An estimated-break unit root test lets the data pick the date of a one-time trend break instead of fixing it in advance. Economists use it to check whether a series like GNP is a random walk or is trend-stationary around one structural shift. Zivot and Andrews (1992) apply this test in Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis. They retest Perron's (1989) fourteen Nelson-Plosser (1982) series (T = 62 to T = 111) and postwar quarterly real GNP (T = 159). At the 5% level, they cannot reject the unit root null for 4 of the 10 series Perron rejects.
What the Study Found
Using estimated-break critical values, Zivot and Andrews cannot reject the unit root null for 4 of the 10 series Perron rejects at the 5% level. They still reject the unit root null for 6 of the series, including real GNP, nominal GNP, and industrial production. Contrary to Perron, they cannot reject the unit root null for postwar quarterly real GNP at the 5% or 10% level. Industrial production still rejects the unit root null at the 1% level, with a minimum t-statistic of -5.95. Applying Perron's own 5% critical value to the estimated-break statistic gives an actual test size of 55.1% for the level-break model.
"Using our "estimated break point" asymptotic distributions, we find less conclusive evidence against the unit root hypothesis than Perron finds for many of the data series."
Zivot and Andrews (1992), Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis, p. 21.
Methodology
Zivot and Andrews (1992) reanalyze the fourteen Nelson-Plosser (1982) annual macroeconomic series and the postwar quarterly real GNP series (GNP82). The annual series range from T = 62 to T = 111 observations, and the quarterly GNP series has T = 159 observations. The augmented regressions include k lagged first-differences of each series, selected by a sequential t-significance rule, to remove serial correlation. The break fraction is estimated by minimizing the one-sided t-statistic for the unit root null across every candidate break date.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Min. t-statistic, Model A | -5.58 | Real GNP, estimated break 1929, still rejected at 1% |
| Min. t-statistic, Model A | -5.95 | Industrial Production, estimated break 1929, still rejected at 1% |
| Min. t-statistic, Model A | -4.61 | Real per capita GNP, estimated break 1929, p = .091 |
| Min. t-statistic, Model A | -4.12 | GNP Deflator, estimated break 1929, p = .278 |
| Min. t-statistic, Model A | -4.34 | Money Stock, estimated break 1929, p = .174 |
| Min. t-statistic, Model C | -4.74 | Real Wages, estimated break 1940, p = .119 |
| Min. t-statistic, Model B | -3.99 | Quarterly real GNP, estimated break 1973:II, p = .131 |
| Actual size, nominal 5% test | 55.1% | Model A, using Perron's fixed-break critical value |
Estimated Break vs Fixed Break
| Measure | Estimated Break | Perron's Fixed Break |
|---|---|---|
| Model A, 5% critical value | -4.80 | -3.74 (average) |
| GNP deflator, unit root rejected at 5%? | No (p = .278) | Yes |
| Money stock, unit root rejected at 5%? | No (p = .174) | Yes |
| Postwar quarterly real GNP, unit root rejected at 5%? | No (p = .131) | Yes |
Why This Matters
The comparison shows that letting the break date float changes which macroeconomic series look non-stationary. Picking a break date after inspecting the data inflates the evidence against a unit root, so fixed-break tests can overstate rejections. The result cautions against choosing a structural-break date by eye before running a unit root test. Because the reversal is not universal across series, the finding does not amount to a blanket case for the random walk hypothesis.