Unit root test results.
Abstract
Inflation uncertainty maintains its importance in emerging economies as well as in others. Increases in the level of inflation uncertainty constitute an important risk factor by affecting macroeconomic variables in the markets that are sensitive to price changes. The stabilization programs implemented in Turkey during 1980–2003 could not reduce the sensitivity of economic structure to inflationary shocks. Between 2003 and 2015, changes occurred, switching from high inflation to the singledigit inflation rates, in Turkey with transition to the inflationtargeting regime. Within the scope of this study, the effect of inflation uncertainty on inflation, economic growth and selected monetaryfiscal policy variables was examined using multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) models. The dynamic conditional covariance model is designed to reflect the strong timedependent correlation structure. While the inflationtargeting regime studies in developing countries focus on either the adoption or nonadoption of such a regime and its feasibility, this study evaluates the success of the regime in Turkey as an emerging economy.
Keywords
 inflation uncertainty
 inflation targeting
 monetary policy
 fiscal policy
 MGARCH models
1. Introduction
The phenomenon of high inflation arising from the 1970s oil crisis and the collapse of Bretton Woods’s system has brought price stability to the base of the monetary policy. While inflation, growth, exchange rate and interest rate should be in harmony in order to prevent financialbased crises, to eliminate income distribution imbalances and to increase prosperity, the implicit relationship between monetary and fiscal policies should not be ignored in developing countries that are subject to the inflationtargeting regime.
Inflation uncertainty has an effect not only on monetary and fiscal policy variables but also on economic growth and indirectly on the real sector by affecting both real net revenues and price system efficiency in resource allocation. In emerging markets economies, interest rate and exchange rate, which are indicative variables, have a decisive influence on the real and nominal sectors for sustainable development and a stable economy. Changes in interest rates and exchange rates affect domestic and foreign investment decisions and consumer behaviors. High interest rates increase risk perception as they cause inflationary expectations. Moreover, volatility that may be experienced at interest rates creates exchange rate uncertainties. Thus, the exchange rate instability affects the real sector and it causes economic instability. In open economies, exchange rates are controlled through interest rates (usually short term) when it is necessary.
Tax revenues follow a fluctuating structure in emerging economies where the economies are not fully managed due to the influence of political structure. Tax revenues can be seen as a means of development by the direct or indirect effect of resource allocation in developing countries. Macroeconomic balances are realized at a lower cost in the shorter term as the tax revenues are directed toward the financing of the growth. The longer the average collection period of taxes, the greater the magnitude of the corrosive effect on tax revenues is related with inflation. Depending on inflation, inflation rate increases by increased risk premiums due to economic uncertainty and instability. Funds used in the financing of the growth by excluding investments shift to nontaxable areas. The economic contraction due to the diminishing of investments reduces the taxable potential.
Tax revenues create economic conditions for stability and growth by reducing the debt burden of the public sector and alleviate the pressure on interest and inflation. Therefore, public expenditures also have an effect on the relation between inflation and tax revenues. The change in public expenditure activates the multiplier mechanism and causes a change in income, consumption and tax revenues. The high public debt burden may affect inflation expectations and can constitute difficulties to meet the inflation target. Government revenues increase as total savings, and taxable potential increases in moderate inflation periods.
Imbalances between government revenues/expenditures, elimination of existing debts by borrowing, problems in banking system, deficiencies in risk management processes, monetary and fiscal policy approaches which are far from rationality and the environment where shortterm capital movements for speculative purposes are widespread due to increasing globalization and economic liberalization movements make an inflation spiral in emerging economies as well as in Turkey.
The effectiveness of inflexible monetary policies has disappeared because of the fluctuations in the variables used as main or intermediate target. High inflation, floating growth rates, high public deficits and a dollarized economy emerged between 1989 and 2001 in Turkey because of not only the shortterm capital movements started to be effective in the economic structure but also unrealizable financial and structural reforms. In this period, monetary policy approaches that target interest rate, foreign currency exchange rate and monetary aggregates had been used in the economic system. Interestexchange rate targeting has been abandoned because of the changes in shocks in the economic structure and highfloating inflationary periods that make interest targeting difficult. The increase in capital movements and the decrease in flexibility against global shocks made the use of the exchange rate ineffective. Monetary aggregates could not be applied as intermediate targets owing to the structural changes and financial liberalization, and programs had resulted in disappearance of stability in the currency speed of money, the emergence of new financial instruments and the destabilization of the money demand caused by fastgrowing financial sector. The exchange rate policy has been changed to the floating exchange rate regime because of the anticipation that it could be effective in closing the current account deficit and the monetary policy gained independence. Inflation had been adversely affected because the foreign exchange rate, which is sensitive to external shocks, exhibited a volatile structure and the perception that the interventions made on the interest rate were considered as interventions to the exchange rates.
In order to achieve price stability in the Turkish economic structure, it has been decided to implement the inflationtargeting regime, a monetary policy approach that targets directly inflation without using any intermediate targets. In Turkey, due to domestic debt stock and high interest rates, the transition to the inflationtargeting regime could not be possible immediately. With the transition to the inflationtargeting regime, which had been implemented in 2003, inflation and the level of dollarization had started to decrease. With the transition to the inflationtargeting regime in 2006, inflation reached single digits and the aim changed as price stabilization. Due to the difficulty of keeping inflation under control in emerging economies and the delayed/prolonged effects of the monetaryfiscal policy instruments on inflation, the longterm internal and external shocks experienced in Turkey between 2002 and 2009 created disruptions in the operation of the regime.
Since the relationship between uncertainty and macroeconomic variables is sensitive to various factors such as sampling period, model classification and uncertainty identifications, different results have been determined in studies among inflation, output growth, interest rate and inflation uncertainty. Almost none of the studies have been found within the scope of the developed economies or the developing economies on the interactions of inflation uncertainty with real effective exchange rate, tax revenues and government expenditures.
Cukierman et al., Azariadis et al., Friedman and Deveraux [1, 2, 3, 4] argue that there is a positive relationship between inflation and inflation uncertainty. Baillie et al. [5] conclude that the CukiermanMeltzer hypothesis is valid only in high inflationary countries. Pourgerami et al., Ungar et al. and Grier et al. [6, 7, 8] argue that there is an inverse relationship between inflation uncertainty and inflation rate. Bhar et al. [9] have concluded that inflation uncertainty has diminished inflation after inflation targeting. Holland [10] argues that higher inflation uncertainty may be associated with lower average inflation. While Dotsey and Sarte [15] find that inflation uncertainty has a positive effect on growth, Friedman, Pindyck, Beaudry et al.,Tommasi and Fountas et al. [1, 11, 12, 13, 14] determine an inverse relationship between inflation uncertainty and output growth. Bhar et al. [9] point out that inflation uncertainty reduces the growth rate after inflation targeting. Chan [16] suggests that uncertainty reduces output growth by reducing consumption and investment spending with interest rates when there is a positive relationship between inflation uncertainty and interest rates. Berument et al. [17] show that inflation uncertainty increases 3month deposit interest. Omay et al. [18] show that the effect of the inflation risk on the interest rates is regime dependent.
In case of uncertainty, determining the interaction of real and nominal economic variables with inflation uncertainty is important in shaping economic policies of countries experiencing problems with inflation. In this study, it is investigated whether the inflationtargeting regime causes a structural change in the economic system exposed to high and lowinflation periods. It is aimed to contribute to the literature by focusing on the effect of inflation uncertainty on inflation, output growth and selected monetaryfiscal policy instruments under the inflationtargeting regime. Within the scope of the study, inflationtargeting period was accepted between 2003 and 2015 and preinflationtargeting period was between 1987 and 2003. The effect of inflation uncertainty on real and nominal economic indicators is examined using multivariate generalized autoregressive conditional heteroscedasticity (MGARCH) model. Because volatility is a quantitative measure of the risk that individual investors and financial institutions face, it is one of the noteworthy features of financial data. Because of the fact that financial changes move together over time, the ability to envision and forecast the dependency of seconddegree moments of return is important in financial econometrics. The multivariate GARCH models, which are developed based on the fact that financial asset volatilities move together over time, provide efficiency gains. In order to handle all the possible interactions in a system equation, solutions are obtained by using fullinformation maximumlikelihood method.
In this way, with the help of an equations system that is stated in a multivariate structure, all the possible interactions are tackled together and solutions are obtained based on complete information. In addition, with the help of a slope dummy variable, which was defined to differentiate the periods before and after 2003, the effects of inflation and output uncertainty have been assessed for both high and low inflation periods. The study first takes a general look at the related literature about inflation uncertainty. It then moves on to defining the model and obtaining empirical findings which were established over the model. The study concludes with an assessment section in which the empirical findings obtained are evaluated.
2. Model structure
The generalized autoregressive conditional heteroscedasticity (GARCH) approach includes the time dependencies between conditional variances and covariances between various markets and assets. Although multivariate GARCH (MGARCH) models fundamentally resemble univariate GARCH models, the significant difference between the two is the definitions of the equations that show how the covariances of multivariate models move over time. To elicit these changes, performing analysis within the framework of multivariate modeling allows the researcher to obtain results that are more realistic. From the financial perspective, it facilitates taking better risk management decisions.
Expansion from the univariate GARCH model to a model with n variables requires that random variables
This model class makes the theoretical structure of unconditional moment, ergodicity and stationarity conditions easier (He and Terasvirta, [20]). Since it is difficult to secure
can be written as BEKK (1,1,K) model. Eq. (1) is positive definite under weak conditions. In addition, because the model contains all positivedefinite diagonal representations and almost all positivedefinite VEC representations, it is adequately general. The BEKK model directly concentrates on the model structure, notably as A and B matrices. The main advantage of this is that because there is no constraint requirement necessitating
Using conditional variance and correlation in direct modeling of conditional covariances is a relatively new approach. Conditional correlation models are much more convenient alternatives in the estimation and interpretation of parameters. These models, which are nonlinear combinations of univariate GARCH models, allow for separate determination of individual conditional variances on the one hand, and of a conditional correlation matrix between the individual series on the other, or of another dependency criterion. Timedependent correlations are usually calculated by the cross product of returns and by multivariate GARCH models that are linear in their squares. The dynamic conditional correlation (DCC) model takes the change of conditional correlation over time into account. The multivariate models that are called DCC have the flexibility of parsimonious parametric models and relevant univariate GARCH models for correlations. In other words, the DCC estimators have the flexibility of univarate GARCH; however, they refrain from the complexity of multivariate GARCH. Despite being nonlinear, they can be calculated by twostep methods or singlevariable methods that are based on probability function. These models, which directly parameterize the conditional correlations, can be estimated in two steps: the first being a series of univariate GARCH estimations and the second being correlation estimation. It is observed that under many circumstances they function well and provide reasonable empirical results.
When
The dynamic conditional correlation model, which is a generalized form of the constant conditional correlation (CCC) estimator, is shown as follows:
The only difference in the dynamic conditional correlation model is that R changes over time (Engle, [22]). Parameterization of R requires that conditional variances are in integrity, and it has the same requirements as H.
The possible simplest and best method is exponential smoothing, which is expressed as a geometrical weighted average of normalized residuals. Another alternative is obtained using the GARCH (1,1) model. When the equation is written as
the below equation
is obtained. Assuming that the unconditional expectation of the cross product is
When S is an unconditional correlation matrix of epsilons, the matrix forms of these estimators are written as
As long as unconditional moments are adapted to a simple correlation matrix, in order to parameterize the correlations, more complex positivedefinite multivariate GARCH models can be used.
3. Effects of inflation uncertainty on economic policies
Quarterly data (1987:Q1–2015: Q3) were used to examine the effect of inflation uncertainty for Turkey on the variables of consumer price index, real gross domestic product, real effective exchange rate, 12month deposit interest rate, government expenditures and tax revenues. The data set was taken from the Central Bank of the Republic of Turkey (CBRT) electronic data distribution system (EVDS). Different term dates for different base years are organized according to the 1987 base year. The seasonal structure in the real gross national product, government expenditures and tax revenue variables is eliminated by using the Tramo/Seat method. The government expenditures and tax revenues series are divided by the seasonally adjusted nominal gross national product and multiplied by 100. Growth measures expressed as percentage changes are obtained by taking the logarithmic firstorder differences, multiplying by 100, of the consumer price index, real gross domestic product, 12month deposit interest rate and real effective exchange rate.
MGARCH model structure by using inflation (
is performed. The meanmodel structure consists of Eqs. (8)–(13). Agumented DickeyFuller (ADF), KwiatkowskiPhillipsSchmidtShin (KPSS) and PhillipsPerron (PP) unit root tests were applied in Table 1 to set out the stationarity of the variables. It is decided that all variables are stationary, generally, when the ADF, KPSS and PP stationarity test results are evaluated for all variables.
ADF test statistics  KPSS test statistics  PP test statistics  


Level  −2.199  0.159***  −9.539** 

Level  −7.599**  0.087**  −12.743** 

Level  −10.836**  0.141**  −12.830** 

Level  −9.754**  0.095**  −9.717** 

Level  −6.332**  0.081**  −6.332** 

Level  −7.304**  0.157***  −7.654** 
Figure 1
shows the tendencies of the series used in the model construction with respect to time. When the inflation series is examined, it is observed that there has been a fluctuation in the period of 2003 with the transition to the inflationtargeting regime. A dummy variable has been added to the model structure to reveal the effects of this period. Dummy variable(
In the onedimensional case, the mean equation for the model should be decided. In addition, the first condition that must be satisfied before dealing with the general structure of the variance equation in the multivariate GARCH model is that the series should be a white noise vector process. Residuals should be serially uncorrelated to each other, as well as have zero correlation with the lags of other components. It is suggested to use loworder VAR models to get rid of nested autocorrelation structure. Table 2 shows the optimal lag length calculated for the model structure.
Lag length  SC  HQ  AIC  FPE  

Model C  0  30.7841788  30.6922946  30.6311298  808155.7 
1  30.4943727*  29.8511831*  29.4757366*  239794.0  
2  31.3253894  30.1308945  29.5447431  219511.0*  
3  32.3555313  30.6097310  29.9389591  247924.9  
4  33.3434204  31.0463148  30.4465451  272942.8  
5  34.4803294  31.6319184  31.2983202  356934.9  
6  35.7085147  32.3087984  32.4907265  527368.6  
7  36.9301733  32.9791516  34.0022509  805829.9  
8  37.5814766  33.0791495  35.3800101  733320.2  
9  37.9362941  32.8826617  37.0656734  530976.8  
10  38.1716960  32.5667583  39.5027360  373253.0  
11  38.5220873  32.3658442  43.3755930  332466.6  
12  38.9348464  32.2272979  49.4561719  374125.8 
Detection of autocorrelation in residuals and/or squared residuals within the framework of established VAR (1) model leads to the use of MGARCH models. A preliminary multivariate ARCH effect test was performed in order to question the existence of the ARCH effect on the model constructed. In Table 3 , it is shown that the absence of the ARCH effect is strictly rejected. Since the null hypothesis, constant and all other lagged parameters are equal to zero and are rejected, it can be said that there is no constant correlation and a dynamic structure can be mentioned with strong timedependency correlation between the selected variables.
Multidimensional ARCH effect test statistic  Significance level 

1898.86  0.000 
Within the scope of the study, the model structure is examined as a dynamic conditional correlation model to determine the effect of inflation uncertainty on economic variables. For this reason, the volatilities of the involved variables are restricted within the DCC framework. The DCC model established in the study states that there are unstable interactions of the series concerned with conditional correlation and that this correlation affects the correlations with a one lagperiod. The DCC model estimation results are shown in Table 4 . According to the result of the multivariate Q statistic in Table 4 , no residuals were found to be serially correlated, and the ARCH effect was no more observed in the model. It is found that there is no autocorrelation problem when considering the autocorrelation function of residuals and its squares. When these results are taken into consideration, the effect of uncertainty in the inflation can be evaluated using the DCC model. The DCC model provides more precisely the dynamic structure of the correlation between inflation uncertainty and macroeconomic variables.
Panel A: Model parameter tahminleri  








Constant  4.10*  Constant  0.65*  Constant  −0.750  Constant  −1.013*  Constant  2.001*  Constant  −1.327* 

0.630* 

−0.026 

0.120 

0.105* 

−0.101 

0.242 

0.126 

−0.042 

0.114 

0.526* 

0.522 

0.982** 

−0.567 

0.043* 

0.092 

−0.308** 

0.092* 

0.443* 

0.033** 

−0.028* 

0.083* 

0.190* 

0.874* 

−0.323* 

0.001 

−0.021 

0.314 

0.093* 

0.021 

0.084 

0.074 

0.013 

0.053* 

0.042 

0.092* 

0.463* 

−0.48* 

−0.095* 

0.995 

0.689* 

−1.000* 

0.154* 

0.479* 

0.155** 

0.045 

−0.093* 

0.679** 

−0.18* 

−0.12* 

−0.362* 

0.023 

0.102* 

−0.878* 

0.247* 
Panel B: GARCH parameter estimates  
C(1)  3.019***  C(4)  4.620***  A(1)  0.546*  A(4)  0.409**  B(1)  0.245***  B(4)  0.480*** 
C(2)  2.009*  C(5)  8.372***  A(2)  0.365  A(5)  0.352***  B(2)  0.514***  B(5)  0.583*** 
C(3)  5.267**  C(6)  9.157***  A(3)  0.709***  A(6)  0.222***  B(3)  0.235*  B(6)  0.534 
Panel C: Correlation parameter estimates  
DCC(1)  0.120***  DCC(2)  0.672***  
Multivariate Q (10) statistic  390.851*  
Multivariate ARCH statistic  3416.55** 
The dummy variable used for inflation targeting was found to be statistically insignificant for exchange rate changes, while statistically significant for inflation, output growth, interest rate change, governmet expenditure and tax revenues. This result indicates the effect of inflation uncertainty on selected variables differs pre2003 and post2003 periods. In other words, the effects of inflation uncertainty on real and nominal economic indicators are not the same in high and low inflationary periods. Inflation uncertainty had a positive and statistically significant effect on inflation, a positive and statistically significant effect on output gowth, a positive and statistically insignificant effect on exchange rate change, a negative and statistically significant effect on interest rate change, a positive and statistically significant effect on government expenditures and negative and statistically significant effect on tax revenues pre2003 period. In the post2003, inflation uncertainty affects inflation positively and statistically, output growth negatively and statistically significant, exchange rate change positively and statistically insignificant, interest rate change positively and statistically significant, government expenditures negatively and statistically significant, and tax revenues positively and statistically significant.
4. Findings and remarks
As unexpected inflation increases with rising inflation uncertainty, the more inflation uncertainty increases inflation for the pre2003 and post2003. It is noteworthy that increases in the period after 2003 are less than the previous period. In the period before 2003, the more inflation uncertainty is an increasing effect on economic growth. In this period, as consumption expenditures were made for saving, the increase in inflation uncertainty has led to a shift in commodity markets. Since consumption expenditures are not made for saving, more inflation uncertainty makes the reducing effect on economic growth in the post2003 period.
Inflation uncertainty increases domestic prices, and so nominal exchange rate is also increased for both of the periods. While an exchange rate regime system was based on the “devaluation as much as inflation” idea in the period before 2003 (excluding the period between December 1999 and February 2001), flexible exchange rate system was implemented under implicit and explicit inflationtargeting regime in the post2003 period. Due to the fact that the adequate adjustment is provided in nominal exchange rate, inflation uncertainty has no effect on the reel exchange rates for the pre2003 and post2003 periods.
The increase in inflation uncertainty reduces the nominal interest rate in the period before 2003. Although the reduction of the nominal interest rate as inflation uncertainty increases, or the negative impact of inflation uncertainty on the nominal interest rate, seems contradictory at first glance, this result describes the features of the period before 2003. A severe increase in government borrowing needs is the basic phenomena that determine market interest rate for the pre2003 period. In case that the state borrowing to repay the debt is a key factor in determining the market interest rates. The banks become main actors in financing the government. Given that deposits be a source of funding for banks, the decreasing effect of more inflation uncertainty on deposit interest rates is a reflection of the behavior of the banks’ increasing profit margin, because bank is shrouded in a structure that they collect the deposits to the state as a debt in the period before 2003.
The increase in nominal interest rate as an impact of more inflation uncertainty is an expected result in the period after 2003. The most capital inflow to Turkey was experienced in the post2003 period. It is a period in which it becomes very important that interior interest rates are too sensitive to outside interest rates and foreign interest rate is extremely high in the determination of domestic interest rates in Turkey. The supply of funds in the financial markets is largely shaped by a capital flow to Turkey. Capital flows to Turkey largely consist of hot money flows. In this sense, nominal interest rates are increasing due to the reduction in hot money flows as inflation uncertainty increases.
In addition, the inflation uncertainty and nominal interest rate relationship obtained from the study findings support the findings of inflation uncertainty and growth relationship. Consumption spending has become sensitive to interest rates due to the increase in financing consumption spending with credits (the most common example of a credit card) in the post2003 period. If our findings are being analyzed, in the period after 2003, inflation uncertainty has an impact on nominal interest rate increase.
The fiscal policies implemented before the 2003 period and the conjunctural situation of the country caused the inflation rates to be considerably higher than the developed countries especially. Inflation uncertainty has led to the realization of the Tanzi effect, known as inflation cause to erode the real value of the tax revenues, in the pre2003 period. In the same period, there was no inverse Tanzi effect, which means a decrease in the real value of public expenditures due to high inflation. When the post2003 period was passed, the opposite effect was observed.
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