Distribution of the Estimators for Autoregressive Time Series with a Unit Root

Dickey, David A.; Fuller, Wayne A.

doi:10.1080/01621459.1979.10482531

Cited by 11,029 publications

(5,364 citation statements)

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“…In a first step, we test for the existence of unit roots. Standard augmented Dickey-Fuller (Dickey and Fuller 1979) tests indicate that there is a unit root in the level of real GDP, inflation and the short term interest rate in this sample. The null hypothesis of a unit root can, however, be rejected for the series in first differences (Table 1).…”

Section: Unit Root and Cointegration Testsmentioning

confidence: 78%

The Macroeconomic Effects of Exogenous Fiscal Policy Shocks in Germany: A Disaggregated SVAR Analysis

Tenhofen

Wolff

Heppke-Falk

2010

Jahrbücher Für Nationalökonomie Und Statistik

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Abstract:We investigate the short-term effects of fiscal policy shocks on the German economy following the SVAR approach by Blanchard and Perotti (2002). We find that direct government expenditure shocks increase output and private consumption on impact with low statistical significance, while they decrease private investment, though insignificantly. For the sub-category government investment -in contrast to government consumption -a positive output effect is found, which is statistically significant until 12 quarters ahead. Allowing for anticipation effects of fiscal policy does not change the sign of the positive consumption response. Anticipated expenditure shocks have significant effects on output when the shock is realized, but not in the period of anticipation.In sum, effects of expenditure shocks are only short-lived. Government net revenue shocks do not affect output with statistical significance. However, when splitting up this aggregate, direct taxes lower output significantly, while small indirect tax revenue shocks have little effects. Compensation of public employees is equally not effective in stimulating the economy.Keywords: Fiscal policy, government spending, net revenue, policy anticipation, structural vector autoregression. JEL-Classification: E62, H30. Non-technical summaryIn this paper, we investigate the effects of fiscal policy shocks on the German economy. Most studies investigate fiscal policy in the US. For Europe, the number of papers appears to be limited. As for Germany, few studies exist (e.g., Höppner (2003) and Perotti (2005) However, it is difficult to draw conclusions on the effects of large structural changes of tax rates in this context. We go beyond existing studies by providing a disaggregated analysis and employing a comparatively long sample (1974:1 -2004:4). We find that in the short run direct government expenditure shocks increase output and private consumption with low statistical significance, while they decrease private investment, though insignificantly.These effects disappear after a few quarters, thereby indicating the vanishing character of effects on GDP stemming from one-off government expenditure increases. The possible long-term effects on government debt are discounted in this model. According to our estimation results government investment as sub-component of direct government expenditure -in contrast to government consumption -has positive effects on output, being reflected in statistical significance lasting until 12 quarters ahead. Allowing for the possibility of one period ahead anticipation of fiscal policy in the framework of this estimation approach does not change the sign of the positive consumption response. In our model, we find that anticipated expenditure shocks have significant effects on output when the shock is realized, but not in the period of anticipation.Small shocks to government net revenue do not affect output with statistical significance. However, when splitting up this aggregate, direct tax shocks lower output significantly, while ...

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Section: Unit Root and Cointegration Testsmentioning

confidence: 78%

The Macroeconomic Effects of Exogenous Fiscal Policy Shocks in Germany: A Disaggregated SVAR Analysis

Tenhofen

Wolff

Heppke-Falk

2010

Jahrbücher Für Nationalökonomie Und Statistik

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“…The problem of the evaluation of stationarity of time series has been extensively discussed in econometrics, resulting in the development of the Kwiatkowski-PhillipsSchmidt-Schin (KPSS) test for trend-or mean-stationarity (Kwiatkowski et al 1992), the class of tests for the presence of unit roots-the Dickey-Fuller (DF) test, the augmented Dickey-Fuller (ADF) test (Dickey and Fuller 1979;Said and Dickey 1984), or the Phillips-Perron (PP) test (Phillips and Perron 1988)-and the White test for variance-stationarity (White 1980). We studied the stationarity of MEG time series by means of these statistical tests.…”

Section: Tests For the Stationarity Of Time Seriesmentioning

confidence: 99%

“…Let us assume that the time series has at most one unit root. The wellestablished tests to verify such a hypothesis are the DickeyFuller class tests-the DF and the ADF test introduced by Dickey and Fuller (1979) and by Said and Dickey (1984), respectively. They are based on the assumption that the residuals in the time-series model represent a white-noise process WN(0, σ 2 ), which, however, is a simplified assumption.…”

Section: The Phillips-perron Test For Unit Rootmentioning

confidence: 99%

Application of modern tests for stationarity to single-trial MEG data

et al. 2011

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Stationarity is a crucial yet rarely questioned assumption in the analysis of time series of magneto-(MEG) or electroencephalography (EEG). One key drawback of the commonly used tests for stationarity of encephalographic time series is the fact that conclusions on stationarity are only indirectly inferred either from the Gaussianity (e.g. the Shapiro-Wilk test or Kolmogorov-Smirnov test) or the randomness of the time series and the absence of trend using very simple time-series models (e.g. the sign and trend tests by Bendat and Piersol). We present a novel approach to the analysis of the stationarity of MEG and EEG time series by applying modern statistical methods which were specifically developed in econometrics to verify the hypothesis that a time series is stationary. We report our findings of the application of three different tests of stationarity-the Kwiatkowski-Phillips-Schmidt-Schin (KPSS) test for trend or mean stationarity, the Phillips-Perron (PP) test for the presence of a unit root and the White test for homoscedasticity-on an illustrative set of MEG data. For five stimulation sessions, we found already for short epochs of duration of 250 and 500 ms that, although the majority of the studied epochs of single MEG trials were usually mean-stationary (KPSS test and PP test), they were classified as nonstationary due to their heteroscedasticity (White test). We also observed that the presence of external auditory stimulation did not significantly affect the findings regarding the stationarity of the data. We conclude that the combination of these tests allows a refined analysis of the stationarity of MEG and EEG time series.

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“…As for many countries there are only annual data available, the span usually covers no more than 20-30 years. However, it is well-known that standard time series tests, such as the augmented Dickey-Fuller unit root test (Dickey and Fuller, 1979) and the Johansen (1991Johansen ( , 1995 cointegration test, have low statistical power, especially when the span of data is short, (Campbell and Perron, 1991). In response, recent studies have used panel data to extend the time series dimension by the cross-sectional dimension and, hence, exploit additional information.…”

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confidence: 99%

Energy Consumption and Economic Growth Revisited: Structural Breaks and Cross-Section Dependence

Dobnik

2011

SSRN Journal

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Distribution of the Estimators for Autoregressive Time Series with a Unit Root

Cited by 11,029 publications

References 6 publications

The Macroeconomic Effects of Exogenous Fiscal Policy Shocks in Germany: A Disaggregated SVAR Analysis

The Macroeconomic Effects of Exogenous Fiscal Policy Shocks in Germany: A Disaggregated SVAR Analysis

Application of modern tests for stationarity to single-trial MEG data

Energy Consumption and Economic Growth Revisited: Structural Breaks and Cross-Section Dependence

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