How does TFP growth turn into a long-run equity return forecast?

Short answer: TFP growth feeds into trend GDP growth, which approximately equals trend corporate earnings growth, which combined with dividend yield equals long-run real equity returns. The chain runs through the Gordon growth model logic, and TFP is the key input that determines whether long-run growth is sustainable or stalls.

Reading the symbols: $g_A$ = TFP growth; $g_K$ = capital growth; $g_L$ = labor growth; $\alpha$ = capital share; $g_Y$ = trend GDP growth; $D/P$ = dividend yield; $r_e$ = expected real equity return.

The full chain

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Step by step:

Step 1: Growth accounting gives trend GDP growth.

$$g_Y = g_A + \alpha g_K + (1-\alpha) g_L$$

For the US: $g_A \approx 1.5\%$, $g_K \approx 2\%$, $g_L \approx 0.5\%$, $\alpha = 0.30$.

$$g_Y \approx 1.5\% + 0.3 \times 2\% + 0.7 \times 0.5\% \approx 2.4\%$$

Step 2: Trend earnings growth approximately equals trend GDP growth.

In the long run, corporate earnings cannot grow faster than the economy as a whole (or corporate profits would consume all of GDP, which is impossible). So real trend earnings growth $\approx g_Y$. This is the Grinold-Kroner-style approximation.

Step 3: Gordon growth model says expected equity return = earnings growth + dividend yield.

$$r_e = g_Y + \frac{D}{P}$$

For the US with about 2% dividend yield:

$$r_e \approx 2.4\% + 2.0\% \approx 4.4\%$$

This says real US equity returns SHOULD trend around 4.4% per year over the long run.

Why TFP is the highest-leverage input

Of the three inputs to trend GDP, TFP is by far the most uncertain — and the most consequential. Compare:

Input	Typical range	Confidence
Labor growth $g_L$	0% to 2%	High (demographics are predictable)
Capital growth $g_K$	1% to 4%	Moderate (depends on savings/investment)
TFP growth $g_A$	0% to 3%	LOW (depends on technology, institutions)

A 1% swing in TFP forecast moves trend GDP by 1% — and thus equity return forecast by 1%. Over a 30-year horizon, that compounds to ~35% in cumulative-return difference.

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This is why CFA candidates spend so much time on TFP — it is the single most important input to long-run return forecasts, and the most uncertain.

Cross-country implications

Apply the framework to forecast long-run real equity returns for several economies:

Country	$g_A$	$g_K$	$g_L$	$\alpha$	$g_Y$	$D/P$	Forecast $r_e$
US	1.5%	2.0%	0.5%	0.30	2.45%	2.0%	4.5%
Japan	0.8%	1.5%	-0.5%	0.30	0.90%	2.5%	3.4%
India	3.0%	6.0%	1.0%	0.40	6.0%	1.5%	7.5%
Switzerland	1.2%	1.5%	0.3%	0.30	1.86%	3.0%	4.9%

(All real terms, illustrative.) The framework shows India should anchor higher long-run equity returns than Japan, primarily because of demographic and TFP differences.

The exam-day pattern

When a CFA vignette gives you values for input growth and capital share, you should be able to:

1. Compute trend GDP using $g_Y = g_A + \alpha g_K + (1-\alpha) g_L$
2. Add dividend yield to anchor long-run real equity return
3. Optionally adjust for valuation reversion (if P/E is mean-reverting)

For more on growth accounting and CME see our TFP article.