could be earnings, benefits, household services, medical expenses, retirement pay, or some other item of loss. Economists do seem to prefer a history of growth in any of these items as their indicator of the future increases in their value. So the economist using current interest rates must combine that with historical growth rates.

Those using historical interest rates normally make a very persuasive argument that it is not the absolute level of the rate but, rather, the relationship between the growth rate and the interest rate. Their premise is that this relationship tends to remain relatively stable over time. In other words, they argue that it does not matter whether the interest rate is 6% and the growth rate 3%, or the interest rate is 5% and the growth rate is 2%. What matters is that the relationship of the difference between the two appears to be consistent, or stable, over time. The jury is still out over this issue of stability. Since 1975 there have been over 50 studies completed that attempt to determine whether or not there is stability. Some adamantly conclude that stability has not been maintained over long periods of time. Others conclude just as strongly that there is stability between them.

(Mathematically, the difference using subtraction between 6% and 3% is 3% and the difference between 5% and 2% is also 3%. Technically, this is not correct when using a net discount rate (NDR). When the NDR is correctly calculated algebraically in discrete time, when using 6% and 3% the NDR is 2.91%. Using 5% and 2% yields an NDR of 2.94%. The difference is not large, but is does exist.)

Lastly are those who believe forecasts of the interest rates are the best measure to use. They rely on forecasts of the Social Security Trustees, the Federal Reserve Board, the Congressional Budget Office, or one of the many private forecasting services. It is not uncommon to see these economists using a combination of forecast interest rates and forecast increases in wages. While the number using this approach appears to be small, these economists are also implicitly assuming a stable relationship between the two variables.

In summary, those using either historical or forecast rates are assuming that stability does exist over time between the interest rate and the growth rate. Those using current interest rates are less concerned with stability and more concerned with how the plaintiff will invest the funds.

#### §1222      Historical Interest Rate Research

The following is an excerpt taken from the conclusion in a paper that is under review for publication.

“Historical Net Discount Rates and Future Economic Losses: Refuting the Common Practice,” Bradley Braun, Junsoo Lee, and Mark C. Strazicich. January 23, 2004

Thus, using a historical mean or trend in net discount rates to determine future economic losses will not ensure optimal hedging against future uncertainty. Instead, these findings suggest that the currentnet discount rate may be the most useful reference to estimate a plaintiff’s award in wrongful death and personal injury litigation.

This recent paper supports what Dr. Havrilesky said in his 1989 publication discussed in the preceding section. Going back to 1975, there is a rich collection of studies examining this issue. Some have found that there is no structural change over a long time period, but the majority of researchers have concluded, as did Dr. Havrilesky, that it is not always prudent to use historical interest rates to select a discount rate to be used in the evaluation of a future loss.

There seems to be a growing trend among forensic economists to move away from the use of historical interest rates and to use currently available market rates in their evaluations. This seems substantiated in a survey of NAFE members conducted by Drs. Michael Brookshire, Michael Luthy, and Frank Slesnic. This is the sixth in a series of surveys that began in 1990. In the first survey, released in 1990, 57.6% of the economists responding reported using historical interest rates, while only 24.6% reported using current interest rates. Jumping ahead to the sixth survey in 2003, the numbers had shifted to show that those using historical rates had declined to 37.7%, while those using current rates had increased to 47.1%. The remaining small percentage reported using some other method.

Perhaps that trend is the result of the many studies that have received publicity within the ranks of economists in recent years, such as the quote at the beginning of this section. Your economist should have access to these studies in the event that he or she is challenged about the choice of using historical or current interest rates. For that reason, a bibliography on the stability of historical interest rates has been compiled from research beginning in 1975 and is included here.

1. McConnico, S.E. “Inflation and the Future Loss of Earnings,” Baylor Law Review, vol. 27, no. 2, 1975.

2. Carlson, J.A. “Economic Analysis v. Courtroom Controversy: The Present Value of Future Earnings,” The American Bar Association Journal, vol. 62, May 1976.

3. Harris, William G. “Selecting Income Growth and Discount Rates in Wrongful Death and Injury Cases: Comment,”Journal of Risk and Insurance, vol. 58, 1977.

4. Franz, W.W. “A Solution to Problems Arising from Inflation When Determining Damages,” Journal of Risk and Insurance, vol. 45, no. 2, 1978.

5. Beveridge, S. and C. Nelson. “A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the ‘Business Cycle’,” Journal of Monetary Economics, vol. 7, 1981.

6. Hosek, W.R. “Problems in the Use of Historical Data in Estimating Economic Loss in Wrongful Death and Injury Cases,” Journal of Risk and Insurance, June 1982.

7. Nelson, C.R., and C. I. Plosser. “Trends and Random Walks in Macroeconomic Time Series”, Journal of Monetary Economics, vol. 10, 1982.

8. Brody, M. “Inflation, Productivity, and the Total Offset Method of Calculating Damages for Lost Future Earnings,”University of Chicago Law Review, vol. 49, 1982.

9. Harris, W.G. “Problems in the Use of Historical Data in Estimating Economic Loss in Wrongful Death and Injury Cases,” Journal of Risk and Insurance, March 1984.

10. Lambrinos, J. “On the Use of Historical Data in the Estimation of Economic Losses,” Journal of Risk and Insurance, vol. 52, no. 3, 1985.

11. Schilling, D. “Estimating the Present Value of Future Income Losses: An Historical Simulation 1900-1982,” Journal of Risk and Insurance, vol. 52, March 1985.

12. Lane, J., and D. Glennon. “The Estimation of Age/Earnings Profiles in Wrongful Death and Injury Cases,” Journal of  Risk and Insurance, vol. 52, no. 4, December 1985.

13. Clark, P., “The Cyclical Component ofU.S.Economic Activity,” Quarterly Journal of Economics, vol. 102, 1987.

14. Bryan, W.R., and C.M. Linke. “Estimating Present Value of Future Earnings,” Journal of Risk and Insurance, vol. 55, June 1988.

15. Colella, Francis. “Controversial Issues: Selecting a Discount Rate,” Journal of Forensic Economics, vol. II. no. 2, 1989.

16. Palaez. R.F. “The Total Offset Method,” Journal of Forensic Economics, vol. II, no. 2, 1989.

17. Lewis, Cris W. “On the Relationship Between Age, Earnings, and the Net Discount Rate,” Journal of Forensic Economics, vol. II, no. 3, August 1989.

18. Albrecht, Gary, and John Moorhouse. “On the Derivation and Consistent Use of Growth and Discount Rates for Future Earnings,” Journal of Forensic Economics, vol. II, no. 3, August 1989.

19. Anderson, G.A., and D.L. Roberts. “Stability in the Present Value Assessment of Lost Earnings,” Journal of Risk and Insurance, vol. 56, 1989.

20. Havrilesky, Thomas. “Those Who Only Remember the Past May Be Doomed to Repeat Its Mistakes,” Journal of Forensic Economics, vol. III, no. 1, December 1989.

21. Perron, P. “The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,” Econometrica, vol. 57, 1989.

22. Nowak, Laura. “Empirical Evidence on the Relationship Between Earnings Growth and Interest Rates,” Journal of Forensic Economics, vol. IV, no. 2, Spring/Summer 1991.

23. Lewis, Cris W. “On the Relative Stability and Predictability of the Interest Rate and Earnings Growth Rate,” Journal of Forensic Economics, vol. V, no. 1, Winter 1991.

24. Haslag, J.H., M. Nieswiadomy, and D. J. Slottje. “Are Net Discount Rates Stationary?: Implications for Present Value Calculations,” Journal of Risk and Insurance, vol. 58, 1991.

25. Pelaez, Rolando F. “Valuation of Earnings Using Historical Growth-Discount Rates,” Journal of Forensic Economics, vol. V, no. 1, Winter 1991.

26. Rowe, John W., Jr. “The Net Discount Rate in a Model of Long-Run Growth Equilibrium,” Journal of Forensic Economics, vol. V, no. 1, Winter 1991.

27. Bonham, Carl, and Summer J. La Croix. “Forecasting Earnings Growth and Discount Rates: New Evidence from Time Series Analysis,” Journal of Forensic Economics, vol. V, no. 3, Fall 1992.

28. Benich, J. “On the Relative Stability and Predictability of the Interest Rate and Earnings Growth Rate,” Journal of Forensic Economics, vol. VI, no. 1, 1992.

29. Haydon, Randall, and Samuel Webb. “Selecting the Time Period Over Which the Net Discount Rate is Determined for Economic Loss Analysis,” Journal of Forensic Economics, vol. V, no. 2, Spring/Summer 1992.

30. Romans, J.T., and F.G. Floss. “Four Guidelines for Selecting a Discount Rate,” Journal of Forensic Economics, vol. V, no. 3, 1992.

31. Schmidt, P., and P. C. B. Phillips. “LM Tests for a Unit Root in the Presence of Deterministic Trends,”Oxford Bulletin of Economics and Statistics, vol. 54, 1992.

32. Zivot, E., and D. W. K. Andrews. “Further Evidence on the Great Crash, the Oil Price Shock and the Unit Root Hypothesis,”Journal of Business and Economic Statistics, vol. 10, 1992.

33. Gamber, Edward, and Robert Sorensen. “On Testing for the Stability of the Net Discount Rate,” Journal of Forensic Economics, vol. VII, no. 1, Winter 1993.

34. Schieren, George. “Is There an Advantage in Using Time-Series to Forecast Lost Earnings?,” Journal of Legal Economics, vol. 4, no. 3, Winter 1994.

35. Gamber, E.N., and R. L. Sorensen. “Are Net Discount Rates Stationary?: The Implications for Present Value Calculations: A Comment,” Journal of Risk and Insurance, vol. 61, no. 3, 1994.

36. Haslag, J.H., M. Nieswiadomy, and D.J. Slottje. “Are Net Discount Ratios Stationary?: Some Further Evidence,” Journal of Risk and Insurance, vol. 61, no. 3, 1994.

37. Lawlis, Frank, and Robert Male. “Methodological Issues: Interest Rate and Wage Growth Forecasting,” Journal of Legal Economics, vol. 4, no. 3, Winter 1994.

38. Hamilton, James D. “Time Series Analysis,”PrincetonUniversityPress, New Jersey, 1994.

39. Kim, C. “Dynamic Linear Models with Markov-Switching,” Journal of Econometrics, vol. 60, 1994.

40. Schwenk, A.E. “Introducing Weights for the Employment Cost Index,” Compensation and Working Conditions, vol. 105, no. 6, 1995.

41. Amsler, C., and J. Lee. “An LM Test for a Unit-Root in the Presence of a Structural Change,” Econometric Theory, vol. 11, 1995.

42. Pelaez, Rolando F. “Mean-Reversion in the Net Discount Rate: The Evidence from the Manufacturing Sector,” Journal of Legal Economics, vol. 6, no. 2, Fall 1996.

43. Rodgers, J.D., M.L. Brookshire, and R. J. Thornton. “Forecasting Earnings Using Age-Earnings Profiles and Longitudinal Data,” Journal of Forensic Economics, vol. IX, no. 2, 1996.

44. Johnson, Walter, and Gregory Gelles. “Calculating Net Discount Rates: It’s Time to Recognize Structural Changes,” Journal of Forensic Economics, vol. IX, no. 2, Spring/Summer 1996.

45. Horvath, Philip, and Edward Sattler. “Calculating Net Discount Rates – It’s Time To Recognize Structural Changes: A Comment,” Journal of Forensic Economics, vol. X, no. 3, Fall 1997.

46. Linke, C.M. “Another Perspective of the (i-g) Differential for Discounting Future Earnings,” Journal of Forensic Economics, vol. 10, no. 3, 1997.

47. Lumsdaine, R., and D. Papell. “Multiple Trend Breaks and the Unit-Root Hypothesis,” The Review of Economics and Statistics, vol. 79, no. 2, 1997.

48. Nunes, L., P. Newbold, and C Kuan. “Testing for Unit Roots with Breaks: Evidence on the Great Crash and the Unit Root Hypothesis Reconsidered,”Oxford Bulletin of Economics and Statistics, vol. 59, 1997.

49. Payne, J. E., Bradley Ewing, and Michael Piette. “Stationarity of the Net Discount Rate,”Litigation Economics Digest, vol. 3, no. 1, 1998.

50. Payne, James, Bradley Ewing, and Michael Piette. “An Inquiry into the Time Series Properties of Net Discount Rates,”Journal of Forensic Economics, vol. XII, no. 3, Fall 1999.

51. Payne, Michael, B.T. Ewing, and M.J. Piette. “Mean Reversion in Net Discount Rates,” Journal of Legal Economics, vol. 9, no. 1, 1999.

52. Kim, C., and C. Nelson. “Friedman’s Plucking Model of Business Fluctuations: Tests and Estimates of Permanent and Transitory Components,” Journal of Money, Credit, and Banking, vol. 331, part 1, 1999.

53. Kim, C., and C. Nelson. “State-Space Models with Regime Switching, Classical and Gibbs-Sampling Approaches with Applications,” The MIT Press, Cambridge, MA, 1999.

54. Sen, Amit, Gregory Gelles, and Walter Johnson. “A Further Examination Regarding the Stability of the Net Discount Rate,” Journal of Forensic Economics, vol. XIII, no. 1, Winter 2000.

55. Hays, P., M. Schrieber, J.E. Payne, B.T. Ewing, and M. Piette. “Are Net Discount Ratios Stationary? Evidence of Mean Reversion and Persistency,” Journal of Risk and Insurance, vol. 67, no. 3, 2000.

56. Ireland, T.R. “Total Offsets in Forensic Economics: Legal Requirements, Data Comparisons, and Jury Comprehension,” Journal of Legal Economics, vol. 9, no. 2, 2000.

57. Bowles, Tyler J., and W. Cris Lewis. “A Time Series Analysis of the Medical Care Price Index: Implications for Appraising Economic Losses,” Journal of Forensic Economics, vol. XIII, no. 3, Fall 2000.

58. Bowles, Tyler J., and Cris Lewis. “Time Series Properties of Medical Net Discount Rates,” Journal of Legal Economics, vol. 10, no. 2, Winter 2000.

59. Bowerman, B.L., and S. J. La Croix. Business Statistics in Practice, 2nd edition, Irwin McGraw-Hill, New York, 2001.

60. Payne, James, Bradley Ewing, and Michael Piette. “Total Offset Method: Is It Appropriate? Evidence from ECI Data,”Journal of Legal Economics, vol. 11, no. 2, Fall 2001.

61. Lee, J. “On the End-Point Issue in Unit Root Tests in the Presence of a Structural Break,” Economics Letters, vol. 68, 2001.

62. Lee, J., and M. Strazicich. “Break Point Estimation and Spurious Rejections with Endogenous Unit Root Tests,”Oxford Bulletin of Economics and Statistics, vol. 63, no. 5, 2001.

63. Ang, Andrew, and Geert Bekaert. “The Term Structure of Real Rates and Expected Inflation,”ColumbiaUniversityand NBER Working Paper, June 2003.

64. Lee, J., and M. Strazicich. “Minimum LM Unit Root Test with Two Structural Breaks,” The Review of Economics and Statistics, vol. 85, no. 4, 2003.

65. Braun, B., J. Lee, and M. Strazicich. “Historical Net Discount Rates and Future Economic Losses: Refuting the Common Practice,” Economic Foundations of Injury and Death Damages, Edward Elgar Publishing, U.K. 2005, edited by Kaufman, Rodgers, and Martin.

#### §1230  The Mathematics of the Partial Offset

A common error made by many economists who should know better is to subtract the growth rate from the interest rate and use the difference as the discounting factor in the partial offset method. For example, if the interest rate is 8% and the growth rate is 5%, they will simply subtract to get 3% and use this as the discount rate with a 0% growth rate.

The correct procedure is to change the percentages to decimal numbers and add one to each. Thus an 8% interest rate becomes .08 to which we add one to get 1.08. The formula then is

d = (1 + i/1 + g) – 1 = (1.08/1.05) -1 = .02857 = 2.857%

where d is the discount rate, i is the interest rate, and g is the earnings growth rate.

Of course, any time these calculations are based on historical data for interest rates rather than on currently available data, the calculation is suspect. A still better method requires separate calculations of the real interest rate and the real wage growth rate. Real interest rates should be based on the nominal rate currently available adjusted for expected inflation. Real growth rates should be based on the nominal growth rate and the historical level of inflation. There are formulas available for these, but you need not master them.. They are given here only to allow you to examine the economists report to determine whether he is using something similar or just subtracting.

Letting the nominal wage growth be n, the inflation rate be p, and the real growth rate be d, the formula for real growth is

g = (n – p)/(1 + p).

Letting the nominal interest rate be I, the inflation rate be p, and the real interest rate be d, the formula for real interest is

d = (i – p)/(l + p).

The use of these formulas does not negate the criticisms of the partial offset method, but their use, particularly the use of expected inflation and nominal current interest rates as variables, does enhance the method and make it a bit more realistic.

#### §1240  Periodic Payments Required in Medical Malpractice Cases

Calculating damages in a medical malpractice action presents a peculiar problem to the economist, particularly those who use either a form of the offset method or the real rates method because, in many cases, the economist does not know how the payment for future damages will be made. Normally, a jury awards a lump sum following the trial, but that is not always the case in a medical malpractice case.

The problem can best be shown by examining the language in the California Code of Civil Procedure, section 667.7 (Medical Malpractice Actions).

(a) In any action for injury or damages against a provider of health care services, a superior court shall, at the request of either party, enter a judgment ordering that money damages or its equivalent for future damages of the judgment creditor be paid in whole or in part by periodic payments rather than by a lump-sum payment if the award equals or exceeds fifty thousand dollars (\$50,000) in future damages. In entering a judgment ordering the payment of future damages by periodic payments, the court shall make a specific finding as to the dollar amount of periodic payments which will compensate the judgment creditor for such future damages. §667.7(b)(1). The judgment ordering the payment of future damages by periodic payments shall specify the recipient or recipients of the payments, the dollar amount of the payments, the interval between payments, and the number of payments or the period of time over which payments shall be made.

Section 667.7(e)(f) “Future Damages” includes damages for future medical treatment, care or custody, loss of future earnings, loss of bodily function, or future pain and suffering of the judgment creditor.

While this rule applies in California. many states have similar or modified versions; therefore, inform your economist of the law in your state.

Under this rule, the economist must go to court not only with the traditional estimate of losses in present value, but must also have an undiscounted payment schedule showing what must be paid in actual dollars in each future year of the loss as either party may request periodic payments in lieu of a lump sum. In order to have such a schedule available, a forecast of future losses must by made. If an economist uses an offset method and merely takes the difference between some historical cost or earnings growth rate and a historical interest rate, he will not have such a schedule. If, instead of the offset method. he uses a real rates method wherein inflation has been removed from wage and cost growth and interest rates, then the value of future losses will be grossly understated.

The best way to demonstrate this problem is to take a hypothetical example and key in on just one year. Suppose that the current level of lost wages at the time of the incident was \$10,000 per year, the loss will continue many years into the future, and we want to know what payment should be made in the 20th year. Similarly, annual medical costs will continue for life and are \$20,000 per year in current prices. If the economist uses the total offset method where the interest rate is assumed equal to the growth rate, then he does not use a growth rate and the earnings and medical costs in 20 years would be exactly what they are today. Obviously, this will not happen as both wages and prices continue to increase over time. The economist will be forced to make an estimate, or forecast, of the rate of increase in both wage rates and medical costs for many years into the future and then calculate what will be needed in each of the future years or the plaintiff will be undercompensated. The same result holds when only “real” inflation free growth rates are used. No discounting is done on the future payments as they will not be made until due in the future.

Usually, the jury will not know if a periodic payment election has been requested and will deal with the case on a lump-sum basis. After an award has been made, the judge will then set the payment schedule. At that time, be prepared to present him an estimate of what the future, undiscounted payments should be. Otherwise, it is his discretion to determine what the rate of increase will be and order an annuity purchased to incorporate that rate. A complete listing of future values by your economist can be very helpful in this phase.

#### §1250  Runoff Interest Rates

One of the common actuarial methods used to calculate the present value of an annuity, or series of payments stretching into the future, is to use a runoff rate. The time periods can vary, but 15 years seems to be a common breaking point. The first step the actuary will take is to determine the number of years a stream of future payments will be paid. If it covers a period of no more than 15 years, he will often simply use the current yield available on U.S. Treasury bonds or notes that mature in the same number of years in which the payments will be made. For example, to determine the present value of a 10-year stream of payments, he will discount those payments at the rate available on 10-year Treasury bonds or notes.

When the period extends beyond 15 years, he will begin to make adjustments by weighing in what is called the runoff rate. The runoff rate can change over time. One option is to use the Social Security forecast of interest rates for the next 75 years as the runoff rate. The calculation beyond 15 years is made using a weighted average. Suppose the period is 20 years and the current rate is 5%. The first 15 of the 20 years will be given a value of 5% for each year and the last 5 years of the 20 year period will be given a value of 6% for each year. It is not necessary for you to do the calculations, as Table 39 has been prepared so that you may simply look up the answer. Just enter Table 39 at the current rate of 5% on the left side and read across to the 20 year column. You find that the weighted average over the full 20 year period is just over 5% and you could use this as your discount rate.

For those mathematically inclined and would like to have all this information in a programmable hand held calculator, you can store a 1-line formula that looks like this:

R = ((I x 15) + (5.8 x (n – 15))) / n

Where:

R = the derived discount rate.

I = the current rate on 15 year Treasury bonds.

N = the total number of years payments will be made.

5.8 = the runoff rate.

Using our example above from the tables we would find that:

R = ((5 x 15) + (5.8 x (20 – 15))) / 20 = 5.2% (the same answer found in the table).

The advantage of using a formula rather than a table is that you can enter fractions instead of whole numbers. It is quite simple to use a current rate of 5.22% on Treasury bonds and a 22.45 year time period. Just enter them as the value for I and n.

#### §1251      Laddered Interest Rates

Still another method of evaluation you may see used by some economists relies on the use of laddered interest rates. This refers to the use of short-term securities for losses in the first few future years, and increasingly longer term securities for increasingly longer periods into the future. Use of this method typically requires using current rates, and then for periods longer than the maturity of securities available in the market, a runoff rate is used. (See §1250 for a discussion of the runoff rate.) The result is what may be referred to as a ladder of interest rates, with each step being to a higher interest rate, which is the natural result of using securities with progressively increasing maturity periods.

As an example, assume a trucker was injured and the vocational and medical experts testify that he will never be able to return to any kind of gainful employment. For this worker, the economist can determine his pre-injury earnings, the rate of increase in those earnings, the amount of employer paid benefits, and his Worklife expectancy. The economist then checks the current rates, or yields, on U.S. Treasury securities available in the market. He may decide to use a ladder of maturities from the two-year T-Bill to the 20-year T-Bond. The interest rates on these securities become the rates at which he discounts future earnings to their present value. He may discount the first three years of losses at the two-year rate, years four to six at the five-year rate, and so on. If he calculates this in a manner that displays each year separately, there is no need to use a Net Discount Rate (NDR).

There are two Printouts within this section. The first illustrates the information used by the economist to make the calculations, with a summary of the loss shown at the bottom. NDRs are shown for information only on this sheet and are not used in the calculations. The second Printout illustrates the actual year by year calculations. For the section dealing with losses from the date of injury to the trial date, there is no discounting. In the section showing the future losses, note that the discount rate for each year is given. The information page, or the first Printout, has an interest rate for a 20-year bond, but as this evaluation extends less than 14 years into the future that rate is not used.

The codes of ethics of the three major associations to which forensic economists belong require that the methods of the economist be in sufficient detail that an opposing economist be able to duplicate the results. A calculation such as this should satisfy that requirement, as every calculation is detailed with nothing hidden.

#### §1260  Net Discount Rate (NDR)

In any case in which your economist must make a projection of a future loss of earnings, there are two basic steps he or she must include in the calculations. First, there must be some consideration for future increases in wages. Second, there must be some consideration for discounting those wages to their present value. In other words, there must be a wage growth rate and an interest rate for discounting. While economists may disagree over just what those rates should be in any particular case, there are really only two ways in which these two items are incorporated in the analysis. First, an economist may use a wage growth rate and calculate what future wages will be and then use a discount rate to calculate their present value. Here, he or she has two choices: use nominal rates or use real rates. The only difference is that the nominal rates include an estimate for inflation while the estimate for inflation has been removed from both rates to get at the real rates. This being the only difference, it really shouldn’t matter which rates are used as both should provide the same present value.

The second method is to use a Net Discount Rate (NDR), which begins by taking either the real rates or the nominal rates just mentioned, and then working with the difference between the two rates. This somewhat simplifies the economist’s calculations as the mathematical procedure inherently provides that wages remain the same over the future period, and are discounted at a much lower rate, the NDR.

Deriving the NDR can be done by basing the difference in the rates on historical data, or by using forecasts of future growth rates and discount rates. There is logic supporting either method, so you only need to be concerned that your economist is able to justify the method chosen. You should note, however, that if an economist uses historical data, then the period of years chosen to derive the difference can be different from a different set of years. For example, using ten years of historical data will not yield the same NDR as one would get from using a 20-year period. Further, there is some disagreement that the NDR remains stable over time, evidenced by the fact that choosing different time periods seems to result in different NDR’s.

#### §1260.1   The Mathematics of the Net Discount Rate

Over time, there has been a slow but steady movement by economists to use the Net Discount Rate (NDR) in making their estimates of future losses, whether it is earnings, benefits, household service value, or life care plan needs. As discussed in Section 1260 above, the NDR is a method for combining the growth rate with the discount rate in order to simplify the calculations used in measuring future losses. One of the problems in determining the correct NDR is in the mathematics. The obvious, and simplest way, is to simply decide what growth rate and what discount rate the economist wants to use, and simply subtract the growth rate from the discount rate. This is incorrect. Without getting into a long discussion of the difference between continuous time mathematics and discrete time calculations, we offer only a brief description of the differences. This description is primarily for the economists who use this guide. As an attorney you likely have little interest in the distinction between the two kinds of time, and may safely skip the next paragraph.

Continuous time takes on a value at every point in time, whereas discrete time is only defined at integer values of the time variable. While discrete time values can be easily stored and processed on a computer, it is impossible to store the value of continuous time for all points along the real continuum. To derive an accurate continuous time variable, the proper selection of the spacing on the time continuum is crucial for an efficient and accurate approximation of continuous values. Excessively close spacing will lead to too much data whereas excessively distant spacing will lead to a poor approximation of continuous tie. An important implication of a strictly continuous time scale is that the probability that two events occur at the same time is zero. In discrete time models, only the outcomes for discrete time periods are considered and no reference is made to the timing of events within a period. The basic continuous time approach appears to be much more simple but also much less flexible than discrete time models. The strictly sequential order of events in a continuous time framework is an appealing property but it rests on the assumption of a perfect modes specification with conditionally independent partial processes. If this assumption is violated, the standard competing risk approach will no longer be adequate. Discrete time models do not require the assumption of conditional independence. Due to the aggregation over time and the resulting loss of information on the ordering of events within a period, one would even expect stochastic dependencies to exist between partial outcomes in discrete time modes. Simply put, the present value variables used in forensic evaluations are based on discrete time and the use of the simplified continuous time formulation is not appropriate. An example of a continuous time calculation to determine NDR would be:

NDR = Discount Rate – Growth Rate.

In discrete time, the calculation would be:

NDR = ((1 + Discount Rate) ÷ (1 + Growth Rate) – 1) x 100.

While the discrete time formula is more complicated, it is also more accurate for evaluation purposes.

In present value calculations, there are only six variables the economist must deal with, and we believe that an economist should be able to discuss each of them and explain their relations with each other. Dr. Gary Skoog, a leading statistician and mathematician at DePaulUniversity, and this author created a spreadsheet that illustrates all the possible combinations of these six variables and how each is used to find the value of other of the six variables. This spreadsheet was presented at the annual meeting of the AmericanAcademyof Economic and Finance Experts in Las Vegas in April 2003. In this Guide, we reproduce only the last of the six pages of the spreadsheet, which we call the Magic Box. For anyone wanting the entire spreadsheet, which is written in Excel, Version 10, it can be downloaded at no charge from the following address:http://www.nafe.net/

There are several files located there, and the spreadsheet is titled “S & M Magic Box.”

After a thorough search of the literature, neither Dr. Skoog nor this writer could locate a source that combined all the six variables, their relationships, and the formulae needed to make the necessary calculations. The six variables are:

R = a nominal discount rate

r = a real discount rate (the nominal rate with inflation removed.)

G = a nominal rate of growth

g = a real rate of growth (the nominal rate with inflation removed.)

pi = the percent change in the Consumer Price Index (CPI)

NDR = the Net Discount Rate*

Table 39A is a reproduction of the last of the six spreadsheet pages. In that table, all the rules that govern which variables can and cannot be combined to produce the value of another variable. The Binary formulae mentioned refer to the solutions that may be found by combining just two of the six variables. The Tertiary formulae refer to the combination of three of the variables to determine the value of a fourth. The column titled: “Then the disallowed input is:” refers to the variable for which a solution is being sought given the input of the variables in the column titled: “If your set contains.” In the Magic Box at the bottom of Table 39A, values are entered only in the column titled: “Input Value.” The values in the “Output Value” column are those values that can be calculated from the entries made in the “Input Value” column. Finally, the “Consistent Set” column shows all the input and output variables that can be calculated from the variables entered as input.

With this spreadsheet, one can easily do two things. First, a correct calculation can be made for use in estimating future losses. Second, a quick check can be made to determine whether the NDR calculations of an opposing economist are consistent with the values he or she is using to determine NDR.

We offer one last note on using this spreadsheet. This spreadsheet does not determine what input variables the economist should be using. Growth and discount rates, whether real or nominal, may be used. The source of those rates may be from historical data, current values, or forecasts of what those variables may be in the future. That is a decision we leave to the economist. This spreadsheet is designed only to describe the relationships and to allow the verification that, once a set of input variables is chosen, the correct mathematical procedure is used to produce the NDR.

#### §1261      Total Offsets in Forensic Economics

“Total offset” refers to the assumption that the rate of increase in wages is exactly equal to the discount rate. Under this assumption, the economist need only multiply the current wage by the number of years of future loss to arrive at a present value. At one point in time, this was referred to as the Alaska Method, and later the Pennsylvania Method. These names are unfair to the states as both allow other methods, so the more appropriate generic term now used is “total offset.” It is really nothing more than one variation of the Net Discount Rate (NDR) where the difference between the two rates of concern is zero.

Dr. Thomas Ireland, Professor of Economics at the University of Missouri at St. Louis, a practicing forensic economist and prolific author, has studied the historic relationship between growth rates and discount rates, and created a set of tables showing the differences in the NDR over various time periods. In Tables 40 and 41, he has examined the relationship between interest rates and the wage growth rate. In Tables 42 and 43, he has extended the analysis to cover medical care by making a similar comparison between the medical care component of the Consumer Price Index and in the discount rates. He has also provided an accompanying text explaining the methods and logic in his research. The remainder of this section was written by Dr. Ireland.

Total Offsets in Forensic Economics:
Legal Requirements, Data Comparisons, and Jury Comprehension

Thomas R. Ireland

April 4th, 2008

Introduction

“Total offsets” in forensic economics are assumptions that one set of variables will have impacts that can be completely “offset” by another set of variables in such a way both sets of variables can be eliminated from a damage calculation. The term “total offset” is often used to refer to an assumption that wage growth and an appropriate discount rate for reducing future values to present values exactly offset each other, two other “total offset” assumptions as well.

In forensic economics, the term “total offset” typically refers to either a complete offset between increases in wages and discount rates (the “Alaska Rule,” which was used in Alaska until 1986) or to a complete offset between rates of price increase and the discount rate (the “Pennsylvania Rule,” which still applies in Pennsylvaniatoday). A third total offset involving discount rates is an assumed offset between increases in medical care costs and the discount rate. There are also other “total offsets” that are sometimes used by economic experts in personal injury and wrongful death damage analysis, but these will not be considered in the current paper.1

This paper considers these six total offset assumptions from the standpoint of three criteria: (1) what is required by law?; (2) what is most accurate from the standpoint of economic practice and theory?; and (3) what will be most helpful to a jury that is trying to assign damages in a case at hand?

The first criterion is a sine qua non for being an economic expert witness and consultant. In terms of admissible testimony, legal restrictions trump issues of theoretical accuracy and jury comprehension. If testimony does not conform to the requirements of law, it will not be permitted. The second criterion of accuracy focuses on how much empirical justification exists for the assumed offset. The third criterion of helpfulness to a jury takes into account the fact that a theoretically accurate and precise measurement of damages is not meaningful if a jury cannot comprehend and assess the method by which measurement was made. The social goal of expert testimony is having juries better informed and more able to assess complicated issues. As such, it may be important in some instances to sacrifice measurement precision to increase jury comprehension as long as this is done in a way that is not biased toward the plaintiff or the defendant. By its nature, any total offset calculation represents a simplification of the calculation process; therefore any total offset method will have some advantages according to the third criterion.

Total Offset

When the term “total offset” is used in forensic economics, it typically refers to a total offset between wage increases and the discount rate. This is the rule that was mandated by the Alaska Supreme Court from 1967 to 1986; for that reason, it is sometimes referred to as the “Alaska Rule.2” In 1986, however, the Alaska legislature eliminated the Alaska Rule and this author is not aware of any legal venues that require this specific offset to be made, though it may be frequently used in Pennsylvania (see below under the “Pennsylvania Rule”). This method is specifically mentioned and, with sufficient justification,3 it is specifically allowed under the Jones & Laughlin Steel Corp. v. Pfeifer 103 S. Ct. 2541 (1983) decision, which is the central precedent for lost earnings analysis in federal cases.4 It is, however, not a favored method in that decision.

The advantage of this approach is its simplicity. If wage increases can be assumed to totally offset the discount rate needed to reduce future values to present values, wage loss can be assessed by multiplying the wage loss by the number of years over which the loss is projected to continue. From the standpoint of jury comprehension, this method gets the highest possible rating, though the need for an economic expert to make this calculation seems questionable. In a case where this method is used, arguments may center around the worklife period over which losses should be projected, but a base year loss figure and the number of years of losses are the only necessary variables for an instant calculation of loss. Under the Pfeifer decision, this is a legally permissible method only if given proper evidentiary foundation. This is not an easy feat, given the lack of consistency of this method with basic wage growth and interest rate data for the American economy over the past 40 years. Thus, this method fails from the standpoint of accuracy.

The lack of accuracy of this method is shown in Tables 40 and 41 at the end of this paper. The data contained in these tables is all taken from The Economic Report of the President, 2008, showing annual discount rates for five different interest rates and two wage series. The data covers the forty-year period from 1965 to 2007. Data for the Employer Cost Index (ECI) for earnings became available only in 1981. Arithmetic averages are calculated at the bottom of the table for five-year, ten-year, fifteen-year, nineteen-year, twenty-year, twenty-five-year, thirty-year, and thirty-five-year periods that end with 2007.5

Table 41 uses the averages for different time periods calculated for Table 40 to calculate net discount rates for corresponding periods. An explanation of the specific processes that were used is provided in the notes to Table 41. Net Discount Rates were calculated for all available periods using the “Average Weekly Earnings of All American Workers (Av.Wk.%)” series and the “Total Compensation Series of the Employer Cost Index (E Cost).” Net discount rates are calculated through 40 years using the “Av. Wk. %” and through 25-year periods using “E Cost %,” which is the longest period available in recent versions of the Economic Report of the President. The final two columns show 0.00 comparison values when each series is compared to itself and provide measures of the differences between the two growth series when compared with each other. The only period and only discount rate for which one can find net discount rates approach close to total offset are five- and ten-year periods ending in 2007 with the 91-day Treasury Bill rate.

The Pennsylvania Rule—An Offset Between the CPI and the Discount Rate

The “Pennsylvania Rule” is confined to the state of Pennsylvania.6 State law requires that an offset be assumed between the rate of inflation, represented by the Consumer Price Index and the discount rate. Since the first criterion for being an economic expert is to conform one’s calculations to existing law, experts in that state have no choices about this particular issue. It was, in fact, this issue that prompted the ruling federal precedent in Jones & Laughlin Steel v. Pfeifer (1983), 103 S. Ct. 2541. Howard Pfeifer, a longshoreman in western Pennsylvania had won an award for damages under the Longshoremen’s and Harbor Worker’s Compensation Act, which had been, according to Pennsylvanialaw, calculated by the total offset method. The United States Supreme Court ruled that, contrary to Pennsylvania law, the total offset method was not mandated in federal courts in Pennsylvania. For this reason, the Supreme Court vacated the trial court decision and remanded the case for further consideration of damages.

In reading Pfeifer and cases following Pfeifer, it is not always clear that the courts have been cognizant of the difference between total offset as an offset between wages and the discount rate and total offset as an offset between the CPI and the discount rate. Indeed, over the past 20 years, calculations under the two different total offsets would have had quite similar results since wage increases, until the very recent past, have been quite similar to the rate of inflation, implying very little increase in real earnings. The difference between these two forms of total offset occurs when there are productivity increases in earnings. In other words, in theory, one could add productivity increases in earnings under the Pennsylvania Rule since the mandated total offset is between inflation and the discount rate. Some forensic economists in Pennsylvania, however, have not chosen to do so, realizing that the mandated offset between inflation and the discount rate already implies overcompensation for lost earnings, at least for workers 35 and older. In general, the only uses of the Pennsylvania total offset method have been in the state of Pennsylvaniaand only because of the requirements of state law. Effectively, this means that the criteria of accuracy and clarity to a jury are moot issues.

Tables 42 and 43 are structured similarly to Tables 40 and 41, but with the CPI-U and the Medical CPI substituted for the growth rates in Average Weekly Earnings and the Employer Cost Index. Using the CPI effectively makes the net discount rates from Table 41 become real interest rates (RDR’s) in Table 43. Medical Net Discount rates are shown as MDR’s. As is indicated in Table 43, the smallest real discount rate is the five-year rate using the 91-day U.S. Treasury Bill rate. For that five-year period using the 91-day Treasury Bill, there was a slightly negative average return. Real rates using 10-year Treasury Bonds varied from 1.28% for five years to 3.68% for 30 years.

Total Offset Between Medical Care Cost Increases and the Discount Rate

It is common in the medical economics literature to assume a total offset between rates of medical care increase and the discount rate.7 Many forensic economists do this as well with respect to life care costs when an individual has been catastrophically injured and costs of a life care plan are part of damages in personal injury cases. As Table 43 suggests, a total offset between medical care costs and selected discount rates is much less unreasonable than an assumed total offset between earnings of an average worker and the discount rate. The average annual rate of medical care increase is reasonably similar to the three-month Treasury Bill rate for all historical periods in Table 42 except for the past five-year period, when medical increase rates were lower. If other historical discount rates are used, a total offset assumption would overstate projected future costs of medical care, but by much smaller amounts than with earnings projections.

However, this semblance of parity between rates of medical care increase and discount rates is sometimes misused to characterize rates of cost increase in life care plans. Life care plans, especially life care plans with large values, contain large component costs for attendant care. Costs of trained attendants and even Licensed Practical Nurses have not increased at the rates indicated in Tables 42 and 43 for the Medical Care CPI. Neither have many basic medical commodities, like wheelchairs and other basic types of equipment. Further, many items in life care plans are simply ordinary commodities made necessary because of the life care needs of the injured individual. This use of a total offset for the total annual costs of a life care plan would significantly overstate the true expected rates of increase for the majority of components in the plan, even assuming that a total offset for medical care itself is reasonable. That, of course, requires the use of the “parking value of money” 91-day U.S. Treasury Bill rate. Other rates would result in higher net discount differences. With medical care cost increases, it also must be understood that historical rates of increase were so far above the average for other types of goods and services that they could not have been expected to continue at historical rates in any case.

From the standpoint of the legal criterion, this total offset poses no special problem. Neither the states nor the federal courts have special rules for dealing with rates of cost increase for medical or life care plans relative to discount rates used to reduce future costs to present value. From the standpoint of economic accuracy, an assumption of total offset between medical care costs and the discount rate is less unreasonable than total offsets between earnings and the discount rate or general price inflation and the discount rate. But this assumption still overstates future increases in medical care cost unless the discount rate used is the three-month Treasury Bill rate. And it certainly overstates the rates of cost increase for most life care plans, especially those with large components for attendant care. From the standpoint of jury comprehension, there is usually little problem for jurors in understanding that medical care increases have been greater than other cost increases.

References

Economic Report of the President, 2008, and earlier editions.

Endnotes

1. Other “total offsets” include: (a) An assumed offset between income taxes on lost earnings and income tax liabilities on interest paid on balances in loss replacement accounts. In most states, income taxes that would have to have been paid on lost earnings are not taxable, so this offset would be irrelevant. However, in federal personal injury litigation and inHawaii and South Carolina (and perhaps other states) taxes are subtracted from lost earnings. For loss calculations in those venues, some economic experts try to argue that the taxes owed on income would offset taxes owed on the interest on the loss replacement fund that both can be ignored. (b) An assumed offset between income taxes owed on lost earnings in the same venues, and fringe benefits that a worker would have received in addition to income. (c) Still another “total offset,” in use in Canada, is an assumed total offset between negative employment contingencies (mainly unemployment and non-participation) and job-related fringe benefits.

2. The “Alaska Rule” originated with Beaulieu v. Elliott, 434 P.2d 665 (Alaska 1967). It was modified somewhat by State v. Quinn, 555 P.2d 530 (Alaska 1976), which affirmed the Court’s earlier Beaulieu ruling of no growth and no discount, but allowed plaintiffs to include known step increases that existed in current contracts. Quite interestingly, while sticking with Beaulieu andGuinn, the Court decided that pensions should be reduced to present value in Alaska Airlines v. Sweat, 568 P.2d 916 (Alaska 1977) and again in the same original case Alaska Airlines v. Sweat, 584 P.2d 544 (Alaska 1978). The “Alaska Rule” was eliminated in 1986 by statute AS 09.17.040(b), which requires explicit consideration of inflation, real growth, and reduction to present value for all actions arising after passage in 1986. The author thanks Paul Taylor for this review of the history of the “Alaska Rule.”

3. This is discussed in the next section in the context of the “Pennsylvania Rule” since Pfeifer represented a specific challenge to the “Pennsylvania Rule” in federal actions in Pennsylvania.

4. This approach is used by only a very small number of forensic economists, but is commonly associated with employees of Vocational Economics, a business centered inLouisville,Kentucky that has branches in a number of states. It appears to be a business practice of Vocational Economics for this method to be used in all lost earnings cases and for the use of this practice to be justified in a particular way. A few other practitioners, including Dr. Charles Linke of theUniversityof Illinois, argue for a total offset approach, but offer different types of justification for this method.

5. Calculating geometric averages for the same periods involves an extensive process of formula development. Geometric averages were calculated for periods up to 22 years and showed very little difference from simple arithmetic averages of annual rates. Therefore, arithmetic averages were used in all calculations in both Tables 1 and 2.

6. This is based on Kaczkowski v. Bolubasz, 491 Pa.561, 421 A.2d 1027 (1980). Based on the name of the defendant, Bolubasz, this case is sometimes referred to by Pennsylvaniaattorneys as the “soup” case. This author thanks James D. Rodgers for this citation.

7. The author thanks Ted R. Miller for suggesting this item.

Gerald D. Martin holds a doctorate in Finance from Arizona StateUniversity. He is a Professor Emeritus at California State University,Fresno. He began his consulting service in 1974 and has testified in both state and federal courts across the country. He has an extensive list of papers, publications, and presentations to various groups. He has served on the board of editors of the Journal of Forensic Economics and the Journal of Legal Economics. Dr. Martin is a charter member of the National Associations of Forensic Economics and the AmericanAcademy of Economic and Finance Experts. He has consulted on several thousand cases in his career, divided near equally between plaintiff and defendant. Dr. Martin is the author of Determining Economic Damages, from which this article is excerpted.