Editorial Type: ARTICLES
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Online Publication Date: 16 Apr 2024

Two-Step Medical Inflation Forecasts: Econometric Performance and Related Issues

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Article Category: Research Article
Page Range: 49 – 68
DOI: 10.5085/JFE-492
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Abstract

This paper examines medical inflation forecasting based on a two-step method proposed by Gilbert (2019), whereby the medical inflation rate is forecast via the sum of two terms: a broad inflation published forecast and a historical average of the inflation gap—this being the difference between medical inflation and broad inflation. In a simple forecasting experiment, the two-step method compares favorably to the one-step method of forecasting medical inflation based on its past values alone. Stationarity tests applied to the inflation gap mostly support stationarity, with a possible historical break. The econometric results generally support the use of the two-step method, with a limited historical window for inflation gap averaging, consistent with Gilbert (2019).

I. Introduction

Forensic economists are often charged with the valuation of life care plans in catastrophic injury cases. The valuation of a life care plan entails projecting future price changes of plan items and services, and discounting future plan costs to present value. The two economic inputs are the price growth rate and the discount rate. This article will focus on the price growth rate for medical care and the gap between medical price growth and broad Consumer Price Index (CPI) growth, with medical price represented by the medical services CPI index and its subcomponents. Econometric analysis of such gaps, between medical price growth and broad CPI growth, first appeared in the forensic economic literature in Scott D. Gilbert (2019).

In Gilbert (2019), the rationale for considering medical inflation gaps is that an analysis of such gaps may be useful for forecasting medical prices when appraising a life care plan.1 The inflation rate for any CPI medical component can always be written as the sum of two terms: the broad CPI inflation rate and the difference, or gap, between the medical component and broad inflation rates. Forecasts are available for broad CPI inflation over a 10-year future period via the Federal Reserve Bank of Cleveland (FRBC) and the Federal Reserve Bank of Philadelphia (FRBP).2, 3 Simple econometric methods—including moving averages—are available to the forensic economist for forecasting the inflation gap. A feasible forecast of medical component CPI inflation is the sum of a broad inflation published forecast and a simple econometric forecast of the gap. This two-step forecasting approach leverages any macroeconomic knowledge contained in the published forecast about macroeconomic trends or developments, and the gap forecast completes the approach in the absence of published forecasts for CPI medical components.

This article builds on Gilbert (2019) in two ways. First, while Gilbert (2019) reports on the accuracy of econometric forecasts of inflation gaps, he does not report on the accuracy of the two-part forecast of medical inflation itself. Second, Gilbert (2019) discusses the relevance of moving average forecasts for both stationary and non-stationary time series but does not test for stationarity or non-stationarity.

The present work evaluates the accuracy of medical inflation forecasts and finds that the two-step approach achieves greater forecast accuracy than does the published broad CPI forecast or a historical average of medical inflation rates. The present work also tests for stationarity and non-stationarity, finding support for inflation gap stationarity in the 2000-2020 period, with mixed results for the longer 1948-2020 time period.4

Section II of this article is a review of the forensic economic literature that broaches the subject of formulating medical care inflation rate forecasts or projections for life care plan valuation. Section III describes and interprets the historical performance of published forecasts of broad inflation. Section IV describes the two-step forecast method of medical inflation forecasting, Section V reports on the accuracy of forecast methods and medical inflation gap stationarity, Section VI interprets the technical results from the standpoint of life care plan valuation, and Section VII is the conclusion.

II. Literature Review

On the topic of medical inflation and its role in life care plan valuation, the articles in the forensic economics literature can be grouped into the following categories: stationarity of medical inflation rates, stationarity of medical net discount rates, medical price inflation forecasting, and the choice of inflation data sources.

A. Stationarity of Medical Inflation Rates

Bowles and Lewis (2000a) tested the stationarity of medical inflation—based on the CPI medical care services price index—with mixed results for the post-World War II historical period but clear support for stationarity in years 1982 onward. The authors interpret these results as supportive of using post-1982 average historical medical inflation as a forecast of future medical inflation, with the caveat that large, sustained gaps between medical and broad inflation may be unsustainable in the long-run.

B. Stationarity of Medical Net Discount Rates

Bowles and Lewis (2000b) tested the stationarity of medical net discount rates for calculating the present value of medical expenses. For the CPI medical care price index, the medical commodities index, and the medical care services index, the net discount rate—net of a one-year Treasury bill yield or a 10-year Treasury bond yield from 1967 through 2000—the authors found the net discount rates to be stationary. Bradley T. Ewing, James E. Payne, and Michael J. Piette (2001) come to similar conclusions for the time period 1980 through 2000, as do Schap, Guest, and Kraynak (2013) for the period 1981 through 2012. Bauman and Schap (2015) extend the work of Schap et al. (2013), finding particularly strong evidence of stationarity in years 2001 onward.

Christensen (2019) is the most recent article to examine the stationarity of medical net discount rates. The article reviewed prior net discount rate research and examined net discount rates for medical care, medical care commodities, and medical care services using data from 1953 through 2018. The main finding was that net discount rate stationarity depends on the time period examined, with general support for stationarity when based on historical periods of 30 years.

C. Forecasts of Medical Inflation Rates

As noted earlier, Bowles and Lewis (2000a) interpret stationarity of medical inflation rates as support for using a historical average medical inflation rate to forecast future inflation rates; however, they do not actually carry out a forecasting exercise. There is a dearth of forensic economics literature—and the economics literature more broadly—on the econometrics of medical inflation forecasting. An exception is Qing Cao, Bradley Ewing, and Mark A. Thompson (2012) who used linear autoregressive and moving average models, and some non-linear neural network models, to forecast medical inflation in the short-run, finding support for non-linear models. Since their focus in on short-run forecasts, the results are of limited use for longer-term forecasts common in life care plan valuation.

Gilbert (2019) is the only article in the forensic economic literature to study the econometrics of medical price inflation forecasting.5 This paper examines the performance of forecasts based on moving averages, for the general CPI, the medical CPI, and the gap between the general CPI and the Medical CPI (MC), for the following forecast horizons: one, two, three, four, five, ten, and twenty years. Using data for the period 1948 through 2017 and measuring forecast performance via mean squared error and mean absolute error, moving averages based on a 10- to 20-year time window do well when forecasting the gap between medical inflation and broad inflation, while shorter time windows worked better when forecasting the broad and medical inflation rate series. The paper also proposes the two-step method studied here, forecasting medical price inflation via the sum of i) a published forecast of broad inflation, and ii) a moving average forecast of the difference or gap between medical inflation and broad inflation.

D. Alternative Medical Inflation Data Sources

The U.S. Bureau of Labor Statistics (BLS) publishes data on the CPI and its medical components, and other sources of medical price data are the U.S. Bureau of Economic Analysis—via its Personal Consumption Expenditures (PCE) indexes, and the CMS via its PHCPI noted earlier. Each yields estimates of medical inflation, with CPI more representative of “out-of-pocket”6 price increases to consumers of medical goods and services, see Abe C. Dunn, Scott D. Grosse and Samuel H. Zuvekas (2018) and Rosenberg and Keehan (2019) for recent discussion.7

In the forensic economics literature, Gene A. Trevino (2013) examined the design and the attributes of the CPI, the PCE, and PHC medical price indices, with differences in the indexes attributable to third-party payers, formula differences, relative weighting of items, and the scope of items included in the index. Rosenberg and Keehan (2019) further compared the CPI and PHC indexes, concluding that there are no right answers in choosing a data source, and discussed PHC forecasts which have been available on request from the CMS—albeit in unpublished form. Most recently, Patrick A. Gaughan and Viviane Luporini (2020) compared CPI and PCE with an eye toward life care plan valuation, and Patrick A. Gaughan (2021) studied the problem of future pricing for medicines or drugs that switch from prescription to generic at some point. Because published consensus forecasts of expected inflation form the basis for the two-step model examined herein, the following section reviews the performance of these forecasts.

III. Inflation Forecasting and Published Forecasts

Published inflation forecasts, specifically those provided by the FRBC and FRBP, leverage the insights of multiple professional forecasters, and as noted earlier this has proven helpful in application to inflation forecasting—see Keane and Runkle (1990), Ang, Bekaert, and Wei (2007), and Haubrich, Pennachci and Ritchken (2011). Professional forecasters have at their disposal a variety of econometric models for computing inflation forecasts, and the fact that consensus forecasts have outperformed specific econometric models' forecasts, such as that of autoregressive models, may reflect the limitations of such models for capturing sudden yet sustained shifts in the level and persistence of inflation, as in the inflationary 1970s versus the relatively stable and low-inflation period of 1990 onward.

Published broad inflation forecasts at long horizons, such as 10 years ahead, can be especially helpful in application to life care plans that involve decades of future projected costs. Figure 1 shows the 10-year forecast of broad (CPI-U) inflation rate, provided by the FRBC, and broad inflation itself, for years starting in 1992 which matches the first published FRBC 10-year forecast reported in year 1982. From the graph, the forecast value lies above actual inflation in most years, most strikingly in the 1990s, reflecting the fact that forecasters in the 1980s faced a much more inflationary environment then than in later decades.

Figure 1.Figure 1.Figure 1.
Figure 1. Broad Inflation and Its 10-Year Published FRBC Forecast

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

If the transition from high-inflation to low-inflation environment in the 1990s could have been anticipated in the 1980s, the 10-year published forecast values made in the 1980s would reasonably have been lower than they were, but the economics profession had no such foreknowledge, and the differences between published forecast value and actual inflation in Figure 1 reflect inflation shocks rather than forecast bias.

To further illustrate the difference between inflation surprises and inflation forecast bias, consider an econometric forecast of broad inflation, via a first-order autoregressive AR(1) model. With the annual inflation rate in year , in the AR(1) model the current inflation rate is related to the previous year's rate via a linear regression with regression intercept , slope , and error . The forecast of future value , periods ahead of time , takes the following form in the AR(1) model8

Applying this econometric forecast method to broad inflation, by fitting an AR(1) model to inflation in years 1948,…,, for = 1982,…,2010, and making 10-year forecasts based on fitted models for each period,9Figure 2 shows the econometric 10-year forecast and the actual inflation rate.

Figure 2.Figure 2.Figure 2.
Figure 2. Broad Inflation and Its 10-Year Forecast from an AR(1) Model

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

As with the published FRBC forecast shown in Figure 1, the econometric forecast in Figure 2 is typically higher than the actual inflation value, and the contrast between forecast and actual inflation is more pronounced for the econometric forecast. If the econometric model were correctly specified, then forecasts from the fitted model would be unbiased—at least in large samples—and the observed contrast in Figure 2 would be consistent with inflation surprises manifest as persistent stochastic swings in inflation over time. To further illustrate this principle, Figure 3 shows a simulated AR(1) time series, for years 1959,…,2020, with parameter values matching a fitted AR(1) model for broad inflation in years 1948,…,2020, and the 10-year AR(1) forecast—based on the known parameter values—of the simulated series.

Figure 3.Figure 3.Figure 3.
Figure 3. Simulated AR(1) Time Series and Its 10-Year Forecast

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

In Figure 3, the 10-year forecast of the simulated AR(1) time series takes advantage of known parameter values, and is exactly unbiased, yet the forecast value tends to lie below the actual time series for long time blocks, and above it in others. While the simulated time series is dissimilar to broad inflation except in matching the AR(1) model's parameters calibrated to inflation, owing to randomly drawn errors10 in the simulation process, a pattern common to historical inflation and the simulated time series is strong serial correlation and persistence: the AR(1) model's slope parameter measures this persistence, and its fitted value is 0.694 for broad inflation in the historical period 1948-2020.

Published forecasts of broad inflation have forecast errors which tend to be larger at long horizons than at short ones, and this is true of econometric forecasts from the AR(1) model and similar ones. The relatively large errors at long horizons are consistent with inflation surprises—and bigger surprises at long horizons. Consistent with Figures 1 and 2, forecast errors tend to be smaller for the published FRBC forecast than for the econometric AR(1) forecast, during the 1992-2020 period, based on root mean square and mean absolute error measures, shown in Table 1.11

Table 1 Performance of Published and Econometric Forecasts of Broad Inflation
Table 1

A reason that inflation forecasts published by the Federal Reserve may reasonably continue to provide results at least as accurate as those based on a specific econometric model is that the Federal Reserve (and the forecasters it relies on) has at its disposal econometric models and other resources too. For example, from the theory of financial economics the Irving Fisher (1907) equation applied to two bond markets, one with nominally riskless bonds having repayment in future dollars, and another with real riskless bonds having repayment in inflation-adjusted dollars takes the form12 with the nominal interest rate, real interest rate, and inflation expectation, respectively.

In the market for U.S. Treasuries, the interest rate on Treasury Inflation Protected Securities (TIPS) is a proxy for the real rate , and the rate on ordinary Treasuries is a proxy for , yielding a computable inflation forecast .

Figure 4 shows this inflation forecast, based on interest rate differences or yield spreads on 10-year Treasury bonds,13 for years 2013 onward when TIPS data is available, via the Federal Reserve Bank of St. Louis,14 the result being similar to the 10-year published FRBC inflation forecast, but somewhat less accurate.

Figure 4.Figure 4.Figure 4.
Figure 4. Broad Inflation and Its 10-Year Forecasts via Yield Spread and FRBC

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

Other financial markets may shed additional light on market participant expectations of future inflation, and forecasts published by the Federal Reserve can usefully incorporate this sort of information.15

The foregoing discussion has demonstrated that published consensus forecasts of expected inflation have performed better than econometric forecasts. Persistent errors in both the published consensus and the econometric forecasts can be attributable to inflationary shocks rather than bias. During times of high inflation, such as the current environment, the use of consensus forecasts is prudent given their ability incorporate knowledge of current economic conditions.

IV. Inflation Data and the Two-Step Forecast Method

As in Gilbert (2019), price data for this research are the broad CPI for all urban consumers, and its Medical Care sub-index (MC) each produced by the BLS, with annual price levels for years 1947-2020 available online from the BLS or FRED provided by the Federal Reserve Bank of St. Louis. Annual inflation rates are yearly percent changes in price levels, as depicted in Figure 5.

Figure 5.Figure 5.Figure 5.
Figure 5. Time Plot of Broad & Medical CPI Inflation Rates, Years 1948-2020.

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

To model a given component of the CPI, such as Medical Care Services, let be the inflation rate in that component between year and year t. As in Gilbert (2019), assume that includes random fluctuation over time, and let be the expectation of inflation periods in the future, conditional on information available at time . This expectation is formed at time and is an optimal econometric forecast—minimizing mean squared prediction error. This forecast incorporates any relevant macroeconomic information known at time , as well as any microeconomic information specific to component or sector . For forensic economic application to medical price inflation, a challenge is that there is no consensus about the optimal forecast value. However, there is some consensus about the optimal forecast of broad CPI inflation . To make use of this consensus, write medical component inflation as broad inflation plus the gap between component and broad inflation:For the medical inflation component of CPI, Figure 6 shows the historical gap between the medical component and broad inflation for years 1948-2020, and in Figure 5 this gap is the vertical distance between the medical inflation and broad inflation.

Figure 6.Figure 6.Figure 6.
Figure 6. Time Plot of the Medical Inflation Gap, Years 1948-2020.

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

Applying conditional expectations to the left- and right-hand side of (1), and using the additive property of expectations, the optimal forecast of medical component inflation equals the optimal forecast of broad inflation plus the optimal forecast of the inflation gap:

A consensus about provides a proxy for this value in (2), reflecting current macroeconomic information and policies. The inflation gap, to the extent that it reflects microeconomic conditions but not macroeconomics ones, may be relatively easy to forecast, and if so (2) provides a two-step forecast method: in (2), plug in a consensus forecast for broad inflation, and a simple econometric forecast for medical component inflation gap. In Gilbert (2019), the result is a long-run medical inflation forecast of 3.651% for years 2020 onward, based on 2.2% consensus forecast of broad inflation and a 20-year historical average of 1.451% for the medical inflation gap. The present work examines the econometrics of this two-step forecast method in more detail.

For the second step in the two-step forecasting method (2), a historical average of inflation gaps serves as a proxy for the gaps' optimal forecast in later years. Gilbert (2019) finds that a historical average window of 10 to 20 years works well for long-run forecasting of medical inflation gaps.

To apply these principles, let the forecast period h be 10 years, and let the consensus inflation forecast be the 10-year inflation forecast from the FRBC, available to forecast years 1992-2020. The two-step forecast method uses an average of historical gaps between medical and broad inflation rates. Table 2 shows some historical averages of broad CPI, MC, and the gap between MC and CPI.

Table 2 Historical Averages of Broad and Medical Inflation, and their Gap
Table 2

From the vantage point of year 2020, Table 3 shows two-step forecasts of future medical inflation with the number “p” of past averaged years being 10, 20, and 30.16 Also shown are “one-step” forecasts, these being the historical averages of medical inflation itself—shown in Table 2.

Table 3 Forecasts of Medical Inflation from Year 2020
Table 3

As an additional visual guide to these inflation forecasts, Figures 7 through 9 show more time plots. Recalling that two-step forecast method uses the published inflation forecast shown in Figure 1 and a moving average of the medical inflation gap, Figure 7 shows these gap moving averages—with averaging over 10, 20, and 30 years.

Figure 7.Figure 7.Figure 7.
Figure 7. Time Plot of Moving Averages for the Medical Inflation Gap.

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

Combining Figures 1 and 7, Figure 8 shows two-step medical inflation forecasts, each the sum of the broad inflation forecast (Figure 1) and one of the moving averages in Figure 7.17

Figure 8.Figure 8.Figure 8.
Figure 8. MC and 2-Step Forecasts (10, 20, 30 year GAP averaging), Years 1992-2020.

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

Figure 9 shows one-step forecasts of medical inflation, each a moving average of medical inflation itself. Comparing these two figures, the two-step method appears to provide better forecasts of medical inflation, overall, than does the one-step method. Section V states this comparison more objectively via forecast performance statistics.

Figure 9.Figure 9.Figure 9.
Figure 9. MC and 1-Step Forecasts (10, 20, 30 year MC averaging), Years 1992-2020.

Citation: Journal of Forensic Economics 31, 1; 10.5085/JFE-492

V. Forecast Performance and Stationarity of Medical Inflation Gap

Under the assumptions made earlier, Table 4 reports medical inflation forecasting performance in terms of root mean squared error and mean absolute error—as in Gilbert (2019) and the econometric forecasting literature.

Table 4 Performance of Medical Inflation Forecasts, During years 1992-2020
Table 4

As shown, the two-step method performs better in this forecasting exercise, with the best two-step forecast about twice as accurate as the best one-step forecast. For modern application to life care plan valuation, the two-step method of medical inflation forecasting is most useful if the inflation gap is simple to forecast. Gilbert (2019) reports on the performance of moving average long-term forecasts of the inflation gap, and moving averages are simple historical averages of a given length p and a successively updated end-point. Moving averages can be useful for long-term forecasting of stationary time series and also non-stationary ones, provided that optimal forecasts of such series are suitably convergent—see Appendix B of Gilbert (2019) for discussion. For stationary time series, historical averages with long length can be useful, while for non-stationary series a short length can be better.

Table 5 reports Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) tests of the unit root non-stationarity null hypothesis versus a stationary alternative, applied to the medical inflation gap for the whole historical period 1948-2020 and more recent periods 1980-2020 and 2000-2020.18

Table 5 Tests of the Non-Stationary Unit Root Hypothesis, Medical Inflation Gap
Table 5

Each test rejects the non-stationarity null hypothesis in favor of stationarity, at the 1% significance level. As a counterpoint, Table 6 reports Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests of the stationarity hypothesis versus a unit root alternative: these tests fail to reject stationarity of medical inflation for the whole-sample period 1948-2020 and for the sub-sample 1980-2020, while marginally rejecting it (at the 5% but not 1% level) for the more recent sub-sample 2000-2020.

Table 6 KPSS Tests of the Stationarity Hypothesis Versus Non-Stationarity, Medical Inflation Gap
Table 6

On the whole, the ADF and the KPSS tests are mostly consistent with inflation gap stationarity. A middle-ground, between stationarity and non-stationarity, is the hypothesis that a time series is stationarity until the occurrence of a structural break—represented by a shift in long-run mean—after which the time series exhibits stationarity about a shifted or changed mean value. The Zivot-Andrews test pits the non-stationary unit root hypothesis versus the alternative of two distinct periods of stationarity—pre- and post-break.19 Applying the Zivot-Andrews test to the medical inflation gap, over the 1948-2020 period, the test endogenously selects year 1980 as the break year, rejecting the non-stationarity null hypothesis at the 1% level, in favor of stationarity in two distinct periods:20 1948-1979 and 1980-2020,21 see Table 7.

Table 7 Zivot-Andrews Tests of the Unit Root Hypothesis Versus Stationarity With a Structural Break, Medical Inflation Gap
Table 7

If indeed the inflation gap is consistent with stationarity in the 1980-2020 period but not the whole post-war period, it may be useful to forecast this gap using a historical average that includes years in 1980-2020 but excludes earlier ones. Even within the 1980-2020 period, there may be changes in the gap's level that could motivate an inflation gap forecast based on, say, years 2000-2020 alone. Gilbert (2019) explores a variety of historical windows, for gap averaging purposes, and finds the best forecast results when the window is 10-20 years.22

VI. Medical Care Components and Implications for Life Care Plan Evaluation

For life care plan appraisal, it may be helpful to forecast separately the inflation rates of medical care components such as medical services and medical commodities. To this end, this section extends the preceding analysis to these components as well as physician services and prescription drugs.

Table 8 reports historical averages of medical component inflation series for the period 2000-2020. Table 9 shows forecasts of the medical component inflation series, made from the year 2020 using the one-step and two-step methods discussed earlier. Table 10 reports on the historical performance of such forecasts over the 1990-2020 period, with results: the two-step method outperforms the one-step method for each time series. Table 11 reports tests of stationarity and non-stationarity hypotheses for component medical inflation gaps, during years 2000-2020, with results mostly supporting stationarity.

Table 8 Historical Average of Medical Component Inflation Rates, Years 2000-2020
Table 8
Table 9 Forecasts of Medical Component Inflation, from Year 2020
Table 9
Table 10 Performance of Medical Component Inflation Forecasts, During Years 1990-2020
Table 10
Table 11 Stationarity Tests, Medical Component Inflation Gaps, Years 2000-2020
Table 11

Overall, the econometric results for component medical inflation forecasts are similar to those for medical inflation overall: the two-step forecast method performs relatively well and—in recent times—the medical inflation gap appears stationary or nearly so.

There are other components of CPI medical inflation, and the forecast methods discussed earlier also apply to them. For some of these, such home care CPI,23 data availability starts sometime after year 2000, and conclusions from formal econometric analysis of such series are limited by small sample sizes and await future research.24

For the purpose of valuing life care plans today, the upshot of the foregoing technical discussion is additional support for the Gilbert (2019) two-step method for forecasting medical inflation. Combining the results in Gilbert (2019) with those here, the first step of this method is to look up a consensus forecast of broad inflation, and the second is to add to this forecast a historical average of the gap between medical and broad inflation, with the historical time window subject to choice but usefully in the range of 10-20 years or perhaps longer. An alternative is simply to average the medical inflation rate by itself and use that as a forecast of future medical inflation. This one-step method is simple—a virtue in forensic economics practice, but the two-step method also has some appeal. One appeal of the two-step method is that it leaves to consensus any relevant analysis of macroeconomic factors or trends impacting both broad and medical inflation, and analyses only the gap. A second appeal is that, based on the analysis in Section V of this paper, the two-step forecasting method may be much more accurate than the one-step method.

VII. Conclusion

Consensus forecasts of broad inflation, plus available historical data on medical and broad inflation, provide a simple two-step to medical inflation forecasting, proposed in Gilbert (2019) and studied there and here in econometric terms. The econometric results are generally supportive of the two-step method as was demonstrated using the medical care price index and the following subcomponents: medical commodities, medical services, physician services, and prescription drugs.

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  1. 1

    For economists that use current interest rates to reduce expected future costs to present value, forecasts of medical prices are useful. An alternative is to apply a net discount rate (NDR) to current-dollar plan costs, see Tyler J. Bowles, and W. Cris Lewis (2000a, 2000b), David J. Schap, Lauren Guest and Andrew C. Kraynak (2013), Robert W. Baumann and David J. Schap (2015), Kurt V. Krueger, (2016), and Eric W. Christensen, (2019) on medical NDRs.

  2. 2

    The FRBC has published a 10-year forecast of inflation since 1982, and the FRBP has published one since 1991. Each forecasts the annual average inflation rate of headline (CPI) inflation over the next 10 years. The FRBP forecast, published in its quarterly Survey of Professional Forecasters (SPF), is based on a consensus of professional forecasters. The FRBC inflation forecast, in its Inflation Expectations monthly update online, currently takes as input the FRBP 10-year consensus forecast (since 1991), plus shorter-term Blue Chip Economic Indicator forecasts (since 1982), and applies econometric modelling to produce monthly forecasts; see FRBC online documentation and also Joseph G. Haubrich, George Pennachi and Peter Ritchken (2011). As noted in the latter, Andrew Ang, Geert Bekaert, and Min Wei (2007) find that SPF consensus-based inflation forecasts significantly outperform a variety of other inflation predictions. See Michal. P. Keane and David. E. Runkle (1990) for similar findings.

  3. 3

    These forecasts, published by the Federal Reserve, leverage consensus views among professional forecasters about future events, a useful approach—especially when faced with major unforeseen events like the New Economy period of the late 1990s, the Great Recession, and the Covid-19 pandemic.

  4. 4

    Readers interested in forecasting inflation in medical costs should see a new paper by David Rosenbaum and Christopher Mann on the topic in this issue of the JFE.

  5. 5

    As discussed earlier, the Federal Reserve publishes forecasts of broad (CPI) inflation. It does not publish similar forecasts of medical price inflation, nor do such forecasts appear in other high-profile outlets like the Blue Chip Economic Indicators, which motivates the econometric analysis of medical inflation forecasts in forensic economics. The Centers for Medicare and Medicaid Services (CMS) computes a Personal Health Care Price Index (PHCPI), and in year 2020 CMS researchers published—in the journal Health Affairs—a 10-year forecast or projection for that index over the period 2019-2028, see Sean P. Keehan, Gigi A. Cuckler, John A. Poisal, and Andrea M. Sisko (2020). PHCPI forecasts do not appear in the more recent 2021-2030 edition of the CMS projections in Health Affairs, but that edition does include forecasts of the chain-weighted National Health Expenditures deflator, see John A. Poisal, Andrea M. Sisko, Gigi Cuckler, Sheila Smith, Sean P. Keehan, Jacqueline A. Fiore, Andrew J. Madison, and Kathryn F. Rennie (2022). Keehan, a co-author of these studies, has provided on request by forensic economists some additional—albeit unofficial—forecasts or projections of medical care prices; see Joseph I. Rosenberg and Sean P. Keehan (2019) for discussion of these projections. Some or all of these resources may be of use for medical inflation forecasting by forensic economists.

  6. 6

    In the market for health care, included in CPI “out-of-pocket” costs are household costs of health insurance, on top of co-pays for actual goods and services receive. These exceed the literal out-of-pocket co-pay cost on a typical doctor visit, for example. See Rosenberg and Keehan (2019) for discussion.

  7. 7

    The purpose of the CPI is to inform households (and others) about the typical prices for goods and services they may face as consumers in the marketplace. By comparison, PCE—as part of the National Income and Product Accounts—tracks all consumption expenditures, by households and others. The Office of the Actuary of the CMS, tasked with supporting a sustainable budget for Medicare and Medicaid, studies health care costs and prices from that vantagepoint; and their PHCPI index may be ideal for that purpose.

  8. 8

    This forecast formula results from repeated application of the AR(1) modelling relationship at successively earlier periods: expressing Yt in terms of Yt−1 with the latter expressed in terms of Yt−2, and so on. See James D. Hamilton (1994, equation 4.2.19) for an equivalent formula under the assumption that Yt is a stationary time series.

  9. 9

    The authors estimate the AR(1) using EViews 11 software via the “Equation” command with default specifications, and computer code for replicating these and other EViews results is available from the authors.

  10. 10

    The errors are normally distributed and generated in EViews with a “seed” value equal to 1 for the random number generator.

  11. 11

    The fitted AR(1) models discussed earlier have estimated slope (β) values in the range (-1,1), which corresponds to a stationary time series. An alternative is to impose a non-stationary I(1) or “unit root” restriction on the time series, and for an AR(1) model of inflation the relevant restriction is α = 0, β = 1, in which case Yt is a random walk, and the AR(1) model performs better in the 1992-2020 period with this approach than without it, achieving forecast error root mean squared error = 1.627 and mean absolute error = 1.353.

  12. 12

    See Fisher (1907, page 359), and for more recent discussion in monetary and financial markets see Fredric S. Mishkin (2013, Chapter 5) and Jordi Gali (2015, Chapters 2 and 3).

  13. 13

    From the Fisher (1907) equation, if both r and πe are close to zero then πe ≈ i − r, with a yield spread. We can see this because . After dropping the last term because it is the product of two numbers close to zero, we get or .

  14. 14

    The data series is the “10-Year Breakeven Inflation Rate,” available in the Federal Reserve Economic Data (FRED) online.

  15. 15

    For example, the FRBC's inflation forecasts incorporate information on “inflation swaps''—contracts which one party makes fixed payments to a second party, and the latter makes payments to the first on an inflation-adjusted basis.

  16. 16

    These two-step forecasts are each the sum of: (a) the published/consensus forecast of broad inflation, published in year 2020, and (b) an average inflation gap appearing in the rightmost column of Table 2.

  17. 17

    Ex post the medical care inflation forecasts were much higher than actual medical inflation in year 1997, but converged toward the latter as years progressed. The big contrast in year 1997 reflects historic shifts in the course and behavior of broad (CPI) inflation—from high inflation and persistence in the 1980s to lower inflation and persistence in later decades. From Figure 6, the gap between medical and broad inflation has a similar but more muted contrast in behavior, moving from the 1970s and 1980s to later decades. Medical inflation forecasts that are systematically higher than realized values are possible, depending on the nature of the time series to be forecast, but do not in itself imply that the forecast method is suboptimal. The consensus (CPI) inflation forecast is arguably the best method available (as discussed in footnotes 2 and 3, with literature references), and overshoots inflation 10 years out for most years in Figure 1 (including year 1997). For the inflation gap, over- and under-shooting happens in Figure 7, and combining broad inflation and the inflation gap, Figure 8 shows the composite result of adding forecasts from Figures 1 and 7: here the major forecast overshoot of medical inflation in year 1997 is mainly due to the consensus forecast's overshoot of broad inflation, but in later years the inflation gap's forecast overshoot contributes notably to the forecast overshoot of medical inflation itself.

  18. 18

    The forensic economics literature discusses these econometric tests at length, and others such as the KPSS test of stationarity and the Zivot-Andrews test of stationarity with a one-time break, see Baumann and Schap (2015) and articles referenced therein. Testing here is via EViews 11 software with default settings: these include an intercept but no linear time trend in the models, and use of the Bayes/Schwarz information criterion for choosing the number of included lags in dynamic models.

  19. 19

    See Bauman and Schap (2015) for additional discussion and references to the econometric literature.

  20. 20

    For the second of these periods, its starting point 1980 coincides with emerging monetary policy changes, and in the health care sector the arrival of managed care by the late 1980s reduced care costs, with some offset by the regulation of managed care by the 1990s.

  21. 21

    By comparison, Christensen (2019) tests the medical net discount rate—which contrasts medical inflation and an interest rate, mostly finding evidence of stationarity when using historical data windows ending in year 2018 and starting 30 years or more earlier, as in Tables 3 and 4 “Without Trend” columns that correspond to ADF and PP test statistics here.

  22. 22

    The recent Covid-19 pandemic, like the Great Recession, increased economic uncertainty in subsequent years, and challenged economic forecasters to anticipate its consequences. The two-step forecasting method uses a published forecast of broad inflation, incorporating consensus views from many professional economists, which may be especially helpful in times of great uncertainty. The gap, between medical and broad inflation, may reasonably remain stationarity in such periods, provided that the fundamentals of health care markets do not change greatly.

  23. 23

    See the Care of Elderly at Home component of CPI, series SEMD03.

  24. 24

    Relatively short time horizons are one limitation of some CPI component time series. For Nursing Home Services (series SEMD02), another may be that the CPI methodology is geared to non-institutionalized persons whereas those persons in nursing homes may better classified as institutionalized.

Copyright: © 2024 by the National Association of Forensic Economics 2024
Figure 1.
Figure 1.

Broad Inflation and Its 10-Year Published FRBC Forecast

Figure 2.
Figure 2.

Broad Inflation and Its 10-Year Forecast from an AR(1) Model

Figure 3.
Figure 3.

Simulated AR(1) Time Series and Its 10-Year Forecast

Figure 4.
Figure 4.

Broad Inflation and Its 10-Year Forecasts via Yield Spread and FRBC

Figure 5.
Figure 5.

Time Plot of Broad & Medical CPI Inflation Rates, Years 1948-2020.

Figure 6.
Figure 6.

Time Plot of the Medical Inflation Gap, Years 1948-2020.

Figure 7.
Figure 7.

Time Plot of Moving Averages for the Medical Inflation Gap.

Figure 8.
Figure 8.

MC and 2-Step Forecasts (10, 20, 30 year GAP averaging), Years 1992-2020.

Figure 9.
Figure 9.

MC and 1-Step Forecasts (10, 20, 30 year MC averaging), Years 1992-2020.

Contributor Notes

*

Scott D. Gilbert, Associate Professor of Economics, Southern Illinois University Carbondale, IL; Gene A. Trevino, Economic Evidence, San Antonio, TX. The authors want to thank the Editor and anonymous referees for suggestions that greatly improved this work.

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