Nominal Illusion

Nominal Illusion

Nominal illusion (also called money illusion or the inflation illusion) is the bounded-rationality hypothesis that investors fail to correctly adjust between nominal and real terms when discounting future cash flows. The textbook valuation rule requires consistency on both sides of the present-value equation:
$V=\frac{D^{\text{nom}}}{r^{\text{nom}}}\text{or}V=\frac{D^{\text{real}}}{r^{\text{real}}},$
where $D^{\text{nom}}$ and $r^{\text{nom}}$ are nominal cash flows and discount rates and $D^{\text{real}}$, $r^{\text{real}}$ are their real (inflation-adjusted) counterparts.

The Modigliani-Cohn ($1979$) hypothesis is that investors discount real (inflation-adjusted) cash flows at nominal discount rates:
$V^{\text{naive}}=\frac{D^{\text{real}}}{r^{\text{nom}}}.$
This is internally inconsistent — it deflates the numerator but not the denominator — and produces systematic mispricing whenever expected inflation deviates from zero.

• High-inflation regimes ($r^{\text{nom}}$ large because of inflation): the naive valuation $D^{\text{real}}/r^{\text{nom}}$ is too low, so stocks are undervalued.
• Low-inflation regimes ($r^{\text{nom}}$ small): the naive valuation is too high, so stocks are overvalued.

Modigliani and Cohn applied this hypothesis to U.S. data from the $1970$s, when inflation ran near double digits and the stock market traded at exceptionally low price-earnings multiples — outcomes that pure-rational-pricing models had difficulty explaining without invoking an implausible rise in equity risk premia. The illusion gave a simple alternative: investors deflated real earnings forecasts by an inflation-augmented nominal discount rate without realizing the deflation had already been done in the numerator.

Modern evidence. Campbell-Vuolteenaho ($2004$) construct a long sample of U.S. price-dividend ratios and decompose its variation into rational components (cash-flow news, discount-rate news) and a residual associated with expected inflation. They find that a $1$-percentage-point increase in expected inflation predicts a roughly $20\%$ decline in the price-dividend ratio over the next decade — a magnitude that requires, under rational pricing, an implausibly large rise in the equity risk premium with inflation. The illusion-based explanation matches the data more parsimoniously.

Intuition

The rational present-value rule respects a simple consistency requirement: if the cash flows you are projecting are stated in real terms, you must discount them with a real rate; if they are stated in nominal terms, with a nominal rate. The two routes give the same answer because the inflation premium in the nominal discount rate exactly cancels the inflation built into nominal cash-flow projections. Mixing the two — as the naive investor does — leaves uncancelled inflation in the denominator, distorting valuations whenever inflation is high or low relative to zero.

Why would investors make this mistake? The simple answer is that real and nominal numbers do not look very different in everyday financial reporting. Earnings forecasts are published in nominal dollars, but the analyst doing the projection has typically held something like the firm’s real earnings constant — the firm earns the same goods-and-services equivalent — and inflation enters only through revisions to the nominal denominator. The investor reading the forecast may not realize that the projection is implicitly real even though stated in nominal dollars, and may discount it as if it were a true nominal projection.

The illusion is bounded-rationality rather than belief-bias because the investor is processing a smaller information set than the rational benchmark requires. A fully attentive investor would extract the implicit inflation assumption from the forecast and use it consistently on both sides of the present-value equation; a bounded-rational investor reads off the nominal earnings number and applies whatever nominal discount rate the bond market gives her. The mismatch is mechanical.

Properties

(Direction of Mispricing) Undervaluation in high-inflation regimes; overvaluation in low-inflation regimes.

The naive valuation $V^{\text{naive}}=D^{\text{real}}/r^{\text{nom}}$ scales inversely with the nominal discount rate. When expected inflation is high, $r^{\text{nom}}$ is high and $V^{\text{naive}}$ is too low. When expected inflation is low (or negative), $r^{\text{nom}}$ is low and $V^{\text{naive}}$ is too high. The 1970s — when inflation was running $8$–$10\%$ and U.S. stock-market price-earnings ratios fell to historic lows ($\approx 7$) — fit the high-inflation prediction. The late $1990$s and post-$2008$ low-rate environments fit the low-inflation prediction.

(Modigliani-Cohn 1979 Original Application) The 1970s undervaluation puzzle.

Modigliani and Cohn ($1979$) noted that throughout the 1970s the U.S. stock market traded at price-earnings ratios well below historical norms despite earnings remaining strong in real terms. Pure-rational explanations required the equity risk premium to have risen sharply, but there was no obvious reason — risk-aversion changes, productivity-growth slowdowns — that would justify such a rise. The nominal illusion provided a parsimonious alternative: investors were correctly perceiving real earnings but discounting them at the inflation-inflated nominal long-bond rate (then near $14\%$), producing valuations far below the rational benchmark.

(Campbell-Vuolteenaho 2004) Inflation as a third factor in the price-dividend ratio.

Campbell and Vuolteenaho ($2004$) use the present-value identity to decompose movements in the U.S. price-dividend ratio into (i) news about future cash flows, (ii) news about future discount rates, and (iii) news about future inflation. Under fully rational pricing, only (i) and (ii) should drive the decomposition. They find that (iii) — expected inflation — has substantial explanatory power, with elasticities consistent with the Modigliani-Cohn hypothesis. The result is one of the cleanest tests of nominal illusion in aggregate U.S. data.

(Cross-Sectional Test) Stocks with longer-duration cash flows are most affected.

Cohen, Polk, and Vuolteenaho ($2005$) test the illusion at the cross-section. If the illusion is real, stocks whose cash flows are most sensitive to long-horizon discount-rate changes — high-duration stocks like growth and tech — should be most undervalued in high-inflation regimes and most overvalued in low-inflation regimes. The data support this: the cross-sectional spread between high-duration and low-duration stocks is correlated with inflation in exactly the direction the illusion predicts.

(Bond-Market Analogue) Inflation-protected securities reveal the rational benchmark.

The introduction of TIPS (Treasury Inflation-Protected Securities) in $1997$ allows the rational discount rate to be observed directly. Researchers can now compare the nominal discount rate that nominal-illusion investors plausibly apply to equities with the real rate they should apply. The TIPS-implied real rate is typically $2$–$4$ percentage points below the nominal long-bond rate at any given time, and the difference is exactly the wedge that drives the illusion-based mispricing in equities. This confirms that the magnitudes are economically plausible.

(Limits of the Illusion Story) Recent macro-finance work explores rational alternatives.

Critics argue that part of the inflation-valuation correlation reflects rational links between inflation and risk premia (high inflation correlates with macroeconomic uncertainty and recession risk). Bekaert and Engstrom ($2010$) propose a rational model in which inflation co-moves with consumption-growth risk, generating a negative inflation–valuation correlation without illusion. The empirical literature has not fully resolved how much of the observed correlation is illusion and how much is rational risk re-pricing. Most syllabus treatments retain the illusion as the leading explanation but flag the rational-alternative literature.

Examples

The 1970s puzzle

In $1979$, U.S. CPI inflation was running at $11\%$, the $10$-year Treasury yield was approximately $11\%$, and the S&P $500$ price-earnings ratio was approximately $7$ — historically very low. A naive investor applying $V=D^{\text{real}}/r^{\text{nom}}$ would arrive at exactly such a low valuation: with real earnings essentially flat and a nominal discount rate of $11\%$, the perpetuity-style multiple would land near $1/0.11\approx 9$. A rational investor applying $V=D^{\text{real}}/r^{\text{real}}$ with a real discount rate of $4\%$ would arrive at $1/0.04=25$, much closer to the long-run historical average. The naive valuation matches the data; the rational benchmark requires an implausibly large rise in the equity risk premium to do so.

Working through the mismatch algebraically

Let dividends grow at the nominal rate $g^{\text{nom}}=g^{\text{real}}+\pi$, where $\pi$ is the inflation rate, and the nominal discount rate be $r^{\text{nom}}=r^{\text{real}}+\pi$. The rational Gordon valuation is
$V^{\text{rat}}=\frac{D_1^{\text{nom}}}{r^{\text{nom}}-g^{\text{nom}}}=\frac{D_1^{\text{nom}}}{r^{\text{real}}-g^{\text{real}}}.$
The inflation terms cancel; the rational valuation is independent of $\pi$. The nominal-illusion valuation, in contrast, applies $r^{\text{nom}}$ to the real growth rate:
$V^{\text{naive}}=\frac{D_1^{\text{real}}}{r^{\text{nom}}-g^{\text{real}}}=\frac{D_1^{\text{real}}}{r^{\text{real}}+\pi -g^{\text{real}}}.$
The $\pi$ in the denominator does not cancel. As $\pi$ rises, $V^{\text{naive}}$ falls. Setting realistic numbers — $r^{\text{real}}=4\%$, $g^{\text{real}}=2\%$, $\pi =8\%$ — gives $V^{\text{rat}}\propto 1/0.02=50$ and $V^{\text{naive}}\propto 1/0.10=10$. A five-fold valuation gap from a $\pi =8\%$ inflation environment.

Why the illusion may have weakened

Some empirical work suggests the inflation-valuation correlation has weakened in recent decades, particularly after the broad introduction of TIPS in $1997$ made real rates directly observable. If investors gradually learned to discount real cash flows at observable real rates rather than at unadjusted nominal rates, the illusion would attenuate. The post-$2010$ low-inflation, high-valuation regime is consistent with the illusion still being present (low $\pi \Rightarrow$ low $r^{\text{nom}}\Rightarrow$ high $V^{\text{naive}}$), but the magnitudes are smaller than in the 1970s, suggesting partial learning.

See Also

• 8.11. Bounded Rationality — parent hub.
• 8.3. Challenges to Rational Pricing — places nominal illusion among the broader set of valuation puzzles.
• 8.11.1. Limited Attention and PEAD — sibling: under-attention to slow-moving fundamentals.
• 8.11.5. Categorical Thinking and Comovement — sibling: another category-level cognitive shortcut affecting valuation.
• 8.6.6. Anchoring — distinct cognitive bias also operating on numeric inputs to valuation.