Kim-Nelson (1999a) Friedman's Plucking Model of Business Fluctuations: Tests and Estimates of Permanent and Transitory Components

Summary

Kim and Nelson (1999a) provide the first formal econometric model capable of testing Friedman's (1964) "plucking" model of business fluctuations against a symmetric trend-plus-cycle alternative. Output is decomposed into a stochastic trend ceiling and a transitory cycle whose shock is a mixture of a discrete asymmetric recession component ( $\pi S_t$ , $\pi < 0$ ) and a symmetric continuous component, with a two-state Markov-switching variable governing the regime. Estimated via Kim's (1994) approximate maximum likelihood estimation (MLE) on U.S. real GDP and unemployment (1951:1–1995:3), the results strongly favour plucking: the symmetric shock is essentially zero for GDP, apparent persistence drops sharply once asymmetry is modelled, and implied regime probabilities align with NBER dates. Three phases emerge — normal (near the trend ceiling), recessionary, and high-growth recovery — with differing implications for which macroeconomic theory applies.

Key Claims

Plucking identification: $\hat{\pi} = -0.011$ (std 0.003) — highly significant negative asymmetric recession shock; joint test $\sigma_{u0} = \sigma_{u1} = 0$ is accepted at high $p$ -value, so the symmetric shock plays no role for GDP.
Reduced apparent persistence: $\phi_1 + \phi_2 = 0.797$ in the asymmetric model vs. 0.946 in Clark's (1987) linear unobserved-components (UC) model; accounting for asymmetry substantially lowers estimated transitory-component persistence (consistent with Perron (1990) on unit-root bias under regime switching).
Three business cycle phases: normal (output near trend ceiling, permanent shocks dominate), recessionary (output plucked below ceiling by transitory discrete shock), and high-growth recovery (fast reversion as transitory effects dissipate, as noted by Sichel 1994).
Log-likelihood gains: 585.71 (plucking, Model 1) vs. 577.83 (Clark linear UC, Model 5); stochastic trend growth $\sigma_w$ also becomes significant once asymmetry is captured (likelihood-ratio, LR = 3.44).
Unemployment: Asymmetric shock is positive ( $\hat{\pi} > 0$ , unemployment plucked upward), more persistent ( $\phi_1+\phi_2 = 0.927$ ), symmetric shock significant; transitory component of unemployment correlated −0.694 with that of GDP, with lag and higher persistence.
Structural interpretation: During normal times output is driven by permanent shocks — real business cycle (RBC) models appropriate. During recessions and recovery, transitory shocks dominate — monetary and demand-side models more appropriate.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"Empirical results for real GDP suggest that output during normal times is driven mostly by permanent shocks: Real business cycle models may be more relevant in explaining the output dynamics during normal times. During the recessionary and high-growth recovery periods, real GDP is driven mostly by transitory shocks: Macroeconomic theories such as monetary models or other models that emphasize demand-oriented shocks may be more appropriate."

My Take

The main contribution is methodological: the first estimable model that nests symmetric UC and asymmetric plucking within a single state-space framework, using the Kim (1994) approximate MLE filter. The finding that the symmetric shock is essentially zero for GDP is striking. One limitation is that the Kim filter approximation introduces a bias that is absent from the Gibbs-sampling approach in Kim-Nelson (1998); a fully Bayesian treatment of this model would be a natural extension. The regime-dependent implication — that which macroeconomic theory applies depends on the phase of the cycle — is an underappreciated insight that motivates time-varying structural models.