557699

Investigating the Cross-Country Relationship Between Economic Growth, Physical Capital Stock and Age-Structured Population

1. Introduction

There have been numerous attempts to explain economic growth and its determinants over the years, with these theories wide ranging in their explanations. The neoclassical economists such as Solow (1952) stressed the importance of free markets, privatisation and open economies for economic growth. They regarded physical factors of production like capital and labour to be the determinants of economic growth. To understand the nature of economic growth, we must also start by understanding the relationship economic growth has with the people who produce it. Cuaresma, Lutz and Sanderson (2009) concluded that the size of the population with the technologies they produce is the root cause of economic growth.

For development economics, sustained growth in GDP per capita is arguably the most important determinant of living standards since other measures of living standards, such as life expectancy and the Human Development Index (HDI), typically move together with GDP per capita. Therefore understanding the causes of economic growth is of great importance if we 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 depends on the savings rate, the capital-output ratio, and the depreciation rate. This model assumes that by increasing the savings rate, that this will increase investment and therefore augment the capital stock. In this paper we are endogenizing this effect by considering growth in the physical capital stock instead of changes to the savings rate. A major criticism of this model however 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 of growth of labour and growth of capital. Using the model, economic growth was derived as g=n, meaning economic growth is equal to labour growth. This model found growth to be exogenous because growth of the labour force was not part of the model; however we are endogenizing this effect by including age-structured population growth in the model. This paper will explore this relationship by undertaking a cross-country analysis of the relationship between economic growth, as the dependent variable, and age-structured population growth and physical capital stock growth as explanatory variables.

2. Inspecting the Data

The data being used to investigate the possible relationships will be from 20 worldwide countries of varying development stages1. Therefore the number of cross-sections in the data will be i=1 , …, N ; where N=20. The data will cover the period of 1960 to 2000, therefore t=1 , …,T ;where T=41. The data will be analysed as a balanced panel using the econometric

1 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

557699

software Eviews. The physical capital stock for each country will be measured in thousands of US dollars and be denoted in Eviews as CAP; this variable is transformed into 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, which represents the school age population up to age 14; POP1564, which represents the working age population of people from 15 to 64 years old; finally POP65P, which represents people aged 65 or the retired population. These three population variables will be log differenced as well to produce Pop014growth, Pop1564growth and Pop65pgrowth, which represent population growth for the three age brackets. RGDP denotes the real GDP per capita for each country 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 between periods t and t−1. This calculation can be carried out in Eviews by generating the following equation using the pool object

Growth?=d ¿

This paper is therefore examining how percentage changes to the physical capital stock and age-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 people aged 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 reject normality for all three of these countries and for Sri Lanka we can reject normality even at the 1% significance level. The Kurtosis value for each cross-section can also be analysed to understand the shape of the data with standard normally distributed data having a Kurtosis value of 3. As you can see from the graph in the appendix, the Kurtosis for Sri Lanka looks to be significantly different from 3 as it has a Kurtosis value of 4.07075 and it is the only leptokurtic cross-section in the data. All the other cross sections have a Kurtosis value of less than 3 which indicates they could be more platykurtic in shape, meaning the data has a lower and broader peak with shorter and thinner tails than a standard normal distribution. Finally we can look at the skewness of the POP014 variable for each cross-section. Non-skewed and normally distributed data will have a skewness of 0. It can be seen that Mexico and Morocco are moderately skewed to the left as they have a skewness value of -0.759313 and -0.605342 respectively. More extremely, Sri Lanka has a skewness value of -1.323122 showing that it is highly skewed to the left. These results signify that there are some questionable features in this variable.

Next we can analyse the descriptive statistics for the POP1564 variable for the working aged population between the ages of 15 to 64. The data series’ for this variable are much more normal than the POP014 however there is still some features which seen non-normal. The series’ for Namibia, Niger and Nigeria all have moderately positive skewness, shown by a

2

557699

skewness value of 0.750231, 0.591596 and 0.5052 respectively. All of the cross-sections are possibly platykurtic in shape as the Kurtosis values for all cross-sections are less than 3 but we cannot be sure if they are significantly less than 3, but the kurtosis value of 1.52529 for Lesotho does seem to be significantly less than 3. However the Jarque-Bera statistic for each cross-section has probability values of greater than the 10% significance level so we cannot reject the null hypothesis of normality, therefore concluding that the POP1564 is a generally normal variable.

The POP65P variable for people aged 65 and over is similar to the previously discussed variable as it seems generally normal with a few discrepancies. In terms of skewness; Lesotho, Mexico, Mali, Malawi, Namibia, Niger, Nicaragua and Nepal are all moderately positively skewed in their distribution which means they have longer tails to the right. More worryingly for this variable when considering the Jarque-Bera statistic for normality is that one cross-section is significantly non-normal at the 5% level (Malawi with a probability value 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 that one 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 the Jarque-Bera statistic, we can reject normality at the 1% significance level for Mexico Mauritania, Malawi, Nicaragua, and New Zealand. We can also reject normality at the 5% significance level for Sri Lanka, Luxembourg, Morocco, Mali, Niger, Nigeria, the Netherlands, and Nepal. Finally we can reject normality at the 10% significance level for Mozambique and Malaysia. 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 ordinary least squares estimation undertaken below produces. This data could be not normally distributed due to the difficulty in generating this variable because economists have struggled to 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 is also some skewness in the data with Luxembourg, Mauritius, Namibia and Nepal all being highly positively skewed.

Finally, the real GDP growth variable which was produced using the previous formula in Eviews also seems to be very non-normal. Examining the Jarque-Bera statistic first again shows 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 Kurtosis values 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 because there are many values close to zero.

3.1. Estimating Possible Relationships: Pooled Estimation

3

557699

The 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 set for growth is stacked into a single column containing all the cross-sectional and time-series observations and the same for all the explanatory variables as well. This equation is then estimated using ordinary least squares. We use the pooled estimation method as it is a simple way to estimate the relationships between variables because it assumes homogeneity among the cross-sections and over time. The equation to be estimated is the following

Growth¿=c+a1 Pop 014 growth¿+α 2 Pop 1564 growth¿+α3 Pop 65 pgrowth¿+α 4 Capgrowth¿

Where ‘c’ is the intercept,a1 is the coefficient on the Pop014growth variable,a2 is the

coefficient on the Pop1564growth variable, a3 is the coefficient on the Pop65Pgrowth

variable, and a4 is the coefficient on the Capgrowth variable.

To undertake this analysis in Eviews, first the pool object is opened and then the estimate button is clicked which brings up the pool estimation menus. On this menu, ‘growth_?’ is entered as the dependent variable, where the ‘_?’ captures the cross-sectional element of the data. The regressors are chosen as ‘pop014growth_?’, ‘pop1564growth_?’, ‘pop65pgrowth_?’, ‘capgrowth_?’ and a constant term ‘c’. These inputs create the following pooled estimation output in Eviews

Dependent Variable: GROWTH_?Method: Pooled Least SquaresDate: 03/13/12 Time: 12:39Sample (adjusted): 1961 2000Included observations: 40 after adjustmentsCross-sections included: 20Total pool (balanced) observations: 800

Variable Coefficient Std. Error t-Statistic Prob.

C 0.030666 0.006153 4.984061 0.0000POP014GROWTH_? -0.293921 0.177507 -1.655828 0.0982

POP1564GROWTH_? -0.663378 0.285869 -2.320565 0.0206POP65PGROWTH_? 0.062482 0.108355 0.576641 0.5643

CAPGROWTH_? -0.000269 0.002672 -0.100509 0.9200

R-squared 0.019565    Mean dependent var 0.012709Adjusted R-squared 0.014632    S.D. dependent var 0.061980S.E. of regression 0.061525    Akaike info criterion -2.732526Sum squared resid 3.009304    Schwarz criterion -2.703247Log likelihood 1098.010    Hannan-Quinn criter. -2.721278F-statistic 3.966174    Durbin-Watson stat 1.720148Prob(F-statistic) 0.003406

Analysing the results of this pooled OLS regression, first we can examine the significance of the explanatory variables.

We can see that the constant term is significantly different from zero because the probability that it is equal to zero is 0.000. It also shows there is a positive constant growth effect from

4

557699

its coefficient 0.030666. The constant term signifies that there is an exogenously determined level of growth in the economy. The fact that other variables are significant shows that economic growth is both exogenously and endogenously determined.

Next the Pop014growth variable is significantly different from zero at the 10% significance level as it has a probability that it is zero of 0.0982. The coefficient for this variable −0.293921 shows that a 1% increase in the population aged 0 to 14 will decrease GDP growth by 0.294%. This effect could be occurring because an increase in people of this age will 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 a result.

The Pop1564growth variable is significantly different from zero at the 5% level, as shown by its p value of 0.0206. The coefficient for this variable is −0.663378 which indicates that a 1% 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 would be positively contributing towards real GDP growth as they are working, producing and spending. This result could possibly have arisen due to the pooled estimation method not taking into account the cultural differences between counties. It might be easier to understand why this effect is occurring if this age bracket was split into categories for peoples education levels so we could understand the effect that the level of peoples education has on GDP growth. It might be that for this age bracket in some countries there is a lot of highly educated people, whereas in other countries the average education level is much lower; therefore making this age bracket contribute negatively to GDP growth.

The Pop65pgrowth variable results show that this variable has no effect on GDP growth because the probability that the coefficient is different from zero is 0.5643 which fails at all 3 important significance levels. In some developing countries, the level of wealth that retired people have might be so low that they are just living on government benefits, hence not contributing 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 GDP growth because it has a 92% probability that its coefficient is equal to zero. This finding obviously flies in the face of most current research and theory. This could have arisen due to the method used to calculate the capital stock, because there are many techniques available to use.

Therefore, the OLS regression model for economic growth is given by a pooled estimation is

GDP Growth¿=0.030666−(0.293921 ) Pop 014 growth¿−¿

The R-squared value of 0.019565 from the regression shows that only 1.96% of the variance in 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 which may not be the most efficient method of estimation as the countries might have different cultural and technological characteristics making the estimation of a common

5

557699

coefficient for each variable and for each country unsuitable. This low R-squared value also indicates that there may be other explanatory variables which explain economic growth which aren’t included in this model; these variables could be physical factors, technological influences or other demographic variables such as education levels, or birth rates. Human capital growth theory, for example, suggests that education is the most prominent factor in economic growth and that countries with lower levels of education will suffer from less innovation, a slower pace of learning by doing, and also less technical changes. Another variable 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 the unemployment rate.

Analysing the Durbin-Watson statistic of 1.72 we can conclude that there is no autocorrelation 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 a few parameters, it also has several limitations. Firstly, pooling the data implicitly assumes that the relationships between the variables and the average value for these variables are constant both over time and across all cross-sections of the sample. This assumption for simplification affects the validity of the model because in the context of this paper it also assumes that all countries have the same cultural and geographical variations. Intuitively this would seem to be unrealistic as the sample has both developed and developing countries of various sizes, which would point to them having different coefficients. Therefore, estimating the data as a pool means we lose individual heterogeneity. To solve this problem we can estimate the data again using the fixed effects method.

3.2. Estimating Possible Relationships: Fixed Effects Method

The fixed effects method considers country specific effects by allowing the intercept in the regression model to differ cross-sectionally but not over time. Because the intercept is not allowed to change over time, it therefore captures a fixed effect which is why the model has its name. It treats observations for the same individual as having something specific in common such that they are more ‘like’ each other than observations from two or more different countries. We use the fixed effects method because it captures all the effects which are specific to a country. The fixed effects in the context of this paper take into account geographical factors, natural endowments, and other factors which vary between countries but not over time. This means that we cannot include other variables which do not vary over time but do vary cross-sectionally, such as country size, because these variables would be perfectly co-linear with the fixed effect. The fixed effects method can be extended by including 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 over time but are common across the whole panel. This paper will utilise the fixed effects method with cross-sectional dummies only as we are comparing the cross-country relationship. Two

6

557699

methods to estimate the fixed effects method this paper will explore are the Least Squares Dummy Variable (LSDV) method and the within-groups method.

To explain the LSDV approach, we can first consider this simple two variable model below

y¿=α+ β X¿+ε¿ ε ¿ N (0 , σ2)

Where y¿ is the dependent variable, α is the intercept term, X ¿ is the explanatory variable, β is the coefficient on the explanatory variable, and ε ¿ is the stochastic error term which can be split up into an individual specific effect, ui, and a remainder disturbance term, v¿ , such that

ε ¿=u i+v¿

This expanded error term can then be plugged back into the model to produce

y¿=α+ β X¿+ui+v¿

ui now represents all of the variables that affect y¿ cross-sectionally but not over time, the

fixed effect; such as a person’s gender, the sector a firm operates in, or in this paper’s case the country. This model can now be estimated using dummy variables which is then called the Least Squared Dummy Variable Approach

y¿=β X¿+u1 D1+u2 D2+…+uN DN+v¿

Or

y¿=β X¿+∑i=1

N

ui Di+v¿

Where D1, D2,…,DN are dummy variables indicating the groups and where u1, u2,…, uN are their regression coefficients which must be estimated. For the dummy variables, D1=1 when i=1 and 0 otherwise. Similarly, D2=1 when i=2 and 0 otherwise, and so on for the N number of cross-sections. The intercept term α has been removed from this regression model in order to 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 can undertake a transformation called a “within-transformation” which then provides the second approach, ‘the within-groups method’.

The within-groups method works by transforming the data by subtracting the mean of each entity away from the values of the variable. Starting with the regression model

y¿=α+ β X¿+ε¿

We can define the group means as

X i=1T ∑

t

X¿

7

557699

y i=1T ∑

t

y¿

Now we can subtract the means from each variable to obtain a regression containing demeaned variables only. This regression does not require an intercept term because the dependent variable will have zero mean by construction. Undertaking this transformation gives the following model

y¿− y i=β ( X¿−X i )+(ε¿−εi)

or

y¿=β X¿+ε ¿

Where double dots denote demeaned values. This within-groups method provides identical estimates 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 and sum of products

W xxi=∑t

( X ¿−X i)2

W yyi=∑t

( y¿− y i)2

W xyi=∑t

( X¿−X i) ( y¿− y i )

Now Q=∑¿

( y¿−α i− β X¿) must be minimised with respect to α i∧β i

dQd αi

=0=¿∑t

( y¿−α i− β X¿)=0

or α i= y i− β X i (1)

dQd β i

=0=¿∑t

X¿ ( y¿− αi− β X¿ )=0 (2)

Next equation (1) is substituted into equation (2) and simplified to give

β=W xx−1W xy

In the case where the model includes several explanatory variables then Wxx is a matrix, and

β and Wxy are vectors.

Since we have defined β, we can define α i as

α i= y i− β ' X i.

8

557699

These estimates are known as within-group estimates and often denoted βW.

The advantage of using the fixed effects method over the pooled estimation method is that it controls for all possible fixed characteristics of the individual countries in the study. It also allows for more heterogeneity than the pooled estimation because of this.

However, there are disadvantages of using the fixed effects method to estimate this relationship. First; when the number of cross-sections, N, is large it is unpractical to specify so many dummy variables as it would take a lot of time and money to compute those in a large study. The fixed effects method is also inefficient if the ui terms are uncorrelated with X ¿, this is because these characteristics make the random effects method the appropriate method to use. Finally; the use of the fixed effects method can exacerbate biases from other types of specification problems, especially measurement errors.

To estimate the relationship in Eviews using the fixed effects method, we must first select the pool object and then click the estimate button which brings up the pool estimation menus. On this menu, ‘growth_?’ is entered as the dependent variable and the regressors are chosen as ‘pop014_growth?’, ‘pop1564_growth?’, ‘pop65p_growth?’, ‘cap_growth?’ and a constant term ‘c’. This is currently the same as the pooled estimation except now under estimation method, 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 effects method, not a two-way fixed effects method. These inputs create the following fixed effects estimation output in Eviews

Dependent Variable: GROWTH_?Method: Pooled Least SquaresDate: 03/13/12 Time: 14:12Sample (adjusted): 1961 2000

9

557699

Included observations: 40 after adjustmentsCross-sections included: 20Total pool (balanced) observations: 800

Variable Coefficient Std. Error t-Statistic Prob.

C 0.019472 0.010577 1.840932 0.0660POP014GROWTH_? 0.480704 0.245099 1.961268 0.0502

POP1564GROWTH_? -0.733022 0.421396 -1.739510 0.0823POP65PGROWTH_? 0.043773 0.109685 0.399079 0.6899

CAPGROWTH_? -0.000687 0.002651 -0.258987 0.7957Fixed Effects (Cross)

LKA--C 0.015778LSO--C 0.002839LUX--C 0.015977MAR--C 0.016757MEX--C 0.012095MLI--C -0.017151

MDG--C -0.024539MOZ--C -0.027105MRT--C -0.007329MUS--C 0.032287MWI--C 0.001716MYS--C 0.031352NAM--C -0.006058NER--C -0.030094NGA--C -0.022851NIC--C -0.022772NLD--C 0.013482NOR--C 0.014642NPL--C -0.000709NZL--C 0.001682

Effects Specification

Cross-section fixed (dummy variables)

R-squared 0.081617    Mean dependent var 0.012709Adjusted R-squared 0.054397    S.D. dependent var 0.061980S.E. of regression 0.060270    Akaike info criterion -2.750407Sum squared resid 2.818845    Schwarz criterion -2.609869Log likelihood 1124.163    Hannan-Quinn criter. -2.696419F-statistic 2.998405    Durbin-Watson stat 1.841619Prob(F-statistic) 0.000004

To begin analysing the results from the fixed effects method we can first look upon the intercept in the regression model which is now allowed to differ cross-sectionally but not over time. In the Eviews output, the fixed effects for each country as listed as deviations from the overall group intercept term. This way of calculating the model stops the problem of multicollinearity. The probability that there is no constant level of growth is 0.066 meaning that at the 10% we can reject that there is no constant level of growth and hence conclude that there is a constant endogenous level of growth for the countries. Since we now know that the intercept is significant, we can also look at its effect cross-sectionally. We can see that for some countries real GDP growth grows constantly, whereas for others real GDP growth is shrinking. This could be occurring due to technological differences between developing and developed countries. This is supported by developed European countries like the Netherlands

10

557699

and Luxembourg showing a positive intercept value of 0.032954 and 0.035449 respectively, whereas many of the developing African countries have a negative intercept; such as Niger (−0.01062), Mozambique (−0.000763), Madagascar (−0.00507) and Nicaragua (−0.0033). The variety of estimates for the constant term across the cross-sections would be an indicator that the pooled regression might not perform as well as the fixed effects method because the variety of estimates for the constant reflects the technical and cultural differences between countries. The constant term is showing that there is a stable exogenous effect which differs between the countries. This could be government spending for example, which could mean 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 tended to be negative.

The fixed effects estimation of the Pop014growth variable has changed when compared with the pooled estimation. In the pooled estimation, a change in the population aged 0 to 14 negatively 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 is significant at the 10% significance level but just misses the 5% significance level with a probability of 0.0502. This finding confirms the findings by An and Jeon (2006) who showed that demographic changes appear to affect economic growth in an inverted U-shape, first increasing then decreasing economic growth.

Next the Pop1564growth variable has slightly changed from the pooled regression. It is less significant as it is only significant at the 10% level for this fixed effects method, shown by a probability 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 GDP growth as larger than under the pooled estimation. This model estimates that a 1% increase in the population aged 15 to 64 decreases GDP growth by 0.733%, which is a reduction in GDP growth of 0.07% more than under the pooled estimation.

Similarly to the pooled estimation, the fixed effects method finds both the Pop65pgrowth and Capgrowth variables insignificantly different from zero, shown by p values of 0.6899 and 0.7957 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 which explain 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 no autocorrelation 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 model explained 1.9565% of the variance in real GDP growth, however this fixed effects method is able to explain 8.1617% of the variance in real GDP growth. Therefore we can say that the fixed model explains more of the variance in real GDP growth than the pooled estimation does but to decide which performs better we need to undertake an F-test.

11

557699

Before undertaking the F-test, we can also see that the fixed effects method is more efficient than the pooled estimation method because it has a smaller residual sum of squares, 2.818845 compared to 3.009304.

The F-test is used to test which of the pooled and fixed effects methods performs best. It tests the null hypothesis that the pooled estimation method is most efficient and that there is no unobserved heterogeneity

H 0 :α 1=α 2=…=α N=α

It is tested against the alternative hypothesis that at least some of the intercept terms are not equal, meaning the fixed effects method is most efficient. The formula to calculate the F-statistic is given by

F(n−1 ,nT −n−k)=(RU

2 −RP2 /n−1)

(1−RU2 /nT−n−k )

Where ' RU2 ' is the R2 from the fixed effects method, ' RP

2 ' 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 F critical 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 of 0.081617, with number of cross-sections, 20, the number of years, 40, and finally the number of explanatory variables, 23, into the equation produces

F (19,757 )=(0.081617−0.019565/19 )

(1−0.081617 /20∗40−20−23 )=2.691995

This value can now be compared to the F critical values which are

F19,7571% =1.93

F19,7575% =1.6

F19,75710% =1.44

Comparing the F-statistic to the F critical value at each significance level we can see that F>Fc so we can reject the null hypothesis at the 1%, 5% and 10% significance levels and so conclude that at least some of the intercept terms are not equal and that the fixed effects method performs better than the pooled estimation. This result seems intuitive as the data has a mix of developed and developing countries so cultural differences would indicate that homogenous coefficients are unsuitable.

12

557699

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, a random effects method can be used to estimate the relationship between the variables which allows the constant term to be stochastic.

3.3. Estimating Possible Relationships: Random Effects Method

In the random effects method, the α iare treated as random variables rather than fixed constants like in the fixed effects approach. The model assumes that the intercepts for each cross-section arise from a common intercept term α , plus a random variable ε i that varies

cross-sectionally but is constant over time. ε i measures the random deviation of each country’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 ε i terms. This model can also be called the variance components model or the error components model. We can understand why it is called the error components model by considering the following simple two variable regression model

y¿=α i+ β X¿+u¿

Where, α i is made up of a global constant term ' α ' , and a random error termε i

α ¿=α+εi,

Therefore y¿=α+ β X¿+ω¿, where ω¿=εi+u¿

ω¿ is the composite error term. It is also assumed that ε i IID (o , σ εi

2 ) and it is also independent

of both X ¿ and u¿. The reason it is called the error components model is that we have broken down the error term into the unobserved heterogeneity in the cross-sectional units and the random error term. We cannot run this model in ordinary least squares because even though α and β are estimated consistently, they are not estimated efficiently because of autocorrelation. Autocorrelation arises due to the presence of ε i which produces a correlation among 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) to get efficient estimates. Mundlak (1978) confirmed that GLS estimators are BLUE and therefore the desired estimation method, however since GLS is associated with the random effects method its use had to be justified by arguing that economic effects are random and not fixed. We can test whether this holds once results from the random effects method have been attained 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 a weighted mean of each variable over time. The model to estimate using GLS is also a weighted average of the estimates produced by the between estimator and the within estimator using OLS, which is as follows

13

557699

( y¿−θ y i )= (1−θ ) α+ ( X¿−θ X¿) θ+(1−θ ) εi+(u¿−θ ui)

Where θ=1−√ σu2

T σε2+σ u

2, u¿ is the idiosyncratic error with variance σu

2, and

ε i is theunobserved heterogeneity with variance σ ε2. This transformation ensures that there is no

auto-correlation in the error terms. The above equation is then estimated using GLS to provide estimates of the variables.

The advantages of using the random effects approach is that there are fewer parameters to estimate 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 observations within 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 that it is only valid when the composite error term ω¿ is uncorrelated with all of the explanatory variables. If they are uncorrelated, the random effects approach can be use; otherwise the fixed effects method is preferable. Another disadvantage of using this model is that we need to make specific assumptions about the distribution of the random components.

To estimate whether a relationship exists using the random effects method in eviews, we must first select the pool object and then click estimate. On this menus ‘growth_?’ is entered as the dependent variable and the regressors are chosen as ‘pop014_growth?’, ‘pop1564_growth?’, ‘pop65p_growth?’, ‘cap_growth?’ and a constant term ‘c’. Next under estimation method we change to cross-sections option to random. These inputs then estimates the relationship using the random effects approach which produces the following output

Dependent Variable: GROWTH_?

14

557699

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 0.0001POP014GROWTH_? -0.050100 0.196670 -0.254743 0.7990

POP1564GROWTH_? -0.805182 0.320585 -2.511605 0.0122POP65PGROWTH_? 0.050634 0.107561 0.470746 0.6380

CAPGROWTH_? -0.000408 0.002634 -0.155042 0.8768Random Effects (Cross)

LKA--C 0.004388LSO--C 0.001725LUX--C 0.004357MAR--C 0.008146MEX--C 0.006311MLI--C -0.006652

MDG--C -0.009350MOZ--C -0.012003MRT--C -0.001415MUS--C 0.011354MWI--C 0.003371MYS--C 0.016287NAM--C 3.74E-05NER--C -0.010818NGA--C -0.008033NIC--C -0.008364NLD--C 0.000732NOR--C 0.002051NPL--C 0.001044NZL--C -0.003170

Effects SpecificationS.D. Rho

Cross-section random 0.009409 0.0238Idiosyncratic random 0.060270 0.9762

Weighted Statistics

R-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 Statistics

R-squared 0.017176    Mean dependent var 0.012709Sum squared resid 3.016639    Durbin-Watson stat 1.716834

To begin analysing the results from the random effects method we can first look upon the cross-sectional random error which is given as a deviation from the ‘global’ intercept ‘c’.

15

557699

These terms are significant at the 1% significance level, as seen by the probability value of 0.0001. This shows that there are significant exogenous determinants of growth which are random between cross-sections. Even though the interpretations of the constant terms are slightly different in the fixed and random effects methods, they both find the constant a significantly positive determinant of growth at the 10% level, but the random effects method estimates constant terms which are significant at the 1% significance level.

The Pop014growth variable in the random effects approach has been estimated to have zero effect on GDP growth as it fails to reject the null that it is equal to zero, shown by the probability value of 0.799. This is obviously in stark contrast to the fixed effects approach which 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 negative effect on GDP growth as a 1% increase in this population group will decrease GDP growth by 0.805%. The magnitude of this effect has been estimated to be higher in the random effects 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. Economic interpretation of this finding could be that there is excess supply in the labour market meaning that any extra people would find it tough to enter the labour market and as such would live on state benefits. The increase in unemployed living on state benefits would reduce the government’s freedom to spend money on goods and services which would have helped 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 would support the conclusions from these results. If we could analyse the trend in unemployment rates, 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 human capital which in-turn negatively affected economic growth. He found that if Southern Asia and Sub-Saharan Africa had no gender inequality in education in 1960, then their economic growth would have been up to 0.9% per year faster than in reality. Gender inequality in employment in these regions has also been shown to reduce economic growth by another 0.3% annually. Therefore if we could also have used a dummy variable for gender, we may be able to offer extra insight into some of these findings.

The Pop65pgrowth and Capgrowth variables have found similar conclusions in the random effects as in the fixed effects approaches in that they both conclude that these variables have no impact on the growth rates of real GDP.

Next we can analyse the differences in the regression statistics. Eviews reports both weighted and unweighted statistics in the random effects output. The unweighted statistics are calculated using the GLS coefficient results estimated using the original data, whereas the weighted statistics are estimated after the GLS transformations have been undertaken. It is the GLS transformed weighted statistics that we are interested in.

16

557699

First looking at the R-squared value we can see that the random effects method is explaining a lot less of the variance in GDP growth than in the fixed effects method, 1% in the random effects approach compared to 8% in the fixed effects approach. The fixed effects method is also more efficient at estimating this data as it has a sum of squared residuals of 2.818845 compared to the random effects approach’s sum of squared residuals of 2.927659. The Durbin-Watson statistic of 1.769 shows that there is no autocorrelation in the data which was the same finding as the fixed effects approach.

Both the fixed effects and random effects approaches have been used to estimate the relationships and both have different estimations and assumptions, but which approach is most efficient and should be used? To decide this we can use a specification test devised by Hausman (1978) who modified a test based on the idea that under the null hypothesis of no correlation, both OLS and GLS are consistent but OLS is not efficient. While for alternative hypothesis OLS is consistent but GLS isn’t. Given a panel data model for which the fixed effects method is appropriate to use, the Hausman test examines whether the random effects approach will estimate as good as the fixed. Therefore we are testing the null hypothesis of no correlation between the α i∧X ¿ meaning the random effects approach is more consistent and efficient, against the alternative hypothesis that the random effects are inconsistent meaning that the fixed effects approach is more appropriate. The Hausman test statistic is calculated using the following formula

H=( βFE− β ℜ)' [Var ( βFE )−Var ( β ℜ) ]−1( βFE− βℜ) χ2(k )

Once the Hausman test statistic is calculated, it is then compared to Chi-Squared critical values.

We can undertake the Hausman test by first estimating the random effects method. Then selecting View=>Fixed/Random Effect Testing=>Correlated Random Effects-Hausman test. Selecting this test then produces the following output in Eviews

Correlated Random Effects - Hausman TestPool: POOLTest cross-section random effects

Test SummaryChi-Sq. 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 0.0003POP1564GROWTH_? -0.733022 -0.805182 0.074800 0.7919POP65PGROWTH_? 0.043773 0.050634 0.000461 0.7494

CAPGROWTH_? -0.000687 -0.000408 0.000000 0.3639

17

557699

The 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 random effects method is efficient, and therefore conclude that the fixed effects method is the most consistent model and therefore the model of choice. This also means that α i∧X ¿ are correlated. We could have identified that the fixed effects method is also more appropriate as we are not taking our cross-sections in the sample from a random draw of some underlying distribution.

4. Panel Stationarity Testing

Something which has not been considered so far in this paper is the issue with stationarity. In panel data estimation it is important to consider the degree of heterogeneity between the cross-sections. In particular, it is important to understand that all the countries in the panel may not have the same characteristics or properties. Therefore it is possible that not all the cross-sections in the panel may be stationary.

When using panel data, individual units are stacked assuming a common system between the cross-sections. This can cause a stochastic shock in one of the cross-sectional units to ripple across and disrupt the other cross-sections. Non-stationarity of a time series implies that the mean 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 chaotic dynamics and system failure. The advantage of unit roots tests being carried out on panel data rather than time series is that the power of panel unit root tests increases with an increase in the number of cross-sections. Two panel unit root tests this paper will consider is the test by Levin, 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 appropriate and will produce reliable results using this data. Structural breaks are an important consideration to take when performing a unit root test because structural change can make time series appear to be non-stationary. In panel data, a structural break in one cross-section will cause the LLC test to fail to reject a false null and conclude non-stationarity overall because the LLC test assumes that ρ is the same for all cross-sections, as explained below. In other 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 trend terms are correctly specified and when there are structural breaks, the deterministic terms will change at some point in time.

For example; empirical work by many economists has found that unit roots are present in most macroeconomic time series, however Perron (1989) argued that when either the great crash of 1929 or the oil shock of 1973 are taken into account, these results change dramatically 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 for the observations over time, with can be found in Appendix 2. A structural break will be an

18

557699

event where the trend in the data changes suddenly. Considering the graphs, it can be seen that some exhibit a constant growing trend over time, such as for GDP in the Netherlands or Norway, others are much more chaotic in nature, such as Nigeria or Mali, which would indicate a unit root process. However for Namibia, it seems that there is a structural change in the data. Considering the graph below for the real GDP of Namibia, it is clear to see that prior to 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 of GDP which is trending around a constant level of GDP.

3,000

3,500

4,000

4,500

5,000

5,500

6,000

6,500

1960 1965 1970 1975 1980 1985 1990 1995 2000

RGDP_NAM

In order to confirm that there is a structural break occurring in 1980, we can undertake some tests on the following AR(1) model

Rgd pNam=Rgd pNam (−1 )+e t

We can now use some stability diagnostics in Eviews to test our predictions that a structural break is present. First we can use recursive estimation of the residuals which shows whether there are any anomalies in the residuals from the above regression model. The table below shows that in 1980 the residuals spike out of the ±2 standard error bands which confirm the thoughts that a structural break occurring at that date.

19

557699

-2,000

-1,500

-1,000

-500

0

500

1,000

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 no break is present in 1980. The Eviews output for this test is below

Chow Breakpoint Test: 1980Null Hypothesis: No breaks at specified breakpointsVarying regressors: All equation variablesEquation Sample: 1961 2000

F-statistic 46.87814 Prob. F(2,36) 0.0000Log likelihood ratio 51.28556 Prob. Chi-Square(2) 0.0000Wald Statistic 93.75629 Prob. Chi-Square(2) 0.0000

Looking at the F-statistic for this test of 46.878, with the corresponding P value of 0.0000, we can conclusively reject the null hypothesis and therefore conclude that a structural break is occurring in 1980 in the real GDP data for Namibia. Because a structural break has been identified, we need to deal with it appropriately. Firstly we will estimate the LLC unit root tests below excluding Namibia from the estimation, then again with Namibia included in order 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 Namibia as if other countries are stationary it will show up in the results.

4.1. Panel Unit Root Test- Levin, Lin and Chu test

In 1992 Levin and Lin developed their first unit root test designed to be used on panel data. The original model was designed as such

Y ¿=ρ Y i ,t−1+z¿' γ+e¿, where e¿ IID(0 , σe

2)

20

557699

However, this 1992 model did not take into account problems with autocorrelation and Heteroskedasticity and so they created their 1993 model which was published in 2002 with Chu as co-author. This new model is given by

∆ Y ¿=ρ¿Y i ,t−1+∑l=1

L

θl Y i , t−l+z¿' γ+e¿

Where ρ¿=ρ−1 because the dependent variable has been differenced;θk is the coefficient on the lagged dependent variables; and e¿ is the stochastic error term. This new test now allows for different lags across the cross-sections in the model. The model also allows for

heterogeneity via two-way fixed effects, where z¿' =αi+δt with α i capturing the unit specific

fixed effects and δ tcapturing the unit specific time effects. The unit-specific fixed effects are very important to the model because they are allowing for individual heterogeneity since the coefficient on the lagged Yit is restricted to be homogenous across all units of the panel.

As before, this model assumes that e¿ IID(0 , σe2) meaning individual processes for each

cross-section are cross-sectionally independent and there is also no serial correlation. Under this 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 no cointegrating relationships and they found that LLC, as well as IPS, often over reject the null hypothesis of non-stationarity which indicates that these tests have poor size properties.

The model has three versions, each with separate null and alternative hypotheses

1). ∆ Y ¿=ρ¿Y i ,t−1+∑l=1

L

θl Y i , t−l+e¿, where H 0 : ρ=0 ,H 1 : ρ<0.

2).∆ Y ¿=αi+ρ¿Y i , t−1+∑l=1

L

θk Y i ,t−l+e¿, where H 0 : ρ=αi=0 , H 1 : ρ<0∧α i≠ 0.

3). ∆ Y ¿=αi+δ i t +ρ¿Y i ,t−1+∑l=1

L

θl Y i ,t−l+e¿, where H 0 : ρ=δi=0 , H 1 : ρ<0∧δ i≠ 0.

Model 1 contains no deterministic terms. Model 2 has an individual-specific mean, but no time trend. Model 3 has both an individual-specific mean and a time trend. Similarly to single time series unit root tests, if a deterministic element is present but it is not included in the regression model then the unit root test will not be consistent. Conversely, if deterministic terms are wrongly included in the regression procedure then the statistical power of the unit root test will be reduced (Levin, Lin and Chu, 2002).

To implement this model, Levin and Lin recommended a three-step procedure to implement this test:

Step 1: First, separate ADF regressions are undertaken for each cross-section in the panel on the following regression model

21

557699

∆ Y ¿=ρ Y i , t−1+∑l=1

L

θl ∆ Y i ,t−l+u¿

Because 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 which works by choosing the maximum lag order and then using t tests to decide whether a smaller lag order is preferable. Next we have to run two auxiliary regressions to generate orthogonalized residuals, meaning they are independent and uncorrelated. This is achieved by regressing ∆ Y ¿∧Y i , t−1 against ∆ Y ¿−l where (l=1,…,L), shown below

∆ Y ¿=∑l=1

L

θ l ∆Y i ,t−l+e¿

Y i ,t−1=∑l=1

L

θl ∆ Y i , t−l+εi ,t−1

Then the residuals e¿ and ε i ,t−1 from these regressions are saved. To allow for heterogeneity

across individuals we must normalise e¿ and ε i ,t−1 by the regression standard error

~e¿=e¿

σui

¿~ε¿=εi ,t−1

σui

Where σ ui 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 by calculating the following

σ yi2 = 1

T−1∑t=2

T

∆ y¿2+2∑

l=1

L

wLl[ 1T−1

∑t=2+l

T

∆ y¿∆ y i ,t−l]However, if model 2 from above is being used we need to replace ∆ Y ¿ for ∆ Y ¿−∆ Y ¿, where ∆ Y ¿ is the average value of ∆ Y ¿ for each cross-section. wL l 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 and time series observations in order to estimate

~u¿=γ ~εi , t−1+~e¿

Which is based on the total of N~T observations, where ~T=T−L−1 is the average number of

observations per individual in the panel, and L= 1N∑i=1

N

Li is the average lag order for the

individual ADF regressions which were carried out in step 1. The regression t-statistic for testing γ=0 is given by

t γ=γ

STD ( γ )

22

557699

Where

γ=∑i=1

N

∑t=2+L i

T~εi , t−1

~e¿

∑i=1

N

∑t=2+L i

T

~εi ,t−12

Therefore STD ( γ )=σu[∑i=1

N

∑t+2+Li

T~εi ,t−1

2 ]And σ u

2=¿

Therefore we can test the null hypothesis that γ=0.

Harris and Tzavalis (1999) found that the assumption built into this test that T → ∞ yields a test 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 whether there is a unit root for real GDP in these countries. To undertake this test we must first open all the cross-sectional data for real GDP in one window. Then unit root tests are selected and the following options are selected

In the test equation, both intercept and trend deterministics are included because if we analyse the graphs in Appendix 2 we can clearly see that many of the cross-sections exhibit a gradual upward trend. From these options the following result is produced

23

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_NZLDate: 03/15/12 Time: 15:20Sample: 1960 2000Exogenous variables: Individual effects, individual linear trendsAutomatic selection of maximum lagsAutomatic lag length selection based on SIC: 0 to 2Newey-West automatic bandwidth selection and Bartlett kernelTotal number of observations: 789Cross-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  40RGDP_LSO -0.25826  5099.8  524.22  0  9  39.0  40RGDP_LUX  0.05117  488015  513001  0  9  0.0  40RGDP_MAR -0.49985  12513.  5285.0  1  9  6.0  39RGDP_MDG -0.14692  858.79  1051.5  0  9  3.0  40RGDP_MEX -0.09610  50446.  68087.  0  9  2.0  40RGDP_MLI -0.22069  2310.9  2610.9  0  9  0.0  40

RGDP_MOZ -0.13749  12963.  15090.  0  9  4.0  40RGDP_MRT -0.13368  21514.  20503.  0  9  6.0  40RGDP_MUS  0.01747  76555.  87250.  0  9  2.0  40RGDP_MWI -0.34846  1247.8  200.62  2  9  29.0  38RGDP_MYS -0.05980  18544.  24225.  1  9  0.0  39RGDP_NAM -0.18874  121226  72743.  0  9  8.0  40RGDP_NER -0.24288  5247.8  5191.9  0  9  2.0  40RGDP_NGA -0.46164  6302.8  2947.5  1  9  9.0  39RGDP_NIC -0.17481  35806.  45641.  1  9  0.0  39RGDP_NLD -0.09901  58141.  130551  1  9  3.0  39RGDP_NOR -0.20757  59641.  133077  1  9  3.0  39RGDP_NPL  0.06413  683.09  554.34  2  9  1.0  38RGDP_NZL -0.38424  190085  279272  1  9  2.0  39

Coefficient t-Stat SE Reg mu* sig* ObsPooled -0.09173 -5.929  1.039 -0.640  0.878  789

The LLC test produces the test statistic of 1.08357 with a p value of 0.8607. Therefore we cannot reject the null hypothesis that there is a unit root and therefore conclude that this panel is 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

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_NZLDate: 03/15/12 Time: 15:46Sample: 1960 2000Exogenous variables: Individual effects, individual linear trendsAutomatic selection of maximum lagsAutomatic lag length selection based on SIC: 0 to 2Newey-West automatic bandwidth selection and Bartlett kernelTotal number of observations: 749Cross-sections included: 19

Method Statistic Prob.**Levin, Lin & Chu t*  1.26001  0.8962

** Probabilities are computed assuming asympotic normality

As you can see there is most definitely unit root processes in the real GDP variable with or without Namibia. This could be occurring because other countries have less obvious structural breaks but if we analyse the graph in Appendix 2 again we can clearly see that many 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 limitation with 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 explored below relaxes this assumption to allow different values of ρ for each cross-section.

4.2. Panel Unit Root Test- Im, Pesaran and Smith test

Im, Pesaran and Shin (2003) proposed a unit root test for dynamic heterogeneous panels based 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 also a modified version of this test which allows for situations where the errors in the individual DF regressions are serially uncorrelated. When errors in individual DF regressions are serially uncorrelated, and normally and independently distributed across groups, it is shown that the proposed Lagrange Multiplier-bar (LM ¿ test statistic is distributed as standard normal for 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/T tending to k, where k is a finite positive constant.

The IPS model is given by:

∆ y¿=α i+ρi y i ,t−1+∑k=1

n

θk ∆ y i ,t−k+δi t+ε¿

25

557699

Where α i is the intercept, δ i t is the trend term, ε ¿ is the random error term, ∆ y i , t−k is the

change in the dependent variable used to remove autocorrelation with θk its coefficient and ρi is the coefficient on the lagged dependent which indicates whether or not a unit root is present.

To test the null hypothesis of that there is a unit root in all cross-sections, we test if ρi=0.

The alternative hypothesis is that ρi<0 for at least some cross-sections. This is in contrast to the LLC test which assumes that all series are stationary under the null hypothesis. A limitation of this model is that it has been created under the restrictive assumption that it is tested on a balanced panel, such that T is the same for all cross-sections. We must use a balanced panel to calculate their t statistic, which shows the average of the individual ADF t-

statistics for testing that ρi=0 (denoted t ρi ) :

t= 1N∑i=1

N

t ρi

We can now use this value to derive t ¿ , which has been shown that under specific

assumptions t ρi converges to this value over time. We also must calculate the mean and

variance for t ¿. Based on those values the IPS test statistic, t IPS, can be calculated and is given by:

t IPS=√N ¿¿

Where E ( t ¿|ρi=0 ) is the mean and Var ( t ¿|ρi=0) is the variance for t ¿ . Im, Pesaran, and Shin

proved using Monte Carlo simulations that their test has better finite sample properties than the LLC undertaken above.

We can undertake the IPS test in Eviews in the same way as the LLC test except by choosing the option for IPS as the test type. We have kept the lag length selection as Schwartz information criterion and have included Namibia as the presence of structural change in Namibia 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

Null Hypothesis: Unit root (individual unit root process)

26

557699

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_NZLDate: 03/16/12 Time: 12:48Sample: 1960 2000Exogenous variables: Individual effects, individual linear trendsAutomatic selection of maximum lagsAutomatic lag length selection based on SIC: 0 to 2Total number of observations: 789Cross-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

MaxSeries t-Stat Prob. E(t) E(Var) Lag Lag Obs

RGDP_LKA -1.4508  0.8297 -2.173  0.655  0  9  40RGDP_LSO -2.3893  0.3792 -2.173  0.655  0  9  40RGDP_LUX  1.3764  1.0000 -2.173  0.655  0  9  40RGDP_MAR -2.7277  0.2317 -2.177  0.692  1  9  39RGDP_MDG -1.7477  0.7109 -2.173  0.655  0  9  40RGDP_MEX -1.4769  0.8210 -2.173  0.655  0  9  40RGDP_MLI -2.1915  0.4811 -2.173  0.655  0  9  40

RGDP_MOZ -1.6147  0.7693 -2.173  0.655  0  9  40RGDP_MRT -1.9228  0.6241 -2.173  0.655  0  9  40RGDP_MUS  0.3621  0.9983 -2.173  0.655  0  9  40RGDP_MWI -2.4571  0.3463 -2.115  0.713  2  9  38RGDP_MYS -1.3811  0.8510 -2.177  0.692  1  9  39RGDP_NAM -2.2468  0.4520 -2.173  0.655  0  9  40RGDP_NER -2.0706  0.5458 -2.173  0.655  0  9  40RGDP_NGA -3.3215  0.0777 -2.177  0.692  1  9  39RGDP_NIC -2.8785  0.1802 -2.177  0.692  1  9  39RGDP_NLD -1.3965  0.8464 -2.177  0.692  1  9  39RGDP_NOR -3.0583  0.1303 -2.177  0.692  1  9  39RGDP_NPL  0.7339  0.9995 -2.115  0.713  2  9  38RGDP_NZL -3.1177  0.1165 -2.177  0.692  1  9  39

Average -1.7489 -2.168  0.674

As with the LLC test, the IPS test have conclusively identified that there is a unit root in all the cross-sections as it has a probability that there is a unit root of 98.89%, meaning we fail to reject the unit root null hypothesis. This finding could possibly have arisen because other series, as well as Namibia, have structural breaks in them but we have not dealt with the presence of the structural break as unit root tests for panel data with structural breaks are very complex to implement and are beyond the scope of this paper. This result would indicate that real GDP for these 20 countries follows a stochastic trend and shocks will therefore induce persistent changes in the level of the series and not decay over time.

Murthy and Anoruo (2009) found that in a panel of 27 African countries, the real GDP per capita series in the panel are stationary with multiple structural breaks that are taking place in

27

557699

different countries at different times. They therefore concluded that the series are stationary with broken trends. These results are contrary to this results from my paper, however from analysing the graphs in appendix 2, it can be seen that there may be multiple structural breaks occurring in most time series. We could therefore carry out additional analysis in another paper 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 after controlling for two sources of nonlinearity, asymmetric adjustment and nonlinear trends, then real 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 would have enormous implications. For instance, using non-stationary time series in OLS regression analysis would lead to spurious results and the forecasts based on the series would cease to be reliable, in addition to rendering monetary and fiscal policy actions based on these series permanent and not mean-reverting. Real GDP being a non-stationary process means that it is a random walk with only stochastic shocks affecting it. This would mean that government policy instruments would have negligible effect on GDP growth.

Azomahou, Diebolt and Mishra (2009) have shown that in recent years, demographic dynamics have had noticeable effects on both the volatility and nonlinearity of cross-country economic growth. In concluding that a unit root is present, these demographic shocks would persist as the economy has a long memory and therefore increase the volatility of economic growth.

5. Concluding Remarks in Light of the Results from the Unit Root Tests

In section 3 we found that the fixed effects method is the most efficient model to use to estimate 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 would lead to spurious results which would be unreliable; however because we have estimated the fixed effects method using log differenced variables, we do not need to change the specification of the test because these variables would be stationary and therefore OLS would produce unbiased estimates.

Following the work of Prskawetz, Kögel, Sanderson and Scherbov (2007), we could examine the 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, used as uncertainty (h¿¿ in the subsequent analysis of the following model

∆ y¿=α 0+α 1h¿+α 2 Pop 014¿+α 3 Pop 1564¿+α 4 Pop 65 p¿+α5 Cap¿+u¿

We could also use a dynamic model to measure the persistence of GDP growth. If we were to use a basic dynamic model without logarithmic differences, for example

y¿=α i+ βi X¿+γ y i , t−1+u¿

28

557699

The introduction of the lagged dependent variable removes any autocorrelation and it also models a partial adjustment based approach.

However the use of this dynamic model means that traditional OLS estimators are biased and therefore different methods of estimation will need to be used. This arises because of the correlation between the lagged dependent variables with the individual specific random or fixed effects. Since yit is a function of αi, then yi,t-1 is also a function of αi. This means that the explanatory variable yi,t-1 is correlated with the error term which will lead to biased and inconsistent estimates. Similarly; applying the random effects method using GLS means that we would have to quasi- demean the data, however this causes the demeaned dependent variable to be correlated with the demeaned residuals; thus causing the GLS estimator to be biased and inconsistent.

6. Review of Literature on Demographic volatility and Economic Growth

Following on from research by Kelley and Schmidt (1995, 2001); Mishra and Diebolt (2010) have proposed that empirical economic growth models should account for stochastic demographic 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 for which they have relaxed the conventional assumption that population growth is considered stationary; in favour of assuming a long-memory, non-stationary process. They augmented the economic growth model with the evolutionary pattern of the demographic system, allowing them to model economic growth with the conventional assumption of stationarity universally assumed in existing growth models to be a special case of the more general stochastic demographic system. Demographic variables such as birth rates, life expectancy at birth rates, mortality rates, and population density have been found to have statistically significant impacts on economic growth and including these additional demographic can improve the explanatory power; although they found that we cannot understand the relationship between economic growth and demography without considering stochastic shocks.

Mishra and Diebolt use panel estimation techniques to estimate the following model, which is the same specification as Kelley and Schmidt used:

(Y|N gr )i(t ,t+n)=αi+ηt +β ln ¿

They then use 3 empirical specifications with each increasing variables, model 3 is the most general specification. Model 3 was also found to be the best model with the highest R2. The first model regresses output growth on log of per capita income, aggregate population growth, population density and the interaction term. The second model includes the contemporaneous birth and death rates, and the third model includes lagged values of the birth rates.

29

557699

They used the fixed estimation method over the random effects method because even though random is theoretically better than fixed for efficiency, it produces biased estimates if α i∧ηt are correlated with the explanatory variables. The Fixed effects method is also more appropriate as they are not taking their cross-sections as a sample from a random draw of an underlying distribution. Use of the Hausman specification test confirmed that the fixed effects method 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 in recent decades for developed countries but in developing countries it was found to be negative. This was a result of poor resources and higher birth rates which caused depression in developing countries economy. Intuitively, there are large effects from falls in the death rate which positively contribute to economic growth in each decade. However, an important conclusion that emerged from their analysis was that very little gain could be expected from further reductions in mortality in the developing countries.

Future extensions that they are considering to take are to analyse the long-run equilibrium relationship between Yt and Vit given different orders of integration. They want to know the impacts that a linear combination of various orders of integrated process of age-structures will have on the order of the dependent variable.

Words (510)

Appendix 1

30

557699

31

557699

32

557699

33

557699

Appendix 2

34

557699

35

1,00

0

1,50

0

2,00

0

2,50

0

3,00

0

3,50

0

6065

7075

8085

9095

00

RG

DP

_L

KA

600

800

1,00

0

1,20

0

1,40

0

1,60

0

6065

7075

8085

9095

00

RG

DP

_L

SO

10,0

00

20,0

00

30,0

00

40,0

00

50,0

00

6065

7075

8085

9095

00

RG

DP

_L

UX

1,00

0

1,50

0

2,00

0

2,50

0

3,00

0

3,50

0

4,00

0

6065

7075

8085

9095

00

RG

DP

_M

AR

700

800

900

1,00

0

1,10

0

1,20

0

1,30

0

6065

7075

8085

9095

00

RG

DP

_M

DG

3,00

0

4,00

0

5,00

0

6,00

0

7,00

0

8,00

0

9,00

0

6065

7075

8085

9095

00

RG

DP

_M

EX

700

800

900

1,00

0

1,10

0

6065

7075

8085

9095

00

RG

DP

_M

LI

400

800

1,20

0

1,60

0

2,00

0

2,40

0

6065

7075

8085

9095

00

RG

DP

_M

OZ

400

800

1,20

0

1,60

0

2,00

0

2,40

0

6065

7075

8085

9095

00

RG

DP

_M

RT

0

4,00

0

8,00

0

12,0

00

16,0

00

6065

7075

8085

9095

00

RG

DP

_M

US

400

500

600

700

800

900

6065

7075

8085

9095

00

RG

DP

_M

WI

2,00

0

4,00

0

6,00

0

8,00

0

10,0

00

6065

7075

8085

9095

00

RG

DP

_M

YS

3,00

0

4,00

0

5,00

0

6,00

0

7,00

0

6065

7075

8085

9095

00

RG

DP

_N

AM

600

800

1,00

0

1,20

0

1,40

0

1,60

0

1,80

0

6065

7075

8085

9095

00

RG

DP

_N

ER

600

800

1,00

0

1,20

0

1,40

0

6065

7075

8085

9095

00

RG

DP

_N

GA

1,00

0

2,00

0

3,00

0

4,00

0

5,00

0

6065

7075

8085

9095

00

RG

DP

_N

IC

8,00

0

12,0

00

16,0

00

20,0

00

24,0

00

28,0

00

6065

7075

8085

9095

00

RG

DP

_N

LD

8,00

0

12,0

00

16,0

00

20,0

00

24,0

00

28,0

00

6065

7075

8085

9095

00

RG

DP

_N

OR

600

800

1,00

0

1,20

0

1,40

0

1,60

0

6065

7075

8085

9095

00

RG

DP

_N

PL

10,0

00

12,0

00

14,0

00

16,0

00

18,0

00

20,0

00

6065

7075

8085

9095

00

RG

DP

_N

ZL

557699

References

An, C.B., and Jeon, S.H., 2006. Demographic Change and Economic Growth: An Inverted-U Shape Relationship. Economics Letters, 92, pp.447-454.

Banerjee, A., Cockerell, L., and Russell, B., 2001. An I(2) Analysis of Inflation and the Markup, Journal of Applied Econometrics, 16(3), pp. 221-240.

Bloom, D.E., Canning, D., and Fink, G., 2008. Population Aging and Economic Growth, Commission on Growth and Development, Working Paper No.32.

Cuaresma, J.P., Lutz, W., and Sanderson, W., 2009. The Dynamics of Age Structured Human Capital and Economic Growth. New Directions in the Economic Analysis of Education, Milton Friedman Institute, University of Chicago. November 20-21.

Cuestas, J.C., and Garratt, D., 2008. Is Real GDP Per Capita a Stationary Process? Smooth Transitions, Nonlinear Trends and Unit Root Testing. Discussion Papers in Economics, Nottingham Trent University, July 16.

Klasen, S., 1999. Does Gender Inequality Reduce Growth and Development? Evidence from Cross-Country Regressions, The World Bank, Development Research Group/ Poverty Reduction and Economic Management Network, Working Paper no.7, Nov.

Harris, R.D.F., and Tzavalis, E., 1999. Inference for unit roots in dynamic panels where the time dimension is fixed, Journal of Econometrics, 91, pp.201-226.

Hausman, J.A., 1978. Specification Tests in Econometrics, Econometrica, 46(6), pp.1251-1271.

Im, K.S., Pesaran, M.H., and Shin, Y., 2003. Testing for Unit Roots in Heterogenous Panels, Journal of Econometrics, 115, pp.53-74.

Levin, A., Lin, C.F., and Chu, C.S.J., 2002. Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties, Journal of Econometrics, 108(1), pp.1-24.

Mundlak, Y., 1978. On the Pooling of Time Series and Cross Section Data, Econometrica, 46(1), pp.69-85.

Murthy, V.N.R., and Anoruo, E., 2009. Is Real GDP Per Capita Panel Stationary With Structural Breaks in African Countries? Econometric Evidence. Indian Journal of Economics and Business, 8(2), pp.395-412.

Perron, P., 1989. The Great Crash, The Oil Price Shock, and the Unit Root Hypothesis. Econometrica, 57(6), pp.1361-1401.

Solow, R.M., 1952. Technical Change and the Aggregate Production Function. Review of Economics and Statistics, 39, pp.312-320.

36

557699

Zhuang, H., and St. Juliana, R., 2010. Determinants of Economic Growth: Evidence from American Countries. International Business & Economics Research Journal, 9(5), pp.65-69.

37