Anna Bykhovskaya, James A. Duffy
arXiv 5 Oct 2022 · Econometrics · publishedJournal of Econometrics (2024) · 4 citations (OpenAlex)
arXiv:2210.02599 · PDF · DOI · OpenAlex · Extracted main text
This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive. Surprisingly, despite the presence of censoring, the OLS estimators of the model parameters are consistent. We show that this allows OLS-based inferences to be drawn on the overall persistence of the process (as measured by the sum of the autoregressive coefficients), and for the null of a unit root to be tested in the presence of censoring. Our simulations illustrate that the conventional ADF test substantially over-rejects when the data is generated by a dynamic Tobit with a unit root, whereas our proposed test is correctly sized. We provide an application of our methods to testing for a unit root in the Swiss franc / euro exchange rate, during a period when this was subject to an occasionally binding lower bound.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | de Jong, R. and Herrera, A. M (2011) Dynamic censored regression and the Open Market Desk reaction function | 1.000 | 7 | 3 | 100% |
| 2 | –- (2005) Limited time series with a unit root | 1.000 | 5 | 4 | 100% |
| 3 | Bykhovskaya, A (2023) Time series approach to the evolution of networks: prediction and estimation self | 0.974 | 13 | 6 | 92% |
| 4 | Cavaliere, G (2004) The asymptotic distribution of the Dickey–Fuller statistic under nonnegativity constraint | 0.843 | 4 | 3 | 75% |
| 5 | –- and Xu, F (2014) Testing for unit roots in bounded time series | 0.843 | 3 | 3 | 100% |
| 6 | Duffy, J. A., Mavroeidis, S. and Wycherley, S (2022) Cointegration with occasionally binding constraints, arXiv:2211.09604 self | 0.811 | 4 | 2 | 100% |
| 7 | Liu, W., Ling, S. and Shao, Q.-M (2011) On non-stationary threshold autoregressive models | 0.737 | 3 | 2 | 100% |
| 8 | Andrews, D. W. K. and Chen, H. Y (1994) Approximately median-unbiased estimation of autoregressive models | 0.644 | 2 | 2 | 100% |
| 9 | –-, Tjstheim, D. and Yin, J (2013) Estimation in threshold autoregressive models with a stationary and a unit root regime | 0.644 | 2 | 2 | 100% |
| 10 | Liebscher, E (2005) Towards a unified approach for proving geometric ergodicity and mixing properties of nonlinear autoregressive processes | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 57 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Cointegration with Occasionally Binding Constraints | 0.956 | 8 | 6 |
| 2 | Estimation of a Dynamic Tobit Model with a Unit Root | 0.663 | 24 | 7 |
| 3 | Stationarity with Occasionally Binding Constraints | 0.405 | 1 | 1 |