**4. Methodology**

The main purpose of this study is to explore long-run relationship among liquidity risk and credit expansion in the Turkish banking sector. This study adopts dynamic panel econometric methodology. It consists of four steps. First, the crosssectional dependence of the units (banks) is investigated with the Pesaran CDLM test developed by Pesaran [14]. Second, Delta tests are applied to analyze whether the parameters change according to the units. Third, CIPS panel unit root test developed by Pesaran [15] is used to determine order of the integration of the variables. Finally, panel cointegration test developed by Westerlund [16] is conducted in order to explore the existence of the long-run relationship among the variables. In this section, theoretical background of methodology is explained.

#### **4.1 Investigation of cross-sectional dependence**

One of the important concepts that affects the choice of method to be used in dynamic panel data analysis is inter-units correlation. The inter-units correlation, in other words, cross-sectional dependence is the simultaneous correlation of series that may occur due to excluded, observed common factors, spatial spillover effects, and all common effects observed or not observed [17].

Model for panel data analysis can be written as in Eq. (3) [18]:

$$LR\_{it} = \mu\_i + \beta\_i \mathbf{C} \mathbf{E}\_{it} + \varepsilon\_{it} \tag{3}$$

the weight which is difference between variances of OLS and within estimator. The

Pesaran and Yamagata [22] developed Swamy test by two different test statistics [22]. These two statistics differ according to the size of sample. They are delta (*Δ*~) for large samples and delta adjusted (*Δ*~*adj*) for small samples. These tests explore whether slope coefficients are homogenous or not. Delta for large samples and delta

> *N* p *N*�1^

*N* p *N*�1^

The first factor to be considered in panel unit root tests is whether the units forming the panel are correlated to each other. According to the existence of correlation between units, panel unit root tests are divided into two as first- and secondgeneration tests. Levin et al., Harris and Tzavalis, Breitung and Hadri are firstgeneration unit root tests that do not take into account cross-sectional dependence [24–27]. In these tests, all units are assumed to have a common autoregressive parameter. However, an autoregressive parameter changing according to the units is a more realistic approach. The second-generation unit root tests have been developed for this purpose. They deal with cross-sectional dependence in three different ways. First, first-generation unit root tests were transformed by reducing the correlation between the units by taking the difference from the cross-sectional averages, but unable to eliminate some types of correlation. As a result, these versions of tests are not used much in the literature [28]. Second, there are panel unit root tests such as the multivariate augmented Dickey-Fuller (MADF) panel unit root test and seemingly unrelated augmented Dickey-Fuller (SURADF) panel unit root test based on system estimation [29–32]. Third, there are panel unit root tests that eliminate cross-sectional dependence by modeling it via common factor [15, 33–40].

In this study, since the cross-sectional dependence was determined among the banks forming the panel, the stationarity of the series was tested by using the second-generation panel unit root tests. Cross-sectionally augmented Im, Pesaran, and Shin (CIPS) unit root test developed by Pesaran [15] was used to in order to determine stationarity of the series. CIPS unit root test is an extension of Im, Pesaran, and Shin (2003) unit root test. This method adds cross-sectional averages of the lagged series and first differences of series as factors to DF or ADF regression to eliminate correlation between units [15]. Dynamic heterogenous panel data

*LRit* ¼ 1 � *ϕ<sup>i</sup>* ð Þ*μ<sup>i</sup>* þ *ϕiLRit*�<sup>1</sup> þ *εit i* ¼ 1 … *N*, *t* ¼ 1 … *T* (9)

*εit* ¼ *φ<sup>i</sup> ft* þ *ϵit* (10)

*S* is Swamy test statistic, *k* is number of regressors, and *SE* denotes

*S* � *k* 2*k* !

*S* � *k SE T*ð Þ , *k* ! � *<sup>χ</sup>*<sup>2</sup>

*<sup>k</sup>* (7)

� *N*ð Þ 0, 1 (8)

test statistic is *<sup>χ</sup>*<sup>2</sup> distributed with *kx*(*<sup>N</sup>* � 1) degrees of freedom.

Large samples : *<sup>Δ</sup>*<sup>~</sup> <sup>¼</sup> ffiffiffiffi

Small samples : *<sup>Δ</sup>*~*adj* <sup>¼</sup> ffiffiffiffi

in which ^

standard errors.

**4.3 Investigation of unit roots**

model without autocorrelation is as Eq. (9).

**209**

*εit* with a single factor structure is shown in Eq. (10).

adjusted for small samples are calculated as follows [23]:

*More Credits, Less Cash: A Panel Cointegration Approach*

*DOI: http://dx.doi.org/10.5772/intechopen.93778*

where *i* = 1 … *N* denotes cross section dimension, which is banks here, *t* = 1 …*T*, is time series dimension which is the quarterly period. *LRit* shows the liquidity risk, *CEit* is a variable of credit expansion. *μ<sup>i</sup>* represents the intercept of the model. The slope coefficients are *β<sup>i</sup>* which vary across the cross section units. *εit* is the error term which may be cross-sectionally dependent.

The null hypothesis (*<sup>E</sup> <sup>ε</sup>itεjt* � � <sup>¼</sup> <sup>0</sup> *for all* <sup>i</sup> 6¼ *<sup>j</sup>*) used to investigate whether there is a correlation between units in the error term of this model.

Rejecting the null hypothesis shows existence of the cross-sectional dependence. Pesaran [14] proposed a simple cross-sectional dependence test that can be applied to heterogeneous panel series with both stationary and unit roots [14]. The test statistic, *CD*, is the average of the pairwise correlation coefficients of the ordinary least squares residuals obtained from the individual regression coefficients. The test statistic is calculated as Eq. (4) [19]:

$$\text{CD} = \sqrt{\frac{2T}{N(N-1)} \left(\sum\_{i=1}^{N-1} \sum\_{j=i+1}^{N} \hat{\rho}\_{\vec{\eta}}\right)} \tag{4}$$

where ^*ρij* represents pairwise correlation coefficient and can be formulated by ^*ρij* <sup>¼</sup> ^*ρji* <sup>¼</sup> <sup>P</sup>*<sup>T</sup> <sup>t</sup>*¼<sup>1</sup>^*εit*^*εjt<sup>=</sup>* <sup>P</sup>*<sup>T</sup> <sup>t</sup>*¼<sup>1</sup> ^*ε*<sup>2</sup> *it* � �<sup>1</sup>*=*<sup>2</sup> P*<sup>T</sup> <sup>t</sup>*¼<sup>1</sup> ^*ε*<sup>2</sup> *jt* � �<sup>1</sup>*=*<sup>2</sup> . ^*εit* shows the ordinary least square (OLS) estimate of *εit* which is based on *T* number of observation in each unit. Pesaran CD test works well even when there are few years and many units (*N* > *T*) [20].

#### **4.2 Investigation of homogeneity**

Homogeneity means that constant and slope parameters do not change according to the units. Delta test which is an extension of Swamy S test is used to test homogeneity of parameters in this study. The purpose of the Swamy S test is to explore whether there is a difference between OLS estimator and weighted average matrices of within estimator. OLS estimator does not take into account panel structure of units. Conversely, within estimator considers panel-specific estimates with weighted average of parameters.

The null hypothesis of Swamy S test is *H*0: *β<sup>i</sup>* ¼ *β i* ¼ 1 … *N* which represents homogeneity of parameters estimated by two different estimation methods, OLS and within estimator [21].

Test statistic of Swamy [21] can be written as Eq. (5):

$$\hat{\mathbf{S}} = \chi\_{k(N-1)}^2 = \sum\_{i=1}^{N} \left( \hat{\boldsymbol{\beta}}\_i^{\text{OLS}} - \boldsymbol{\beta}^{\text{WWE}} \right) \mathbf{V}\_i^{-1} \left( \hat{\boldsymbol{\beta}}\_i^{\text{OLS}} - \boldsymbol{\beta}^{\text{WWE}} \right) \tag{5}$$

$$\boldsymbol{\beta}^{\text{WWE}} = \left(\sum\_{i=1}^{N} \hat{\boldsymbol{V}}\_{i}^{-1}\right)^{-1} \sum\_{i=1}^{N} \hat{\boldsymbol{V}}\_{i}^{-1} \hat{\boldsymbol{\beta}}\_{i}^{\text{OLS}} \tag{6}$$

*β*^*OLS <sup>i</sup>* indicates estimation of coefficients from ordinary least squares. *βWWE* is the estimation of weighted (by *<sup>V</sup>*^ �<sup>1</sup> *<sup>i</sup>* ) average of parameters from within estimator. *<sup>V</sup>*^*<sup>i</sup>* is *More Credits, Less Cash: A Panel Cointegration Approach DOI: http://dx.doi.org/10.5772/intechopen.93778*

Model for panel data analysis can be written as in Eq. (3) [18]:

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

term which may be cross-sectionally dependent.

*CD* ¼

*<sup>t</sup>*¼<sup>1</sup> ^*ε*<sup>2</sup> *it* � �<sup>1</sup>*=*<sup>2</sup>

Test statistic of Swamy [21] can be written as Eq. (5):

*N*

*β*^*OLS <sup>i</sup>* � *<sup>β</sup>WWE* � �

*N*

*<sup>V</sup>*^ �<sup>1</sup> *i* !�<sup>1</sup>

*<sup>i</sup>* indicates estimation of coefficients from ordinary least squares. *βWWE* is the

*i*¼1

*i*¼1

*<sup>β</sup>WWE* <sup>¼</sup> <sup>X</sup>

*k N*ð Þ �<sup>1</sup> <sup>¼</sup> <sup>X</sup>

is a correlation between units in the error term of this model.

2*T N N*ð Þ � 1

> P*<sup>T</sup> <sup>t</sup>*¼<sup>1</sup> ^*ε*<sup>2</sup> *jt* � �<sup>1</sup>*=*<sup>2</sup>

Homogeneity means that constant and slope parameters do not change according to the units. Delta test which is an extension of Swamy S test is used to test homogeneity of parameters in this study. The purpose of the Swamy S test is to explore whether there is a difference between OLS estimator and weighted average matrices of within estimator. OLS estimator does not take into account panel structure of units. Conversely, within estimator considers panel-specific estimates with

The null hypothesis of Swamy S test is *H*0: *β<sup>i</sup>* ¼ *β i* ¼ 1 … *N* which represents homogeneity of parameters estimated by two different estimation methods, OLS

> *V*�<sup>1</sup> *<sup>i</sup> <sup>β</sup>*^*OLS*

X *N*

*<sup>V</sup>*^ �<sup>1</sup> *<sup>i</sup> <sup>β</sup>*^*OLS*

*<sup>i</sup>* ) average of parameters from within estimator. *<sup>V</sup>*^*<sup>i</sup>* is

*i*¼1

*<sup>i</sup>* � *<sup>β</sup>WWE* � �

*<sup>i</sup>* (6)

The null hypothesis (*E εitεjt*

statistic is calculated as Eq. (4) [19]:

*<sup>t</sup>*¼<sup>1</sup>^*εit*^*εjt<sup>=</sup>* <sup>P</sup>*<sup>T</sup>*

**4.2 Investigation of homogeneity**

weighted average of parameters.

^ *<sup>S</sup>* <sup>¼</sup> *<sup>χ</sup>*<sup>2</sup>

estimation of weighted (by *<sup>V</sup>*^ �<sup>1</sup>

and within estimator [21].

*β*^*OLS*

**208**

^*ρij* <sup>¼</sup> ^*ρji* <sup>¼</sup> <sup>P</sup>*<sup>T</sup>*

where *i* = 1 … *N* denotes cross section dimension, which is banks here, *t* = 1 …*T*, is time series dimension which is the quarterly period. *LRit* shows the liquidity risk, *CEit* is a variable of credit expansion. *μ<sup>i</sup>* represents the intercept of the model. The slope coefficients are *β<sup>i</sup>* which vary across the cross section units. *εit* is the error

Rejecting the null hypothesis shows existence of the cross-sectional dependence. Pesaran [14] proposed a simple cross-sectional dependence test that can be applied to heterogeneous panel series with both stationary and unit roots [14]. The test statistic, *CD*, is the average of the pairwise correlation coefficients of the ordinary least squares residuals obtained from the individual regression coefficients. The test

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

X*<sup>N</sup> j*¼*i*þ1 ^*ρij*

. ^*εit* shows the ordinary least square

(4)

(5)

X*<sup>N</sup>*�<sup>1</sup> *i*¼1

� � <sup>s</sup>

where ^*ρij* represents pairwise correlation coefficient and can be formulated by

(OLS) estimate of *εit* which is based on *T* number of observation in each unit. Pesaran CD test works well even when there are few years and many units (*N* > *T*) [20].

*LRit* ¼ *μ<sup>i</sup>* þ *βiCEit* þ *εit* (3)

� � <sup>¼</sup> <sup>0</sup> *for all* <sup>i</sup> 6¼ *<sup>j</sup>*) used to investigate whether there

the weight which is difference between variances of OLS and within estimator. The test statistic is *<sup>χ</sup>*<sup>2</sup> distributed with *kx*(*<sup>N</sup>* � 1) degrees of freedom.

Pesaran and Yamagata [22] developed Swamy test by two different test statistics [22]. These two statistics differ according to the size of sample. They are delta (*Δ*~) for large samples and delta adjusted (*Δ*~*adj*) for small samples. These tests explore whether slope coefficients are homogenous or not. Delta for large samples and delta adjusted for small samples are calculated as follows [23]:

$$\text{Large samples}: \tilde{\Delta} = \sqrt{N} \left( \frac{N^{-1} \hat{\mathbf{S}} - k}{2k} \right) \sim \chi^2\_k \tag{7}$$

$$\text{Small samples}: \tilde{\Delta}\_{adj} = \sqrt{N} \left( \frac{N^{-1} \hat{\mathbf{S}} - k}{\text{SE}(T, k)} \right) \sim N(0, 1) \tag{8}$$

in which ^ *S* is Swamy test statistic, *k* is number of regressors, and *SE* denotes standard errors.

#### **4.3 Investigation of unit roots**

The first factor to be considered in panel unit root tests is whether the units forming the panel are correlated to each other. According to the existence of correlation between units, panel unit root tests are divided into two as first- and secondgeneration tests. Levin et al., Harris and Tzavalis, Breitung and Hadri are firstgeneration unit root tests that do not take into account cross-sectional dependence [24–27]. In these tests, all units are assumed to have a common autoregressive parameter. However, an autoregressive parameter changing according to the units is a more realistic approach. The second-generation unit root tests have been developed for this purpose. They deal with cross-sectional dependence in three different ways. First, first-generation unit root tests were transformed by reducing the correlation between the units by taking the difference from the cross-sectional averages, but unable to eliminate some types of correlation. As a result, these versions of tests are not used much in the literature [28]. Second, there are panel unit root tests such as the multivariate augmented Dickey-Fuller (MADF) panel unit root test and seemingly unrelated augmented Dickey-Fuller (SURADF) panel unit root test based on system estimation [29–32]. Third, there are panel unit root tests that eliminate cross-sectional dependence by modeling it via common factor [15, 33–40].

In this study, since the cross-sectional dependence was determined among the banks forming the panel, the stationarity of the series was tested by using the second-generation panel unit root tests. Cross-sectionally augmented Im, Pesaran, and Shin (CIPS) unit root test developed by Pesaran [15] was used to in order to determine stationarity of the series. CIPS unit root test is an extension of Im, Pesaran, and Shin (2003) unit root test. This method adds cross-sectional averages of the lagged series and first differences of series as factors to DF or ADF regression to eliminate correlation between units [15]. Dynamic heterogenous panel data model without autocorrelation is as Eq. (9).

$$LR\_{it} = (1 - \phi\_i)\mu\_i + \phi\_i LR\_{it-1} + \varepsilon\_{it} \qquad i = 1 \ldots N, t = 1 \ldots T \tag{9}$$

*εit* with a single factor structure is shown in Eq. (10).

$$
\varepsilon\_{\it t} = \varrho\_{\it} f\_{\it t} + c\_{\it t} \tag{10}
$$

where *ft* is unobserved common factors, *ϵit* is individual specific error term. If we rearrange Eq. (9)., it is displayed in Eq. (11).

$$
\Delta LR\_{it} = a\_i + \beta\_i LR\_{it-1} + \varphi\_i f\_t + \epsilon\_{it} \tag{11}
$$

where *dt* represents deterministic components vector (intercept and trend),

*<sup>i</sup>* is the long-term parameter, *ϑij* and *γij* are short-term parameters. Westerlund [16] test is based on four statistics. Two of them are group mean statistics (*Gα*, *GT*Þ. Autoregressive parameter in group mean statistics varies from

*<sup>α</sup>*^*i*ð Þ<sup>1</sup> , *GT* <sup>¼</sup> <sup>1</sup>

in which *SE* denotes the standard error of *α*^*i*. Other two statistics of Westerlund [16] are panel statistics (*Pα*, *PT*Þ. They are calculated by using whole information on

The rejection of the hypothesis of interest (*H*<sup>0</sup> : *β<sup>i</sup>* ¼ 0 *for all i*Þ in both groups of tests signifies the existence of a cointegration relationship. If the variables are longterm cointegrated, the cointegration model can be estimated in different ways depending on whether the long-term covariance is homogeneous or not. Since the long-term covariance is homogeneous in this study, the panel dynamic least squares (PDOLS) estimator by Kao and Chiang [42] is used to estimate long-term relation. Kao and Chiang PDOLS estimator can be obtained by estimating regression model

*q*

*j*¼�*q*

where *β* is long-term parameter. According to Kao and Chiang's Monte Carlo simulation results, the PDOLS estimator and t statistics are successful in all cases of

The aim of this study is to examine the long-term relationship between liquidity risk and credit expansion for the period from 2014.Q1 to 2017.Q4 using data from 20 banks in the Turkish banking sector. Since biased results can be obtained due to correlation between units forming panel data, the presence of cross-sectional dependence should be tested first. In this context, the presence of cross-sectional dependence of residuals obtained from error correction model and cross-sectional dependence of the liquidity risk and credit expansion variables were tested by

According to the results represented in **Table 1**, the null hypothesis of crosssectional dependence test states no correlation between units. There is enough

CD [14] 3.88 0.000 3.84 0.000 0.54 0.589

**LR CE Model Statistic p-Value Statistic p-Value Statistic p-Value**

*<sup>P</sup><sup>α</sup>* <sup>¼</sup> *<sup>T</sup>α*^, *PT* <sup>¼</sup> *<sup>α</sup>*^

*N* X *N*

*i*¼1

*α*^*i SE*ð Þ *α*^*<sup>i</sup>*

*SE*ð Þ *<sup>α</sup>*^ (17)

*cijΔCEit*þ*<sup>j</sup>* þ *vit* (18)

(16)

unit to unit. Group mean statistics can be formulated as in Eq. (16).

*Tα*^*<sup>i</sup>*

*LRit* <sup>¼</sup> *<sup>α</sup><sup>i</sup>* <sup>þ</sup> *CEit<sup>β</sup>* <sup>þ</sup> <sup>X</sup>

Pesaran [14] CD test. The test results are given in **Table 1**.

homogeneous and heterogeneous panels.

**5. Empirical results**

**Table 1.**

**211**

*Test results of cross-sectional dependence.*

*i*¼1

panel. Panel statistics are shown in the following equations:

*<sup>G</sup><sup>α</sup>* <sup>¼</sup> <sup>1</sup> *N* X *N*

*More Credits, Less Cash: A Panel Cointegration Approach*

*DOI: http://dx.doi.org/10.5772/intechopen.93778*

*λ*0 *i* =�*αiβ*<sup>0</sup>

below [42]:

in which *α<sup>i</sup>* ¼ 1 � *ϕ<sup>i</sup>* ð Þ*μi*; *β<sup>i</sup>* ¼ � 1 � *ϕ<sup>i</sup>* ð Þ and *ΔLRit* ¼ *LRit* � *LRit*�1. Pesaran [15] used the cross-sectional average of *LRit* (*LRt*Þ and average of lagged values (*LRt*�1, *LRt*�2, … Þ as instrumental variable for common factor ( *ft* ). Crosssectionally augmented ADF (CADF) regression with intercept is defined as follow same as Equation 54 in Pesaran [15].

$$
\Delta LR\_{it} = \alpha\_i + \beta\_i LR\_{it-1} + \alpha\_i \overline{LR}\_{t-1} + \sum\_{j=0}^{p} \nu\_{ij} \Delta \overline{LR}\_{t-j} + \sum\_{j=1}^{p} n\_{ij} \Delta LR\_{it-j} + \epsilon\_{it} \tag{12}
$$

The unit root hypothesis of interest is: *H*<sup>0</sup> : *β<sup>i</sup>* ¼ 0 *for all i*; whereas alternatives are: *H*<sup>1</sup> : *β<sup>i</sup>* < 0 *i* ¼ 1, 2 … *N*1, *β<sup>i</sup>* ¼ 0, *i* ¼ *N*<sup>1</sup> þ 1, *N*<sup>1</sup> þ 2 … *N:* In order to test this hypothesis of interest, CIPS statistic is calculated as average of CADF.

$$\text{CIPS} = \frac{1}{N} \sum\_{i=1}^{N} \text{CADF}\_i = \frac{1}{N} \sum\_{i=1}^{N} t\_i \tag{13}$$

where *ti* denotes the OLS t-ratio of *β<sup>i</sup>* in the Eq. (12). Critical values were given by Pesaran [15].

#### **4.4 Investigation of long-run relationship**

Cointegration is the long-run equilibrium relationship between the variables despite permanent shocks affecting the system. Panel cointegration tests were developed to investigate long-run relationship in the panel data. They can be divided into two according to the existence of cross-sectional dependence. Firstgeneration panel cointegration tests (Kao (1999); Pedroni (1999, 2004); McCoskey and Kao (1998); [16]) do not take into account correlation between units, while second-generation tests [16] with bootstrapping critical values (Gengenbach, Urbain and Westerlund (2016)) do. In this study, Westerlund [16] cointegration test was used to investigate long-run relationship between variables.

Westerlund [16] is an error-correction based panel cointegration test. In the test, the presence of long-run relationship is explored by deciding whether each unit has its own error correction [16]. So rejecting hypothesis of interest shows that there is not error correction and it means absence of the long-run relationship between variables. Error correction model is shown in Eq. (14) [41]:

$$
\Delta LR\_{it} = \delta\_i' d\_t + a\_i \left( LR\_{it-1} - \beta\_i' CE\_{it-1} \right) \\
+ \sum\_{j=1}^{m\_i} \theta\_{ij} \Delta LR\_{it-j} + \sum\_{j=-q\_i}^{m\_i} \gamma\_{ij} \Delta CE\_{it-j} + e\_{it} \tag{14}
$$

Eq. (14) can be rewritten as below:

$$
\Delta LR\_{it} = \delta\_i' d\_t + a\_i LR\_{it-1} + \lambda\_i' \mathbf{CE}\_{it-1} + \sum\_{j=1}^{m\_i} \theta\_{i\bar{j}} \Delta LR\_{it-j} + \sum\_{j=-q\_i}^{m\_i} \gamma\_{i\bar{j}} \Delta \mathbf{CE}\_{it-j} + \varepsilon\_{it} \tag{15}
$$

*More Credits, Less Cash: A Panel Cointegration Approach DOI: http://dx.doi.org/10.5772/intechopen.93778*

where *ft* is unobserved common factors, *ϵit* is individual specific error term. If

in which *α<sup>i</sup>* ¼ 1 � *ϕ<sup>i</sup>* ð Þ*μi*; *β<sup>i</sup>* ¼ � 1 � *ϕ<sup>i</sup>* ð Þ and *ΔLRit* ¼ *LRit* � *LRit*�1. Pesaran [15]

sectionally augmented ADF (CADF) regression with intercept is defined as follow

*p*

*j*¼0

The unit root hypothesis of interest is: *H*<sup>0</sup> : *β<sup>i</sup>* ¼ 0 *for all i*; whereas alternatives are: *H*<sup>1</sup> : *β<sup>i</sup>* < 0 *i* ¼ 1, 2 … *N*1, *β<sup>i</sup>* ¼ 0, *i* ¼ *N*<sup>1</sup> þ 1, *N*<sup>1</sup> þ 2 … *N:* In order to test this

where *ti* denotes the OLS t-ratio of *β<sup>i</sup>* in the Eq. (12). Critical values were given

Cointegration is the long-run equilibrium relationship between the variables despite permanent shocks affecting the system. Panel cointegration tests were developed to investigate long-run relationship in the panel data. They can be divided into two according to the existence of cross-sectional dependence. Firstgeneration panel cointegration tests (Kao (1999); Pedroni (1999, 2004); McCoskey and Kao (1998); [16]) do not take into account correlation between units, while second-generation tests [16] with bootstrapping critical values (Gengenbach, Urbain and Westerlund (2016)) do. In this study, Westerlund [16] cointegration

Westerlund [16] is an error-correction based panel cointegration test. In the test, the presence of long-run relationship is explored by deciding whether each unit has its own error correction [16]. So rejecting hypothesis of interest shows that there is not error correction and it means absence of the long-run relationship between

*j*¼1

*j*¼1

*<sup>ϑ</sup>ijΔLRit*�*<sup>j</sup>* <sup>þ</sup> <sup>X</sup>*mi*

*<sup>ϑ</sup>ijΔLRit*�*<sup>j</sup>* <sup>þ</sup> <sup>X</sup>*mi*

*j*¼�*qi*

*j*¼�*qi*

*γijΔCEit*�*<sup>j</sup>* þ *εit* (14)

*γijΔCEit*�*<sup>j</sup>* þ *εit* (15)

*CADFi* <sup>¼</sup> <sup>1</sup>

*N* X *N*

*i*¼1

used the cross-sectional average of *LRit* (*LRt*Þ and average of lagged values

(*LRt*�1, *LRt*�2, … Þ as instrumental variable for common factor ( *ft*

hypothesis of interest, CIPS statistic is calculated as average of CADF.

test was used to investigate long-run relationship between variables.

variables. Error correction model is shown in Eq. (14) [41]:

*i CEit*�<sup>1</sup> � � þX*mi*

*i*

*CEit*�<sup>1</sup> <sup>þ</sup>X*mi*

*i*¼1

*CIPS* <sup>¼</sup> <sup>1</sup> *N* X *N*

*ΔLRit* ¼ *α<sup>i</sup>* þ *βiLRit*�<sup>1</sup> þ *φ<sup>i</sup> ft* þ *ϵit* (11)

*<sup>ψ</sup>ijΔLRt*�*<sup>j</sup>* <sup>þ</sup><sup>X</sup>

*p*

*j*¼1

). Cross-

*nijΔLRit*�*<sup>j</sup>* þ *ϵit* (12)

*ti* (13)

we rearrange Eq. (9)., it is displayed in Eq. (11).

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

same as Equation 54 in Pesaran [15].

by Pesaran [15].

*ΔLRit* ¼ *δ*<sup>0</sup>

*ΔLRit* ¼ *δ*<sup>0</sup>

**210**

*i*

*i*

*dt* þ *α<sup>i</sup> LRit*�<sup>1</sup> � *β*<sup>0</sup>

Eq. (14) can be rewritten as below:

*dt* þ *αiLRit*�<sup>1</sup> þ *λ*<sup>0</sup>

*<sup>Δ</sup>LRit* <sup>¼</sup> *<sup>α</sup><sup>i</sup>* <sup>þ</sup> *<sup>β</sup>iLRit*�<sup>1</sup> <sup>þ</sup> *<sup>ω</sup>iLRt*�<sup>1</sup> <sup>þ</sup><sup>X</sup>

**4.4 Investigation of long-run relationship**

where *dt* represents deterministic components vector (intercept and trend), *λ*0 *i* =�*αiβ*<sup>0</sup> *<sup>i</sup>* is the long-term parameter, *ϑij* and *γij* are short-term parameters. Westerlund [16] test is based on four statistics. Two of them are group mean statistics (*Gα*, *GT*Þ. Autoregressive parameter in group mean statistics varies from unit to unit. Group mean statistics can be formulated as in Eq. (16).

$$G\_a = \frac{1}{N} \sum\_{i=1}^{N} \frac{T\hat{\alpha}\_i}{\hat{\alpha}\_i(\mathbf{1})}, \qquad G\_T = \frac{1}{N} \sum\_{i=1}^{N} \frac{\hat{\alpha}\_i}{\text{SE}(\hat{\alpha}\_i)} \tag{16}$$

in which *SE* denotes the standard error of *α*^*i*. Other two statistics of Westerlund [16] are panel statistics (*Pα*, *PT*Þ. They are calculated by using whole information on panel. Panel statistics are shown in the following equations:

$$P\_a = T\hat{a}, \qquad P\_T = \frac{\hat{\alpha}}{\text{SE}(\hat{\alpha})} \tag{17}$$

The rejection of the hypothesis of interest (*H*<sup>0</sup> : *β<sup>i</sup>* ¼ 0 *for all i*Þ in both groups of tests signifies the existence of a cointegration relationship. If the variables are longterm cointegrated, the cointegration model can be estimated in different ways depending on whether the long-term covariance is homogeneous or not. Since the long-term covariance is homogeneous in this study, the panel dynamic least squares (PDOLS) estimator by Kao and Chiang [42] is used to estimate long-term relation. Kao and Chiang PDOLS estimator can be obtained by estimating regression model below [42]:

$$LR\_{it} = a\_i + \text{CE}\_{it}\beta + \sum\_{j=-q}^{q} c\_{ij}\Delta\text{CE}\_{it+j} + v\_{it} \tag{18}$$

where *β* is long-term parameter. According to Kao and Chiang's Monte Carlo simulation results, the PDOLS estimator and t statistics are successful in all cases of homogeneous and heterogeneous panels.
