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When Do State-Dependent Local Projections Work?

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Abstract

Many empirical studies estimate impulse response functions that depend on the state of the economy. Most of these studies rely on a variant of the local projection (LP) approach to estimate the state-dependent impulse response functions. Despite its widespread application, the asymptotic validity of the LP approach to estimating state-dependent impulse responses has not been established to date. We formally derive this result for a structural state-dependent vector autoregressive process. The model only requires the structural shock of interest to be identified. A sufficient condition for the consistency of the state-dependent LP estimator of the response function is that the first- and second-order conditional moments of the structural shocks are independent of current and future states, given the information available at the time the shock is realized. This rules out models in which the state of the economy is a function of current or future realizations of the outcome variable of interest, as is often the case in applied work. Even when the state is a function of past values of this variable only, consistency may hold only at short horizons.

Suggested Citation

  • Silvia Goncalves & Ana María Herrera & Lutz Kilian & Elena Pesavento, 2022. "When Do State-Dependent Local Projections Work?," Working Papers 2205, Federal Reserve Bank of Dallas.
  • Handle: RePEc:fip:feddwp:94175
    DOI: 10.24149/wp2205
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    1. Lutz Kilian & Robert J. Vigfusson, 2011. "Are the responses of the U.S. economy asymmetric in energy price increases and decreases?," Quantitative Economics, Econometric Society, vol. 2(3), pages 419-453, November.
    2. Michael T. Owyang & Valerie A. Ramey & Sarah Zubairy, 2013. "Are government spending multipliers greater during periods of slack? evidence from 20th century historical data," Working Papers 2013-004, Federal Reserve Bank of St. Louis.
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    5. repec:adr:anecst:y:2005:i:78:p:01 is not listed on IDEAS
    6. Gonçalves, Sílvia & Herrera, Ana María & Kilian, Lutz & Pesavento, Elena, 2021. "Impulse response analysis for structural dynamic models with nonlinear regressors," Journal of Econometrics, Elsevier, vol. 225(1), pages 107-130.
    7. Michael T. Owyang & Valerie A. Ramey & Sarah Zubairy, 2013. "Are Government Spending Multipliers Greater during Periods of Slack? Evidence from Twentieth-Century Historical Data," American Economic Review, American Economic Association, vol. 103(3), pages 129-134, May.
    8. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1993. "Nonlinear Dynamic Structures," Econometrica, Econometric Society, vol. 61(4), pages 871-907, July.
    9. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
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    Cited by:

    1. Sarah Arndt & Zeno Enders, 2023. "The Transmission of Supply Shocks in Different Inflation Regimes," CESifo Working Paper Series 10839, CESifo.
    2. De Santis, Roberto A. & Tornese, Tommaso, 2023. "Energy supply shocks’ nonlinearities on output and prices," Working Paper Series 2834, European Central Bank.
    3. James Cloyne & Òscar Jordà & Alan M. Taylor, 2023. "State-Dependent Local Projections: Understanding Impulse Response Heterogeneity," Working Paper Series 2023-05, Federal Reserve Bank of San Francisco.
    4. Jessen, Jonas & Jessen, Robin & Galecka-Burdziak, Ewa & Góra, Marek & Kluve, Jochen, 2023. "The Micro and Macro Effects of Changes in the Potential Benefit Duration," IZA Discussion Papers 15978, Institute of Labor Economics (IZA).
    5. Sheng, Xin & Kim, Won Joong & Gupta, Rangan & Ji, Qiang, 2023. "The impacts of oil price volatility on financial stress: Is the COVID-19 period different?," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 520-532.
    6. Sarah Arndt & Zeno Enders, 2024. "The Transmission of Supply Shocks in Different Inflation Regimes," Working papers 938, Banque de France.
    7. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    8. Syed Sadaqat Ali Shah & Muhammad Asim Afridi, 2023. "Cyclical variation of fiscal multipliers in Caucasus and Central Asia economies: an empirical evidence," Economic Change and Restructuring, Springer, vol. 56(6), pages 4531-4563, December.
    9. Bunce, Alan & Carrillo-Maldonado, Paul, 2023. "Asymmetric effect of the oil price in the ecuadorian economy," Energy Economics, Elsevier, vol. 124(C).
    10. Finck, David & Hoffmann, Mathias & Hürtgen, Patrick, 2023. "On the empirical relevance of the exchange rate as a shock absorber at the zero lower bound," Discussion Papers 10/2023, Deutsche Bundesbank.

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    More about this item

    Keywords

    local projections; state-dependent impulse responses; threshold; identification; nonlinear VAR;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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