Econometric Modelling of Income-consumption Relationship: Evidence from Nigeria

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1 British Journal of Economics, Management & Trade 16(2): 1-15, 2017, Article no.bjemt ISSN: X SCIENCEDOMAIN international Econometric Modelling of Income-consumtion Relationshi: Evidence from Nigeria R. K. Ayeni 1* and K. F. Akeju 1 1 Deartment of Economics, Ekiti State University, Ado Ekiti, Nigeria. Authors contributions This work was carried out in collaboration between both authors. Author RKA concetualized and designed the study and analyzed the data. He also did the interretation of results and wrote the first draft of manuscrit. Author KFA managed the literature searches, did critical review and comments on the manuscrit. Author RKA read and aroved the final manuscrit. Article Information DOI: /BJEMT/2017/26967 Editor(s): (1) Chiang-Ming Chen, Deartment of Economics, National Chi Nan University, Taiwan. Reviewers: (1) Afsin Sahin, Gazi University, Turkey. (2) Beatrice Njeru Warue, Africa International University, Kenya. (3) Fabrício Pitombo Leite, Federal University of Rio Grande do Norte, Brazil. Comlete Peer review History: htt:// Original Research Article Received 12 th May 2016 Acceted 2 nd November 2016 Published 26 th January 2017 ABSTRACT This aer seeks to emirically verify the dynamic relationshi between consumtion exenditure and income in Nigeria by exerimenting with two major income hyotheses, the habit ersistence and ermanent income hyotheses. The major research question centred on which of the consumtion theories best describe the relationshi between consumtion and income in Nigeria? Time series data on er caita ersonal consumtion exenditure (PPCE) and er caita disosable income (PPDI) in Nigeria for the eriod were used. The result of the AR() time series estimation showed the weak existence of habit formation by Nigerian consumers. The seed of the short-run adjustment of consumtion exenditure to changes in disosable income is , which is averagely high; an indication that consumtion habits are quickly adjusted to changes in disosable income. Due to the high level of overty, unemloyment and low standard of living, consumers in Nigeria find it difficult to form a consumtion habit for long. Modelling consumtion along the assumtions of Permanent income hyothesis; the results of the ARDL bound testing cointegration showed that the long-run multilier effect of marginal roensity to consume out of ermanent income is ; an indication that consumers save more than send. *Corresonding author: rahayeni@gmail.com;

2 This also imlies that Nigerians on the average have a low ermanent income and a higher transitory income which does not affect consumtion according to the assumtion of Permanent Income of hyothesis. The study therefore recommends that olicies towards reducing the rate of unemloyment and alleviate overty in the Nigeria economy should be ut in lace to encourage good consumtion habits. Keywords: Habit ersistence; ermanent income; er caita ersonal consumtion; er caita income; ARDL. 1. INTRODUCTION Nigeria, mostly referred to as the giant of Africa [1] and endowed with natural resources is characterized by overty, oor savings geared by high consumtion for basic needs among her eole and high rate of unemloyment. This feature tends to be a general form of the sub Sahara region thereby resulting into stagnation of the region. [2] attested to this by identifying that the rates of saving in the ast three decades doubled in East Asia and stagnated in Sub- Saharan Africa, Latin America and the Caribbean constituted to oor growth and develoment of the region. Consumtion which can be described as the final urchase of goods and services by individuals is largely determined by income level. Many theories view the resonse of household consumtion to household economic resources; [3]' General Theory in 1936 identified the relationshi between income and consumtion as a key macroeconomic relationshi. The theory asserts that as income rises, consumtion also rises but not necessarily with the same amount. Rich eole are exected to consume a lower roortion of their income than oor eole. Habit ersistence hyothesis of [4] identified ast consumtion habits as a major determinant of resent growth rate of consumtion. The ermanent income hyothesis of [5] on the other hand is a theory of consumer sending which states that eole will send money at a level consistent with their exected long term average income. The consumtion attern of households in Nigeria is such that is determined by their income, ast behaviour, or future exectations thus leading to a dynamic aroach to the study. Peole in different ositions in resect to income have different structures of consumtion. National saving at the macro level is low because Nigeria s economy is a consuming nation with a low national income as a result of low consumtion of locally made roducts in the country. The ersistent budget deficit in Nigeria is an indication of high exenditure and of this, consumtion occuies the share of gross domestic exenditure comosition. The major objective of this aer is to study the dynamic relationshi between consumtion exenditure and income in Nigeria by exerimenting with the Habit Persistence and Permanent Income Hyotheses resectively. The major research question is which of the consumtion theories best describe the relationshi between consumtion and income in Nigeria? The aer is divided into five sections. Section two after the introduction is the review of literature. Section three is the data and descritive analysis, section four is the theoretical framework and emirical analysis. Section five is the conclusion and olicy recommendations. 2. REVIEW OF LITERATURE [6] conducted a research on the imact of change in income on Private Consumtion Exenditure in Nigeria from 1981 to 2010 with the use of Ordinary Least Regression techniques. Their analysis indicated that a ositive significant imact of Gross Domestic Product /income is felt on Private Consumtion Exenditure in the country. This conforms to a riori exectation but the use of ordinary least regression technique is not statistically sufficient and robust for the analysis and this renders their work invalid. [7] analysed relations between er caita consumtion exenditure and ersonal income in India using ordinary least square technique, Granger Causality and Koyck transformation aroach for the eriod covering 1950 to The result indicated that unidirectional causality flows from er caita consumtion exenditure to ersonal disosal income in the country while the Koyck Model indicates that er caita ersonal 2

3 consumtion exenditure adjusts to ersonal disosable income within a relatively long eriod of time. This is an indication that major art of the eole s income is being sent on consumtion exenditure in India thus militating against savings. [8] analysed how rivate saving in Nigeria is determined using data covering using the Error-Correction modelling rocedure and found that savings rate increases as the interest on deosits with banks and the disosable income of individuals increases. He concluded that income based for the nation must be increased to enhance savings. [9] emirically verified if the habit ersistence hyothesis holds in the Jamaican economy. He used the Generalized Method of Moments time series estimation on Jamaican data of income, domestic interest rate inflation and exchange rate from 1980 to His results show that the existence of habit formation is very high among the Jamaicans and ast consumtion and habits of the consumers have effect on the consumtion growth rate in the country. He concluded that to encourage good consumtion habits and confidence, domestic interest rate inflation rates and exchange rate have to be adjusted moderately. [10], while attemting to gauge the marginal roensity to consume (MPC) and the average roensity to consume (APC) in Nigeria in the eriod found conformity in both MPC and APC result with the Keynesian roosition. Argument against this study lies in the used of co-integration regression estimate with dataset of only 25 years san which is not acceted under asymtotic analysis. [11], analysed household consumtion exenditures in EA-18 using anel data model with data between and found that a one dollar increase in gross domestic roduct will have an increase of 0.57 dollar on household consumtion. The study used gross domestic roduct as a roxy for income and concentrated on the effect of increase in gross domestic roduct on household consumtion without consideration on the role of saving on the household consumtion exenditure. [12] identified the effect of consumtion function on aggregate demand and the multilier effect on the Nigerian economy. Using ordinary least square techniques with quarterly data between 2009 and 2014, the study found that the erformance of the economy was better in the ost global financial recession eriod than the eriod that recede it. Macroeconomic variables such as Consumtion, balance of trade, investment and government exenditure also exhibit ositive relationshi with the growth of aggregate demand in the eriod. 3. DATA AND DESCRIPTIVE ANALYSIS This study uses both statistical and descritive analysis to model income-consumtion relationshi in Nigeria using data sanning from 1980 to The statistical analysis involved the use of airwise granger causality, the Koyck's transformation Model and the Auto Regressive Distribution Lag model which hels in modeling the relationshi existing between consumtion exenditure and disosable income in Nigeria using both the habit ersistence hyothesis and the ermanent income hyothesis. This section resents the trend analysis of the er caita ersonal consumtion exenditure (PPCE) in relation to er caita disosable income (PPDI) in Nigeria for the eriod The data measured in million current US dollar, were sourced from the World Bank data bank. From the trend analysis above income (PCDI) aears to be more volatile than consumtion (PPCE). While consumtion (PPCE) looks stable or durable over the years, income fluctuates. The more stable or durable consumtion may imly that consumers may find it difficult to form consumtion habit and sustained it for long. Also the more volatile income follows the Permanent Income hyothesis tenet that believes that individuals base their consumtion on a longer term view of an income measure. There is a jum in consumtion between 2000 and 2008 and from 2011 in Fig. 1. These eriods were the eriod of minimum wage increase in Nigeria. The dro in PCDI witnessed from 2008 to 2010 was robably due to high tax rate which led to clamouring for a new minimum wage that eventually took effect from January It is necessary that we study the direction of causality between the two variables. The result of the air wise Granger causality test is shown in Table 1. The test is sensitive to the lag length, the choice of 2 lags was made using the iterative method, that is gradually increasing the lag length until there is no further imrovement in the decision making [13]. 3

4 PPCE PCDI Fig. 1. Trend in er caita ersonal consumtion exenditure and er caita disosable income in Nigeria ( ) Table 1. Pairwise granger causality Null hyothesis Obs. F-statistic Prob. Decision PCDI does not Granger Cause PPCE Reject PPCE does not Granger Cause PCDI Reject The idea behind causality test is that, although regression analysis deals with the deendence of one variable on the other variable, it does not necessarily imly causation. In other words the existence of a relationshi either the dynamic or equilibrium, between variables does not rove causality or the direction of influence. Table 1 resents the direction of influence between the variables in a air-wise manner. The decision whether to reject or accet the null hyothesis is made based on the robability of the F statistics. Wherever the null hyothesis is rejected it imlies the accetance of the alternative hyothesis. At 0.05 level of significance, the result shows that there is a bidirectional causality between PPCE and PCDI. That is rivate ersonal consumtion exenditure granger cause er caita disosable income and vice-versa as shown by the robabilities. Following our objective, PPCE is a made the endogenous variable for this study. 4. THEORETICAL BACKGROUND, MODEL SPECIFICATION AND ESTIMA- TION 4.1 Habit Persistence Hyothesis Model If we base our consumtion function on the Habit Persistence Hyothesis of [4], the model follows a distributed lag system, DL () where is the lag length. The lag length here reresents the length of consumtion habit already formed by the consumer. Following the assertion that habit fades away but gradually, we can assume that the imact of the habit on resent consumtion follows a declining lag. Thus we have: 2 PPCE α + β PCDI + β λpcdi + β λ PCDI + L + u...(1.0) t = 0 t 0 t 1 0 t 2 t 4

5 If we rationalise our choice of distributed lags of ast consumtion exenditure in equation 1.0 using the Koyck s transformation, the Habit ersistence model for this study is defined as an AR() model as follows: PPCEt = α + β0pcdi t + λppcet j + ut...(2.0) where α = α (1 λ); v t = ( u t λu t 1 ), a moving average λ is such that 0 < λ < 1 = rate of decline of the distribute d lag. PPCE t = er caita ersonal consumtion exenditure PCDI t = er caita disosable income Exlaining equation 2.0 in terms of Euler s relation, λ is the arameter reresenting habit ersistence which is exected to be less than zero if there is evidence of habit formation and greater than zero if the effect durability dominates. If both effects are resent the sign of the coefficient which of the two effects dominates. Habit ersistence imlies that the coefficient of lagged consumtion exenditure is negative, while durability imlies ositive coefficient for the variable [14]. Equation 2.0 was estimated using the OLS. But a major hindrance is the choice of the number of lag. We resort to the method of iteration, testing for serial correlation using the LM test and heteroscedasticity using the ARCH test in each case. Lag 2 was chosen as free from serial correlation and heteroscedasticity roblem. The result of the AR (2) estimation of consumtion exenditure is resented in Table 2. The two coefficients of lagged consumtion are both ositive, imlying that there is evidence of durability rather than habit formation in the consumtion exenditure in Nigeria. If we assume the distribution effect of ast consumtion exenditure on the resent consumtion exenditure follows the Koyck s relation [15], the rate of decline of the distributed lag is λ which is the median lag is log 2 = logλ λ = λ And the Mean lag is Table 2. Koyck's model of consumtion exenditure in Nigeria Deendent variable: PPCE Variable Coefficient Std. Error t-statistic Prob. PCDI C AR(1) AR(2) R-squared F-statistic Adj. R-squared Prob(F-statistic) Breusch-godfrey serial correlation LM test: F-statistic Prob. F(2,25) Obs*R-squared Prob. Chi-Square(2) Heteroskedasticity test: ARCH F-statistic Prob. F(1,28) Obs*R-squared Prob. Chi-Square(1) Inverted AR Roots

6 The median lag is the time required for the first half, or 50 ercent, of the total change in consumtion exenditure following a unit sustained change in er caita disosable income. Here it is that is, in less than 1 eriod of time, 50% of the total resonse of rivate ersonal consumtion exenditure resonds to changes in er caita disosable income. On the average it seems as if consumtion exenditure adjusts to er caita disosable income in a relatively short time (0.2048) which is very fast. This also suggests that consumtion exenditure shows durability rather than habit formation. This imlies Nigeria consumers find it difficult to form habit in their consumtion decision for long eriod. The next model exlains both the Habit Formation and Exected income simultaneously. 3.2 Permanent Income Hyothesis Model On the other hand if we model our consumtion function following the Permanent Income Hyothesis of [5], the ingredients of such model are ermanent consumtion ( ce ), ermanent income ( cdi ), transitory consumtion and transitory income. Present income is the sum of ermanent and transitory income and consumtion at time t is the sum of the ermanent and transitory comonents. Friedman also ostulated that there is no correlation between the ermanent and the transitory comonents. That is an increase or decrease in transitory income does not affect ermanent consumtion. The equation determining ermanent consumtion is given by: ce = k( r, z) cdi (3.0) Where k(r,z) is the average (or marginal) roensity to consume out of ermanent income. This deends on the rate of interest r and the taste shifter variable z. Adjusting equation 3.0 by differentiating totally we have dce = krdcdi + kzdcdi dce = kzdcdi + krdcdi ce ** t = β + β cdi 0 1 ** t + u t β = kzdcdi... change in taste shift factor 0 β = kr... m arg inal roensity toconsume out of 1 ermanent income Where ce and ** t cdi are desired change in ersonal consumtion exenditure (ermanent ** t consumtion) and exected change in income (ermanent income) resectively. These are not directly observable; we used the artial adjustment mechanism to derive the desired consumtion exenditure and the adative exectation model for the exected level of income, called the ermanent income. The resultant model is an ARDL model [13]. Since Permanent income hyothesis is a long run measure of relationshi between consumtion exenditure and income, cointegration analysis was therefore emloyed. Table 3. Unit root tests AT levels 1 st difference I() Variable ADF test 1% C.V. 5% C.V. Prob. ADF test 1% C.V. 5% C. V. Prob. PCDI I(1) PPCE I(1) 6

7 To test for stationarity of the variables, the Augmented Dickey Fuller (ADF) and Phili Peron (PP) unit root tests were conducted on each series. The correct secification is to include trend variable and intercet since the descritive analysis in Fig. 1 shows that the two variables are trended. Accordingly the null hyothesis in each case is that there is a unit root in each series that is each variable is non-stationary. The result is resented in Table 3. The results of the ADF unit root test in Table 3 shows that the variables are integrated of the same order. Likewise the result of the PP unit root test did not deviate from the ADF. (see Aendix 1). This imlies that the condition for cointegration using the Johannsen method was met by the series. The major objective of this study is to analyse both the long run and short run dynamic relationshi between the two variables via the ARDL. The Bound test cointegration aroach develoed by [16] was used along with the Johanssen technique, to test the long-run equilibrium relationshi between the variables. The result of the Johannsen technique is resented in Aendix 2. Only the trace test reorts the resence of one cointegrating equation. We refer to use the ARDL aroach because it effectively corrects for ossible endogenity of exlanatory variables [17], and the estimates exhibit desirable small samle roerties and our samle is not too large. The bound test regression is theoretically secified in two ways, the original version as shown in equation 5.0 and the E-views version. The original version of the secification (log cet ) = β 0 + β j (log cet 1) + γ 1 (log cdit j ) + θ 0 log( cet 1) + θ1 log( cdit 1) + et where j = 0,1,2, Equation 5.0 is the ARDL model of the consumtion-income relationshi which is also known as the unrestricted ECM. It was used to estimate the short-run (cointegrating form) of the ermanent income hyothesis and the long run coefficients. Using E-views 9 version, the maximum lag for the endogenous and exogenous variables was selected in such a way that the degree of freedom (defined as n-k) must not be less than 30. The Linear Trend otion was also selected because the two variables were trended. The aroriate lag selection for the otimal lag was determined using the Schwartz (SC) criterion. One lag was selected as otimal for the PPCE while zero lag was selected for PCDI. The result as shown in Aendix 3, is the referred regression on which the Bound test was conducted. The Bound test was conducted on the unrestricted ECM in Aendix 3, by conducting the F statistics of the hyothesis, H θ = θ = θ 0 against the alternative. As a check we erform a Bounds 0 : = F-test of H 0, if the F-statistic is greater than the Critical Value Bounds for the uer bound I(1), 0 = this would suort the conclusion that there is a long-run relationshi between the variables. If the comuted F statistic falls below the lower bound we would conclude that the variables are I(0), so no cointegration is ossible by definition. Finally if the F statistics falls between the bounds, the test is inconclusive, we may rely on the result of Granger causality and/or the short-run analysis. The result is shown in Table 5. To test for the resence of cointegration in the ermanent income model, we comare the F-statistics of the null hyothesis with Critical values. In Table 4. the value of our F-statistic is , which is greater than the uer bound at 10% level of significance. As the value of our F statistic exceeds the uer bound at the 10% level we can conclude that there is evidence of a long-run relationshi, even though weak, between PPCE and PCDI. This suorts the results of the Johannsen method earlier discussed. To give room for seasonality in the variables, as suggested by the trend analysis in Fig. 1, a dummy exogenous variable was included in equation 5 and we exerimented by tesing for cointegration using the two methodologies. The result of the Johannsen technique is not different from when no dummy variable was included. The result of the Bound Test with dummy variable did not erform better either. The two results are resented in Aendix 4 and 5 resectively. Our referred result is the result in Table 4. 7

8 Table 4. ARDL bounds test H0: No long-run relationshi exist Test statistic Value K F-statistic Critical value bounds Significance I(0) Bound 10% % % % I(1) Bound We can therefore estimate both the short-run and the long-run dynamics form of the underlying ARDL result of Aendix 3. The result is shown in Table 5. The long-run marginal roensity to consume from ermanent income is derived from the following equation. The ARDL Result in Table 5. resents both the short-run dynamic, that is error correction mechanism and the long-run dynamics of the imact of income on consumtion exenditure. Recall that the major objective of this study is to study the dynamics of Consumtion-Income relationshi by exerimenting with the Habit Persistence and the Permanent Income Hyotheses. Our selection of ARDL over the Johannsen technique was based on the fact that the former model the two hyotheses simultaneously. The results in Table 5. are interreted in three dimensions. The first is the short-run adjustment of consumtion exenditures to changes in er caita income. This is the comonents of habit formation catured by the coefficients of cointeq.1, which is the ECM(-1) coefficient. The coefficient is , significant at 5% as shown by the robability (0.0024). This imlies that consumers in Nigeria form habit in their consumtion, but not ermanently. The seed of adjustment is , which imlies that consumers quickly adjust to changes in their disosable income by shelving their former consumtion habits. This result can also be exlained in direction of irregular ayments of wages, high rate of inflation, witnessed in Nigeria that always lower the real income of consumers. The second influence is catured by the coefficients of DLOG (PCD). This is a measure of the imact of short-run income on consumtion decision, the short-run marginal roensity to consume. The short-run MPC is ositive ( ) and significant at 5% as shown by the robability (0.0402). This imlies that as income increases, consumers in Nigeria tend to increase their consumtion exenditure. A one ercent increase in income leads to a less than one ercent increase in exenditure. The third influence is the imact of ermanent (exected long-run) income on consumtion decision. This is catured by the long-run coefficient of PCDI, which is ositive ( ), and significant at 5% as shown by the robability (0.0015). This imlies that the influence of longrun or exected income on resent consumtion exenditure is high and significant. Consumers are conscious of their ermanent income when taking resent consumtion exenditure decisions. It also imlies that resent consumtion decisions among consumers in Nigeria are influenced by ermanent income rather than the current income or ast habit. Table 5. ARDL Cointegrating and long run form Cointegrating form (Short-run estimates) Variable Coefficient Std. error t-statistic Prob. DLOG(PCDI) D(@TREND()) CointEq(-1) Long run coefficients Variable Coefficient Std. Error t-statistic Prob. LOG(PCDI) C Cointeq = LOG(PPCE) - (0.2953*LOG(PCDI) *@TREND) 8

9 5. CONCLUSION AND POLICY RECOMMENDATIONS The objective of this aer was to study the dynamic relationshi between consumtion exenditure and income in Nigeria by exerimenting with the Habit Persistence and Permanent Income hyotheses. The major research question is which of the consumtion hyotheses of Habit ersistence and ermanent income best describe the relationshi between consumtion and income in Nigeria. The study revealed that on the average, consumtion exenditure adjusts to changes in er caita disosable income quickly. That means consumers tend to shelve their higher consumtion habit in resonse to a fall in er caita disosable. This imlies Nigeria consumers do form consumtion habits but find it difficult to sustain such habit in their consumtion decision for long. This result artially suorts the findings of [9] in Jamaican economy. On the other hand, modelling consumtion along the assumtions of Permanent income hyothesis shows that the long-run effect of marginal roensity to consume out of ermanent income is ositive but very low (0.2952); an indication that consumers save more than send. 29 ercent of increase in ermanent income is devoted to consumtion while the rest 71 ercent is saved. The kind of saving common among consumers in Nigeria is savin with informal financial institutions where they would borrow for caital roject in a very near future. This may not mean that consumers in Nigeria have oor consumtion attern. The best argument for this is that Nigerians on the average have a low ermanent income and a higher transitory income which does not affect consumtion according the assumtion of Permanent Income Hyothesis. This result suorts the findings of [18], which found that ermanent income hyothesis hold for five develoing African countries, Nigeria inclusive. There are observable macroeconomic conditions in Nigeria that suort these conclusions. i. Poverty is ramart in Nigeria, a henomenon that suggests that transitory income which does not affect consumtion, is larger than ermanent income in Nigeria. ii. Unemloyment in also high in Nigeria, a henomenon that makes self-emloyed and unemloyed larger than the salaried workers or farm household larger than non-farm households. iii. Self emloyed and unemloyed have larger transitory comonents to their income. In concluding this aer it is to be noted that only ermanent fiscal and monetary olicies that are discretionary in nature may have a sustained imact on consumtion in Nigeria, given this results. We therefore recommend that government should regulate interest rate a major determinant of the marginal roensity to consume out of ermanent income. Also the shift factor of the roensity which is the taste shifter has a direct link with the tye of emloyment and rate overty. Government should therefore device olicies towards reducing the rate of unemloyment and alleviate overty in the Nigeria economy. COMPETING INTERESTS Authors have declared that no cometing interests exist. REFERENCES 1. Ojukwu CC, Shoeju JO. Elite corrution and the culture of rimitive accumulation in 21 st century Nigeria. International Journal of Peace and Develoment Studies. 2010;1(2): Loayza, Schmidt-Hebbel, Serven. Does income inequality raise aggregate saving? Journal of Develoment Economics. 2000;61: Keynes JM. The general theory of emloyment, interest and money; Brown TM. Habit ersistence and lags in consumer behaviour. Econometrica. 1952; 20(3). 5. Friedman M. A theory of the consumtion function, National Bureau of Economic Research, Princeton, NJ; Akekere J, Yousuo PO. Emirical analysis of change in income on rivate consumtion xenditure in Nigeria evidences from 1981 to International Journal of Academic Research in Business and Social Sciences. 2012;2(12). ISSN: Lingaraj Mallik, Kalandi Charan Pradhan. Per caita consumtion exenditure and ersonal disosal income in India-an econometric analysis. International Journal 9

10 of Economics Res. 2012;3(2): ISSN: Adelakun OJ. The nexus of rivate savings and economic growth in emerging economy: A case of Nigeria. Journal of Economics and Sustainable. 2011;2(6). 9. Oluwafemi OB. The habit ersistence hyothesis: Evidence from Jamaica, Munich Personal RePEc Archive, MPRA 2013; Available:htt:// 10. Tsenkwo JB. Testing Nigeria s marginal roensity to consume (MPC) within the eriod Journal of Innovative Research in Management and Humanities. 2011;2(1): Tasin G, Hesang A. An analysis of household consumtion exenditure in EA-18. Euroean Scientific Journal. 2014;10(16). 12. Okwori J, Sule A, Abu J. The multilier effect of consumtion function on aggregate demand in Nigeria: Aftermath of the global financial recession. The Journal of Business and Management (ISSN ). 2016;4(5): Gujarati DN, Sangeetha. Dynamics econometric models, Basic Econometrics. 1 st ed. New Delhi, Tata McGraw-Hill Publishing Comany. 2007; chater 17: Ferson WE, Constantinides GM. Habit ersistence and durability in aggregate consumtion. National Bureau of Economic Research Working Paer No Develoment ISSN (Paer). ISSN ;2(6):201. Available: htt:// 15. Koyck LM. Distributed lags and investment analysis. Amsterdam, North Holland Publishing Comany; Pesaran MH, Shin Y, Smith RJ. Bounds testing aroaches to the analysis of level relationshi. Journal of Alied Econometrics. 2001;16(3). 17. Sahin, Afsin, Cengiz, Sibel. Another brick for the aggregate consumtion uzzle in Turkey. International Research Journal of Finance and Economics. 2010;45: Nwala K. Does ermanent income hyothesis hold for some selected African countries? Emirical evidence. African Journal of Business and Economic Research. 2010;5(2&3):

11 APPENDIX 1 Phili Peron Unit Root Tests for PPCE at Levels and First Difference Null Hyothesis: PPCE has a unit root Exogenous: Constant Bandwidth: 1 (Newey-West automatic) using Bartlett kernel Adj. t-stat Prob.* Phillis-Perron test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided -values. Residual variance (no correction) HAC corrected variance (Bartlett kernel) Null Hyothesis: D(PPCE) has a unit root Exogenous: Constant Bandwidth: 2 (Newey-West automatic) using Bartlett kernel Adj. t-stat Prob.* Phillis-Perron test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided -values. Residual variance (no correction) HAC corrected variance (Bartlett kernel)

12 Phili Peron Unit Root Tests for PCDI at Levels And First Difference Null Hyothesis: PCDI has a unit root Exogenous: Constant Bandwidth: 3 (Newey-West automatic) using Bartlett kernel Adj. t-stat Prob.* Phillis-Perron test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided -values. Residual variance (no correction) HAC corrected variance (Bartlett kernel) Null Hyothesis: D(PCDI) has a unit root Exogenous: Constant Bandwidth: 3 (Newey-West automatic) using Bartlett kernel Adj. t-stat Prob.* Phillis-Perron test statistic Test critical values: 1% level % level % level *MacKinnon (1996) one-sided -values. Residual variance (no correction) HAC corrected variance (Bartlett kernel)

13 APPENDIX 2 Result of the Johansen Method Cointegration Test Trend assumtion: Linear deterministic trend (restricted) Series: PPCE PCDI Lags interval (in first differences): 1 to 2 Unrestricted Cointegration Rank Test (Trace) Hyothesized Trace 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * At most Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hyothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) -values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hyothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None At most Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hyothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) -values Unrestricted Cointegrating Coefficients (normalized by b'*s11*b=i): PPCE Unrestricted Adjustment Coefficients (alha): D(PPCE) D(PCDI) Cointegrating Equation(s): Log likelihood Normalized cointegrating coefficients (standard error in arentheses) PPCE ( ) ( ) Adjustment coefficients (standard error in arentheses) D(PPCE) ( ) D(PCDI) ( ) 13

14 APPENDIX 3 Results of ARDL Model of PCDI on PPCE Deendent Variable: LOG(PPCE); Selected Model: ARDL(1,0) Variable Coefficient Std. Error t-statistic Prob.* LOG(PPCE(-1)) LOG(PCDI) C R-squared Mean deendent var Adjusted R-squared S.D. deendent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood Hannan-Quinn criter F-statistic Durbin-Watson stat Prob(F-statistic) APPENDIX 4 Johansen Cointegration Test Using Seasonal Dummy Variable Johansen cointegration test using seasonal dummy Series: PPCE PCDI DUM Lags interval (in first differences): 1 to 1 Hyothesized Trace 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * At most At most Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hyothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) -values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hyothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None At most At most Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hyothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) -values 14

15 APPENDIX 5 ARDL Bounds Test with Dummy Variable ARDL bounds test (Seasonal dummy included) H0: No long-run relationshi exist Test Statistic Value K F-statistic Critical value bounds Significance I(0) Bound I(1) Bound 10% % % % Ayeni and Akeju; This is an Oen Access article distributed under the terms of the Creative Commons Attribution License (htt://creativecommons.org/licenses/by/4.0), which ermits unrestricted use, distribution, and reroduction in any medium, rovided the original work is roerly cited. Peer-review history: The eer review history for this aer can be accessed here: htt://sciencedomain.org/review-history/