Perron (1989) The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis

Summary

Perron (1989) shows that standard Dickey-Fuller unit root tests have zero asymptotic power against trend-stationary processes interrupted by a single large exogenous shock. Treating the 1929 stock market crash and the 1973 oil price shock as known exogenous break dates, he specifies three models (A: mean shift; B: slope shift; C: both), derives the limiting distributions of the unit root test statistics as functionals of Brownian motion indexed by the break fraction $\lambda = T_B/T$ , and tabulates model-specific critical values. Applied to the 13 Nelson-Plosser (1982) macroeconomic series, 11 reject the unit root null at the 1% or 2.5% level once the break is accommodated — reversing the benchmark Nelson-Plosser finding.

Key Claims

Three break models. Model A (crash model): intercept shifts at $T_B$ — null $y_t = \mu + dD(T_B)_t + y_{t-1} + e_t$ vs. alternative $y_t = \mu_1 + \beta t + (\mu_2-\mu_1)DU_t + e_t$ . Model B (changing growth): slope shifts — null $y_t = \mu_1 + y_{t-1} + (\mu_2-\mu_1)DU_t + e_t$ vs. alternative $y_t = \mu + \beta_1 t + (\beta_2-\beta_1)DT^*_t + e_t$ . Model C: both intercept and slope shift at $T_B$ .
Theorem 1 (zero power under the alternative). Under the trend-stationary alternative, the ordinary least squares (OLS) AR coefficient estimate $\bar\alpha$ from the misspecified test regression converges to a probability limit strictly less than 1 for Model A (crash) but converges to exactly 1 for Model B (changing growth). The DF test is therefore inconsistent against the changing-growth alternative — its power vanishes asymptotically.
Theorem 2 (limiting distribution under the null). Under the unit root null, $T(\hat\alpha^i - 1) \Rightarrow H_i/K_i$ and $t_{\hat\alpha^i} \Rightarrow (\sigma/\sigma_e) H_i / (g_i K_i)^{1/2}$ , where $H_i$ , $K_i$ , $g_i$ are functionals of a standard Brownian motion $W(r)$ that depend on $\lambda = T_B/T$ . The limiting distributions differ from the standard DF distributions and must be tabulated separately for each model and each $\lambda \in \{0.1, 0.2, \ldots, 0.9\}$ .
Critical values shift substantially. 5% critical value for the $t$ -statistic: Model A $\approx -3.76$ ; Model B $\approx -3.96$ ; Model C $\approx -4.24$ (vs. the standard DF value of $-3.41$ with a constant and trend). Failing to account for the break leads to over-rejection of the unit root null.
AO versus IO specification. The Additive Outlier (AO) model allows an instantaneous level change and is used for Model A (1929 crash). The Innovational Outlier (IO) model allows a gradual change transmitted through the AR polynomial and is used for Model B (1973 oil shock). The two specifications yield different test regression forms.
Empirical results (Table VII). 11 of 13 Nelson-Plosser series reject the unit root: real GNP, nominal GNP, industrial production, employment, and wages at the 1% level; real per capita GNP, GNP deflator, money stock, common stock prices, and real wages at 2.5%. Three series fail to reject: consumer prices, velocity, and the interest rate. Quarterly real GNP (not in the NP dataset): $\hat{t} = -3.98$ , $\hat\alpha = 0.86$ , lag $k = 10$ .
Exogeneity postulate. The break dates 1929 and 1973 are treated as exogenous historical events, not realizations of an endogenous switching process. Perron acknowledges that treating $T_B$ as unknown would require different critical values; this extension is left for future work (later addressed by Zivot-Andrews 1992).
Perron-Vogelsang (1993) erratum. The asymptotic distributions for the AO model in the original paper contained errors; corrected distributions and critical values were published. The IO model results and the empirical conclusions of the paper are unaffected by the erratum.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"The purpose of this paper is to analyze the effects of a single exogenous structural change on the power of Dickey-Fuller tests and to show that many macroeconomic time series are in fact trend stationary." (p. 1361)

"The unit root hypothesis…is rejected for 11 of the 13 Nelson-Plosser series when the structural change is taken into account." (p. 1392)

My Take

The paper's influence is outsized relative to its length: it reversed the Nelson-Plosser unit root consensus for most macroeconomic series and established structural breaks as a first-order concern in persistence testing. The core insight — that unmodelled trend breaks inflate apparent persistence — is theoretically clean (Theorem 1) and empirically decisive. The main limitation, which Perron acknowledged, is the exogeneity postulate: treating 1929 and 1973 as known fixes the break fraction $\lambda$ and delivers sharper critical values than an endogenous search would. Zivot-Andrews (1992) showed that with data-determined $T_B$ , fewer series reject, and the breaks are sometimes mis-timed by one period. The AO-model erratum (Perron-Vogelsang 1993) is a genuine technical correction but does not overturn the empirical conclusions since the IO model results were unaffected.