Feldstein-Horioka Puzzle

Definition

The Feldstein-Horioka puzzle refers to the empirical finding (Feldstein-Horioka 1980) that national saving and investment rates are highly correlated across Organisation for Economic Co-operation and Development (OECD) countries — implying that capital is less mobile than theory predicts, since perfect capital mobility should sever the link between domestic saving and domestic investment financing.

Key Ideas

• Original ordinary least squares (OLS) finding: Feldstein-Horioka (1980) regressed $(I/Y)$ on $(S/Y)$ across 16 OECD countries and found slope $\beta \approx 0.89$, interpreted as evidence against perfect capital mobility.
• Capital mobility interpretation: Under perfect mobility, investment is funded from a global pool; domestic saving should not predict domestic investment — $\beta \approx 0$.
• Solvency constraint alternative (Coakley-Kulasi-Smith 1996): Even with perfect capital mobility, a country's current account must be stationary (no-Ponzi / transversality condition), forcing $S$ and $I$ to cointegrate with coefficient $\beta = 1$ in the long run. So $\beta \approx 1$ is consistent with capital mobility, reinterpreted as a long-run solvency constraint rather than short-run saving retention.
• Specification sensitivity (Mark-Ogaki-Sul 2003): Results differ sharply between $S/Y$ and $I/Y$ ratios vs. log-levels:
  • Ratios, non-European countries (Australia, Canada, Japan, US): restricted dynamic seemingly unrelated regression (DSUR) $\beta = 0.777$ ($t = -3.60$, significantly $< 1$) — appears to reject full capital mobility.
  • Log-levels, non-European: restricted DSUR $\beta = 1.019$ ($t = 1.36$, insignificant) — consistent with solvency constraint.
  • European countries (8): in ratios, homogeneity of $\beta$ strongly rejected ($\chi^2_8 = 29.10$, $p = 0.000$); in log-levels, homogeneity not rejected ($\chi^2_8 = 4.487$, $p = 0.722$); restricted $\beta = 0.974$ (insignificant).
• Geographic pooling: DSUR requires splitting samples by geography to ensure cross-equation error correlations are plausibly high within each subsystem.

How It Works

The regression is $I_{it} = \alpha_i + \beta S_{it} + u_{it}$, where both $S$ and $I$ are potentially I(1) and cointegrate. Estimation challenges: (1) endogeneity of $S$ (simultaneous determination); (2) cross-country correlation in equilibrium errors. DSUR addresses both: leads/lags of $\Delta S$ correct endogeneity; seemingly unrelated regression (SUR) generalized least squares (GLS) exploits cross-country correlation. Restricted DSUR pools the estimate of $\beta$ across countries when the Wald test of homogeneity ($\beta_i = \beta$ for all $i$) does not reject.

Why It Matters

One of the most studied puzzles in international macroeconomics for four decades. The resolution has implications for understanding capital market integration, current account sustainability, and the effectiveness of domestic fiscal policy. The Coakley-Kulasi-Smith solvency reinterpretation has partially dissolved the puzzle theoretically, but the empirical question of how close $\beta$ is to 1 — and whether the answer depends on functional form — remains open.

Open Questions

• Does the puzzle weaken with more recent data (post-1990s financial globalization)?
• Is the ratio vs. log-levels ambiguity a fundamental identification problem or a measurement issue?
• How does $\beta$ vary across development levels, exchange rate regimes, and capital account openness?

Related

• Dynamic Seemingly Unrelated Regression
• Cointegration
• Nelson Mark