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Estimating and Inferring the Nonlinear Autoregressive Distributed Lag Model by Ordinary Least Squares

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  • Jin Seo Cho

    (Yonsei University)

Abstract

This study examines the large sample behavior of an ordinary least squares (OLS) estimator when a nonlinear autoregressive distributed lag (NARDL) model is correctly specified for nonstationary data. Although the OLS estimator suffers from an asymptotically singular matrix problem, it is consistent for unknown model parameters, and follows a mixed normal distribution asymptotically. We also examine the large sample behavior of the standard Wald test defined by the OLS estimator for asymmetries in long- and short-run NARDL parameters, and further supplement it by noting that the long-run parameter estimator is not super-consistent. Using Monte Carlo simulations, we then affirm the theory on the Wald test. Finally, using the U.S. GDP and exogenous fiscal shock data provided by Romer and Romer (2010, American Economic Review), we find statistical evidence for long-and short-run symmetries between tax increase and decrease in relation to the U.S. GDP.

Suggested Citation

  • Jin Seo Cho, 2024. "Estimating and Inferring the Nonlinear Autoregressive Distributed Lag Model by Ordinary Least Squares," Working papers 2024rwp-227, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2024rwp-227
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    References listed on IDEAS

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    1. Dakyung Seong & Jin Seo Cho & Timo Teräsvirta, 2022. "Comprehensively testing linearity hypothesis using the smooth transition autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 41(8), pages 966-984, September.
    2. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    3. Olivier Blanchard & Roberto Perotti, 2002. "An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1329-1368.
    4. Severin Borenstein & A. Colin Cameron & Richard Gilbert, 1997. "Do Gasoline Prices Respond Asymmetrically to Crude Oil Price Changes?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(1), pages 305-339.
    5. Ghassibe, Mishel & Zanetti, Francesco, 2022. "State dependence of fiscal multipliers: the source of fluctuations matters," Journal of Monetary Economics, Elsevier, vol. 132(C), pages 1-23.
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    Keywords

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory

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