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Modelling Time-Varying Parameters in Panel Data State-Space Frameworks: An Application to the Feldstein–Horioka Puzzle

Computational Economics volume 56, pages 87–114 (2020)Cite this article

Abstract

In this paper, we develop a very flexible and comprehensive state-space framework for modeling time series data. Our research extends the simple canonical model usually employed in the literature, into a panel-data time-varying parameters framework, combining fixed (both common and country-specific) and varying components. Under some specific circumstances, this setting can be understood as a mean-reverting panel time-series model, where the mean fixed parameter can, at the same time, include a deterministic trend. Regarding the transition equation, our structure allows for the estimation of different autoregressive alternatives, and include control instruments, whose coefficients can be set-up either common or idiosyncratic. This is particularly useful to detect asymmetries among individuals (countries) to common shocks. We develop a GAUSS code that allows for the introduction of restrictions regarding the variances of both the transition and measurement equations. Finally, we use this empirical framework to test for the Feldstein–Horioka puzzle in a 17-country panel. The results show its usefulness for solving complexities in macroeconomic empirical research.

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Notes

  1. The code can be downloaded at http://econweb.ucsd.edu/~jhamilto/KALMAN.ZIP.

  2. Excellent textbook treatments of state-space models are provided in Harvey (1993, 1989), Hamilton (1994a, b), West and Harrison (1997), or Kim and Nelson (1999), among others. They all use different conventions, but the notation used here is based on James Hamilton’s, with slight variations.

  3. A very simple example proposed by Faragher (2012) is what happens to the trajectory of a rocket when fuel injection is activated during flight.

  4. Parameter instability in dynamic econometric models has often been integrated in the form of structural change models (see Perron 1989). Markov-switching models, as in Hamilton (1989), constitute a less ambitious approach, despite the advantage of easily allowing the parameters to change gradually over time. The simplest TVP framework can be estimated by rolling regressions, while the Kalman filter is the most popular framework due to its simplicity. Our proposal, compared to the other alternatives, has the advantage of implementing a smooth time-varying transition overtime instead of discreet changes.

  5. See Rosenberg (1973), Hsiao (1974), Hsiao (1975), Ck and Zellner (1993), Swamy and Mehta (1977), Zellner et al. (1991) among others.

  6. Also known as “dispersed coefficient models” (Schaefer et al. 1975) or “mean reverting models”.

  7. Ohlson and Rosenberg (1982) formulation of the MRV model that allows for both autocorrelated (predictable) and random (unpredictable) variation within the same model, combining mean reversion to a random mean for parameters, where \(\left( \beta _{t}-\bar{\beta }\right) -\xi _{t}={\varPhi }\left[ \left( \beta _{t-1}-\bar{\beta }\right) -\xi _{t}\right] +\nu _{t}\). In this model, the constant “true” mean of the parameter, \(\bar{\beta }\), is affected by a random variable, \(\nu _{t}\), with zero mean and a variance \(\lambda \) (if \(\lambda =0\), then this model becomes the MRV presented above). \(y_{t}=\left( \bar{\beta }+\xi _{t}\right) x_{t}+\left[ \beta _{t}-\left( \bar{\beta }+\xi _{t}\right) \right] x_{t}+\omega _{t}\). This model allows for a heteroskedastic variance in the measurement equation, induced by the tendency of the parameter’s mean to fluctuate randomly about its “true” value, with \(u_{t}=x_{t}\xi _{t}+\omega _{t}\).

  8. Note that our Gauss code allows for multiple common-factors as well as the inclusion of potential restrictions on them.

  9. Increasing signal-to-noise ratio would weigh the observation heavier in the correction equations of the Kalman filter.

  10. See Wyplosz (1999) , Pagoulatos (1999) and Camarero et al. (2002) for a detailed description of this process.

  11. Exhaustive reviews can be found at Coakley et al. (1998) or Apergis and Tsoumas (2009).

  12. See also Tw (2002), Telatar et al. (2007), Mastroyiannis (2007), Özmen and Parmaksiz (2003) Kejriwal (2008) or Ketenci (2012).

  13. The predictions of the partial equilibrium inter-temporal theory of the current account refers to idiosyncratic components (country-specific or regional shocks) of saving and investment rates that, as they do not affect all countries similarly, are unlikely to generate imbalances in the world capital market.

  14. Examples of this are Glick and Rogoff (1995) and Ventura (2003).

  15. Harberger notes that the difference between gross domestic saving and investment to GDP has greater variability and larger absolute value for small countries than for large ones.

  16. An alternative variable for global risk aversion is the CBOE Volatility Index, known by its ticker symbol VIX; this variable was not available for the whole period. Note that CBOE VIX measures the stock market’s expectation of volatility implied by S&P 500 index options, calculated and published by the Chicago Board Options Exchange. Moreover, although the literature finds a relevant role for both proxies, while BAA spread measures risk appetite, a variation in implied volatility on a market may stem from a change in the quantity of risk on this market and not necessarily from a change in the investor’s risk aversion.

  17. The data has been obtained from https://data.worldbank.org/. Gross fixed capital formation (formerly gross domestic fixed investment) includes land improvements (fences, ditches, drains, and so on); plant, machinery, and equipment purchases; and the construction of roads, railways, and the like, including schools, offices, hospitals, private residential dwellings, and commercial and industrial buildings. According to the 1993 SNA, net acquisitions of valuables are also considered capital formation. Gross domestic savings are calculated as GDP less final consumption expenditure (total consumption). As in the literature, both variables have been expressed as a percentage of GDP.

  18. Adapting Bai and Perron (2003) methodology to a panel data framework.

  19. Following Bai and Ng (2004) and Moon and Perron (2004).

  20. An important part of the literature on time-varying parameter models would make this choice.

  21. See Bai and Carrion-i Silvestre (2009) for details.

  22. See Zivot and Andrews (2002), Perron (1997), Vogelsang and Perron (1998), Perron and Vogelsang (1992a, b), among others.

  23. The conventional wisdom is for capital to flow in the opposite direction: insufficient domestic saving is augmented by foreign saving to match investment demand, i.e., capital flows in, and this should be reflected in a current account deficit.

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Acknowledgements

The authors are indebted to James D. Hamilton and J. LL. Carrion-i-Silvestre for providing them with the Gauss codes to implement some of the tests used in the paper. They also thank comments and suggestions from participants in the 5th ISCEF Symposium 2018 (Paris).

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Authors and Affiliations

  1. INTECO Joint Research Unit, Department of Economics, Universitat Jaume I, Campus del Riu Sec, 12071, Castellon de la Plana, Spain

    Mariam Camarero

  2. Faculty of Economics and Management, Catholic University of Valencia, 34 Calle Corona, 46003, Valencia, Spain

    Juan Sapena

  3. INTECO Joint Research Unit, Department of Applied Economics II, University of Valencia, PO Box 22.006, 46071, Valencia, Spain

    Cecilio Tamarit

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  1. Mariam Camarero
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The authors gratefully acknowledge the financial support from AEI/Ministerio de Economía, Industria y Competitividad (MINEIC) and FEDER Project ECO2017-83255-C3-3-P and the Generalitat Valenciana (PROMETEO/2018/102 and GV/2017/052). Authors are also indebted to the Chair “Betelgeux” for a Sustainable Economic Development, for its specific funding of this research. This paper has been developed within the research thematic network ECO2016-81901-REDT financed by MINEIC. The usual disclaimer applies.

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Camarero, M., Sapena, J. & Tamarit, C. Modelling Time-Varying Parameters in Panel Data State-Space Frameworks: An Application to the Feldstein–Horioka Puzzle. Comput Econ 56, 87–114 (2020). https://doi.org/10.1007/s10614-019-09879-x

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Keywords

  • Feldstein–Horioka puzzle
  • Panel unit root tests
  • Multiple structural breaks
  • Common factors
  • Kalman Filter
  • Time varying parameters

JEL Classification

  • C23
  • F32
  • F36