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An econometric analysis of the determinants of economic growth

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My coursework for the 5th assignment of my econometrics university module.

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An econometric analysis of the determinants of economic growth

  1. 1. 557699 Investigating the Cross-Country Relationship Between Economic Growth, Physical Capital Stock and Age-Structured Population 1. IntroductionThere have been numerous attempts to explain economic growth and its determinants overthe years, with these theories wide ranging in their explanations. The neoclassical economistssuch as Solow (1952) stressed the importance of free markets, privatisation and openeconomies for economic growth. They regarded physical factors of production like capitaland labour to be the determinants of economic growth. To understand the nature of economicgrowth, we must also start by understanding the relationship economic growth has with thepeople who produce it. Cuaresma, Lutz and Sanderson (2009) concluded that the size of thepopulation with the technologies they produce is the root cause of economic growth.For development economics, sustained growth in GDP per capita is arguably the mostimportant determinant of living standards since other measures of living standards, such aslife expectancy and the Human Development Index (HDI), typically move together with GDPper capita. Therefore understanding the causes of economic growth is of great importance ifwe want to improve a country‟s long run welfare and stability (Zhuang and St. Juliana, 2010).The Harrod-Domar model of exogenous growth theorises that economic growth only dependson the savings rate, the capital-output ratio, and the depreciation rate. This model assumesthat by increasing the savings rate, that this will increase investment and therefore augmentthe capital stock. In this paper we are endogenizing this effect by considering growth in thephysical capital stock instead of changes to the savings rate. A major criticism of this modelhowever was that it did not include population growth, an issue this paper looks to solve.Neoclassical models, such as Solow-Swan, hypothesize that growth of output is a function ofgrowth of labour and growth of capital. Using the model, economic growth was derived asg=n, meaning economic growth is equal to labour growth. This model found growth to beexogenous because growth of the labour force was not part of the model; however we areendogenizing this effect by including age-structured population growth in the model. Thispaper will explore this relationship by undertaking a cross-country analysis of the relationshipbetween economic growth, as the dependent variable, and age-structured population growthand physical capital stock growth as explanatory variables. 2. Inspecting the DataThe data being used to investigate the possible relationships will be from 20 worldwidecountries of varying development stages1. Therefore the number of cross-sections in the datawill be . The data will cover the period of 1960 to 2000, therefore1 The countries being used in this study are: Sri Lanka (LKA), Lesotho (LSO), Luxembourg (LUX), Morocco(MAR), Mexico (MEX), Mali (MLI), Madagascar (MDG), Mozambique (MOZ), Mauritania (MRT), Mauritius(MUS), Malawi (MWI), Malaysia (MYS), Namibia (NAM), Niger (NER), Nigeria (NGA), Nicaragua (NIC),Netherlands (NLD), Norway (NOR), Nepal (NPL), New Zealand (NZL). 1
  2. 2. 557699 The data will be analysed as a balanced panel using theeconometric software Eviews. The physical capital stock for each country will be measuredin thousands of US dollars and be denoted in Eviews as CAP; this variable is transformedinto physical capital stock growth by log differencing the series, „capgrowth‟. The age-structure of the population will be split up into three different age groups: POP014, whichrepresents the school age population up to age 14; POP1564, which represents the workingage population of people from 15 to 64 years old; finally POP65P, which represents peopleaged 65 or the retired population. These three population variables will be log differenced aswell to produce Pop014growth, Pop1564growth and Pop65pgrowth, which representpopulation growth for the three age brackets. RGDP denotes the real GDP per capita for eachcountry measured at the 1996 purchasing power parity base price, with real GDP growth,denoted Growth, measured in terms of the logarithmic differences between real GDP betweenperiods and . This calculation can be carried out in Eviews by generating the followingequation using the pool objectThis paper is therefore examining how percentage changes to the physical capital stock andage-structured population change real GDP growth.The raw data can be analysed further by considering the descriptive statistics for each series,which has been undertaken in Eviews with the output in Appendix 1.Analysing the descriptive statistics for the POP014 variable showing the effects of peopleaged 0 to 14 first, it can be seen that some of the variables are non-normal. For Sri Lanka,Mexico, and the Netherlands the Jarque-Bera statistic has a probability value of 0.001062,0.070182 and 0.073538 respectively showing that at the 10% significance level we can rejectnormality for all three of these countries and for Sri Lanka we can reject normality even atthe 1% significance level. The Kurtosis value for each cross-section can also be analysed tounderstand the shape of the data with standard normally distributed data having a Kurtosisvalue of 3. As you can see from the graph in the appendix, the Kurtosis for Sri Lanka looks tobe significantly different from 3 as it has a Kurtosis value of 4.07075 and it is the onlyleptokurtic cross-section in the data. All the other cross sections have a Kurtosis value of lessthan 3 which indicates they could be more platykurtic in shape, meaning the data has a lowerand broader peak with shorter and thinner tails than a standard normal distribution. Finallywe can look at the skewness of the POP014 variable for each cross-section. Non-skewed andnormally distributed data will have a skewness of 0. It can be seen that Mexico and Moroccoare moderately skewed to the left as they have a skewness value of -0.759313 and -0.605342respectively. More extremely, Sri Lanka has a skewness value of -1.323122 showing that it ishighly skewed to the left. These results signify that there are some questionable features inthis variable.Next we can analyse the descriptive statistics for the POP1564 variable for the working agedpopulation between the ages of 15 to 64. The data series‟ for this variable are much morenormal than the POP014 however there is still some features which seen non-normal. The 2
  3. 3. 557699series‟ for Namibia, Niger and Nigeria all have moderately positive skewness, shown by askewness value of 0.750231, 0.591596 and 0.5052 respectively. All of the cross-sections arepossibly platykurtic in shape as the Kurtosis values for all cross-sections are less than 3 butwe cannot be sure if they are significantly less than 3, but the kurtosis value of 1.52529 forLesotho does seem to be significantly less than 3. However the Jarque-Bera statistic for eachcross-section has probability values of greater than the 10% significance level so we cannotreject the null hypothesis of normality, therefore concluding that the POP1564 is a generallynormal variable.The POP65P variable for people aged 65 and over is similar to the previously discussedvariable as it seems generally normal with a few discrepancies. In terms of skewness;Lesotho, Mexico, Mali, Malawi, Namibia, Niger, Nicaragua and Nepal are all moderatelypositively skewed in their distribution which means they have longer tails to the right. Moreworryingly for this variable when considering the Jarque-Bera statistic for normality is thatone cross-section is significantly non-normal at the 5% level (Malawi with a probabilityvalue of 0.042773) while 3 more cross-sections are significantly non-normal at the 10%significance level (Lesotho- 0.094135, Mexico- 0.085253, and Mali- 0.099908). The fact thatone fifth of the data is not normal may have effects on the reliability of the results.For the Physical Capital Stock explanatory variable the situation is worse. First examining theJarque-Bera statistic, we can reject normality at the 1% significance level for MexicoMauritania, Malawi, Nicaragua, and New Zealand. We can also reject normality at the 5%significance level for Sri Lanka, Luxembourg, Morocco, Mali, Niger, Nigeria, theNetherlands, and Nepal. Finally we can reject normality at the 10% significance level forMozambique andMalaysia. This means that three quarters of the data for this variable is non-normally distributed. This could have serious implications for the results which the ordinaryleast squares estimation undertaken below produces. This data could be not normallydistributed due to the difficulty in generating this variable because economists have struggledto properly define and measure this variable with full consensus.Analysing the real GDP variable is a stark contrast to the previous variable as only 3 cross-sections are non-normal, shown by the significance of the Jarque-Bera statistic, at the 10%significance level- Mauritius (0.090316), Namibia (0.088383) and Nepal (0.063254). There isalso some skewness in the data with Luxembourg, Mauritius, Namibia and Nepal all beinghighly positively skewed.Finally, the real GDP growth variable which was produced using the previous formula inEviews also seems to be very non-normal. Examining the Jarque-Bera statistic first againshows that at the 1% significance level, we can reject normality for Sri Lanka, Mauritania,Mauritius, Namibia, Niger and Nicaragua. Normality can also be rejected at the 5%significance level for Luxembourg, Mali and Malaysia. There are also some extreme Kurtosisvalues which signify a non-normal distribution- Namibia (17.08135), Nicaragua (8.49808),Niger (7.024593), Mauritania (6.941522) and Mauritius (6.842174). This could arise becausethere are many values close to zero. 3
  4. 4. 557699 3.1. Estimating Possible Relationships: Pooled EstimationThe simplest way to estimate any possible relationships is to estimate a pooled regression.This involves estimating a single equation on all the data collectively such that all the data setfor growth is stacked into a single column containing all the cross-sectional and time-seriesobservations and the same for all the explanatory variables as well. This equation is thenestimated using ordinary least squares. We use the pooled estimation method as it is a simpleway to estimate the relationships between variables because it assumes homogeneity amongthe cross-sections and over time. The equation to be estimated is the followingWhere „c‟ is the intercept, is the coefficient on the Pop014growth variable, is thecoefficient on the Pop1564growth variable, is the coefficient on the Pop65Pgrowthvariable, and is the coefficient on the Capgrowth variable.To undertake this analysis in Eviews, first the pool object is opened and then the estimatebutton is clicked which brings up the pool estimation menus. On this menu, „growth_?‟ isentered as the dependent variable, where the „_?‟ captures the cross-sectional element of thedata. The regressors are chosen as „pop014growth_?‟, „pop1564growth_?‟,„pop65pgrowth_?‟, „capgrowth_?‟ and a constant term „c‟. These inputs create the followingpooled estimation output in Eviews Dependent Variable: GROWTH_? Method: Pooled Least Squares Date: 03/13/12 Time: 12:39 Sample (adjusted): 1961 2000 Included observations: 40 after adjustments Cross-sections included: 20 Total pool (balanced) observations: 800 Variable Coefficient Std. Error t-Statistic Prob. C 0.030666 0.006153 4.984061 0.0000 POP014GROWTH_? -0.293921 0.177507 -1.655828 0.0982 POP1564GROWTH_? -0.663378 0.285869 -2.320565 0.0206 POP65PGROWTH_? 0.062482 0.108355 0.576641 0.5643 CAPGROWTH_? -0.000269 0.002672 -0.100509 0.9200 R-squared 0.019565 Mean dependent var 0.012709 Adjusted R-squared 0.014632 S.D. dependent var 0.061980 S.E. of regression 0.061525 Akaike info criterion -2.732526 Sum squared resid 3.009304 Schwarz criterion -2.703247 Log likelihood 1098.010 Hannan-Quinn criter. -2.721278 F-statistic 3.966174 Durbin-Watson stat 1.720148 Prob(F-statistic) 0.003406Analysing the results of this pooled OLS regression, first we can examine the significance ofthe explanatory variables. 4
  5. 5. 557699We can see that the constant term is significantly different from zero because the probabilitythat it is equal to zero is 0.000. It also shows there is a positive constant growth effect fromits coefficient 0.030666. The constant term signifies that there is an exogenously determinedlevel of growth in the economy. The fact that other variables are significant shows thateconomic growth is both exogenously and endogenously determined.Next the Pop014growth variable is significantly different from zero at the 10% significancelevel as it has a probability that it is zero of 0.0982. The coefficient for this variable shows that a 1% increase in the population aged 0 to 14 will decrease GDPgrowth by 0.294%. This effect could be occurring because an increase in people of this agewill increase the costs of education and welfare benefits for the governments of the countries.A baby boom for instance would stretch the countries resources and would reduce GDP as aresult.The Pop1564growth variable is significantly different from zero at the 5% level, as shown byits p value of 0.0206. The coefficient for this variable is which indicates that a1% increase in the population between the ages of 15 and 64 reduces GDP growth by 0.66%.This result seems to be unintuitive as it would be expected that people of working age wouldbe positively contributing towards real GDP growth as they are working, producing andspending. This result could possibly have arisen due to the pooled estimation method nottaking into account the cultural differences between counties. It might be easier to understandwhy this effect is occurring if this age bracket was split into categories for peoples educationlevels so we could understand the effect that the level of peoples education has on GDPgrowth. It might be that for this age bracket in some countries there is a lot of highly educatedpeople, whereas in other countries the average education level is much lower; thereforemaking this age bracket contribute negatively to GDP growth.The Pop65pgrowth variable results show that this variable has no effect on GDP growthbecause the probability that the coefficient is different from zero is 0.5643 which fails at all 3important significance levels. In some developing countries, the level of wealth that retiredpeople have might be so low that they are just living on government benefits, hence notcontributing towards GDP as what they are costing the government they are spending.Finally the physical capital stock growth variable, capgrowth, also has no effect on GDPgrowth because it has a 92% probability that its coefficient is equal to zero. This findingobviously flies in the face of most current research and theory. This could have arisen due tothe method used to calculate the capital stock, because there are many techniques available touse.Therefore, the OLS regression model for economic growth is given by a pooled estimation isThe R-squared value of 0.019565 from the regression shows that only 1.96% of the variancein economic growth is explained by the physical capital stock and age-structured population.This little variance being explained could arise because a pooled regression is being used 5
  6. 6. 557699which may not be the most efficient method of estimation as the countries might havedifferent cultural and technological characteristics making the estimation of a commoncoefficient for each variable and for each country unsuitable. This low R-squared value alsoindicates that there may be other explanatory variables which explain economic growthwhich aren‟t included in this model; these variables could be physical factors, technologicalinfluences or other demographic variables such as education levels, or birth rates. Humancapital growth theory, for example, suggests that education is the most prominent factor ineconomic growth and that countries with lower levels of education will suffer from lessinnovation, a slower pace of learning by doing, and also less technical changes. Anothervariable which could be included is for the changes in the unemployment rate because„Okun‟s rule of thumb‟ observes that GDP growth depends linearly on changes to theunemployment rate.Analysing the Durbin-Watson statistic of 1.72 we can conclude that there is noautocorrelation present as the statistic is sufficiently close to a value of 2.Although the pooled estimation method is simple because it requires the estimation of only afew parameters, it also has several limitations. Firstly, pooling the data implicitly assumesthat the relationships between the variables and the average value for these variables areconstant both over time and across all cross-sections of the sample. This assumption forsimplification affects the validity of the model because in the context of this paper it alsoassumes that all countries have the same cultural and geographical variations. Intuitively thiswould seem to be unrealistic as the sample has both developed and developing countries ofvarious sizes, which would point to them having different coefficients. Therefore, estimatingthe data as a pool means we lose individual heterogeneity. To solve this problem we canestimate the data again using the fixed effects method. 3.2. Estimating Possible Relationships: Fixed Effects MethodThe fixed effects method considers country specific effects by allowing the intercept in theregression model to differ cross-sectionally but not over time. Because the intercept is notallowed to change over time, it therefore captures a fixed effect which is why the model hasits name. It treats observations for the same individual as having something specific incommon such that they are more „like‟ each other than observations from two or moredifferent countries. We use the fixed effects method because it captures all the effects whichare specific to a country. The fixed effects in the context of this paper take into accountgeographical factors, natural endowments, and other factors which vary between countriesbut not over time. This means that we cannot include other variables which do not vary overtime but do vary cross-sectionally, such as country size, because these variables would beperfectly co-linear with the fixed effect. The fixed effects method can be extended byincluding a set of time dummy variables, which is known as the two-way fixed effect model.The two-way fixed effect model has the advantage of capturing any effects which vary overtime but are common across the whole panel. This paper will utilise the fixed effects 6
  7. 7. 557699methodwith cross-sectional dummies only as we are comparing the cross-countryrelationship. Two methods to estimate the fixed effects method this paper will explore are theLeast Squares Dummy Variable (LSDV) method and the within-groups method.To explain the LSDV approach, we can first consider this simple two variable model belowWhere is the dependent variable, is the intercept term, is the explanatory variable,is the coefficient on the explanatory variable, and is the stochastic error term which can besplit up into an individual specific effect, , and a remainder disturbance term, such thatThis expanded error term can then be plugged back into the model to produce now represents all of the variables that affect cross-sectionally but not over time, thefixed effect; such as a person‟s gender, the sector a firm operates in, or in this paper‟s casethe country. This model can now be estimated using dummy variables which is then calledthe Least Squared Dummy Variable ApproachOrWhere D1, D2,…,DN are dummy variables indicating the groups and where u1, u2,…, uN aretheir regression coefficients which must be estimated. For the dummy variables, D1=1 wheni=1 and 0 otherwise. Similarly, D2=1 when i=2 and 0 otherwise, and so on for the N numberof cross-sections. The intercept term α has been removed from this regression model in orderto avoid the dummy variable trap which causes perfect multicollinearity.However, the LSDV model has N+K parameters to estimate, so with a large number of cross-sections it is unpractical to specify so many dummy variables. In order to avoid this, we canundertake a transformation called a “within-transformation” which then provides the secondapproach, „the within-groups method‟.The within-groups method works by transforming the data by subtracting the mean of eachentity away from the values of the variable. Starting with the regression modelWe can define the group means as 7
  8. 8. 557699Now we can subtract the means from each variable to obtain a regression containingdemeaned variables only. This regression does not require an intercept term because thedependent variable will have zero mean by construction. Undertaking this transformationgives the following modelorWhere double dots denote demeaned values. This within-groups method provides identicalestimates for the parameters that can be achieved by the LSDV model.To estimate the parameters α and β, we must first define the within-group sum of squares andsum of productsNow must be minimised with respect toor (1) (2)Next equation (1) is substituted into equation (2) and simplified to giveIn the case where the model includes several explanatory variables then Wxx is a matrix, and and Wxy are vectors. 8
  9. 9. 557699Since we have defined , we can define as .These estimates are known as within-group estimates and often denoted .The advantage of using the fixed effects method over the pooled estimation method is that itcontrols for all possible fixed characteristics of the individual countries in the study. It alsoallows for more heterogeneity than the pooled estimation because of this.However, there are disadvantages of using the fixed effects method to estimate thisrelationship. First; when the number of cross-sections, N, is large it is unpractical to specifyso many dummy variables as it would take a lot of time and money to compute those in alarge study. The fixed effects method is also inefficient if the terms are uncorrelated with , this is because these characteristics make the random effects method the appropriatemethod to use. Finally; the use of the fixed effects method can exacerbate biases from othertypes of specification problems, especially measurement errors.To estimate the relationship in Eviews using the fixed effects method, we must first select thepool object and then click the estimate button which brings up the pool estimation menus. Onthis menu, „growth_?‟ is entered as the dependent variable and the regressors are chosen as„pop014_growth?‟, „pop1564_growth?‟, „pop65p_growth?‟, „cap_growth?‟ and a constantterm „c‟. This is currently the same as the pooled estimation except now under estimationmethod, the cross-sections option is changed to fixed which creates the fixed effects method.We don‟t change the period to fixed effects as we are only estimating the fixed effectsmethod, not a two-way fixed effects method. These inputs create the following fixed effectsestimation output in Eviews 9
  10. 10. 557699 Dependent Variable: GROWTH_? Method: Pooled Least Squares Date: 03/13/12 Time: 14:12 Sample (adjusted): 1961 2000 Included observations: 40 after adjustments Cross-sections included: 20 Total pool (balanced) observations: 800 Variable Coefficient Std. Error t-Statistic Prob. C 0.019472 0.010577 1.840932 0.0660 POP014GROWTH_? 0.480704 0.245099 1.961268 0.0502 POP1564GROWTH_? -0.733022 0.421396 -1.739510 0.0823 POP65PGROWTH_? 0.043773 0.109685 0.399079 0.6899 CAPGROWTH_? -0.000687 0.002651 -0.258987 0.7957 Fixed Effects (Cross) LKA--C 0.015778 LSO--C 0.002839 LUX--C 0.015977 MAR--C 0.016757 MEX--C 0.012095 MLI--C -0.017151 MDG--C -0.024539 MOZ--C -0.027105 MRT--C -0.007329 MUS--C 0.032287 MWI--C 0.001716 MYS--C 0.031352 NAM--C -0.006058 NER--C -0.030094 NGA--C -0.022851 NIC--C -0.022772 NLD--C 0.013482 NOR--C 0.014642 NPL--C -0.000709 NZL--C 0.001682 Effects Specification Cross-section fixed (dummy variables) R-squared 0.081617 Mean dependent var 0.012709 Adjusted R-squared 0.054397 S.D. dependent var 0.061980 S.E. of regression 0.060270 Akaike info criterion -2.750407 Sum squared resid 2.818845 Schwarz criterion -2.609869 Log likelihood 1124.163 Hannan-Quinn criter. -2.696419 F-statistic 2.998405 Durbin-Watson stat 1.841619 Prob(F-statistic) 0.000004To begin analysing the results from the fixed effects method we can first look upon theintercept in the regression model which is now allowed to differ cross-sectionally but notover time. In the Eviews output, the fixed effects for each country as listed as deviations fromthe overall group intercept term. This way of calculating the model stops the problem ofmulticollinearity. The probability that there is no constant level of growth is 0.066 meaningthat at the 10% we can reject that there is no constant level of growth and hence conclude thatthere is a constant endogenous level of growth for the countries. Since we now know that theintercept is significant, we can also look at its effect cross-sectionally. We can see that for 10
  11. 11. 557699some countries real GDP growth grows constantly, whereas for others real GDP growth isshrinking. This could be occurring due to technological differences between developing anddeveloped countries. This is supported by developed European countries like the Netherlandsand Luxembourg showing a positive intercept value of and respectively,whereas many of the developing African countries have a negative intercept; such as Niger , Mozambique , Madagascar and Nicaragua . The variety of estimates for the constant term across the cross-sections would bean indicator that the pooled regression might not perform as well as the fixed effects methodbecause the variety of estimates for the constant reflects the technical and cultural differencesbetween countries. The constant term is showing that there is a stable exogenous effect whichdiffers between the countries. This could be government spending for example, which couldmean some countries have a stable fiscal policy lending towards positive economic growth,whereas other countries could have a poor fiscal policy which meant economic growth tendedto be negative.The fixed effects estimation of the Pop014growth variable has changed when compared withthe pooled estimation. In the pooled estimation, a change in the population aged 0 to 14negatively affected GDP growth. However the fixed effects method has estimated that 1%change in the population aged 0 to 14 increases GDP growth by 0.48%. This finding issignificant at the 10% significance level but just misses the 5% significance level with aprobability of 0.0502. This finding confirms the findings by An and Jeon (2006) who showedthat demographic changes appear to affect economic growth in an inverted U-shape, firstincreasing then decreasing economic growth.Next the Pop1564growth variable has slightly changed from the pooled regression. It is lesssignificant as it is only significant at the 10% level for this fixed effects method, shown by aprobability value of 0.0823, whereas the pooled estimation was significant at the 5%significance level. This model also estimates the magnitude of this variable‟s effect on GDPgrowth as larger than under the pooled estimation. This model estimates that a 1% increase inthe population aged 15 to 64 decreases GDP growth by 0.733%, which is a reduction in GDPgrowth of 0.07% more than under the pooled estimation.Similarly to the pooled estimation, the fixed effects method finds both the Pop65pgrowth andCapgrowth variables insignificantly different from zero, shown by p values of 0.6899 and0.7957 respectively, which confirms the findings of the pooled estimations.Looking at fixed effects regression results at the 5% level, none of the results are significant.This conclusion indicates that economic growth is endogenous but the variables whichexplain this growth are not included in this model. Since the constant terms are insignificant,economic growth does not depend on any exogenous variables.Analysing the Durbin-Watson statistic of 1.84 we can conclude that there is noautocorrelation present in the data because it is near a value of 2.Next the R-squared value can be analysed. For the pooled estimation it said the modelexplained 1.9565% of the variance in real GDP growth, however this fixed effects method is 11
  12. 12. 557699able to explain 8.1617% of the variance in real GDP growth. Therefore we can say that thefixed model explains more of the variance in real GDP growth than the pooled estimationdoes but to decide which performs better we need to undertake an F-test.Before undertaking the F-test, we can also see that the fixed effects method is more efficientthan the pooled estimation method because it has a smaller residual sum of squares, 2.818845compared to 3.009304.The F-test is used to test which of the pooled and fixed effects methods performs best. It teststhe null hypothesis that the pooled estimation method is most efficient and that there is nounobserved heterogeneityIt is tested against the alternative hypothesis that at least some of the intercept terms are notequal, meaning the fixed effects method is most efficient. The formula to calculate the F-statistic is given byWhere is the R2 from the fixed effects method, is the R2 from the pooled estimation,„n‟ is the number of observations, T is the number of years and „k‟ is the number of variables.To test the hypotheses the F-statistic generated from the above equation is compared to Fcritical values at the 1%, 5% and 10% significance levels.Inputting the pooled R-squared value of 0.019565 and the fixed effects R-squared value of0.081617, with number of cross-sections, 20, the number of years, 40, and finally the numberof explanatory variables, 23, into the equation producesThis value can now be compared to the F critical values which areComparing the F-statistic to the F critical value at each significance level we can see thatF>Fc so we can reject the null hypothesis at the 1%, 5% and 10% significance levels and soconclude that at least some of the intercept terms are not equal and that the fixed effectsmethod performs better than the pooled estimation. This result seems intuitive as the data has 12
  13. 13. 557699a mix of developed and developing countries so cultural differences would indicate thathomogenous coefficients are unsuitable.However, because the fixed effects method assumes individual deterministic constant terms,it is not flexible enough to account for random effects in the economy. To solve this, arandom effects method can be used to estimate the relationship between the variables whichallows the constant term to be stochastic. 3.3. Estimating Possible Relationships: Random Effects MethodIn the random effects method,the are treated as random variables rather than fixedconstants like in the fixed effects approach. The model assumes that the intercepts for eachcross-section arise from a common intercept term , plus a random variable that variescross-sectionally but is constant over time. measures the random deviation of eachcountry‟s intercept term from the „global‟ intercept term. Unlike the fixed effects method,there are no dummy variables to capture heterogeneity in the cross-sectional dimension;instead this occurs via the terms. This model can also be called the variance componentsmodel or the error components model. We can understand why it is called the errorcomponents model by considering the following simple two variable regression modelWhere, is made up of a global constant term , and a random error term ,Therefore , where is the composite error term. It is also assumed that and it is alsoindependent of both and . The reason it is called the error components model is that wehave broken down the error term into the unobserved heterogeneity in the cross-sectionalunits and the random error term. We cannot run this model in ordinary least squares becauseeven though and are estimated consistently, they are not estimated efficiently because ofautocorrelation. Autocorrelation arises due to the presence of which produces a correlationamong the errors of the same cross-sectional unit even though the errors from different cross-sections are independent. Because of this, we have to use Generalised Least Squares (GLS) toget efficient estimates.Mundlak (1978) confirmed that GLS estimators are BLUE andtherefore the desired estimation method, however since GLS is associated with the randomeffects method its use had to be justified by arguing that economic effects are random and notfixed. We can test whether this holds once results from the random effects method have beenattained then we can apply the Hausman specification test to decide which model is best.To be able to use GLS to estimate the data, we must first transform the data by subtracting aweighted mean of each variable over time. The model to estimate using GLS is also a 13
  14. 14. 557699weighted average of the estimates produced by the between estimator and the withinestimator using OLS, which is as followsWhere , , and . This transformation ensures that thereis no auto-correlation in the error terms. The above equation is then estimated using GLS toprovide estimates of the variables.The advantages of using the random effects approach is that there are fewer parameters toestimate compared to the fixed effects approach and it also saves lots of degrees of freedom.It also allows for additional explanatory variables that have equal value for all observationswithin a group, which means we can use dummy variables with this model.However, the random effects approach has a major drawback which arises from the fact thatit is only valid when the composite error term is uncorrelated with all of the explanatoryvariables. If they are uncorrelated, the random effects approach can be use; otherwise thefixed effects method is preferable. Another disadvantage of using this model is that we needto make specific assumptions about the distribution of the random components.To estimate whether a relationship exists using the random effects method in eviews, wemust first select the pool object and then click estimate. On this menus „growth_?‟ is enteredas the dependent variable and the regressors are chosen as „pop014_growth?‟,„pop1564_growth?‟, „pop65p_growth?‟, „cap_growth?‟ and a constant term „c‟. Next underestimation method we change to cross-sections option to random. These inputs then estimatesthe relationship using the random effects approach which produces the following output 14
  15. 15. 557699Dependent Variable: GROWTH_?Method: Pooled EGLS (Cross-section random effects)Date: 03/13/12 Time: 17:47Sample (adjusted): 1961 2000Included observations: 40 after adjustmentsCross-sections included: 20Total pool (balanced) observations: 800Swamy and Arora estimator of component variances Variable Coefficient Std. Error t-Statistic Prob. C 0.029952 0.007498 3.994731 0.0001 POP014GROWTH_? -0.050100 0.196670 -0.254743 0.7990POP1564GROWTH_? -0.805182 0.320585 -2.511605 0.0122 POP65PGROWTH_? 0.050634 0.107561 0.470746 0.6380 CAPGROWTH_? -0.000408 0.002634 -0.155042 0.8768Random Effects (Cross) LKA--C 0.004388 LSO--C 0.001725 LUX--C 0.004357 MAR--C 0.008146 MEX--C 0.006311 MLI--C -0.006652 MDG--C -0.009350 MOZ--C -0.012003 MRT--C -0.001415 MUS--C 0.011354 MWI--C 0.003371 MYS--C 0.016287 NAM--C 3.74E-05 NER--C -0.010818 NGA--C -0.008033 NIC--C -0.008364 NLD--C 0.000732 NOR--C 0.002051 NPL--C 0.001044 NZL--C -0.003170 Effects Specification S.D. RhoCross-section random 0.009409 0.0238Idiosyncratic random 0.060270 0.9762 Weighted StatisticsR-squared 0.010040 Mean dependent var 0.009044Adjusted R-squared 0.005059 S.D. dependent var 0.060838S.E. of regression 0.060684 Sum squared resid 2.927659F-statistic 2.015726 Durbin-Watson stat 1.769013Prob(F-statistic) 0.090400 Unweighted StatisticsR-squared 0.017176 Mean dependent var 0.012709Sum squared resid 3.016639 Durbin-Watson stat 1.716834 15
  16. 16. 557699To begin analysing the results from the random effects method we can first look upon thecross-sectional random error which is given as a deviation from the „global‟ intercept „c‟.These terms are significant at the 1% significance level, as seen by the probability value of0.0001. This shows that there are significant exogenous determinants of growth which arerandom between cross-sections. Even though the interpretations of the constant terms areslightly different in the fixed and random effects methods, they both find the constant asignificantly positive determinant of growth at the 10% level, but the random effects methodestimates constant terms which are significant at the 1% significance level.The Pop014growth variable in the random effects approach has been estimated to have zeroeffect on GDP growth as it fails to reject the null that it is equal to zero, shown by theprobability value of 0.799. This is obviously in stark contrast to the fixed effects approachwhich estimated this variable to have a positive effect which was significant at the 6%significance level.The Pop1564growth variable has been estimated to have a statistically significance negativeeffect on GDP growth as a 1% increase in this population group will decrease GDP growthby 0.805%. The magnitude of this effect has been estimated to be higher in the randomeffects estimation than in the fixed effects and it has also been found to be significant at a 2%significance level whereas the fixed effects is only significant at the 9% level. Economicinterpretation of this finding could be that there is excess supply in the labour marketmeaningthat any extra people would find it tough to enter the labour market and as suchwould live on state benefits. The increase in unemployed living on state benefits wouldreduce the government‟s freedom to spend money on goods and services which would havehelped stimulate the economy. Bloom, Canning and Fink (2008) found that declines labor-force-to-population ratios would lead to modest declines in economic growth, which wouldsupport the conclusions from these results. If we could analyse the trend in unemploymentrates, as well as education levels, this would help to clarify this situation. Results by Klasen(1999) showed that gender inequality in education lowered the average quality of humancapital which in-turn negatively affected economic growth. He found that if Southern Asiaand Sub-Saharan Africa had no gender inequality in education in 1960, then their economicgrowth would have been up to 0.9% per year faster than in reality. Gender inequality inemployment in these regions has also been shown to reduce economic growth by another0.3% annually. Therefore if we could also have used a dummy variable for gender, we maybe able to offer extra insight into some of these findings.The Pop65pgrowth and Capgrowth variables have found similar conclusions in the randomeffects as in the fixed effects approaches in that they both conclude that these variables haveno impact on the growth rates of real GDP.Next we can analyse the differences in the regression statistics. Eviews reports both weightedand unweighted statistics in the random effects output. The unweighted statistics arecalculated using the GLS coefficient results estimated using the original data, whereas theweighted statistics are estimated after the GLS transformations have been undertaken. It is theGLS transformed weighted statistics that we are interested in. 16
  17. 17. 557699First looking at the R-squared value we can see that the random effects method is explaininga lot less of the variance in GDP growth than in the fixed effects method, 1% in the randomeffects approach compared to 8% in the fixed effects approach. The fixed effects method isalso more efficient at estimating this data as it has a sum of squared residuals of 2.818845compared to the random effects approach‟s sum of squared residuals of 2.927659. TheDurbin-Watson statistic of 1.769 shows that there is no autocorrelation in the data which wasthe same finding as the fixed effects approach.Both the fixed effects and random effects approaches have been used to estimate therelationships and both have different estimations and assumptions, but which approach ismost efficient and should be used? To decide this we can use a specification test devised byHausman (1978) who modified a test based on the idea that under the null hypothesis of nocorrelation, both OLS and GLS are consistent but OLS is not efficient. While for alternativehypothesis OLS is consistent but GLS isn‟t. Given a panel data model for which the fixedeffects method is appropriate to use, the Hausman test examines whether the random effectsapproach will estimate as good as the fixed. Therefore we are testing the null hypothesis ofno correlation between the meaning the random effects approach is more consistentand efficient, against the alternative hypothesis that the random effects are inconsistentmeaning that the fixed effects approach is more appropriate. The Hausman test statistic iscalculated using the following formulaOnce the Hausman test statistic is calculated, it is then compared to Chi-Squared criticalvalues.We can undertake the Hausman test by first estimating the random effects method. Thenselecting View=>Fixed/Random Effect Testing=>Correlated Random Effects-Hausman test.Selecting this test then produces the following output in Eviews Correlated Random Effects - Hausman Test Pool: POOL Test cross-section random effects Chi-Sq. Test Summary Statistic Chi-Sq. d.f. Prob. Cross-section random 14.955371 4 0.0048 Cross-section random effects test comparisons: Variable Fixed Random Var(Diff.) Prob. POP014GROWTH_? 0.480704 -0.050100 0.021394 0.0003 POP1564GROWTH_? -0.733022 -0.805182 0.074800 0.7919 POP65PGROWTH_? 0.043773 0.050634 0.000461 0.7494 CAPGROWTH_? -0.000687 -0.000408 0.000000 0.3639 17
  18. 18. 557699The Chi-squared statistic of 14.955, with the corresponding probability value of 0.0048,shows that at the 1% significance level we can reject the null hypothesis that the randomeffects method is efficient, and therefore conclude that the fixed effects method is the mostconsistent model and therefore the model of choice. This also means that arecorrelated.We could have identified that the fixed effects method is also more appropriate aswe are not taking our cross-sections in the sample from a random draw of some underlyingdistribution. 4. Panel Stationarity TestingSomething which has not been considered so far in this paper is the issue with stationarity. Inpanel data estimation it is important to consider the degree of heterogeneity between thecross-sections. In particular, it is important to understand that all the countries in the panelmay not have the same characteristics or properties. Therefore it is possible that not all thecross-sections in the panel may be stationary.When using panel data, individual units are stacked assuming a common system between thecross-sections. This can cause a stochastic shock in one of the cross-sectional units to rippleacross and disrupt the other cross-sections. Non-stationarity of a time series implies that themean and variance vary through time. If some cross-sections in a panel are non-stationary,then slowly-convergent shocks can infect other cross-sectional units causing chaoticdynamics and system failure. The advantage of unit roots tests being carried out on panel datarather than time series is that the power of panel unit root tests increases with an increase inthe number of cross-sections. Two panel unit root tests this paper will consider is the test byLevin, Lin and Chu (LLC) and the test by Im, Pesaran and Smith (IPS).However, before unit root tests can be undertaken we must consider if they are appropriateand will produce reliable results using this data. Structural breaks are an importantconsideration to take when performing a unit root test because structural change can maketime series appear to be non-stationary. In panel data, a structural break in one cross-sectionwill cause the LLC test to fail to reject a false null and conclude non-stationarity overallbecause the LLC test assumes that ρ is the same for all cross-sections, as explained below. Inother words, unit root testing in the presence of structural breaks are biased towards non-rejection of the null. This occurs because unit root tests assume that the deterministic trendterms are correctly specified and when there are structural breaks, the deterministic terms willchange at some point in time.For example; empirical work by many economists has found that unit roots are present inmost macroeconomic time series, however Perron (1989) argued that when either the greatcrash of 1929 or the oil shock of 1973 are taken into account, these results changedramatically and most US macroeconomic time series appear not to have a unit root.We can first consider if there are structural breaks present in the data by analysing graphs forthe observations over time, with can be found in Appendix 2. A structural break will be an 18
  19. 19. 557699event where the trend in the data changes suddenly. Considering the graphs, it can be seenthat some exhibit a constant growing trend over time, such as for GDP in the Netherlands orNorway, others are much more chaotic in nature, such as Nigeria or Mali, which wouldindicate a unit root process. However for Namibia, it seems that there is a structural change inthe data. Considering the graph below for the real GDP of Namibia, it is clear to see that priorto 1980 there is a clear upward trend in GDP, which seems to be growing at a steady rate.However, at 1980 there is a large crash and from then until 2000 there seems to be a level ofGDP which is trending around a constant level of GDP. RGDP_NAM 6,500 6,000 5,500 5,000 4,500 4,000 3,500 3,000 1960 1965 1970 1975 1980 1985 1990 1995 2000In order to confirm that there is a structural break occurring in 1980, we can undertake sometests on the following AR(1) modelWe can now use some stability diagnostics in Eviews to test our predictions that a structuralbreak is present. First we can use recursive estimation of the residuals which shows whetherthere are any anomalies in the residuals from the above regression model. The table belowshows that in 1980 the residuals spike out of the ±2 standard error bands which confirm thethoughts that a structural break occurring at that date. 19
  20. 20. 557699 1,000 500 0 -500 -1,000 -1,500 -2,000 1965 1970 1975 1980 1985 1990 1995 2000 Recursive Residuals ± 2 S.E.A Chow Breakpoint stability test can now be undertaken to test the null hypothesis that nobreak is present in 1980. The Eviews output for this test is below Chow Breakpoint Test: 1980 Null Hypothesis: No breaks at specified breakpoints Varying regressors: All equation variables Equation Sample: 1961 2000 F-statistic 46.87814 Prob. F(2,36) 0.0000 Log likelihood ratio 51.28556 Prob. Chi-Square(2) 0.0000 Wald Statistic 93.75629 Prob. Chi-Square(2) 0.0000Looking at the F-statistic for this test of 46.878, with the corresponding P value of 0.0000, wecan conclusively reject the null hypothesis and therefore conclude that a structural break isoccurring in 1980 in the real GDP data for Namibia. Because a structural break has beenidentified, we need to deal with it appropriately. Firstly we will estimate the LLC unit roottests below excluding Namibia from the estimation, then again with Namibia included inorder to compare if it is affecting the result or if there is a unit root in the data anyway.Because the IPS test allows for individual heterogeneity, we do not need to exclude Namibiaas if other countries are stationary it will show up in the results. 4.1. Panel Unit Root Test- Levin, Lin and Chu testIn 1992 Levin and Lin developed their first unit root test designed to be used on panel data.The original model was designed as such , where 20
  21. 21. 557699However, this 1992 model did not take into account problems with autocorrelation andHeteroskedasticity and so they created their 1993 model which was published in 2002 withChu as co-author. This new model is given byWhere because the dependent variable has been differenced; is the coefficienton the lagged dependent variables; and is the stochastic error term. This new test nowallows for different lags across the cross-sections in the model. The model also allows forheterogeneity via two-way fixed effects, where with capturing the unitspecific fixed effects and capturing the unit specific time effects. The unit-specific fixedeffects are very important to the model because they are allowing for individual heterogeneitysince the coefficient on the lagged Yit is restricted to be homogenous across all units of thepanel.As before, this model assumes that meaning individual processes for eachcross-section are cross-sectionally independent and there is also no serial correlation. Underthis assumption, the pooled OLS estimator for ρ will follow a standard normal distribution.This assumption also ensures that there is no cointegration between groups of cross-sections.However; Banerjee, Cockerill and Russell (2001) explored the consequences of assuming nocointegrating relationships and they found that LLC, as well as IPS, often over reject the nullhypothesis of non-stationarity which indicates that these tests have poor size properties.The model has three versions, each with separate null and alternative hypotheses1). , where .2). , where .3). , where .Model 1 contains no deterministic terms. Model 2 has an individual-specific mean, but notime trend. Model 3 has both an individual-specific mean and a time trend. Similarly to singletime series unit root tests, if a deterministic element is present but it is not included in theregression model then the unit root test will not be consistent. Conversely, if deterministicterms are wrongly included in the regression procedure then the statistical power of the unitroot test will be reduced (Levin, Lin and Chu, 2002).To implement this model, Levin and Lin recommended a three-step procedure to implementthis test:Step 1: First, separate ADF regressions are undertaken for each cross-section in the panel onthe following regression model 21
  22. 22. 557699Because we are using panel data, the lag order of L is permitted to vary across the countries.They recommended using a method suggested by Hall (1990) for selecting lag lengths whichworks by choosing the maximum lag order and then using t tests to decide whether a smallerlag order is preferable. Next we have to run two auxiliary regressions to generateorthogonalized residuals, meaning they are independent and uncorrelated. This is achieved byregressing against where (l=1,…,L), shown belowThen the residuals and from these regressions are saved. To allow for heterogeneityacross individuals we must normalise and by the regression standard errorWhere is the standard error from the first regression model.Step 2: We now can estimate the ratio of long-run to short-run standard deviations bycalculating the followingHowever, if model 2 from above is being used we need to replace for , where is the average value of for each cross-section. is the sample covariance weights,whose value depends on the choice of kernel.Step 3: Now we can compute the panel test statistics by pooling all the cross-sectional andtime series observations in order to estimateWhich is based on the total of observations, where is the average numberof observations per individual in the panel, and is the average lag order for theindividual ADF regressions which were carried out in step 1. The regression t-statistic fortesting is given by 22
  23. 23. 557699WhereThereforeAndTherefore we can test the null hypothesis that .Harris and Tzavalis (1999) found that the assumption built into this test that yields atest with poorer power properties, especially when the sample size is less than 50.Now that the LLC test has been explored, it can be applied to the panel data to test whetherthere is a unit root for real GDP in these countries. To undertake this test we must first openall the cross-sectional data for real GDP in one window. Then unit root tests are selected andthe following options are selectedIn the test equation, both intercept and trend deterministics are included because if weanalyse the graphs in Appendix 2 we can clearly see that many of the cross-sections exhibit agradual upward trend. From these options the following result is produced 23
  24. 24. 557699 Null Hypothesis: Unit root (common unit root process) Series: RGDP_LKA, RGDP_LSO, RGDP_LUX, RGDP_MAR, RGDP_MDG, RGDP_MEX, RGDP_MLI, RGDP_MOZ, RGDP_MRT, RGDP_MUS, RGDP_MWI, RGDP_MYS, RGDP_NAM, RGDP_NER, RGDP_NGA, RGDP_NIC, RGDP_NLD, RGDP_NOR, RGDP_NPL, RGDP_NZL Date: 03/15/12 Time: 15:20 Sample: 1960 2000 Exogenous variables: Individual effects, individual linear trends Automatic selection of maximum lags Automatic lag length selection based on SIC: 0 to 2 Newey-West automatic bandwidth selection and Bartlett kernel Total number of observations: 789 Cross-sections included: 20 Method Statistic Prob.** Levin, Lin & Chu t* 1.08357 0.8607 ** Probabilities are computed assuming asympotic normality Intermediate results on UNTITLED 2nd Stage Variance HAC of Max Band- Series Coefficient of Reg Dep. Lag Lag width Obs RGDP_LKA -0.08420 2991.0 930.57 0 9 9.0 40 RGDP_LSO -0.25826 5099.8 524.22 0 9 39.0 40 RGDP_LUX 0.05117 488015 513001 0 9 0.0 40 RGDP_MAR -0.49985 12513. 5285.0 1 9 6.0 39 RGDP_MDG -0.14692 858.79 1051.5 0 9 3.0 40 RGDP_MEX -0.09610 50446. 68087. 0 9 2.0 40 RGDP_MLI -0.22069 2310.9 2610.9 0 9 0.0 40 RGDP_MOZ -0.13749 12963. 15090. 0 9 4.0 40 RGDP_MRT -0.13368 21514. 20503. 0 9 6.0 40 RGDP_MUS 0.01747 76555. 87250. 0 9 2.0 40 RGDP_MWI -0.34846 1247.8 200.62 2 9 29.0 38 RGDP_MYS -0.05980 18544. 24225. 1 9 0.0 39 RGDP_NAM -0.18874 121226 72743. 0 9 8.0 40 RGDP_NER -0.24288 5247.8 5191.9 0 9 2.0 40 RGDP_NGA -0.46164 6302.8 2947.5 1 9 9.0 39 RGDP_NIC -0.17481 35806. 45641. 1 9 0.0 39 RGDP_NLD -0.09901 58141. 130551 1 9 3.0 39 RGDP_NOR -0.20757 59641. 133077 1 9 3.0 39 RGDP_NPL 0.06413 683.09 554.34 2 9 1.0 38 RGDP_NZL -0.38424 190085 279272 1 9 2.0 39 Coefficient t-Stat SE Reg mu* sig* Obs Pooled -0.09173 -5.929 1.039 -0.640 0.878 789The LLC test produces the test statistic of 1.08357 with a p value of 0.8607. Therefore wecannot reject the null hypothesis that there is a unit root and therefore conclude that this panelis non-stationary.Even if the real GDP series for Namibia, which has been proven to contain structural change,is removed from the unit root test we still get the same result (as shown in the graph below) 24
  25. 25. 557699 Null Hypothesis: Unit root (common unit root process) Series: RGDP_LKA, RGDP_LSO, RGDP_LUX, RGDP_MAR, RGDP_MDG, RGDP_MEX, RGDP_MLI, RGDP_MOZ, RGDP_MRT, RGDP_MUS, RGDP_MWI, RGDP_MYS, RGDP_NER, RGDP_NGA, RGDP_NIC, RGDP_NLD, RGDP_NOR, RGDP_NPL, RGDP_NZL Date: 03/15/12 Time: 15:46 Sample: 1960 2000 Exogenous variables: Individual effects, individual linear trends Automatic selection of maximum lags Automatic lag length selection based on SIC: 0 to 2 Newey-West automatic bandwidth selection and Bartlett kernel Total number of observations: 749 Cross-sections included: 19 Method Statistic Prob.** Levin, Lin & Chu t* 1.26001 0.8962 ** Probabilities are computed assuming asympotic normalityAs you can see there is most definitely unit root processes in the real GDP variable with orwithout Namibia. This could be occurring because other countries have less obviousstructural breaks but if we analyse the graph in Appendix 2 again we can clearly see thatmany of the series seem to be chaotic in appear and so seem to be non-stationary processes.However some countries may in fact be stationary processes, which is the main limitationwith the LLC test because it assumes that there is the same unit root process for all the cross-sections, which is obviously an unrealistic assumption. Instead, the IPS test which is exploredbelow relaxes this assumption to allow different values of ρ for each cross-section. 4.2. Panel Unit Root Test- Im, Pesaran and Smith testIm, Pesaran and Shin (2003) proposed a unit root test for dynamic heterogeneous panelsbased on the average from ADF tests computed for each individual cross-section in the panel.Similar to the LLC test, the IPS test allows for serial correlation of the residuals. There is alsoa modified version of this test which allows for situations where the errors in the individualDF regressions are serially uncorrelated. When errors in individual DF regressions areserially uncorrelated, and normally and independently distributed across groups, it is shownthat the proposed Lagrange Multiplier-bar ( test statistic is distributed as standard normalfor large N and finite T.When errors are serially correlated and heterogeneous across groups,the standardised LM-bar statistic is shown to be valid as T and N tending to infinity, with N/Ttending to k, where k is a finite positive constant.The IPS model is given by: 25
  26. 26. 557699Where is the intercept, is the trend term, is the random error term, is thechange in the dependent variable used to remove autocorrelation with its coefficient and is the coefficient on the lagged dependent which indicates whether or not a unit root ispresent.To test the null hypothesis of that there is a unit root in all cross-sections, we test if The alternative hypothesis is that for at least some cross-sections. This is in contrastto the LLC test which assumes that all series are stationary under the null hypothesis. Alimitation of this model is that it has been created under the restrictive assumption that it istested on a balanced panel, such that T is the same for all cross-sections. We must use abalanced panel to calculate their statistic, which shows the average of the individual ADF t-statistics for testing thatWe can now use this value to derive which has been shown that under specificassumptions converges to this value over time. We also must calculate the mean andvariance for . Based on those values the IPS test statistic, , can be calculated and isgiven by:Where is the mean and is the variance for Im, Pesaran,and Shin proved using Monte Carlo simulations that their test has better finite sampleproperties than the LLC undertaken above.We can undertake the IPS test in Eviews in the same way as the LLC test except by choosingthe option for IPS as the test type. We have kept the lag length selection as Schwartzinformation criterion and have included Namibia as the presence of structural change inNamibia will not affect the result because the value for ρ is allowed to differ for each cross-section. Carrying out the IPS test in Eviews produces the following output 26
  27. 27. 557699 Null Hypothesis: Unit root (individual unit root process) Series: RGDP_LKA, RGDP_LSO, RGDP_LUX, RGDP_MAR, RGDP_MDG, RGDP_MEX, RGDP_MLI, RGDP_MOZ, RGDP_MRT, RGDP_MUS, RGDP_MWI, RGDP_MYS, RGDP_NAM, RGDP_NER, RGDP_NGA, RGDP_NIC, RGDP_NLD, RGDP_NOR, RGDP_NPL, RGDP_NZL Date: 03/16/12 Time: 12:48 Sample: 1960 2000 Exogenous variables: Individual effects, individual linear trends Automatic selection of maximum lags Automatic lag length selection based on SIC: 0 to 2 Total number of observations: 789 Cross-sections included: 20 Method Statistic Prob.** Im, Pesaran and Shin W-stat 2.28632 0.9889 ** Probabilities are computed assuming asympotic normality Intermediate ADF test results Max Series t-Stat Prob. E(t) E(Var) Lag Lag Obs RGDP_LKA -1.4508 0.8297 -2.173 0.655 0 9 40 RGDP_LSO -2.3893 0.3792 -2.173 0.655 0 9 40 RGDP_LUX 1.3764 1.0000 -2.173 0.655 0 9 40 RGDP_MAR -2.7277 0.2317 -2.177 0.692 1 9 39 RGDP_MDG -1.7477 0.7109 -2.173 0.655 0 9 40 RGDP_MEX -1.4769 0.8210 -2.173 0.655 0 9 40 RGDP_MLI -2.1915 0.4811 -2.173 0.655 0 9 40 RGDP_MOZ -1.6147 0.7693 -2.173 0.655 0 9 40 RGDP_MRT -1.9228 0.6241 -2.173 0.655 0 9 40 RGDP_MUS 0.3621 0.9983 -2.173 0.655 0 9 40 RGDP_MWI -2.4571 0.3463 -2.115 0.713 2 9 38 RGDP_MYS -1.3811 0.8510 -2.177 0.692 1 9 39 RGDP_NAM -2.2468 0.4520 -2.173 0.655 0 9 40 RGDP_NER -2.0706 0.5458 -2.173 0.655 0 9 40 RGDP_NGA -3.3215 0.0777 -2.177 0.692 1 9 39 RGDP_NIC -2.8785 0.1802 -2.177 0.692 1 9 39 RGDP_NLD -1.3965 0.8464 -2.177 0.692 1 9 39 RGDP_NOR -3.0583 0.1303 -2.177 0.692 1 9 39 RGDP_NPL 0.7339 0.9995 -2.115 0.713 2 9 38 RGDP_NZL -3.1177 0.1165 -2.177 0.692 1 9 39 Average -1.7489 -2.168 0.674As with the LLC test, the IPS test have conclusively identified that there is a unit root in allthe cross-sections as it has a probability that there is a unit root of 98.89%, meaning we fail toreject the unit root null hypothesis. This finding could possibly have arisen because otherseries, as well as Namibia, have structural breaks in them but we have not dealt with thepresence of the structural break as unit root tests for panel data with structural breaks are verycomplex to implement and are beyond the scope of this paper. This result would indicate thatreal GDP for these 20 countries follows a stochastic trend and shocks will therefore inducepersistent changes in the level of the series and not decay over time. 27
  28. 28. 557699Murthy and Anoruo (2009) found that in a panel of 27 African countries, the real GDP percapita series in the panel are stationary with multiple structural breaks that are taking place indifferent countries at different times. They therefore concluded that the series are stationarywith broken trends. These results are contrary to this results from my paper, however fromanalysing the graphs in appendix 2, it can be seen that there may be multiple structural breaksoccurring in most time series. We could therefore carry out additional analysis in anotherpaper to consider whether there are multiple structural breaks occurring in the panel.However, Cuestas and Garratt (2008) have found that if we test for a unit root aftercontrolling for two sources of nonlinearity, asymmetric adjustment and nonlinear trends, thenreal GDP per capita series in some countries are in fact stationary processes.For economists and policy makers, finding that real GDP is a non-stationary series wouldhave enormous implications. For instance, using non-stationary time series in OLS regressionanalysis would lead to spurious results and the forecasts based on the series would cease to bereliable, in addition to rendering monetary and fiscal policy actions based on these seriespermanent and not mean-reverting.Real GDP being a non-stationary process means that it is arandom walk with only stochastic shocks affecting it. This would mean that governmentpolicy instruments would have negligible effect on GDP growth.Azomahou, Diebolt and Mishra (2009) have shown that in recent years, demographicdynamics have had noticeable effects on both the volatility and nonlinearity of cross-countryeconomic growth. In concluding that a unit root is present, these demographic shocks wouldpersist as the economy has a long memory and therefore increase the volatility of economicgrowth. 5. Concluding Remarks in Light of the Results from the Unit Root TestsIn section 3 we found that the fixed effects method is the most efficient model to use toestimate the relationship between economic growth, physical capital growth and age-structured population growth. In section 4 we found that the real GDP series for all cross-sections are non-stationary. Because real GDP is non-stationary, ordinary least squares wouldlead to spurious results which would be unreliable; however because we have estimated thefixed effects method using log differenced variables, we do not need to change thespecification of the test because these variables would be stationary and therefore OLS wouldproduce unbiased estimates.Following the work of Prskawetz, Kögel, Sanderson and Scherbov (2007), we could examinethe effects of uncertainty on economic growth. To undertake this analysis, a GARCH(1,1)model for real GDP growth must be estimated first in order to obtain the variance series, usedas uncertainty ( in the subsequent analysis of the following model 28
  29. 29. 557699We could also use a dynamic model to measure the persistence of GDP growth. If we were touse a basic dynamic model without logarithmic differences, for exampleThe introduction of the lagged dependent variable removes any autocorrelation and it alsomodels a partial adjustment based approach.However the use of this dynamic model means that traditional OLS estimators are biased andtherefore different methods of estimation will need to be used. This arises because of thecorrelation between the lagged dependent variables with the individual specific random orfixed effects. Since yit is a function of αi, then yi,t-1 is also a function of αi. This means that theexplanatory variable yi,t-1 is correlated with the error term which will lead to biased andinconsistent estimates. Similarly; applying the random effects method using GLS means thatwe would have to quasi- demean the data, however this causes the demeaned dependentvariable to be correlated with the demeaned residuals; thus causing the GLS estimator to bebiased and inconsistent. 6. Review of Literature on Demographic volatility and Economic GrowthFollowing on from research by Kelley and Schmidt (1995, 2001); Mishra and Diebolt (2010)have proposed that empirical economic growth models should account for stochasticdemographic characteristics to gain better information of the evolution of the demography-economic system. As such they proposed a stochastic version of the Solow-Swan model forwhich they have relaxed the conventional assumption that population growth is consideredstationary; in favour of assuming a long-memory, non-stationary process. They augmentedthe economic growth model with the evolutionary pattern of the demographic system,allowing them to model economic growth with the conventional assumption of stationarityuniversally assumed in existing growth models to be a special case of the more generalstochastic demographic system. Demographic variables such as birth rates, life expectancy atbirth rates, mortality rates, and population density have been found to have statisticallysignificant impacts on economic growth and including these additional demographic canimprove the explanatory power; although they found that we cannot understand therelationship between economic growth and demography without considering stochasticshocks.Mishra and Diebolt use panel estimation techniques to estimate the following model, which isthe same specification as Kelley and Schmidt used:They then use 3 empirical specifications with each increasing variables, model 3 is the mostgeneral specification. Model 3 was also found to be the best model with the highest R2. Thefirst model regresses output growth on log of per capita income, aggregate population 29
  30. 30. 557699growth, population density and the interaction term. The second model includes thecontemporaneous birth and death rates, and the third model includes lagged values of thebirth rates.They used the fixed estimation method over the random effects method because even thoughrandom is theoretically better than fixed for efficiency, it produces biased estimates if are correlated with the explanatory variables. The Fixed effects method is also moreappropriate as they are not taking their cross-sections as a sample from a random draw of anunderlying distribution.Use of the Hausman specification test confirmed that the fixed effectsmethod is best as it dominates both the random effects and pooled estimation methods.From their results, we can analyse the partial effect of the contemporaneous birth rates (CBR)and death rates (CDR). Mishra and Diebolt found that CBR has been a positive effect inrecent decades for developed countries but in developing countries it was found to benegative. This was a result of poor resources and higher birth rates which caused depressionin developing countries economy. Intuitively, there are large effects from falls in the deathrate which positively contribute to economic growth in each decade. However, an importantconclusion that emerged from their analysis was that very little gain could be expected fromfurther reductions in mortality in the developing countries.Future extensions that they are considering to take are to analyse the long-run equilibriumrelationship between Yt and Vit given different orders of integration. They want to know theimpacts that a linear combination of various orders of integrated process of age-structureswill have on the order of the dependent variable.Words (510) 30
  31. 31. 557699Appendix 1 31
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