A Production Function Explanation of Saudi Economic Growth 1984-2011

This paper attempts at an explanation of Saudi economic growth along the lines proposed by the neo-classical growth theory. Production function estimates for gross domestic product is provided using Cobb-Douglas function. A wide range of econometric testing is employed. The functional form is estimated using a constant to express the technical progress. The result shows an elasticity of output with respect to capital and labor of about 0.67 and 0.57 respectively. Technical progress has positive contribution to growth rate of output of 8.67% a year. Therefore, it is a difficult task for the policy makers to determine the best policies for the enhancement of capital and labor on economic growth. The major policy implications and recommendations are that Saudi Arabia needs to improve the rate of return to education in order to raise the productivity of labor. That may be occurred by investing large amount of resources in increasing and improving educational attainment for men and women, and by increasing the training levels in industrial and services sectors.


Introduction
As global economic recovery lifted up oil prices in 2010, the Saudi economy recorded high growth and enlarged fiscal spending by the government boosted domestic demand and accelerated the growth in non-oil GDP.On the same line, the actual budget recorded a surplus of SAR 87.7 billion or 5.4 percent of GDP in 2010 against a deficit of SAR 86.6 billion or 6.2 percent of GDP in the previous year.On the other hand, the ratio of public debt to GDP declined from 16.1 percent in 2009 to 9.9 percent in 2010.The current account of the balance of payments recorded a surplus for the twelfth year consecutively amounting to SAR 250.3 billion or 14.9 percent of GDP in 2010 (Saudi Arabian Monetary Agency (SAMA, 2011).
Figures 1, 2 and 3 illustrate the developments of real GDP, real capital formation and total number of employees in Saudi Arabia during the period 1984-2011.The Figures indicate that there are similar directions among real GDP and Gross capital formation and a less degree of similarity with the number of employees.
This study aims at determining the contribution of capital and labor in Saudi economy by applying Cobb-Douglas Production Function in order to determine how the growth rate can be maximized.
Table 1 and Figure 2 illustrate the structure of gross capital formation, it indicates that non-oil private sector absorb the highest share in Saudi capital formation with a percentage reached 42.8% in 2011.While the oil sector ranked second in terms of relative importance and finally the government sector.
Figure 1.Real GDP, real capital formation and total number of employees in Saudi Arabia  Source:  The Total of Employees in Saudi Arabia 1984-2011 (Million Employee) www.ccsenWe also mention that A, α, β, shows the overall significance related to the function, namely "A" is the size factor reflecting overall productivity of production factors, "α" is the elasticity of output relative to the capital formation, and finally "β" is the elasticity of output in relation to work.The factors that influence the productivity level are different and with different impact on the outcome.
If  +  >1, it would imply that the output increase would be more than proportionate to the increase in inputs, if  +  < 1, it would imply that the output increase would be less than proportionate to the increase in inputs and if  +  = 1 the output would just increase proportionately to the rate of increase of inputs.Therefore there will be economies of scale, constant returns to scale or diseconomies of scale depending upon whether  +  is greater than 1, equal to 1, or less than 1 respectively.

The Model and the Methods
The logarithm of both sides of the above Cobb-Douglass production function was taken to convert the equation into linear form; its log transformation is specified below, which is to be estimated by Fully Modified Ordinary Least Squares (FMOLS) approach.FMOLS was originally designed first time by Philips and Hansen (1990) and Philips and Moon (1999) to provide optimal estimates of Co-integration regressions.This technique employs kernal estimators of the Nuisance parameters that affect the asymptotic distribution of the OLS estimator.In order to achieve asymptotic efficiency, this technique modifies least squares to account for serial correlation effects and test for the endogeneity in the regressors that result from the existence of a Co-integrating Relationships.The model that has been estimated is: The variable of "Y" has been expressed by the real Gross Domestic Product, while "K" has been be proxied by real gross capital formation and finally, labor force "L" has been expressed by the number of employees and "ɛ" is the error term.

Data
This study used the annual data from 1984 to 2008 for Saudi Arabia.All data in this study was obtained from Saudi Arabian Monetary Agency (SAMA) and World Bank Development Indicator, the data has been converted to real values (2005 constant prices) by using consumer price index (2005=100).All these factors are illustrated at Table (A-1) in the appendix.

Unit Root and Cointegration Tests
Augmented Dickey-Fuller unit root test is calculated for individual series to provide evidence as to whether the variables are stationary and integrated of the same order.
The results of Augmented Dickey-Fuller (ADF) test for each variable appear in Table 2.The lag parameter in the ADF test is selected by Akaike information criterion (AIC) to eliminate the serial correlation in residual (Akaike, 1973).As shown in Table 3, the null hypothesis of a unit root can't be rejected for all series.However, the unit root hypothesis is rejected for all variables in the first-differenced data.Therefore, we conclude that the series are integrated of order one.The linear combination of the variables may however be stationary.This claim is being supported by the cointegrating relationships explored using 5% critical value.The Johansen approach in Tables 4 and 5 under the trace and Maximal Eigenvalue statistics indicate only one cointegrating equation testifying to the long run relationship among the variables with Y as the dependent variable.The parameter instability approach in Table 5 further confirms this claim of long run relationship among the variables with probability value greater than 0.2 thereby accepting the null hypothesis of existence of cointegrating relationship.Since the two variables are cointegrated, they can be represented equivalently in terms of a long run FMOLS framework.

Model Results
In Table 7, we see the results of the long run FMOLS estimates for equation 3. The explanatory power is high (R 2 =97.4).All the explanatory variables are significant at 1% level.According to above results, A = 8.67, α = 0.67, β = 0.57, provided that α + β >1 and α, β> 0. We also saw that the influence of the capital on the production of GDP is much higher than in the case of labor.We therefore conclude that the national economy is one more capital-intensive and less based on the use of labor in the production process.The 0.67 estimate for α indicates that a 10 percent increase in the capital leads to a 6.7 percent increase in the output level, which implies there is diminishing returns to capital.Similarly, the 0.57 estimate for β indicates that a 10 percent increase in the labor leads to a 5.7 percent increase in the output level, which implies there is diminishing returns to labor.However, the sum 24 . 1 57 .0 67 .0       is greater than one, which implies production exhibits "increasing returns to scale".Increasing returns to scale means a proportionate increase in all inputs leads to a more than proportional increase in the output.For example, doubling all inputs would lead to more than a doubling of output.In this case, 24 . 1     indicates a one hundred percent increase in (or doubling of) the inputs leads to a 124 percent increase in the output level.

Concluding Remarks and Policy Implications
This paper introduces an explanation of Saudi economic growth along the lines proposed by the neo-classical growth theory.Production function estimates for gross domestic product is provided using Cobb-Douglas function.A wide range of econometric testing is employed.The functional form is estimated using a constant to express the technical progress.The result shows an elasticity of output with respect to capital and labor of about 0.67 and 0.57 respectively.Technical progress has positive contribution to growth rate of output of 8.67% a year.Production in Saudi Arabia exhibits "increasing returns to scale."Increasing returns to scale means a proportionate increase in all inputs leads to a more than proportional increase the output.Therefore, it is a difficult task for the policy makers to determine the best policies for the enhancement of capital and labor on economic growth.The major policy implications and recommendations from our analysis are that Saudi Arabia needs to improve the rate of return to education in order to raise the productivity of labor.That may be occurred by investing large amount of resources in increasing and improving educational attainment for men and women, and by increasing the training levels in industrial and services sectors.
Table (A-1) in the appendix.

Table 3 .
Unit root test Notes: ADF-Dickey DA, Fuller WA., (1979)unit root test with the Ho: Variables are I (1); a, b and c indicate significance at the 1%, 5% and 10% levels, respectively.

Table 4 .
Cointegration test based on trace of the stochastic matrix

Table 5 .
Cointegration test based on maximal eigenvalue of the stochastic matrix

Table 6 .
Cointegration result of Hansen parameter instability approach

Table 7 .
FMOLS estimates in the long run