The Feldstein–Horioka puzzle in South Africa: A fractional cointegration approach

ABSTRACT

The Feldstein–Horioka (FH) puzzle, that is the strong correlation between saving and investment in a world where obstacles to capital mobility are limited, has been studied extensively since it was exposed in 1980. Even though the theoretical and empirical literature has examined many of its potential causes, the puzzle persists. This paper aims at shedding further light on the issue by investigating the relationship between saving and investment in South Africa since 1946 using fractional integration and cointegration techniques to account for high persistence in the series. We find evidence of fractional cointegration between saving and investment, indicating some degree of persistence in the gap between the two variables. We also find a structural break in saving and investment ratios to GDP around 1980, which roughly coincides with the start of a financial deregulation process in South Africa. While fractional cointegration holds before the break, it does not thereafter. In other words, while the FH puzzle is observed before the start of financial deregulation, it subsequently disappears. This suggests that financial deregulation may have loosened the link between saving and investment.

KEYWORDS:

• Feldstein–Horioka puzzle
• long memory
• fractional cointegration
• South Africa

JEL Classifications:

• C22
• C32
• E21
• E22
• F41

Acknowledgements

We would like to thank the Editor, Professor David Giles, and two anonymous referees for many helpful comments.

Disclosure statement

The views expressed in this paper are those of the authors and do not necessarily reflect those of the Organisation for Economic Co-operation and Development (OECD) or the governments of its member countries.

Notes

1. As an illustration, the ratios of exports and imports of goods and services to GDP rose, respectively, from 26.9% to 31% and from 24.5% to 33.2% between 2003 and 2013.

2. It must be pointed out that quarterly data on these two variables are also available, starting at 1960:Q1. However, we chose to use annual data, as it allows us to cover a longer time span.

3. Available at: www.resbank.co.za, with codes KBP6286J (savings to GDP) and KBP6282J (investment to GDP).

4. Fixed assets include 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. Inventories are stocks of goods held by firms to meet temporary or unexpected fluctuations in production or sales.

5. As is standard practice in time-series econometrics, we also analyzed the integration properties of the two series using various unit root tests, starting with the standard linear tests: Augmented Dickey Fuller (ADF, 1979), GLS-detrended Dickey-Fuller (Elliot, Rothenberg, and Stock 1996), Phillips–Perron (Phillips and Perron 1988), Kwiatkowksi, Phillips, Schmidt, and Shin (KPSS 1992), Ng and Perron (NP 2001), and the recently developed test of Müller and Watson (2008) for low-frequency data. Then, we conducted four unit root tests with one (Zivot and Andrews 1992), two (Lumsdaine and Papell 1997; Lee and Strazicich 2003), and an unknown (Enders and Lee 2012) number of structural breaks. Also, the Leybourne, Kim, and Taylor (2007) unit root test of change in persistence was used. Furthermore, we also carried out two non-linear unit root tests proposed by Kapetanios, Shin and Shell (KSS 2003), and Sollis (2009). Finally, we also combined the KSS test with the Enders and Lee (2012) tests to accommodate for non-linearity due to regime switching and structural breaks. The results were found to be inconsistent, with degrees of integration changing across the type of unit root tests. Due to the lack of robustness amongst the various unit root tests and the fact that unit root tests have low power when a series is characterized by a fractional integration process (Ben Nasr, Ajmi, and Gupta 2014), we decided to use tests of fractional integration to determine whether a series is stationary or not. The results of the various unit root tests conducted are, however, available upon request from the authors.

6. See Gil-Alana (2004) for approximations of ARMA structures with the model of Bloomfield (1973) in the context of fractional integration.

7. Based on the nonstationary nature of the series, the analysis of fractional integration is conducted on the first differenced data, adding then 1 to the estimated values of d.

8. We use here a procedure suggested by Gil-Alana (2003) and that is based on the tests of Robinson (1994). It follows a similar methodology to the one used in Engle and Granger (1987) though extended to the fractional case.

9. We use here finite sample critical values obtained by simulation (see Gil-Alana 2003). Note that the test statistic is evaluated based on the estimated residuals from the cointegrating regression and, therefore, in finite samples, the residuals series might be biased toward stationarity and, thus, we would expect the null hypothesis to be rejected more often than suggested by the nominal size of Robinson's (1994) tests. A similar problem arises in Engle and Granger (1987) and Cheung and Lai (1993) when testing cointegration.

10. See Hamming (1973) and Smyth (1998) for a detailed description of these polynomials.

11. Note that the wide confidence intervals are a consequence of the small sample sizes used for the analysis in this sub-sample.

12. The fact that the break dates of the two series differ from each other by a year can be considered as a preliminary evidence against the F–H puzzle – something we confirm more formally using statistical tests for the second sub-sample.

13. As a robustness check, we also implemented the autoregressive distributed lag (ARDL) model, also popularly called the bounds testing methodology of Pesaran and Shin (1999) and Pesaran, Shin, and Smith (2001). The advantage of this approach is that, we could test for cointegration without pretesting for the order of integration of the individual series. Our results, in general, were in line with those obtained under the fractional cointegration approach. In other words, we could detect cointegration only at the 10% level of significance (based on small-sample critical values developed by Narayan (2005), but not under the critical values of Pesaran, Shin, and Smith (2001)) for the full and the first sub-sample, but not the second sub-sample. In addition, when we repeated the tests with dummy variables for the year 1979, 1980, and then 1979 and 1980, results were mixed. Specifically, in the first case, we obtained cointegration again at the 10% level under the Narayan (2005) critical values, but an inconclusive result under the 5% critical values of Pesaran, Shin, and Smith (2001), since the F-statistic fell in between the critical values for I(0) and I(1). In the second case, results were inconclusive based on the Narayan's (2005) critical values at the 10% level, but implied cointegration under the Pesaran, Shin, and Smith (2001) critical values. Finally, when we allowed two breaks, the results were similar to the full-sample case without breaks, as discussed above in this endnote. So, overall, with or without breaks, even if we consider cointegration to hold, the evidence in favour of the F–H puzzle is, at best, weak. The fact that we detect nonlinearity in the S-GDP series and not in the I-GDP series could also be driving this weak evidence in the linear framework of the ARDL model.