## wp1912

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### I. Introduction — scope and research question
- Estimates the present value of corporate profits in the United States from 1984 to 2018.
- Data sources used: vintages of five-years-ahead forecast surveys of nominal corporate earnings’ growth and long-term interest rates by professional forecasters.
- Core question: "What is the estimated present value of expected future dividends (as a portion of profits) for a risk-neutral investor relying on the real-time long-range forecasts of market analysts?"
- Main comparisons and diagnostics:
  - Appraised value compared to observed stock price dynamics.
  - Discussion of assumptions and drivers of valuation dynamics.
  - Estimation of the time-varying equity risk premium that would reconcile the estimated valuation with observed data and observed expectations of macroeconomic fundamentals.

### Findings and key observations
- Forecasters’ expectations do not fully incorporate the cyclical nature of earnings; forecasters appear to extrapolate cyclical highs and lows forward.
- This extrapolation leads to a more volatile appraisal of value derived from professional forecasts, in contrast to results in Shiller (1981) where investors were endowed with perfect foresight.
- Valuation using expected earnings and interest rates can be as volatile as observed market prices.
- The long-run expectations of corporate earning growth and their relationship to long-run interest rate expectations ('r−g') fundamentally affect valuation and the implied equity risk premium.
- A decline in long-run interest rates may increase valuations only if long-run income growth expectations do not fall as well.
- Using professionals’ forecasts for valuation is useful for indicating periods of stock market over-valuation relative to expected fundamentals in real time.
- In most periods considered, market prices reflected the expected development in economic fundamentals.
- The largest divergences between the present value of profits and observed stock prices occurred in 1998 (the Dot-Com bubble).

### Valuation approach and methodology
- Core model: discounted-dividend model with two-stage version used:
  - Vt|t = Σ_{s=0}^{T} Dt+s|t / ∏_{p=1}^{s} Rt+p|t  (survey horizon)
  - + (1 / ∏_{p=1}^{T+1} Rt+p|t) * (1+g) D_T|t / (r−g)  (long-run capitalized)
- Specific modelling choices and assumptions:
  - T = 5.
  - Dividends approximated by a constant share of pre-tax corporate earnings using historical average pay-out ratio of 50 percent.
  - Discount factor R derived from expected long-term interest rates from surveys augmented with a constant equity risk premium of four percent.
  - No de-trending or deflation to real values; raw nominal series used to preserve real-time difficulty of distinguishing transitory vs permanent shocks.
  - Taxes ignored in valuation (profits forecasts are for pre-tax profits).

### Data sources and expectation behavior
- Data:
  - Bluechip Economic Indicators survey (ASPEN Publishers) via Haver Analytics — March vintages only, long-range forecasts available from 1984.
  - NIPA corporate earnings before tax and March S&P-500 composite price index from Haver Analytics.
  - Philadelphia FED Survey of Professional Forecasters (SPF) used for quarterly inspection (five-quarter-ahead).
- Key empirical observations:
  - Most level changes in nominal corporate earnings are perceived by forecasters as permanent (both nominal and real terms).
  - Forecasted growth rates quickly revert to long-term growth, but level implications are treated as permanent shifts.
  - Long-term growth expectations change over time; present-value computations are highly sensitive to the (r−g) term.
  - Stylized result: estimated AR(1) across survey vintages yields ρ = 0.17, implying low persistence in growth-rate innovations and permanent level shifts in practice.
  - With quarterly SPF data, from 1990s onwards many quarterly innovations are considered permanent immediately.

### Present-value results and interpretation
- Valuation exercise:
  - Present value of market-expected earnings computed using survey forecasts, 50 percent pay-out, and constant equity premium of 4%.
  - Results compared with observed S&P500 index (March averages), normalized by the net-present value estimate in 1984 for comparability.
- Findings:
  - Fundamental valuation (based on survey expectations) indicates market prices in late 1990s and in 2015–2018 appear above the value implied by expected fundamentals.
  - Periods 1986–1997 show inaccuracies in valuation due to large differentials between nominal corporate earnings growth and nominal interest rates combined with constant equity premium assumption.
  - From 2003 to 2007 both actual earnings growth and long-term growth expectations rose while long-term interest rates declined, producing a rebound in both implied valuation and observed prices until late 2007/early 2008.
  - After 2010 both long-run profit growth expectations and expected long-run Treasury yield decline together until they decouple in 2017.
- Sensitivity:
  - Terminal capitalization relies on (r−g); volatility in forecasts of r and g or changes in equity premium spill strongly into valuation volatility.
  - Larger assumed equity premium dampens the impact of changes in (r−g) on valuations.

### Implied equity risk premium estimates
- Estimation approach: search for a constant equity risk premium (erp_t) added to long-term nominal Treasury forecasts such that model valuation matches observed prices.
- Empirical profile:
  - ERP hovers around 6% in the early 1980s, declines until the late 1990s, increases in the 2000s to around 4%, and is around 4% after year 2000 with a decline in the last couple of years of the sample.
  - When nominal interest rates decline jointly with expected long-term growth, estimated equity risk premium tends to increase.
  - Effective nominal discount rate for equity stakes is relatively stable between 8–10% nominally, consistent with pre-tax rates of return for non-financial corporations.
- Interpretation:
  - To reconcile stock prices from 2016 onwards with the survey data on earnings and interest rates requires assuming a decline in the equity risk premium from its average during 2003–2014.
  - If investors do not accept such a decline in the equity premium, the market is overvalued conditional on the survey forecasts.

### Key quantitative constants and parameters preserved from the analysis
- Pay-out ratio used to approximate dividends from pre-tax earnings: 50 percent.
- Equity risk premium initially assumed in valuations: four percent.
- Survey detailed horizon: T = 5.
- Estimated AR(1) persistence across survey vintages: ρ = 0.17.
- Typical nominal effective required rate of return for equity stakes: between 8–10% nominally.
- Implied ERP historical values highlighted: around 6% in early 1980s, around 4% after year 2000.

### Policy-relevant implications and recommendations
- Monitoring and valuation:
  - The simple, survey-based, non-parametric present-value framework can be used for monitoring markets for over-valuation using multi-year-ahead forecasts from forecasters, central banks, and policy institutions.
- Investor strategy:
  - Investors who better recognize the cyclical nature of earnings (distinguishing transitory shocks from permanent level shifts) may gain an advantage over forecasters who treat most shocks as permanent.
- Interpretation of market high valuations:
  - High market prices in 2015–2018 can only be reconciled with consensus survey expectations by assuming a decline in the equity risk premium; absent such a decline, markets appear overvalued.
- Use for policy institutions:
  - Central banks and regulators with multi-year forecasts can adopt this simple method to provide guidance about stock market valuations implied by macroeconomic forecasts.

### Figures and appendix (captions and plotted scales)
- Figure 9. Quarterly Nominal Corporate Earnings
  - X-axis years shown: 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 2018
  - Y-axis tick labels: 350, 400, 450, 500, 550, 600, 650, 700, 750, 800
  - Series labels: U.S. Corporate Earnings (ex IVA and CCAdj) 5 Q Ahead Market Expectations [100*log]
- Figure 10. Asset Prices Returns
  - X-axis years shown: 1985 1990 1995 2000 2005 2010 2015 2020
  - Y-axis tick labels: -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8
  - Series labels: estimate, S&P500
  - Y-axis title: Growth Rates
- Figure 11. Implied Valuation
  - X-axis years shown: 1980 1985 1990 1995 2000 2005 2010 2015 2020
  - Y-axis tick labels: 0, 2, 4, 6, 8, 10, 12
  - Series labels: estimate, S&P500, constant P/E multiple
  - Y-axis title: NPV of Corporate Earnings (normalized by value estimate in 1984)
- Figure 12. Price-to-Valuation Indicator
  - X-axis years shown: 1980 1985 1990 1995 2000 2005 2010 2015 2020
  - Y-axis tick labels: 0.5, 1, 1.5, 2, 2.5, 3
  - Series label: Implied Price/Value Ratio with Constant Risk Premium

*Source: wp1912 - References (PDF chapter), canonical URL: https://www.imf.org/-/media/files/publications/wp/2019/wp1912.pdf*

### References .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### References

### I. Introduction — scope and research question
- The paper estimates the present value of corporate profits in the United States from 1984 to 2018.
- Data sources used: vintages of five-years-ahead forecast surveys of nominal corporate earnings’ growth and long-term interest rates by professional forecasters.
- Core question: "What is the estimated present value of expected future dividends (as a portion of profits) for a risk-neutral investor relying on the real-time long-range forecasts of market analysts?"
- Main comparisons and diagnostics:
  - The appraised value is compared to observed stock price dynamics.
  - The paper discusses the assumptions and drivers of valuation dynamics.
  - The time-varying equity risk premium that would reconcile the estimated valuation with observed data and observed expectations of macroeconomic fundamentals is estimated.

### Findings and key observations
- Forecasters’ expectations do not fully incorporate the cyclical nature of earnings; instead, forecasters appear to extrapolate cyclical highs and lows forward.
- This extrapolation leads to a more volatile appraisal of value derived from professional forecasts, in contrast to results in Shiller (1981) where investors were endowed with perfect foresight.
- Valuation using expected earnings and interest rates can be as volatile as observed market prices.
- The long-run expectations of corporate earning growth and their relationship to long-run interest rate expectations ('r−g') fundamentally affect valuation and the implied equity risk premium.
- A decline in long-run interest rates may increase valuations only if long-run income growth expectations do not fall as well.
- Using professionals’ forecasts for valuation is useful for indicating periods of stock market over-valuation relative to expected fundamentals in real time.
- In most periods considered, market prices reflected the expected development in economic fundamentals.
- The largest divergences between the present value of profits and observed stock prices occurred in 1998 (the Dot-Com bubble).

### Figures and tables indexed in the source (as listed)
- Figure 1. Corporate Earnings
- Figure 2. Stylized Transitory vs. Permanent Shocks – A Reminder
- Figure 3. Nominal Corporate Earning Forecasts
- Figure 4. Nominal 10Y T-Notes, % p.a.
- Figure 5. Bluechip Survey Long-Run Estimates
- Figure 6. NPV of Corporate Earnings
- Figure 7. Estimated Equity Premium (%)
- Figure 8. Nominal Required Rate of Return (%)
- Figure 9. Quarterly Nominal Corporate Earnings
- Figure 10. Asset Prices Returns
- Figure 11. Implied Valuation
- Figure 12. Price-to-Valuation Indicator

*Source: wp1912 - References (PDF chapter), canonical URL: https://www.imf.org/-/media/files/publications/wp/2019/wp1912.pdf*

### 2015. As of March 2018, the markets seemed to overvalue the present value of expected cor-

### wp1912 - 2015. As of March 2018, the markets seemed to overvalue the present value of expected cor-

### Relationship to the literature
- Paper does not forecast corporate earnings or long-term interest rates with an explicit model; it appraises the value of the corporate earnings stream and distinguishes observed market price from an unobserved value.
- Focus is on valuation (present value of expected income stream) rather than operating in "return space".
- Links to prior work:
  - Shiller (1981): excessive volatility of asset prices relative to present value of future dividends; critique about perfect foresight assumption.
  - Barsky and De Long (1993): importance of uncertainty in long-run growth for price fluctuations; use of simplified Gordon model.
  - Greenwald, Lettau, and Ludvigson (2016): explains stock price level shocks using time-series models.
  - Practitioners’ approach referenced: Graham and Dodd (2009), Damodaran (2012), Mauboussin (2006).
- Rationale: use survey data for forecasters’ short-term and long-term expectations to distinguish level shifts of earnings from changes in long-term growth expectations.

### Valuation approach and methodology
- Core model: discounted-dividend model with two-stage version used:
  - Vt|t = Σ_{s=0}^{T} Dt+s|t / ∏_{p=1}^{s} Rt+p|t  (survey horizon)
  - + (1 / ∏_{p=1}^{T+1} Rt+p|t) * (1+g) D_T|t / (r−g)  (long-run capitalized)
- Specific modelling choices and assumptions:
  - T = 5 (survey dictates five-year detailed horizon).
  - Dividends approximated by a constant share of pre-tax corporate earnings using historical average pay-out ratio of 50 percent.
  - Discount factor R derived from expected long-term interest rates from surveys augmented with a constant equity risk premium of four percent.
  - No de-trending or deflation to real values; raw nominal series used to preserve real-time difficulty of distinguishing transitory vs permanent shocks.
  - Taxes ignored in valuation (profits forecasts are for pre-tax profits).

### Data sources and expectation behavior
- Data:
  - Bluechip Economic Indicators survey (ASPEN Publishers) via Haver Analytics — March vintages only, long-range forecasts available from 1984.
  - NIPA corporate earnings before tax and March S&P-500 composite price index from Haver Analytics.
  - Philadelphia FED Survey of Professional Forecasters (SPF) used for quarterly inspection (five-quarter-ahead).
- Key empirical observations:
  - Most level changes in nominal corporate earnings are perceived by forecasters as permanent (both nominal and real terms).
  - Forecasted growth rates quickly revert to long-term growth, but level implications are treated as permanent shifts.
  - Long-term growth expectations change over time; present-value computations are highly sensitive to the (r−g) term.
  - Stylized result: estimated AR(1) across survey vintages yields ρ = 0.17, implying low persistence in growth-rate innovations and permanent level shifts in practice.
  - With quarterly SPF data, from 1990s onwards many quarterly innovations are considered permanent immediately.

### Present-value results and interpretation
- Valuation exercise:
  - Present value of market-expected earnings computed using survey forecasts, 50 percent pay-out, and constant equity premium of 4%.
  - Results compared with observed S&P500 index (March averages), normalized by the net-present value estimate in 1984 for comparability.
- Findings:
  - Fundamental valuation (based on survey expectations) indicates market prices in late 1990s and in 2015–2018 appear above the value implied by expected fundamentals.
  - Periods 1986–1997 show inaccuracies in valuation due to large differentials between nominal corporate earnings growth and nominal interest rates combined with constant equity premium assumption.
  - From 2003 to 2007 both actual earnings growth and long-term growth expectations rose while long-term interest rates declined, producing a rebound in both implied valuation and observed prices until late 2007/early 2008.
  - After 2010 both long-run profit growth expectations and expected long-run Treasury yield decline together until they decouple in 2017.
- Sensitivity:
  - Terminal capitalization relies on (r−g); volatility in forecasts of r and g or changes in equity premium spill strongly into valuation volatility.
  - Larger assumed equity premium dampens the impact of changes in (r−g) on valuations.

### Implied equity risk premium estimates
- Estimation approach: search for a constant equity risk premium (erp_t) added to long-term nominal Treasury forecasts such that model valuation matches observed prices.
- Empirical profile:
  - ERP hovers around 6% in the early 1980s, declines until the late 1990s, increases in the 2000s to around 4%, and is around 4% after year 2000 with a decline in the last couple of years of the sample.
  - When nominal interest rates decline jointly with expected long-term growth, estimated equity risk premium tends to increase.
  - Effective nominal discount rate for equity stakes is relatively stable between 8–10% nominally, consistent with pre-tax rates of return for non-financial corporations.
- Interpretation:
  - To reconcile stock prices from 2016 onwards with the survey data on earnings and interest rates requires assuming a decline in the equity risk premium from its average during 2003–2014.
  - If investors do not accept such a decline in the equity premium, the market is overvalued conditional on the survey forecasts.

### Key quantitative constants and parameters preserved from the analysis
- Pay-out ratio used to approximate dividends from pre-tax earnings: 50 percent.
- Equity risk premium initially assumed in valuations: four percent.
- Survey detailed horizon: T = 5.
- Estimated AR(1) persistence across survey vintages: ρ = 0.17.
- Typical nominal effective required rate of return for equity stakes: between 8–10% nominally.
- Implied ERP historical values highlighted: around 6% in early 1980s, around 4% after year 2000.

### Policy-relevant implications and recommendations
- Monitoring and valuation:
  - The simple, survey-based, non-parametric present-value framework can be used for monitoring markets for over-valuation using multi-year-ahead forecasts from forecasters, central banks, and policy institutions.
- Investor strategy:
  - Investors who better recognize the cyclical nature of earnings (distinguishing transitory shocks from permanent level shifts) may gain an advantage over forecasters who treat most shocks as permanent.
- Interpretation of market high valuations:
  - High market prices in 2015–2018 can only be reconciled with consensus survey expectations by assuming a decline in the equity risk premium; absent such a decline, markets appear overvalued.
- Use for policy institutions:
  - Central banks and regulators with multi-year forecasts can adopt this simple method to provide guidance about stock market valuations implied by macroeconomic forecasts.

*Source: wp1912 - 2015. As of March 2018, the markets seemed to overvalue the present value of expected cor-*

### REFERENCES

### REFERENCES

### Cited works
- Abel, Andrew. B., and Olivier J. Blanchard, 1986, “The Present Value of Profits and Cyclical Movements in Investment,” Econometrica, Vol. 54, pp. 249–273.
- Barsky, Robert B., and J. Bradford De Long, 1993, “Why Does Stock Market Fluctuate?” The Quarterly Journal of Economics, Vol. 108, No. 2 (May), pp. 291–311.
- Cai, Xiaoming, Wouter den Haan, and Jonathan Pinder, 2016, “Predictable Recoveries,” Economica, Vol. 83, pp. 307–337.
- Campbell, John Y., 2007, “Estimating the Equity Premium,” Working Paper W13423, NBER, Cambridge, MA.
- Campbell, John Y., and Robert J. Shiller, 1988, “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors,” The Review of Financial Studies, Vol. 1, No. 3, pp. 195–228.
- Cochrane, John H., 2011, “Presidential Address: Discount Rates,” Journal of Finance, Vol. 66, No. 4, pp. 1047–1108.
- Damodaran, Aswath, 2012, Investment Valuation: Tools and Techniques for Determinig the Value of Any Asset (Third Ed.) (Wiley Finance).
- Graham, Benjamin, and David L. Dodd, 2009, Security Analysis, Sixth Edition (New York: McGraw-Hill).
- Greenwald, D.L., M. Lettau, and Sydney C. Ludvigson, 2016, “Origins of Stock Market Fluctuations,” mimeo, NYU.
- Hodge, Andrew W., 2011, “Comparing NIPA Profits with S&P 500 Profits,” BEA Breifing pp. 22–27, https://www.bea.gov/scb/pdf/2011/03%20March/0311_profits.pdf, BEA Briefing, Washington DC.
- Mauboussin, Michael J., 2006, “Common Errors in DCF Models: Do You Use Economically Sound and Transparent Models?” mimeo, Legg Mason Capital Management.
- Osborne, Sarah, and Bonnie A. Retus, 2017, “Returns for Domestic Nonfinancial Business,” BEA Breifing https://www.bea.gov/scb/pdf/2017/12-December/1217-returns-for-domestic-nonfinancial-business.pdf, BEA, Washington DC.
- Shiller, Robert J., 1981, “Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?” American Economic Review, Vol. LXXI, pp. 421–435.

### Appendix — Figures (captions and plotted scales)
- Figure 9. Quarterly Nominal Corporate Earnings
  - X-axis years shown: 1968 1973 1978 1983 1988 1993 1998 2003 2008 2013 2018
  - Y-axis tick labels: 350, 400, 450, 500, 550, 600, 650, 700, 750, 800
  - Series labels: U.S. Corporate Earnings (ex IVA and CCAdj) 5 Q Ahead Market Expectations [100*log]

- Figure 10. Asset Prices Returns
  - X-axis years shown: 1985 1990 1995 2000 2005 2010 2015 2020
  - Y-axis tick labels: -0.8, -0.6, -0.4, -0.2, 0, 0.2, 0.4, 0.6, 0.8
  - Series labels: estimate, S&P500
  - Y-axis title: Growth Rates

- Figure 11. Implied Valuation
  - X-axis years shown: 1980 1985 1990 1995 2000 2005 2010 2015 2020
  - Y-axis tick labels: 0, 2, 4, 6, 8, 10, 12
  - Series labels: estimate, S&P500, constant P/E multiple
  - Y-axis title: NPV of Corporate Earnings (normalized by value estimate in 1984)

- Figure 12. Price-to-Valuation Indicator
  - X-axis years shown: 1980 1985 1990 1995 2000 2005 2010 2015 2020
  - Y-axis tick labels: 0.5, 1, 1.5, 2, 2.5, 3
  - Series label: Implied Price/Value Ratio with Constant Risk Premium

*Source: wp1912 - REFERENCES (wp1912 - REFERENCES).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wp1912.pdf_