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Empirical Economics

Erschienen in:

06.01.2016

Real interest rates: nonlinearity and structural breaks

verfasst von: Tolga Omay, Ayşegül Çorakcı, Furkan Emirmahmutoglu

Erschienen in: Empirical Economics | Ausgabe 1/2017

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Abstract

Real interest rate is a crucial variable that determines the consumption, investment and saving behavior of individuals and thereby acts as a key policy tool that the central banks use to control the economy. Although many important theoretical models require the real interest rates to be stationary, the empirical evidence accumulated so far has not been able to provide conclusive evidence on the mean reverting dynamics of this variable. To resolve this puzzle we re-investigate the stochastic nature of the real interest rates by developing unit root tests for nonlinear heterogeneous panels where the alternative hypothesis allows for a smooth transition between deterministic linear trends around which stationary asymmetric adjustment may occur. When the newly developed panel unit root tests are applied to the real interest rates of the 17 OECD countries, we were able to uncover overwhelming empirical support in favor of mean reversion in the short-run and long-run real interest rates. Therefore, these results show that the conclusions drawn from a miss-specified test that ignores the presence of either nonlinearity, structural breaks or cross sectional dependence can give quite misleading results about the stochastic behavior of the real interest rates.

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See Neely and Rapach (2008) for a comprehensive survey of this literature.

In order to consider smooth breaks in the deterministic components of a series, many studies have alternatively developed unit root tests based on Gallant’s (1981) flexible Fourier form. However, as discussed in Omay et al. (2013), the smooth transition methodology has many advantages over the Flexible Fourier form (see also Omay 2015). Thus, in this article we have employed the smooth transition model to handle the structural shifts in the data. Moreover, the dummy variable based structural break unit root testing procedures skip the idea of heterogeneity. The most important conclusion that can be drawn from the simulation studies carried out in this study and the ones in Omay et al. (2013) is that if the panel structural break tests do not estimate the break point heterogeneously, they are insufficient to test the real-life data. Fortunately, the proposed tests in this study have proven to be quite successful in both heterogeneous and homogeneous parameter settings via the Monte Carlo simulation studies.

There are other methods to remedy the CSD problem such as the common correlated effect (CCE) estimator proposed by Pesaran (2006, 2007). The CCE estimator augments the panel regressions by cross-sectional averages of lagged first-difference terms, and this approach is valid for panels where N and T are of the same order of magnitudes (Pesaran 2007) unlike the principal component approach that requires \(N/T\rightarrow 0\). Although Kapetanios et al. (2011) have shown that the CCE estimators have better small sample properties than the factor-based estimators, using the CCE estimator in our present context is quite troublesome since our testing procedure utilizes an indicator function that may produce problems while taking the averages of the independent variables. Hence, we prefer to use the bootstrap methodology which also solves the CSD problem in a multifactor error structure. Besides, the bootstrap methodology is shown to be a better remedy for smooth structural break panel unit root tests with CSD, as opposed to the CCE methodology (Omay et al. 2013).

For further discussions see LNV and Sollis (2004).

The critical values of \(\bar{{t}}_{2p,\alpha }\), \(\bar{{F}}_{2p,\alpha }\), \(\bar{{t}}_{3p,\alpha }\), and \(\bar{{F}}_{3p,\alpha }\) for Models B and C are available upon request.

For two different degrees of cross-sectional dependence, the average pair-wise correlations are computed as 0.01 and 0.816 for \(N=10\), respectively.

For all Monte Carlo simulations, since random parameter values are used, the whole experiment is simulated 5 times and the mean of the empirical sizes and powers obtained from these simulations are reported for different values of N and T. All programs are available upon request in both MATLAB and RATS formats.

As an anonymous referee has, Chang’s (2004, page 277–278) DGP causes there to be weak cross-sectional dependence. Therefore, using Pesaran (2007)’s one factor DGP, the size and power analysis of the tests are conducted only for the values of \(\lambda _i\sim i.i.d.U[1,4]\) that generate high cross-sectional dependence. In this situation, the average pair-wise correlation is computed as 0.816 for \(N=10\). All size analysis are available upon request for Model B and C for Tables 2, 3 and 4.

Leybourne et al. (1998) pointed that Model A is capable to proxy a function containing a linear trend with certain combinations of parameters. In this context, the IPS test with intercept and linear trend is a natural competitor to our proposed \(\bar{{t}}_{1p,\alpha }\) statistic.

A detailed power analysis has been conducted by OHS. For further details refer to Omay et al. (2013).

The data used in this study are retrieved from the Global VAR modeling (GVAR) database, which is publicly available at: https://sites.google.com/site/gvarmodelling/data. A detailed description of the data and sources are also included.

See Neely and Rapach (2008) and the references therein for a discussion of the further challenges involved in econometrically forecasting inflation.

The TAR model estimates are available upon request.

As it can be seen from the second column, we have also found out that 2 out of 17 countries have time varying mean structure, but do not have a significant threshold parameter. Therefore, we neither classify them as having sharp nor smooth structural breaks. It is better to indicate this type of estimates as nonlinear trend. Besides, these two countries, namely Austria and Germany, have significant transition speed parameters. This corroborates the fact that these countries have nonlinear trends.

Also Enders and Granger (1998) have proposed two alternative M-TAR unit root tests. One explicitly estimates the threshold parameter, while the other assumes it to be equal to zero. On the other hand, Sollis (2004) combined LNV structural de-trending with the EG-TAR type of unit root tests, which set the threshold parameter exogenously to zero. This type of structural de-trending (nonlinear attractor) also has a secondary effect. It automatically locates the threshold parameter of the TAR model to zero. Therefore, the threshold parameters obtained in the third column of Table 8 show us that extending Sollis (2004) directly to a panel stetting is a true strategy to follow rather than explicitly finding the threshold level as in Chan (1993).

These 3 countries are indeed found to be nonstationary with the implementation of the PLNV test (Table 7).

Applying the panel unit root tests with the sequential panel selection method (SPSM) proposed by Chortareas and Kapetanios (2009) has allowed us to distinguish the panel into its stationary and nonstationary components. For further technical details on this methodology refer to Chortareas and Kapetanios (2009). On the other hand, recently Costantini and Lupi (2014) have investigated the performance of the SPSM proposed by Chortareas and Kapetanios (2009). The authors suggest that there are some classes of panel unit root tests that are better suited than others to be applied jointly with the SPSM such as the IPS test. Besides, they also recommend that for the Chortareas and Kapetanios (2009) methodology to be used the sample in the investigation must be fairly large and most of the series in the sample should be I(0). Fortunately, our sample fulfills these criteria. For further discussion see Costantini and Lupi (2014).

Following Schaling (2004), the long-run equilibrium value in our model is set to zero.

For nonlinear optimal monetary policy rules see Schaling (2004) and Dolado et al. (2005); and the references therein.

Inflation targeting here is interpreted in strict terms in the sense that it refers to the case in which the central bank only aims to minimize only deviations of inflation from its assigned target. With no weight given to output stabilization in the central bank’s loss function, the real interest rate becomes a nonlinear function of the deviation of the inflation rate from its target (i.e., inflation gap) and the output gap. Thus, a central bank with strict inflation targeting still responds to output gaps. See Schaling (2004) for further details.

Flexible inflation targeting refers to the case in which the goal of monetary policy is to stabilize not only inflation around the target level (as in the case of strict inflation targeting) but also output around its own target level. This causes again the optimal real interest rate to be a nonlinear function of the deviation of the inflation rate from its target and the output gap. See Schaling (2004) for further details.

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Titel: Real interest rates: nonlinearity and structural breaks
verfasst von: Tolga Omay
Ayşegül Çorakcı
Furkan Emirmahmutoglu
Publikationsdatum: 06.01.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 1/2017
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-015-1065-1

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