## The occurrence of the bubbles in question.

The Bubbles ?n (in) Turkish Liras/Dollar Exchange Rate and The Effects of Political and Country Risks: New Evidence From Sequential ADF Tests

Abstract

Thip (This) paper investigates the presence of bubbles in exchange rate market in Turkey and the effects of both political and country risks on so-called bubbles over the period of 1999:M1-2016:M12. We applied sequential ADF tests to detect the bubbles and binary logit model to indicate (show) the effects of political and country risks. We found evidence of explosive fundamental in ratios of exchange rate to non-traded and traded goods. The higher political and country risks increase probability of occurrence of the bubbles in question.

Keywords: Rational bubbles, Exchange rates, Political, Country risks

Jel Codes: C1, F3, B22

Introduction

Rational bubbles in financial markets are of great importance in terms of (in) whether investors give the right decision and accordingly take a position towards risk as well as its effect on financial crises (crisis). Bubbles are excessive increases in asset prices. Brunnemeier (Brunnermeier) (2009) states that bubbles are connected with abrupt asset price inreases (increases) followed by a collapse (collapse). He also expresses that so-called bubbles can occur if financial market participants hold the asset since they expect to sell this asset at a higher price than the others although the asset’s price exceeds its fundamental value.

Fluctuations in asset (an asset) prices impact seriously economy as a whole in terms of (in) real allocation. One of the financial assets is exchange rate. This means that it is identified by current and expected values of Fundamentals. Therefore, academicians and policy makers try to generate models which predict exchange rate behavior (Obstfeld and Rogoff, 1996).

In the literature the studies examining the bubbles in exchange rates are rather extensive. Some of these studies found a (an) evidence of bubbles in exchange rates, others indicated that there are not bubbles. Some researchers (Engel, 1994; Kirikos, 1998; Van Norden and Schaller, 1993; Maldonado et al., 2012; Panopoulou and Pantelidis, 2015) investigated presence of bubbles using Markov Switching model. They set up two-regimes and three-regimes model regarding to (regarding or regard to) the future value of exchange rates to detect the bubbles. However, new methods have been generated to reveal presence of rational bubbles. One of these methods is sequential ADF test including RADF, SADF and GSADF tests. Some of studies (Some of the studies or some studies) investigating bubbles in exchage rates by using GSADF test are Bettendoff and Chen (2013), Jiang et al. (2015), Hu and Oxley (2017).

Purpose of this study is to detect bubbles in Turkish liras/USD exchange rate through right-tailed unit root tests and to indicate the effects of political risk and country risk indices on the exchange rate bubbles. We contribute to the literature in two ways. Firstly, we applied a new method developed by Phillips et al. (2011) to show presence of bubbles in Turkish liras/USD exchange rate. Secondly, we analyzed the effects of both political and country risks on bubbles in Turkish liras/USD exchange rate. Therefore, we aim to fulfill that gap in the literature.

Data and Methodology

In this study we purpose to determine a bubble in the bilateral exchage (exchange) rates between Turkey and United States and to analyze effects of political and country risks on a bubble in question. Thus, we used Turkish Lira/US dollar exchange rate, political risk index and country risk index obtained from Datastream. We also used consumer price index (CPI) and producer price index (PPI) drawn from IMF International Financial Statistics (IFS) database. The data sample covers 216 monthly observations over the period of 1999M1-2016M12. All variables are in a logarithm.

As indicated by Bettendorf and Chen (2013) and Jiang et. al. (et al.) (2015), economic fundamental relating to nominal exchange rate is considered as the price differential (f_t).

f_t=p_t-p_t^*

where p_t and p_t^* respectively exhibit the domestic and foreign price indices in a logarithm. Engel (1999) distinguish goods as traded and non-traded to demonstrate the domestic price index.

p_t=(1-?) p_t^T+?p_t^N

where p_t^T, p_t^N and ? respectively exhibit the traded and non-traded goods in logarithm and the share of non-traded goods component. Similarly, the price differential (f_t) can be rewritten as the combiantion of traded goods and nontraded goods.

(p_t-p_t^* )=(p_t^T-p_t^(T*) )+?(p_t^N-p_t^T )-?(p_t^(N*)-p_t^(T*) )

where first term on the right side of this equation represents the traded goods component (f_t^T ) and second term is the non-traded goods component (f_t^N ).

The producer price index and consumer price index are frequently used as the price level of traded goods and the price level of non-traded goods, respectively.

f_t^T=ln(?PPI?_t )-ln(?PPI?_t^* )

f_t^N=ln(?CPI?_t )-ln(?PPI?_t )-(ln(?CPI?_t^* )-ln(?PPI?_t^* ))

In this study we used recursive right-tailed unit root tests to determine bubbles in nominal Turkish Lira/USD exchange rate s_t and the ratio of the exchange rate to the two types of economic fundamentals.

Right-tailed unit root test including RADF, SADF and GSADF was developed by Phillips et al. (2011). Right-tailed unit root tests are especially used in determining exploding series or slightly exploding series. For example, Diba and Grossman (1988) have applied right-tailed unit root tests for precisely sampled data to find financial bubbles. Phillips et al. (2011) and Phillips and J.Y. (2011) have suggested applying right-tailed unit root tests to recursive sub-samples. The formulation of null and alternative hypothesis and regression model specification are of importance in both left-tailed and right-tailed unit root tests (Phillips, et al., 2014).

One of the right-tailed unit root tests is SADF (sup ADF) test. SADF test is based on recursive estimation of ADF model, and it is acquired as sub-value of the corresponding ADF statistic sequence. In this case, the window size rw expands to 1 from r0 with the result that r0 is the smallest sample window width fraction and 1 is the largest one in the recursion. Initial point r1 constant at zero that’s why the end point of each sample equals to rW and changes to 1 from r0 (Phillips, et al., 2013: 8).

For each xt time series, ADF test is sensitive to the alternative of exploded root (right-tailed). The following autoregressive specification is estimated with least squared (OLS):

x_t=?_x+?? x?_(t-1)+?_(j=1)^J???_j ?x_(t-j) ?+?_(x,t),?_(x,t)~NID(0,?_x^2)

For given some values of lag parameter J, NID is independent and has normal distribution. In unit root tests, null hypothesis is H_0=?=1 and right-tailed alternative hypothesis is H_0=?>1. In recursive regressions, above model repeatedly is estimated increasing one observation at each try.

?ADF?_r?(?_0^r??W ? dW?)/?(?_0^r??W ?^2)??^(1/2)

?sup?_(r?r_0,1) ?ADF?_r??sup?_(r?r_0,1) (?_0^r??W ? dW?)/?(?_0^r??W ?^2)??^(1/2)

Here, W is Standard Browian (Brownian) motion and W ?(r)=W(r)-1/r ?_0^1?W is reduced Browian (Brownian) motion (Phillips, et al., 2011: 206-207).

As SADF test, GSADF test based on the idea of recursively running ADF test on sub-samples as well. Instead, sub-samples are more extensive in comparison with SADF. Also, GSADF test allows the initial point r1 to vary within a feasible sequence on account of switching the end of point of the regression r2 from r0 to 1. GSADF statistic is stated as the largest ADF statistic over all feasible sequences of r1 and r2. GSADF test as follows (Phillps (Phillips), et al., 2013: 10).

GSADF(r_0 )=(sup)?(r_2?)?r_1???0,r_2-r_1? ??r_0,1? ?{?ADF?_(r_1)^(r_2 ) }

Empirical Results

Detected Bubbles in Exchange Rate

Firstly, we focuse (focus) on indicating the bubbles in Turkish liras/USD exchange rate. For this purpose, we applied right-tailed unit root tests. In the study, exchange rate was embraced in three ways and thus, nominal exchange rate, the ratio of exchange rate to the traded goods and the ratio of exchange rate to non-traded goods were used. The results for so-called exchange rates are exhibited in Table 1.

Table 1

The Results of RADF, SADF and GSADF Tests for Bubbles in Turkish Liras/USD Exchange Rate

Variable Sample: 1999 M1-2016 M12

RADF SADF GSADF

s_t 0.852718** -0.263644 0.852718

s_t-f_t^N 0.899056** -0.445028 0.899056

s_t-f_t^T 0.804161* -0.977495 0.804161

CV 1% -0.162387 0.870903 1.657709

CV 5% -0.815928 0.463835 1.233683

CV 10% -1.143328 0.263722 1.020339

Note: s_t,s_t-f_t^Nand s_t-f_t^T state respectively nominal exchange rate, the ratio of the exchange rate to non-treded (non-traded) goods and the ratio of the exchange rate to traded goods.The initial window size is 29 observations for RADF, SADF and GSADF tests. Critical values relating to RADF, SADF and GSADF tests are obtained from Monte-Carlo simulations with 1000 replications. ***,**,* show respectively significance at 0.01, 0.05 and 0.1 levels.

As examined Table 1, RADF (Rolling ADF) test statistic rejected null hypothesis that there is no explosive behavior at significant level 5%. However, this result could be deceptive in case that periodically collapsing bubbles ocur so-called period. Thus, the SADF and GSADF test results should be considered. According to SADF and GSADF test statistics, there is no explosive behavior in nominal Turkish Lira/USD exchage rate in the mentioned period.

According to RADF test statistics, there is explosive behavior for the ratio of the exchange rate to the non-traded goods fundamental s_t-f_t^N. However, we don’t find an evidence about explosiveness for s_t-f_t^N. Similarly, the ratio of the exchage (exchange) rate to the traded goods fundamental s_t-f_t^T don’t show explosive behavior.

Figure 1

The nominal Turkish Lira/USD exchange s_t and its corresponding squence (sequence) of ADF statistics

(b)

Note: Panel (a) shows SADF test and Panel (b) shows GSADF test.The red line represents the 5% critical values

Figure 2

The nominal Turkish Lira/USD exchange s_t-f_t^N and its corresponding squence (sequence) of ADF statistics

(b)

Note: Panel (a) shows SADF test and Panel (b) shows GSADF test.The red line represents the 5% critical values

Figure 3

The nominal Turkish Lira/USD exchange s_t-f_t^T and its corresponding squence of ADF statistics

(b)

Note: Panel (a) shows SADF test and Panel (b) shows GSADF test.The red line represents the 5% critical values

Figure 1 plots log nominal Turkish Lira/USD exchage (exchange) rate and the corresponding sequence of ADF statistics. Panel (a) and Panel (b) show, represently, SADF and GSADF tests. In Figure 1, it is seen that there is no evidence towards explosive behavior the mentioned exchage rate. Figure 2 plots the ratio of nominal Turkish Lira/USD exchage (exchange) rate to non-traded goods and the corresponding sequence of ADF statistics. As seen Figure 2, SADF and GSADF sequences exhibit explicitly presence of bubbles. Firstly, Transition to the Strong Economy Program was carried out in the periods of 2002-2004. In this period, Turkish economy transited to floating exchange rate policy within stand-by agreement made with IMF. Secondly, global financial crisis occured (occurred) in United States and sovereign debt crisis in Europe lead to appreciate excessively nominal Turkish Lira/USD exchage (exchange) rate. Figure 3 plots the ratio of nominal Turkish Lira/USD exchage (exchange) rate to traded goods and the corresponding sequence of ADF statistics. Accordingly, explosive fundamental in the ratio of exchange rate to traded good is seen in the period of 2001-2002 when brusted out (brust out) “The Feburary (February) 28 Crisis” in Turkey.

The Effects of Political and Country Risks

We utilized from logit model to execute the effects of political and country risk on the ratio of exchange rate to both non-traded and traded goods. For this purpose, we generated dummy variables representing the bubble dates. Logit model estimation results are reported in Table 2.

Table 2

Logit Model Estimation Results

Variable Sample: 1999 M1-2016 M12

s_t-f_t^N s_t-f_t^T

Coefficients Marjinal (Marginal) Effects Coefficients Marjinal (Marginal) Effects

Constant -26.33901***

(4.52976) -2.632285***

(2.697115)

Political Risk 0.2247459***

(.06318) 1.252005

(.0791016) 0.0152754***

(.053384) 1.015393

(0.0542057)

Country Risk 0.2456646***

(.0690919) 1.278471

(.088332) 0.3847405

(0.0760321) 1.469233*** (0.1117089)

Log-likelihood -81.775707 -74.939289 -68.445981 -85.150678

LR 31.09*** 44.76*** 33.49*** 33.49***

Note: s_t-f_t^Nand s_t-f_t^T state respectively the ratio of the exchange rate to non-treded (non-traded) goods and the ratio of the exchange rate to traded goods. ***,**,* show respectively significance at 0.01, 0.05 and 0.1 levels. The values in paranthesis (parenthesis) indicate standard errors.

According to Table 2, increases in both political and country risks lead to rise the ratio of exchange rate to non-traded goods. However, country risk enhances the ratio of exchange rate to traded goods while political risk diminshes (diminishes) the mentioned ratio.

Conclusions

In this paper we aim to presence of bubbles in Turkish liras/dollar exchange rate using sequential ADF tests by Phillips et. al. (et al.) (2011a,b). Although we found evidence related to explosive behaviour (British (behaviour), American (behavior) in ratios of exchange rate to both non-traded and traded goods, we didn’t encounter explosiveness in nominal exchange rate. Our results show that prices of non-traded and traded goods have important effect exchange rate movements. We also investigated how political and country risk impact exchange rate bubbles. The results show that probability of apperance (appearance) of bubbles in exchange rate rise as political and country risks increase. These findings are of importance for policy makers and practitioners.