Kim-Kim (1996) Transient Fads and the Crash of '87

Summary

Kim and Kim (1996) propose an unobserved-components model with Markov-switching heteroscedasticity (UC-MS) for monthly real S&P 500 returns (1952:1–1992:12). Stock prices are decomposed into a permanent component following an AR(2) and a transient "fad" component; independent two-state Markov chains govern the innovation variances of each component separately. Maximum-likelihood (ML) estimation via an approximate Kalman filter (Kim 1993, 1994) identifies only two statistically significant fad episodes: the OPEC oil shock (1973–74) and the 1987 crash. Crucially, both episodes are episodes of unwarranted pessimism — the fad component is negative — not speculative bubbles, and the UC-MS model fits substantially better than either a Turner-Startz-Nelson (1989) Markov-switching heteroscedastic model or GARCH(1,1).

Key Claims

• Model structure: $p_t = q_t + u_t$ where $q_t$ is the permanent component (AR(2): $q_t = \phi_1 q_{t-1} + \phi_2 q_{t-2} + v_t$) and $u_t$ is the fad component (AR(1): $u_t = \rho u_{t-1} + e_t$). The innovation variances switch independently: $\mathrm{Var}(v_t) = \sigma_{v,S_{vt}}^2$ with $S_{vt} \in \{0,1\}$ and $\mathrm{Var}(e_t) = \sigma_{e,S_{et}}^2$ with $S_{et} \in \{0,1\}$. With two chains, there are $2^2 = 4$ combined variance states at each period.
• Approximate Kalman filter: Because the Markov chains are independent and each has two states, the exact filter would require tracking $2^4 = 16$ growing mixtures of Gaussians per period. Kim's (1993, 1994) collapsing approximation retains only $2^2 = 4$ mixtures by collapsing the posterior over the lagged combined state back to a product of marginals at each step, enabling tractable ML estimation.
• Estimated AR parameters: $\hat\phi_1 = 1.168$, $\hat\phi_2 = -0.294$ for the permanent component (near-random-walk); $\hat\rho = -0.045$ for the fad (very weak mean reversion).
• Fad state persistence: $\hat{p}_{e1} = 0.647$ — the high-variance fad state has expected duration $1/(1-0.647) \approx 2.83$ months; the low-variance state has $\hat{p}_{e0} = 0.980$ (expected duration $\approx 50$ months). Only 2 fad episodes are statistically significant: OPEC 1973–74 and the 1987 crash.
• Sign of fads: Both identified fad episodes are negative (the transient component $u_t$ is below its mean), indicating unwarranted pessimism rather than speculative overvaluation. This is consistent with Shiller (1984) and Summers (1986) fads-as-pessimism interpretation.
• Volatility comparison: UC-MS variance reverts quickly (mean duration ${\sim}2.8$ months in the high-volatility state), in sharp contrast to GARCH(1,1) where $\hat\alpha + \hat\beta \approx 0.99$ implies near-permanent volatility persistence. The UC-MS model attributes post-crash volatility elevation to a transient Markov state rather than a slowly decaying GARCH process.
• Log-likelihoods: UC-MS $-1383.29$ vs. Turner-Startz-Nelson (1989) $-1387.72$ vs. GARCH(1,1) $-1395.05$. The UC-MS model decisively outperforms both benchmarks despite the additional structural decomposition.
• Variance ratio evidence: The model is consistent with the mean-reversion evidence in Fama-French (1988) and Poterba-Summers (1988) variance ratios and the Lo-MacKinlay (1988) random walk rejection — these patterns are explained by the transient fad component rather than return predictability in the permanent component.

Concepts Introduced or Extended

• Markov-Switching Model
• State-Space Representation
• Kalman Filter

Entities Mentioned

• Chang-Jin Kim
• Myung-Jig Kim

Quotes

"The unwarranted pessimism, rather than speculative bubbles, seems to characterize the fad episodes identified by our model."

"The volatility implied by our model reverts to its normal level much faster than that implied by GARCH."

My Take

The main contribution is methodological: combining an unobserved-components permanent/transitory decomposition with independent Markov-switching variances on each component, estimated via the Kim (1994) approximate filter. The independence assumption makes estimation feasible but is also a maintained restriction — if the permanent and fad variance regimes are correlated (e.g., both spike in crises), the model will misattribute variance. The empirical finding that fads are pessimistic rather than euphoric is interesting but rests on only two episodes over 40 years, which is thin statistical evidence. The volatility comparison with GARCH is compelling: the near-unit-root GARCH persistence has long been considered an artifact of the assumed parametric form, and the MS model offers a cleaner explanation. The log-likelihood advantage over Turner-Startz-Nelson (1989) is modest (${\sim}4$ points for the additional fad decomposition) — a formal likelihood-ratio test is not provided in the paper, but a Bayesian information criterion (BIC) correction would shrink the gap.