Stationary And Unit Root Testing Finance Essay

The chief aim of this survey is to analyse the impact of fiscal services sector on UK economic growing. Although it is clear from the literature that economic growing and fiscal development are positively related but our research aims to happen this relationship in footings of UK because UK is a developed state with such a immense economic system and most significantly has ever been much dependant on its fiscal sector. This chapter throws visible radiation on the fiscal system of UK and analyses the part and importance of fiscal service sector in UK over the period 1992-11. The ground of taking these old ages for the survey is that such extended period of 20 old ages provides a good sample and can give better consequences. Besides this period includes old ages both before and after the fiscal crisis of 2007. This helps analyzing the clear part and importance of fiscal sector for the UK economic system. The theoretical literature discussed above provides clear indicant that fiscal development and economic growing are positively correlated. Empirical grounds from many surveies besides supports the fact that economic growing and fiscal development is positively related. The findings by Christopoulus and Tsionas ( 2004 ) , provides back uping grounds about the co-integration of growing, fiscal development and investings.

3.2 Data Selection and Collection

The informations used for our survey is same as used by different surveies in our literatures. For the empirical analysis the information is collected for the period 2002-2011. Time series theoretical account is used to measure the part of the fiscal services sector on economic growing. Based on the theoretical positions and following the empirical analysis by Abu-Qarn and Abu-Bader ( 2005 ) , King and Levine ( 1993 ) . Levine and Zervos ( 1998 ) , Beck ( 2000 ) , Christopoulos and Tsionas ( 2004 ) , Ang and McKibbin ( 2005 ) , Khan et Al ( 2005 ) and Khan and Qayyum ( 2006 ) , Kargbo and Adamu ( 2009 ) , the fiscal indexs used for our survey will be same as used in these surveies. Along with the fiscal indexs of growing, other major factor of economic growing will besides be taken into consideration for arrested development analysis. The indexs for both of our variables 1 ) fiscal development and 2 ) economic growing are the same as used by research workers in our literatures. Following fiscal development indexs are most normally used by King and Levine ( 1993 ) , Levine and Zervos ( 1998 ) , Abu Qarn and Abu Bader ( 2005 ) and Coleman and Tettey ( 2008 ) ( Table 4.1 ) .


Indexs used

Size of the fiscal system

Fiscal deepness

Ratio of fiscal Assets to GDP

Efficiency of fiscal system

Commercial Bank Assets v/s Central Bank Assetss

Activity of Financial system

Banks private recognition to GDP

Structure of fiscal system

Ratio of chief fiscal establishment ‘s assets to entire fiscal assets

So looking at the indexs, we can acquire an thought that secondary informations is more appropriate for this research so secondary information is used for this research. The ground is that secondary informations is easy to roll up and less expensive. The point to see in secondary informations is that it should be taken from some dependable and trusted resource and for the intent of our research ; informations is taken from following sure beginnings.


Bank of England

World Bank

International Financial Statistics

Central Statistical Office

3.4 Econometric Model

A clip series theoretical account is used to measure the part of fiscal service sector on economic growing. The econometric theoretical account constructed for this survey is as follows:

RGDP=f ( FD, X ) ;

Where RGDP is the index of economic growing, FD is the fiscal development indexs and X is the other independent variables impacting growing. The two indexs of fiscal development used in our survey are M2 and CPS ( recognition to private sector ) . The impact of two indexs impact is analyzed maintaining other variables same. Two econometric theoretical accounts are used to see the affect of both indexs individually and theoretical accounts are as follows:

RGDP= degree Fahrenheit ( INVG, M2, INF, HC ) ( 1 )

RGDP=f ( INVG, CPS, INF, HC ) ( 2 )

Inspired from the surveies by Abu-Qarn and Abu-Bader ( 2005 ) , King and Levine ( 1993 ) . Levine and Zervos ( 1998 ) , Beck ( 2000 ) , Christopoulos and Tsionas ( 2004 ) , Ang and McKibbin ( 2005 ) , Khan et Al ( 2005 ) and Khan and Qayyum ( 2006 ) , Kargbo and Adamu ( 2009 ) , equations ( 1 ) and ( 2 ) are designed as follows to happen the relationship between economic growing and fiscal development:

LRGDPPC= i??iˆ°iˆ«i??iˆ± LINV + i??iˆ?i??iˆ? +i??3INF+i??iˆ?HC+i?? iˆ?iˆ?iˆ©

LRGDPPC=i??iˆ°iˆ«i??iˆ± LINV + i??iˆ?CPS +i??3INF+i??iˆ?HC+i?? iˆ?iˆ?iˆ©

Where, RGDPPC is the dependent variable and is the index of growing. RGDPPC is the existent growing rate of GDP per capita. It is the macroeconomic step of the entire income and end product of the economic system. M2 and CPS are the steps of fiscal deepness, INV represents the investing and it is the ratio of gross fixed capital formation to GDP. The portion of investing is proxied by the ratio of gross fixed capital formation to nominal GDP. This includes the add-on to the physical assets of the state including works and machinery, edifices and other equipments, all valued at market monetary values. INF is the rising prices rate. It is expected to hold a negative impact on the economic system of the state. It affects the economic activities, therefore has an impact on the economic growing of any state. Harmonizing to Coleman and Tettey ( 2008 ) , high rate of rising prices addition the macroeconomic instability status. HC is the human capital which is considered to be an of import determiner of growing ( King and Levine, 1993 ) and vitamin E is an error term. Real GDP, INVG, M2, INF and HC are expressed in natural logarithmic signifier ( Kargbo and Adamu, 2009 )

In our survey, the economic growing index used is RGDPPC which is measured by taking changeless 2000 US $ GDP which takes affect of rising prices as good. The index twelvemonth used is 2000. The two fiscal development indexs are used- ratio of M2 to GDP, ratio of private sector recognition to GDP, and the ratio of private sector recognition in domestic recognition. These fiscal indexs are described below.

M2 to GDP

The ratio of M2 to GDP is calculated by spliting M2 by nominal GDP. M2 is one of the common indexs of fiscal development used in many researches. M2 is the Money and quasi money comprise the amount of currency outside Bankss, demand deposits other than those of the cardinal authorities, and the clip, nest eggs, and foreign currency sedimentations of resident sectors other than the cardinal authorities ( International Financial Statistics ) . M2 to GDP is a step of fiscal deepening, therefore it measures the state ‘s ability to utilize the best of its resources. We expect M2 to hold a positive impact on fiscal service sector and therefore the economic growing. King and Levine ( 1993 ) made usage of M1 to GDP alternatively of M2, but this survey will utilize M2 because this is largely used to estimate the economic pecuniary conditions. Hassan and Jung-Suk ( 2007 ) used the ratio of M3 to GDP as a placeholder of fiscal deepness. They argue that other pecuniary sums like M1 and M2 may be hapless placeholders in economic systems with developing fiscal system, where a high ratio of money to GDP exists because money is used as shop of value in the absence of other more attractive options. Vuranok ( 2009 ) found that M3 to GDP can non be a alone index of fiscal development. M3 is argued because of the failing that it does non reflect the allotment of nest eggs and so may non be an accurate index of the activities of fiscal mediators. M2 is criticized to be used for developing fiscal system whereas UK has good developed fiscal system so it can be a good fiscal development index. Based on the unfavorable judgment on other indexs this survey found M2 to be good index.

CPS ( Credit to Private Sector )

The 2nd step of fiscal development is the ratio of domestic recognition to the private sector to GDP. Recognition to the private sector represents the ability or the size of the banking sector. In the position of King and Levine ( 1993 ) , the recognition allocated to the private sector is clear part to growing alternatively of apportioning recognition to public endeavors which do non take to accomplish the efficient allotment of resources. Private recognition includes all group of fiscal mediators non merely lodge money Bankss. So this is one of the fiscal indexs chosen for our survey because it is most widely accepted and tested by the researches in our literature.

To gauge the relationship between our variables, we will follow a stepwise process. The first measure of the survey is to see the clip series variables that whether they are stationary or non. Largely fiscal clip series has non-stationary mean. Non-stationary variables create the job of specious arrested development. Unit root trials are most normally used to find swerving informations. Augmented Dickey Fuller ( ADF ) trial is the most popular and standard trial for unit root and is most normally used. The variables for the clip series should be stationary. Therefore, logarithms of clip series are taken and Augmented Dickey Fuller Test is used for proving series for stationary.

3.5 Unit Root Test

3.5.1 ADF Test ( Augmented Dicker Fuller )

Stationary and Unit Root Testing

A stationary series have a changeless mean, changeless discrepancy and changeless car covariance for each given slowdown. Some seasonal affects, dazes affect the series tendency. Time series should be made free from all these effects to do a right rating with right theoretical accounts ( Vuranok, 2009 ) . Differences of the clip should be taken until series will be stationary at same degree. One of import hazard of taking these differences is that the series may free the long term relationship possible. Thus it is best if the series is stationary at zero order degree I ( 0 ) which means it has no unit roots.

One of the methods to prove whether series is stationary or non is Dickey-Fuller ( DF ) ( 1979 ) , “ DF trial is really of import in footings of mensurating which degree stationary series have, but it does non see an autocorrelation in disturbance term. If disturbance term contains autocorrelation, DF trial is invalid ” ( Vuranok, 2009 )


3.6.1. Engle and Granger Co-integration Test

A stationary co-integration relationship is performed utilizing Engle and Granger two measure process. “ If there is no co-integration between the variables, it can be continued with Granger Causality Test without including mistake rectification footings. If there is a co-integration between the variables, Granger Causality Test will be failed and it will be surely necessary to be included error rectification term into the theoretical accounts ” ( Vuranok, 2009 ) . Granger Causality trial besides gives information about the short-run relationship between the variables. We will regress our equation utilizing Ordinary Least Squares ( OLS ) to look into if there is co-integration among our variables. Then if there is co-integration, mistake rectification theoretical account is used to look into the short tally consequence.

Chapter 4: Consequences

4.1 M2 to GDP

The first fiscal index of our survey to prove for its impact on economic growing is M2 to GDP. So the arrested development equation to find this relationship is as follows:

RGDPPC= i??iˆ°iˆ«i??iˆ±INVG + i??iˆ?M2 +i??3INF+i??iˆ?HC+i??

Where, RGDPPC = Real gross domestic merchandise per capita

INVG= Ratio of investing to GDP

HC= Human Capital

INF= Inflation Rate

M2= demand sedimentations, foreign currency sedimentations, nest eggs and currency outside Bankss

Below is the drumhead statistics of our variables in logarithmic signifier.

The statistics consequences shown in table 4.1 are converting and show that our informations of the variables can suit in our theoretical account good.

4.2.1 Stationary and Unit Root Testing

Following are the hypothesis to prove series

H1: i?? = 0 ( Yt is non-stationary )

H2: i?? a‰ 0 ( Yt is non non-stationary )

T-statistic value and Dicker Fuller value is obtained and comparing is made. If t-ratios are greater than Dicker Fuller value than we can state that variables are stationary.

It can be decided by comparing these values with ADF trial statistics whether series are stationary or non. If ADF trial statistic is greater than McKinnon critical values perfectly, the series are stationary at that degree.

Table 4.2 ADF Test Statistics

Table 4.2 shows that all of our variables are non-stationary at flat signifier because the value of t-statistic is less than the critical values at 95 % significance degree. So the trial will hold to be carried out at first order degree. The first order degree requires differencing of non-stationary variables so that we can bring forth the stationary series.

Table 4.3 ADF Test at First Difference

Table 4.3 shows the consequences of ADF trial at first difference degree. It can be clearly seen from the consequences that all variables are stationary at first difference degree, as the values of t-statistics are greater than critical values at 5 % assurance degree. The SchwartzBayesian Criterion ( SBC ) and Akaike Information Criterion ( AIC ) are used to find the optimum figure of slowdowns included in the trial. These consequences are obtained utilizing Akaike Information Criterion. Once it is tested from ADF trial that variables behave as incorporate procedure, the following measure is to execute co-integration.

4.1.2 Engle and Granger Co-integration Test

Following hypothesis is tested utilizing granger co-integration trial.

H0: i??= 0 ( there is no co integrating between the series )

H1: i??iˆ a‰ 0 ( there is co integrating between the series )

Table 4.4: OLS ( Ordinary Least Square ) Consequences

No of Observations






Roentgen squared






The co-integration trial consequences are reported in table 4.4 and from the consequences above, our equation can be written as follows:

RGDPPC= -31.40+ 11.71INV+ 0.19M2+ 1.818HC- 0.54INF ( 5 )

The value of our intercept is negative which means that if all the explanatory variables remain changeless so if all other factors increase by 1 % , economic growing will diminish by 31 % . From the coefficient consequences we can see that economic growing is positively related with fiscal index used for our survey ( M2 ) . If there is 1 % addition in M2, economic growing will increase by 0.19 % .

Investings are besides positively related to growing. The magnitude of the coefficient implies that a 1 % addition in investings can do a alteration of 11.71 % in economic growing. Our consequences confirm the literature by Christopoulus and Tsionas that economic growing and investings are correlated.

The coefficient calculated for human capital besides have positive mark which means it is besides positively related to growing. As Barro ( 1991 ) suggested in its survey that states with high degree of human capital have more opportunities to spread out its physical capital and therefore higher ratios of investing.

The coefficient of rising prices is negative from which we can infer that rising prices and economic growing has negative relationship. An addition in 1 % rising prices can diminish the economic growing of UK by 0.54 % , therefore impacting the economic system severely. Our consequences supports the surveies by Barro ( 1995 ) , Bruno and Easterly ( 1998 ) , Bullard and Keating ( 1995 ) , DeGregorio ( 1992 ) , Fischer ( 1993 ) , Levine and Renelt ( 1992 ) , and Wynne ( 1993 ) , that rising prices and economic growing are negatively related to each other.

All the variables in our theoretical account are statistically important therefore they have an of import function in economic growing. All affect the economic growing in one manner or the other.

To prove the co-integration foremost the variables should be stationary at first difference degree and so so the remainders should be tested for stationary utilizing Dicker Fuller Test so our hypothesis is

H0: i??= 0 ( Remainders are non-stationary )

H1: i??iˆ a‰ 0 ( Remainders are stationary )

Where H0 is void hypothesis and H1 is alternate hypothesis.

If we reject the void hypothesis that means that the remainders are stationary and hence, the series are co-integrated.





The consequence obtained for the estimation of residuary mistake to be stationary shows that there is co-integration as the t-statistic is greater than the critical value of Dicker Fuller trial so we reject the void hypothesis. If there is co-integration among variables, this means that we can utilize error rectification theoretical account to find the short tally estimation for our survey.

4.1.3 Error Correction Models

The appraisal consequences of error rectification theoretical account are as follows:

Table 4.5: Short Run Effectss

No of Observations






Roentgen squared






Table 4.5 study the consequences of error rectification theoretical account. From the consequences obtained we can see that 44 % of the fluctuation in economic growing is explained by our theoretical account. The value of F-statistics is 2.055 which mean our variables have explained the growing form of UK. Most significantly the value of mistake coefficient is negative which means that there is a long tally relationship between the variables of our theoretical account.

Turning to the fiscal development index of our theoretical account, it can be seen that its value is smaller than that in the long tally. If the coefficient is smaller than that means that economic growing is sensitive to fiscal development in the short tally and is more dominated by its effects in the short tally. So our consequences suggest that kineticss have small consequence in the long tally than in the short tally.

Our findings suggest that secondary school registration is more of a concern for economic growing in the short tally every bit compared to long run as its value is greater in the short tally. So this determination supports the endogenous growing theory on the importance of human capital for economic growing.

The investing has besides positive coefficient ( 8.555 ) and shows that it is extremely important for our theoretical account as it has the highest coefficient demoing its major impact on economic growing of UK. The positive and important consequence of investing supports the consequences by Khan et Al ( 2005 ) . Turning to rising prices, this has a negative impact on economic growing both in the short and in the long tally. This has about equal short and long tally impact on economic growing. This confirms that rising prices conveys the bad signal for economic growing. The ground explained by many research workers for this impact of rising prices is that as monetary values increases, people ‘s ingestion power lessenings and therefore in the international market, for the trade intent, the economic system become less competitory.

The consequences of short-term dynamic coefficients indicate that the variables have the expected marks as in the long tally. The value of mistake rectification term ( -1.8 ) suggests that the velocity of accommodations from short tally divergences to hanker run equilibrium growing is really low and therefore the consequences are statistically important. It indicates that the behavior of economic growing is dominated by short tally dynamic effects. Therefore from the consequences we can state that UK has a developed fiscal system

4.2 Credit to Private Sector ( CPS )

A 2nd fiscal index of our survey to prove for its impact on economic growing is CPS. For CPS this survey undertake the information of domestic recognition to the private sector as % age of GDP. So the arrested development equation to find this relationship is as follows:

RGDPPC= i??iˆ°iˆ«i??iˆ±INVG + i??iˆ?CPS +i??3INF+i??iˆ?HC+i?? iˆ?iˆ¶iˆ©

Where, RGDPPC = Real gross domestic merchandise per capita

INVG= Ratio of investing to GDP

HC= Human Capital

INF= Inflation Rate

CPS= Credit to Private Sector

Table 4.6 Drumhead Statisticss

Table 3.5 provide the drumhead statistics of our theoretical account in natural logarithmic signifier. The consequences of the statistics support our informations and the theoretical account selected for our survey.

4.2.1 Stationary and Unit Root Testing

The 2nd fiscal index affect will besides be tested utilizing Engle Granger two measure process. First OLS arrested development is performed and reported below in the tabular array.

Table 4.7 OLS Regression consequences

No of Observations






Roentgen squared






Depending on the consequences calculated above in table 4.7, our equation can be written as

RGDPPC= -13.09 + 0.58CPS-0.68INF-2.50HC+11.45INV ( 7 )

The value of our intercept indicates that there are no other factors that can impact economic growing other than our explanatory variables. Although this does n’t look to be practical but this may be due to the restrictions of our survey which involves secondary informations and can besides be due to the clip series taken for our survey.

Our fiscal index has shown a positive relation with economic growing. If there is 1 % addition in CPS, economic growing additions by 0.57 % . Inflation has a negative correlativity with growing which has antecedently cleared by many of the surveies in our literature that rising prices can hold an inauspicious effects on economic growing in the long tally ( Agenor, 2000 ) .Human capital bears negative mark which means if human capital additions by 1 % , economic growing lessenings by 2.5 % points.

From the OLS consequences we can infer that investing has been an of import determiner of growing in instance of UK. Our consequences confirm the positions by different research workers that investing encourages economic growing.





The consequence of the residuary mistake trial for stationary shows that there is co-integration among variables and therefore short tally estimation can be performed utilizing mistake rectification theoretical account.