Exchange rate and relative price variability: Linear and nonlinear time series analysis in Turkey

For national central banks that have a developed and developing attitude towards stability, high or instable price rise is the major issue under investigation in literature. Empirically, the effects of relative price variability on social welfare have been studied and through the integration of economies with global markets, the interaction between the relative price variability with rate of exchange has come to fore. The main objective of this study is to study relative price variability and exchange rates as well as to make comparisons between linear and nonlinear time series. Therefore, it is aimed to compare the long term relations obtained from linear time series, which have been created under linearity assumptions, and the results obtained through co-integration and causality analysis when causation and linearity are abandoned.By using real exchange rate of 1994:1-2010:5 term, obtained from Data Distribution System of Central Bank (DDSCB), and 445 sub-components based on the same year- 1994 obtained from Turkish Statistical Institution (TÜİK), relative price variability indexed according to 13 basic expenditure group has been calculated and it has been isolated from seasonality according to Census-X12 by taking into consideration its natural logarithm. In the first section of the study, it has been tried to build a theoretical framework between relative price variability and real exchange rate has in terms of economics theory.The results of linear time series analysis are included in the second section focused on econometric application. In this section, where linear time series applications are carried out, unit root tests are done. Stationarity of series is tested by using Augmented Dickey-Fuller, Dickey-Fuller based GLS, Ng-Perron and KPSS tests developed by Dickey and Fuller (1981), Elliot, Rothenberg and Stock (1996), Ng-Perron (1996, 2001) and Kwaitkowski, Phillips, Schmidt and Shin (1992), respectively. It has been concluded that series are not stationary on level values. In order to indicate the availability of structural breakage during the same period, for a single endogenous breakage Zivot-Andrews (1992) , for double endogenous breakages Lee-Strazicich (2003) unit root tests and structural break tests, developed by Bai-Perron (2003a, 2003b). Zivot-Andrews (1992) unit root test finds structural breakage for real exchange rate June 1999 in Model A, and for relative price variability February 2001 in Model C. Also Lee-Strazicich (2003) test implies that there are structural breaks for real exchange rate in January 2000 in Model A and for relative price variability in August 2001. Lastly Bai-Perron (2003a, 2003b) test finds structural break for real exchange rate in November 1999 and for relative price variability in June 1999 and May 2005. As a result of cointegration analysis with structural breaks which developed by Kejriwal (2008) and Kejriwal and Perron (2009) to determine long term relationship between variables by considering stationarity level, structural break dates are November 2000, January 2004 and August 2007 and these structural break dates are used to cut the period into parts. When we take into account identification parameter, we find a significant relationship between relative price variability and real exchange rate for periods between January 1994 and November 2000 and December 2000 and January 2004. We employed Granger type linear causality tests developed by Toda ? Yamamoto (1995) and Dolado ? Lütkepohl (1996) to identify the direction of causality. Causality analysis are made for whole period and also for each sub-period identified by cointengration analysis with structural breaks which developed by Kejriwal (2008) and Perron (2009). According to Dolado ? Lütkepohl Granger type causality analysis results, there are only causal realtionship between variables running from relative price variability to real exchange rate for periods 1994: 1- 2000: 11 and 2000: 12 ? 2010: 5.In order to understand asymmetric relation between real exchange rate and relative price variability, we apply non-linear times series analysis in the last section of empirical applications. In this context, initially, we find threshold value and then we use threshold value to find expansion and contraction regimes by employing self-exciting threshold autoregressive (SETAR) analysis. Then we use smooth transition autoregressive model (STAR) and we construct eight different models with the possibility of being logistic or exponential of transition function. Because of absence of economics theory explaining whether the relation between relative price variability and real exchange rate is logistic smoothing threshold autoregressive (LSTAR) or exponential smoothing threshold autoregressive (ESTAR) model, we employee ESTAR model due to data used in the analysis. Parameters belonging expansion and contraction regimes are obtained by ESTAR model. By using non-linear impulse response functions of ESTAR model, positive and negative shocks are captured in the expansion and contraction regimes. Linearity of series is tested by BDS test developed by Brock, Dechert ve Schienkman (1987) and Brock, Dechert, Schienkman and LeBaron (1996). As a result of this test, alternative hypothesis is accepted and results imply that both series are non-linear. According to results of non-linear threshold cointegration test developed by Hansen and Seo (2002), null hypothesis is accepted and there is a long term linear cointegration relationship between variables. Also we employee non-linear Granger type causality analysis developed by Himestra-Jones (1994) and Diks-Panchenko (2005, 2006) to find assymetric causality between variables.