Provincial Public Expenditure and Provincial GDP - A Causal Relationship Analysis 1

Transcription

1 Provincial Public Expenditure and Provincial GDP - A Causal Relationship Analysis 1 Coetzee, Clive KwaZulu-Natal Provincial Government Treasury Department Treasury House 9th Floor 145 Commercial Street Pietermaritzburg 32 South Africa Telephone (33) Fax (33) clive.coetzee@kzntreasury.gov.za 1 The views expressed in this working paper are the views of the author and might not necessarily reflect the views of the Provincial Treasury. All rights reserved - 212

2 1. Introduction and Purpose The question whether or not government expansion causes economic growth has divided policy makers into two distinctive theoretical camps, as proponents of either big government or small government. Economic theory would suggest that on some occasions lower levels of government spending would enhance economic growth while on other occasions higher levels of government spending would be more desirable. From an empirical perspective the evidence generated becomes more confusing as a number of studies favour one or the other approach. A recent study by Bose, Haque and Osborn (23) for example found the following: Firstly, the share of government capital expenditure in GDP is positively and significantly correlated with economic growth, but current expenditure is insignificant. Secondly, at the sectoral level, government investment and total expenditures in education are the only outlays that are significantly associated with growth once the budget constraint and omitted variables are taken into consideration. A study by Loizides and Vamvoukas (24) found, amongst others, that in their sample of countries public expenditure Granger causes growth in national income either in the short or the long run. This was born out by the bivariate as well as the trivariate analysis. Their analysis generally rejects the hypothesis that public expansion has hampered economic growth in sample of countries. Their argument is that the underlying growth rates impact of the public sector has been positive, which means that public spending fosters overall economic development. The recent revival of interest in growth theory has also revived interest among researchers in verifying and understanding the linkages between fiscal policies and economic growth. The primary objective of this study is to examine the growth effects of provincial public expenditure on the provincial economy.

3 2. The Variables, Data and Basic Transformation The audited outcome of the provincial government budget for 26/7, 27/8 and 28/9 financial years were R36,881,397,, R44,482,953, and R55,533,549, representing a 13.5 percent and 14.3 percent increase in real terms, respectively. The audited actual for the 29/1 financial year was R63,89,285, bringing the total increase in the budget to R8,275,736,, representing an increase of 7.8 percent in real terms. The revised estimated budget for the 21/11 financial years was R7,53,213, representing an increase of 6 percent in real terms. Provincial public expenditure as a percentage of the provincial GDP increased from about 1 percent in 2 to 23 percent in 21. This represents a significant increase of about 12 percent per annum over the period. Provincial public expenditure can be classified or occurs per department or per economic classification, i.e., the provincial government consists of a number of departments or more correctly votes and each department or vote account or records their expenditure per economic classification. The various provincial government departments and the various economic classifications of provincial government expenditure are displayed in the table below. It must be noted that a small number of provincial government departments have not been included for example the Provincial Treasury and the Provincial Legislator simply because these departments very seldom incur capital expenditure. The table also shows the abbreviations that will be used through-out the analysis and report. Table 1: Data Legend GDP-R Gross Domestic Product adjusted, quarterly Provincial Government Expenditure per Department Edu Department of Education Health Department of Health Social Department of Social Development Housing Department of Human Settlements Cogta Department of Cooperative Governance and Traditional Affairs

4 Agric Department of Agriculture and Environmental Affairs and Rural Development Works Department of Public Works Roads Department of Transport Arts Department of Arts and Culture Sport Department of Sport and Recreation Dedt Department of Economic Development and Tourism Police Department of Community, Safety and Liaison Provincial Government Expenditure per Economic Classification Sw Compensation of Employees Gs Goods and Services Expenditure Trans Current Transfers and Subsidies Capital Payment of Capital Assets Infr Infrastructure Expenditure Table 2 and 3 displays the actual values for the provincial GDP in constant 25 terms and the audited actual expenditure per department and per economic classification. The values are in R. It is evident that the provincial education and health departments have the largest expenditure and that the departments of community safety and sport and recreation have the least expenditure. It is also evident that expenditure on salaries and wages are the largest and that transfers are the least. It is also fairly obvious that individually each expenditure seems minuscule in comparison with the provincial GDP, but as a collective it s another story. Even at 2 percent of the provincial GDP total provincial public expenditure seems significant. Total provincial public expenditure therefore cannot be ignored in terms of its actual or potential impact on the provincial GDP.

5 Table 2: Provincial GDP and Government Expenditure per Department R GDP-R EDU HEALTH SOCIAL HOUSING COGTA AGRIC WORKS ROADS ARTS SPORT DEDT POLICE 26: : : : : : : : : : : : : : : : : : : :

6 Table 3: Provincial GDP and Government Expenditure per Economic Classification R GDP-R SW GS TRANS CAPITAL INFR 26: : : : : : : : : : : : : : : : : : : :

7 Exhibit 1 displays the variables in log format (natural logarithm). The logarithmic transformation is often useful for series that are greater than zero as well for series that grow exponentially. It also adequately converts non constant variation into constant variation; hence, it stabilizes the variance and thereby increases the effectiveness of the various statistical and econometric applications. The exhibit shows the behavior of the provincial GDP, the departmental expenditures and the expenditure per economic classification from the 2 nd quarter of 26 up to the 1 st quarter of 211 in log format. It seems obvious that all of the variables experienced increasing trends or growth patterns over the period. It also seems evident that the overwhelming number of variables displayed quarterly seasonality, especially the provincial GDP. Expenditure by education and health seems the most stable or varies the least from a departmental expenditure view whilst expenditure on salaries and wages and infrastructure expenditure seems to be the most stable or varies the least from an expenditure per economic classification view. Expenditure by Cogta and transfers seems to be the most unstable or varies the most. What seems intuitively arguable is that the behaviors of the various expenditures by department are very similar. This suggests the exogeneity of the variables which seem plausible given that the expenditures are determined through a political and budget process. The behavior of the various expenditures per economic classification, except for transfers, also seems intuitively very similar. It is also important to point out that a number of expenditures (both per department and per economic classification) contain structural breaks. For example the massive decrease in expenditure by the department of arts in 29 was because of the tourism function that was transferred to the department of economic development. Exhibit 2 displays the Kernel density function of each of the variables (still in log format). It shows the average expenditure value and its distribution, for example provincial GDP is the largest and has one of the smallest distributions whilst economic development and tourism has the largest distributions. Expenditure by the department of Community, Safety and Liaison has been the least of any of the expenditures

8 Exhibit 1: Behaviour of the Variables - Q2 26 to Q1 211 in Log Format LGDPR LEDU LHEALTH LSOCIAL LHOUSING LCOGTA LAGRIC LWORKS LROADS LARTS LSPORT LDEDT LPOLICE LSW LGS LTRANS LCAPITAL LINFR

9 Exhibit 2: Kernel Density of the Variables - Q2 26 to Q1 211 in Log Format Q 3 27Q 1 27Q3 28Q 1 28Q 3 29Q1 29Q 3 21Q 1 21Q 3 211Q 1 LGDPR LEDU LHEALTH LSOCIAL LHOUSING LCOGTA LAGRIC LWORKS LROADS LARTS LSPORT LDEDT LPOLICE LSW LGS LTRANS LCAPITAL LINFR

10 Table 4 displays various descriptive statistics (in log format), but in order to understand and make sense of the statistics it is important to understand the various statistical concepts and calculations displayed in the table, i.e. The mean is the mathematical average of a range of values, calculated by dividing the total of all values by the number of observations. If the total number of values in the sample is even, then the median is the mean of the two middle numbers. The median is a useful number in cases where the distribution has very large extreme values which would otherwise skew the data. The maximum and the minimum is what it says, i.e., the maximum and minimum value for each particular variable and are used to calculate the range (max-min) The standard deviation is a measure of the variability of the distribution of a random variable whereas the skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable. A negative skew indicates that the tail on the left side of the probability density function is longer than the right side and the bulk of the values possibly including the median lie to the right of the mean. A positive skew indicates that the tail on the right side is longer than the left side and the bulk of the values lie to the left of the mean. A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically but not necessarily implying a symmetric distribution. Kurtosis is any measure of the "peakedness" of the probability distribution of a real-valued random variable. A high kurtosis distribution has a sharper peak and longer, fatter tails, while a low kurtosis distribution has a more rounded peak and shorter, thinner tails. Distributions with zero excess kurtosis are called mesokurtic, or mesokurtotic The Jarque Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. A normal distribution is a probability distribution that plots all its values in a symmetrical manner and most of the results are situated around the probability s mean. The bell-shaped curve is described in terms at which its height is a maximum (its mean) and how wide it is (its standard deviation). The normality tests all report a p-value (probability of accepting the null hypothesis).

11 Table 4: Descriptive Statistics of the Variables - Q2 26 to Q1 211 in Log Format Variable Mean Median Max Min Standard Deviation Skewness Kurtosis Jarque Bera Probability LGDPQR LEDU LHEALTH LSOCIAL LHOUSING LCOGTA LAGRIC LWORKS LROADS LARTS LSPORT LDEDT LPOLICE LSW LGS LTRANS LCAPITAL LINFRA

12 The descriptive statistics as displayed in the above table suggesting that all the variables are normally distributed, i.e., all the p-values are bigger than Correlation between Provincial GDP and Expenditure by Department, and Expenditure by Economic Classification Correlation is a statistical measurement of the relationship between two variables and the correlation coefficients (r) range from +1 to 1. A zero correlation coefficient indicates that there is no or very little statistical significant relationship between the variables. A correlation coefficient of 1 indicates a perfect negative correlation, meaning that as one variable increase, the other decrease. A correlation coefficient of +1 indicates a perfect positive correlation, meaning that both variables move in the same direction together. The formula to calculate the correlation coefficient can be expressed as follows: where: x i = the variable x (expenditure per department or per economic classification) y = Provincial GDP Σ = sigma, the symbol for "sum up" (x i - x ) each x-value minus the mean of x (y - y ) each y-value minus the mean of y The hypothesis that will be tested is as follows: H : there is no or very little correlation between provincial GDP and expenditure per Department or per economic classification

13 H 1 : there is some to strong correlation between provincial GDP and expenditure per Department or per economic classification The critical values for the hypothesis are as follows: Accept H when -.65<r<.65 Accept H 1 when -.65>r>.65 Table 5 and 6 displays the correlation coefficients. The results suggest that the expenditures by the Education, Health, Roads, Housing and Police departments (in order from highest to lowest) are significantly correlated with the provincial GDP, suggesting some sort of relationship exists between the mentioned departmental expenditures and the provincial GDP. Capital expenditure is the only expenditure per economic classification that seems not to have a significant correlation or have the weakest relationship with the provincial GDP. Table 5: Correlation between Provincial GDP and Expenditure per Department Department Correlation Coefficient.65<r>-.65 EDU.82 Significant HEALTH.79 Significant ROADS.77 Significant HOUSING.73 Significant POLICE.66 Significant SOCIAL.62 Not significant DEDT.56 Not significant WORKS.53 Not significant SPORT.49 Not significant COGTA.43 Not significant AGRIC.37 Not significant ARTS.25 Not significant

14 Table 6: Correlation between Provincial GDP and Expenditure by Economic Classification Economic Classification Correlation Coefficient.65<r>-.65 SW.82 Significant INFR.77 Significant TRANS.76 Significant GS.74 Significant CAPITAL.57 Not significant 4. Covariance between Provincial GDP and Expenditure by Department, and Expenditure by Economic Classification Covariance is a measure of the relationship between two random variables, designed to show the degree of co-movement between them. Covariance is calculated based on the probability-weighted average of the cross-products of each random variable's deviation from its own expected value. A positive number indicates co-movement (i.e. the variables tend to move in the same direction); a value of indicates no relationship, and a negative covariance shows that the variables move in opposite directions. The formula to calculate the covariance can be expressed as follows: where: x = the x variable y = the y variable x = the mean of the x variable x y = the mean of the y variable y n = umber of data points in the sample Cov(x, y) = the covariance of x and y The hypothesis that will be tested is as follows:

15 H : there is no or very little co-movement between provincial GDP and expenditure per Department or per economic classification H 1 : there is some to strong co-movement between provincial GDP and expenditure per Department or per economic classification The critical values for the hypothesis are as follows: Accept H when p>.5 Accept H 1 when p<.5 The covariance picture (tables 7 and 8) seems very similar to the correlation picture except that expenditure by the departments of human settlements and sport and recreation seems not to have a statistical significant covariance with provincial GDP. Table 7: Covariance between Provincial GDP and Expenditure by Department Department Covariance p - value p - value <.5 ROADS.17.1 Significant HEALTH.7.1 Significant EDU.8. Significant COGTA.8 1. Not significant AGRIC.5 1. Not significant ARTS. 1. Not significant SPORT.9.99 Not significant WORKS.1.94 Not significant DEDT Not significant SOCIAL.7.48 Not significant POLICE.1.22 Not significant HOUSING.18.5 Not significant Table 8: Covariance between Provincial GDP and Expenditure by Economic Classification Economic Classification Covariance p - value p - value <.5

16 GS.7.3 Significant TRANS.11.2 Significant SW.7. Significant INFR.26.1 Significant CAPITAL.7.78 Not significant 5. Cross Correlation between Provincial GDP and Expenditure by Department, and Expenditure by Economic Classification Cross Correlation is a statistical measure timing the movements and proximity of alignment between two different information sets of a series of information. Cross correlation is generally used when measuring information between two different time series. The cross-correlation function gives a measure of the extent to which two signals correlate with each other as a function of the time displacement between them. It is also used to determine to what extent a signal measured at one point originates from a particular source, and with what time delay. We are thus testing whether the various expenditures leads or lags provincial GDP over a specific period. The formula to calculate the cross correlation can be expressed as follows: where: x (i) = variable x y (i) = variable y i =, 1, 2 N-1 mx = mean of variable x my = mean of variable y d (delay) =, 1, 2 N-1 The hypothesis that will be tested is as follows:

17 H : there is no or very little cross correlation between provincial GDP and expenditure per Department or per economic classification (two periods) H 1 : there is some to strong cross correlation between provincial GDP and expenditure per Department or per economic classification (two periods) The critical values for the hypothesis are as follows: Accept H when -.45<r<.45, i = 2 Accept H 1 when -.45>r>.45, i = 2 The departments of agriculture, transport, community safety, health, sport and public works seems all to have a correlation or relationship with the provincial GDP over a specific period of time and in this case over two quarters or six months. The department of economic development has to smallest cross correlation coefficient over two quarters. Salaries and wages and infrastructure expenditure also seems to have a correlation or relationship with the provincial GDP over two quarters or six months where as transfers has the smallest cross correlation coefficient at two quarters. It is interesting that none of the departments or economic classification of provincial public expenditure have significant correlation or relationship with the provincial GDP over four period, i.e., a year. Table 9: Cross correlation between Provincial GDP and Expenditure by Department Department Correlation Coefficient lead *(i=2) AGRIC.62 significant ROADS.58 significant POLICE.53 significant HEALTH.5 significant SPORT.5 significant

18 WORKS SOCIAL ARTS HOUSING COGTA EDU DEDT significant not significant not significant not significant not significant not significant not significant Table 1: Cross correlation between Provincial GDP and Expenditure by Economic Classification Economic Classification SW INFR GS CAPITAL TRANS Correlation Coefficient lead *(i=2) significant significant not significant not significant not significant 6. Granger Causality between Provincial GDP and Department, and Expenditure by Economic Classification Expenditure by The Granger causality testt is a statistical hypothesis test for determining whether one time series is useful in forecasting another. A time series X is said to Granger-cause Y if it can be shown, usually through a series of t-tests and F-tests on lagged values of X (and with lagged values of Y also included), that those X values provide statistically significant information about future values of Y. The formula to calculate the Granger causality can be expressed as follows:

19 where: X 1 (t) and of X 2 (t)= two time series of length t p = the maximum number of lagged observations included in the model (the model order) A = contains the coefficients of the model (i.e., the contributions of each lagged observation to the predicted values of X 1 (t) and of X 2 (t). t and j =lags E 1 and E 2 =residuals (prediction errors) for each time series The hypothesis that will be tested is as follows: H : Expenditure per department or economic classification does not granger cause provincial GDP expenditure per Department or per Department H 1 : Expenditure per department or economic classification does granger cause provincial GDP expenditure per Department or per Department The critical values for the hypothesis are as follows: Accept H when p>.5, p = 4 Accept H 1 when p<.5, p = 4 All the variables (expenditure by department and by economic classification) have p- values greater than.5 using four lags, (except transfers) and we thus cannot reject the null hypothesis. This suggests no or very little granger causality between the provincial GDP and provincial public expenditure. It is also interesting to note that the results remain the same when using 1, 2 or 3 lags. Table 11: Granger Causality between Provincial GDP and Expenditure by Department Null Hypothesis (4 lags): F-Statistic Prob. EDU does not Granger Cause GDPQ

20 HEALTH does not Granger Cause GDPQ SOCIAL does not Granger Cause GDPQ HOUSING does not Granger Cause GDPQ COGTA does not Granger Cause GDPQ AGRIC does not Granger Cause GDPQ WORKS does not Granger Cause GDPQ ROADS does not Granger Cause GDPQ ARTS does not Granger Cause GDPQ SPORT does not Granger Cause GDPQ DEDT does not Granger Cause GDPQ POLICE does not Granger Cause GDPQ Table 12: Granger Causality between Provincial GDP and Expenditure by Economic Classification Null Hypothesis (4 lags): F-Statistic Prob. SW does not Granger Cause GDPQ GS does not Granger Cause GDPQ TRANS does not Granger Cause GDPQ CAPITAL does not Granger Cause GDPQ INFR does not Granger Cause GDPQ Testing for Stationarity of the Variables A concrete set of data (data file or data series) can be regarded as a realization of the underlying stochastic process. A stochastic process is said to be stationary if its mean and variance are constant over time and the value of covariance between two time periods depends only on the distance or lag between the two time periods and not on the actual time at which the covariance is computed. Thus a series is said to be stationary if the mean and autocovariances of the series do not depend on time. Any series that is not stationary is said to be non-stationary. Non-stationarity could be due to a shift in the mean.

21 If a non-stationary time series is being used in a regression analysis the results tend to be unreliable, that is a high R² and t-statistics that appear to be significant, but results that are without any economic meaning. The regression output looks good because the least squares estimates are not consistent and the customary tests of statistical inference do not hold. Because, as pointed out, standard inference procedures do not apply to regressions, which contain an integrated dependant variable, i.e. non-stationary time series, it is important to determine whether a series is stationary or not before using it in regression. The two variables or time series therefore need to be tested for stationarity to determine their order of integration. To perform the Unit Root test on a AR(p) model the following regression will be estimated: where: y t = variable to be tested (national GDP and national fuel consumption) α = constant t = trend = lag operated of the dependent variable u t = white noise innovation The Augmented Dickey-Fuller (ADF) Unit Root Tests is based on the following three regression forms: with constant and trend (τ τ ) with constant (τ µ ) without constant and trend (τ)

22 and the testable hypothesis is β = (i.e., p = 1, y t has a unit root). The hypothesis that will therefore be tested is as follows: H : Expenditure per department or economic classification has a unit root (level format) H 1 : Expenditure per department or economic classification does not have a unit root (level format) The critical values for the hypothesis are as follows: Accept H when t* > ADF crtitical value, i.e., unit root exists. Accept H 1 when If t* < ADF critical value, i.e., unit root does not exist It is evident from table 13 and 14 that all the variables are non-stationary in level format, i.e., they are not I() variables. Table 13: Unit Root Test in Level Format for Provincial GDP and Expenditure by Department Department Format Equation ADF- Statistics F- statistics Results LEDU Level Intercept Non-Stationary Trend & Intercept Stationary None n/a Non-Stationary LHEALTH Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary LSOCIAL Level Intercept Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary LHOUSING Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary LCOGTA Level Intercept Stationary Trend & Intercept Stationary

23 LAGRIC None n/a Non-Stationary Level Intercept Non-Stationary Trend & Intercept Stationary None n/a Non-Stationary LWORKS Level Intercept Non-Stationary Trend & Intercept Stationary None n/a Non-Stationary LARTS Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary LSPORT Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary LDEDT Level Intercept Non-Stationary Trend & Intercept Stationary None.569 n/a Non-Stationary LPOLICE Level Intercept Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary LROADS Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary Table 14: Unit Root Test in Level Format for Expenditure by Economic Classification Economic Classification Format Equation ADF- Statistics F- statistics Results LSW Level Intercept Non-Stationary Trend & Intercept Stationary None n/a Non-Stationary LGS Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary LTRANS Level Intercept Non-Stationary Trend & Intercept Stationary None.5689 n/a Non-Stationary LCAPITAL Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary

24 LINFR Level Intercept Non-Stationary Trend & Intercept Non-Stationary None n/a Non-Stationary Given that the results clearly show that none of the variables are stationary in level format, the variables need to be transformed in order to determine their level of integration. The non-stationary data therefore needs to be differenced. Now if a time series is differenced once and the differenced series is stationary we say that the original series is integrated of the order 1, denoted by I(1). In general, if a time series has to be integrated to be differenced d times, it is integrated of the order d or I(d). Thus any time we have an integrated time series of order I or greater we have a nonstationary time series. If d = the resulting I() process represents a stationary time series. The first difference of a time series is the series of changes from one period to the next. If Y(t) denotes the value of the time series Y at period t, then the first difference of Y at period t is equal to Y(t)-Y(t-1). In Stat graphics, the first difference of Y is expressed as DIFF(Y). If the first difference of Y is stationary and also completely random (not auto correlated), then Y is described by a random walk model: each value is a random step away from the previous value. If the first difference of Y is stationary but not completely random--i.e., if its value at period t is auto correlated with its value at earlier periods-- then a more sophisticated forecasting model such as exponential smoothing or ARIMA may be appropriate. (Note: if DIFF(Y) is stationary and random, this indicates that a random walk model is appropriate for the original series Y, not that a random walk model should be fitted to DIFF(Y). Fitting a random walk model to Y is logically equivalent to fitting a mean. The hypothesis that will therefore be tested is as follows: H : Expenditure per department or economic classification has a unit root (differenced format)

25 H 1 : Expenditure per department or economic classification does not have a unit root (differenced format) The critical values for the hypothesis are as follows: Accept H when t* > ADF critical value, i.e., unit root exists. Accept H 1 when t* < ADF critical value, i.e., unit root does not exist It is evident from table 15 and 16 that all the variables are stationary when differenced once, i.e., they are I(1) variables. Table 15: Unit Root Test in Differenced Format for Provincial GDP and Expenditure by Department Department Format Equation ADF- Statistics F- statistics Results LEDU 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LHEALTH 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LSOCIAL 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LHOUSING 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LCOGTA 1st Difference Intercept Stationery LAGRIC 1st Difference Trend & Intercept Stationery None n/a Stationery Intercept Stationery Trend & Intercept Stationery None n/a Stationery LWORKS 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery

26 LROADS 1st Difference Intercept Non-Stationery Trend & Intercept Non-Stationery None n/a Stationery LARTS 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LSPORT 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LDEDT 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LPOLICE 1st Difference Intercept Stationery Trend & Intercept Non-Stationery None n/a Stationery Table 16: Unit Root Test in Differenced Format for Expenditure by Economic Classification Departments Format Equation ADF- Statistics F- statistics Results LSW 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LGS 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LTRANS 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LCAPITAL 1st Difference Intercept Stationery Trend & Intercept Stationery None n/a Stationery LINFR 1st Difference Intercept Stationery Trend & Intercept Non Stationery None n/a Stationery

27 8. Regression between Provincial GDP and Expenditure by Department, and Expenditure by Economic Classification Regression analysis, in a general sense, means the estimation or prediction of the unknown value of one variable from the known value of the other variable. It is possible to predict the values of y given the values of x by using the equation called the regression equation. I = α + βe + ε where: α = a constant amount; β = the effect that E (independent variable) has on I (dependent variable); ε = the noise term reflecting other factors of influence. The variable I is termed the dependent or endogenous variable; E is termed the independent, explanatory, or exogenous variable. However it is very important to note that regression analysis is based on some fundamental assumptions which if violated will lead to spurious results. The time series needs to be stationary for example. Once a regression model has been constructed, it may be important to confirm the goodness of fit of the model and the statistical significance of the estimated parameters. Commonly used checks of goodness of fit include the R-squared, analyses of the pattern of residuals, and hypothesis testing. Statistical significance can be checked by an F-test of the overall fit, followed by t-tests of individual parameters. The various test statistics that will be reported are discussed as follows: A negative β coefficient implies that the mean of the two variables involved move in opposite directions or independently of each other. A positive β coefficient implies that the mean of the two variables involved move together or in the same direction. In this study, we want to accept only the positive β coefficient. A β coefficient represents the independent contributions of each independent variable to the prediction of the dependent variable. The bigger the coefficient the greater the impact on the provincial GDP.

28 The Adjusted R squared provides a measure of how well future outcomes are likely to be predicted by the model. The R 2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R 2 of 1. indicates that the regression line perfectly fits the data. The t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error and that can be tested against a t distribution to determine how probable it is that the true value of the coefficient is really zero. A rule of thumb is a t-statistics larger than two (2). Durbin Watson statistic is a part of the standard regression output. The Durbin- Watson statistic is a test for first-order serial correlation. The value of d always lies between and 4. If the Durbin Watson statistic is substantially less than 2, there is evidence of positive serial correlation. As a rough rule of thumb, if Durbin Watson is less than 1., there may be cause for alarm. Small values of d indicate successive error terms are, on average, close in value to one another, or positively correlated. If d > 2 successive error terms are, on average, much different in value to one another, i.e., negatively correlated. In regressions, this can imply an underestimation of the level of statistical significance. Table 17 and 18 displays the result for the regression analysis between the provincial GDP and expenditure by department and economic classification in I( 1 ) format. The results show that the departments recorded fairly insignificant β coefficients except the departments of education and transport. A large number of departments also have negative β coefficients which are both surprising and unexpected. The various classifications of expenditure recorded β coefficients less than 1, thus indicating a lower degree of volatility of GDP. Salaries and Wages recorded a t-value greater than 2, thus indicating a greater confidence on the coefficient as a predictor. All the expenditure categories recorded Durbin Watson-values between 2 and 3 suggesting very little or no autocorrelation of the residuals.

29 Table 17: Regression between Provincial GDP and Expenditure by Department in I( 1 ) format Regression Equation β Coefficient T-stat Adjusted R squared DW-stat LGDP= α + β LEDU + Ɛ *** LGDP= α + β LAGRIC+ Ɛ GDP= α + β LHEALTH+ Ɛ GDP= α + β LHOUSING+ Ɛ GDP= α + β LART+ Ɛ GDP= α + β LROADS+ Ɛ GDP= α + β LWORKS+ Ɛ GDP= α + β LSOCIAL+ Ɛ GDP= α + β LSPORT+ Ɛ GDP= α + β LDEDT+ Ɛ GDP= α + β LCOGTA+ Ɛ GDP= α + β LPOLICE+ Ɛ *** Statistically significant at 1% level Table 18: Regression between Provincial GDP and Expenditure by Economic Classification in I( 1 ) format Regression Equation β Coefficient T-stat Adjusted R squared DW-stat GDP= α + β LSW+ Ɛ *** GDP= α + β LSG+ Ɛ GDP= α + β LTRANS+ Ɛ *** GDP= α + β LCAPITAL+ Ɛ GDP= α + β LINFR+ Ɛ *** Statistically significant at 1% level Table 19 and 2 displays the result for the regression analysis between the provincial GDP and expenditure by department and economic classification in I( ) format. All the departments recorded β coefficients less than 1 suggesting insignificant relationship between the various departments of provincial public expenditure and the provincial GDP. All the departments recorded positive β coefficients as expected. All of the t- statistics are greater than 2 suggestion that the β coefficients are indeed statistical significant. However the Durban-Watson test statistics indicate that all of the regression

30 equations suffer from serious autocorrelation of the residuals. This reflects the fact that the regression equation uses non-stationary data and therefore the t-statistics are invalid. Table 19: Regression between Provincial GDP and Expenditure by Department in I( ) format Regression Equation β Coefficient T-stat Adjusted R squared DW-stat LGDP= α + βledu+ Ɛ *** LGDP= α + βlhealth+ Ɛ *** LGDP= α + βlhousing+ Ɛ *** LGDP= α + βlart+ Ɛ LGDP= α + βlroads+ Ɛ *** LGDP= α + βltrans+ Ɛ *** LGDP= α + βlworks+ Ɛ *** LGDP= α + βlsocial+ Ɛ *** LGDP= α + βlsport+ Ɛ *** LGDP= α + βldedt+ Ɛ *** LGDP= α + βlcogta+ Ɛ *** LGDP= α + βlpolice+ Ɛ *** *** Statistically significant at 1% level ** Statistically significant at 5 level * Statistically significant at 1% level The various classifications of expenditure recorded β coefficients less than 1 suggesting insignificant relationship between the various economic classifications of provincial public expenditure and the provincial GDP. All the classifications of expenditure recorded positive β coefficients as expected. All of the t-statistics are greater than 2 suggestion that the β coefficients are indeed statistical significant. However the Durban-Watson test statistics indicate that all of the regression equations suffer from serious autocorrelation of the residuals. This reflects the fact that the regression equation uses non-stationary data and therefore the t-statistics are invalid.

31 Table 2: Regression between Provincial GDP and Expenditure by Economic Classification in I( ) format Regression Equation β Coefficient T-stat Adjusted R squared DW-stat LGDP= α + βlsw+ Ɛ *** LGDP= α + βlgs+ Ɛ *** LGDP= α + βlcapital+ Ɛ *** LGDP= α + βlinfr+ Ɛ *** *** Statistically significant at 1% level ** Statistically significant at 5 level * Statistically significant at 1% level The relevance of the regression analysis at both the stationary and non-stationary level was predominantly to intuitively determine if co-integration analysis could be considered. Intuitively the results of the regression analysis have very little relevance per se, but as an indicator for further analysis are significant. 9. Co-integration between Provincial GDP and Expenditure by Department, and Expenditure by Economic Classification If two or more series are individually integrated (in the time series sense) but some linear combination of them has a lower order of integration, then the series are said to be cointegrated, i.e., x t and y t are said to be cointegrated if there exists a parameter such that u t = y t - αx t is a stationary process. The most well known test, suggested by Engle and Granger (1987) (sometimes known as the EG test) is to run a static regression (after first having verified that y t and x t both are I( )) y t = θ x t + e t

32 where x t is one- or higher-dimensional. The asymptotic distribution of θ is not standard, but the test suggested by Engle and Granger is to estimate θ by OLS and to the test for unit roots in ê t = y t - θ x t Since the unit root tests test the null-hypothesis of a unit root, most co-integration tests test the Null of no co-integration. Enders (24) states that a principle feature of cointegrated variables is that their time paths are influenced by the extent of any deviation from long-run equilibrium. Enders further states that after all, if the system is to return to long run equilibrium, the movements of at least some of the variables must respond to the magnitude of the disequilibrium. The point is that the short-run dynamics must be influenced by the deviation from the long-run relationship. Table 21 and 22 display the results of the co-integration analysis between the Provincial GDP and the expenditure by departments and the expenditure by economic classifications. The tests are performed in I() format similar to the tests displayed in table 19 and 2. However the regression equations have been re-written so that the error terms are the dependent variables. The error terms are then tested for stationarity using the Augmented Dickey-Fuller Unit Root Tests and the testable hypothesis is Ɛ = (i.e., p = 1, Ɛ t has a unit root and therefore no co-integration relationship between the variables). The hypothesis that will therefore be tested is as follows: H : error term contains a unit root and therefore no co-integration relationship H 1 : error term does not contain a unit root and therefore there is a co-integration relationship The critical values for the hypothesis are as follows: Accept H when t* > ADF critical value, i.e., unit root exists.

33 Accept H 1 when If t* < ADF critical value, i.e., unit root does not exist The ADF test statistic are also displayed in table 21 and 22 and must be compared to the critical values (MacKinnon, 2991) at the 99% confidence level, which in this case is It is clear that the test statistic (ADF statistics) in all cases (expenditure by department and expenditure by economic classifications) is greater than the critical value suggesting there are no co-integration relationship between provincial government expenditure and the provincial GDP. Table 21: Tests for Co-integration between Provincial GDP and Expenditure by Department Regression Equation Format Equation Model ADF-Statistics Ɛ= α + βledu - LGDP level Intercept Constant, no trend Ɛ= α + βlhealth - LGDP level Intercept Constant, no trend Ɛ= α + βlhousing - LGDP level Intercept Constant, no trend Ɛ= α + βlarts - LGDP level Intercept Constant, no trend Ɛ= α + βlroads - LGDP level Intercept Constant, no trend Ɛ= α + βltrans - LGDP level Intercept Constant, no trend Ɛ= α + βlworks - LGDP level Intercept Constant, no trend Ɛ= α + βlsocial - LGDP level Intercept Constant, no trend Ɛ= α + βlsports - LGDP level Intercept Constant, no trend Ɛ= α + βldedt - LGDP level Intercept Constant, no trend Ɛ= α + βlcogta - LGDP level Intercept Constant, no trend Ɛ= α + βlpolice - LGDP level Intercept Constant, no trend Table 22: Tests for co integration between GDP and Expenditure by Economic Classification Regression Equation Format Equation Model ADF-Statistics Ű= α + βlsw - LGDP level Intercept Constant, no trend Ű= α + βlgs - LGDP level Intercept Constant, no trend Ű= α + βlcapital - LGDP level Intercept Constant, no trend Ű= α + βlinfr - LGDP level Intercept Constant, no trend