Pension Assets Total & Total: GDP
5.5 EMPIRICAL METHODOLOGY 1 Model specification
This chapter employs the restricted VAR model. The six-variable VAR model comprises pension fund assets (PFA), stock market capitalisation (STK), pension fund assets interacted with stock market capitalisation (INTPFA), population growth (POP), number of listed companies (LST) and gross domestic product per capita (GDP). The choice of variables enables us to see the specific effects of both the pension fund assets separately and jointly when interacting with capital market development. The variables also show the effect of stock market on the growth of the economy.
The use of the VAR framework allows us to measure the relationship between pension fund assets, capital market development, governance and economic growth. It also allows for the use of multivariate cointegration techniques in unravelling long-run behaviour between our variables of interest. Using variance decomposition and impulse response functions, we are able to estimate the variance of the errors for the variables and examine their sensitivity.
First we examine the stationarity of the variables in our model using the ADF and PP unit root tests. This is to avoid specification errors in the model. Once integrating order of the variables is confirmed, next step is to choose appropriate lag order of the variable to apply the Johansen testing approach to cointegration. It is necessary to find out lag order because F-statistic is very much sensitive with the lag order. We use the sequential modified Likelihood Ratio test statistic (LR); Final Prediction Error (FPE); Akaike Information Criterion (AIC); Schwarz Information Criterion (SIC) and Hannan-Quinn Information criterion (HQ) to choose appropriate lag order but we prefer to take decision about appropriate lag following AIC. The AIC provides reliable and consistent information about lag order as compared to other criterion.
Our unit root test shows our variables are first-difference stationary. We then estimate our long-run model. We determine that our variable are cointegrated and then use the VECM to determine our short and long run relationships and derive variance decomposition and impulse responses accordingly.
The model to be estimated is specified as follows:
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The VAR consists of six variables and the long-run equilibrium is tested between all the variables utilising the Johansen cointegration method. The variables were not all stationary at levels. The multivariate Johansen cointegration technique makes use of the maximum likelihood procedure amongst non-stationary variables. Using either the maximum Eigen value and trace statistics we deduce the rank of the cointegrating matrix. This enables us to determine the existence and number of cointegrating vectors in our model.
The multivariate Granger causality based on VECM allows us to determine whether pension funds and capital markets cause growth. This is measured by Granger causality/Block Exogeneity Wald Test in the VECM estimation, using the error correction terms. The long run causality is found by significance of coefficient of lagged error correction term using t-test statistic. The existence of a significant relationship in first differences of the variables provides evidence on the direction of the short run causality. The joint c squared statistic for the first difference lagged independent variables is used to test the direction of short run causality between the variables. The null hypothesis in this instance is that there is no causality, where this is rejected the model confirms the presence of uni- and bi-directional causality. We seek to explore all the economic variables though; however, our principal interest is on whether the deepening of pension assets has through capital market development been channelled to expand growth.
Standard tests were used to select optimal lag length. This study employed the Toda and Yamamoto (1995) approach in order to ensure the robustness of the model. The procedure is an improvement on the Engle and Granger procedure as standard tests in testing the unit root using PP or ADF tests result in low power in mainly small samples. The variables are stationary at both I(0) and I(1), thus differencing procedures are made use of to ensure stationarity of variables. This may have the effect of losing information about the level of variables (Keho, 2007). This test allows more reliable inferences to be made about the causality of variables by reducing transformation bias. This approach is applicable in a VAR estimation in instances of both I(0) and I(1) order of integration and it disregards the cointegration properties required for both unrestricted and restricted VAR. This means that the methodology puts little emphasis on the order of integration of a series and is applicable with cointegration of an arbitrary order. The lag length selection process employed is determined by the variables collected in the kx1 vector, once the VAR order k is ascertained, the technique employs a maximal order of integration (ABCD+k)th order of VAR. The order k is augmented, with extra lag added in the VAR. If the series are I(1) an extra lag is added, if the series are I(0) no additional lag is added to the VAR11. The authors of this method state that this method can complement conventional hypothesis testing while maintaining the asymptotic Chi squared distribution of the Wald statistic (Yamada & Toda, 1998), so the method enables the testing of the significance of VAR parameters using maximal order of integration. We do this in the study for more robust analysis which is needed to further enrich the study.
The robustness of the causality is tested by employing an innovative accounting approach (IAA). In order to estimate the adjustment process that takes place after a shock we make use of the variance decomposition and impulse response analysis. This allows to measure the level of error in a variable, as explained by other variables in the model. Sims (1980) developed the technique particularly in the context of a shock, using the tool to outline the effect of one variable on another amongst the variables in this VAR system.
5.5.2 Variable definition and data
The data used comprises annual data taken from the WDI for the period 1975-2014, allowing for sufficient time trend to derive robust results from the estimation. Total pension assets data
11 The Toda Yamamoto approach is applicable in a VAR estimation in instances of both I(0) and I(1) order of
integration and it disregards the cointegration properties required for both unrestricted and restricted VAR. The usual lag length selection process is employed, the difference is once that is ascertained a k, the technique employs a maximal order of integration. The calculation is explained above as dmx + k – this method complements conventional hypothesis testing yet maintains the asymptotic Chi squared distribution of the Wald statistics.
is derived from the FSB’s Annual Report. South African Registrar of Pension Fund issues the report annually.
In this study all variables are annual and have been transformed to natural logarithm (LN). GDP per capita (GDP) at constant 2005 prices is used as the proxy for economic growth, it constitutes the gross value added by resident producers in an economy, divided by the total population. This measure is the dependent variable in this model. The natural log of per capita GDP becomes the growth rate.
Total pension assets (PFA) are measured using the FSB annual aggregate assets of retirement funds in South Africa to GDP. This comprises all privately-administered funds, underwritten funds, GEPF, Transnet funds, Telkom Pension fund, Post Office Retirement Fund and foreign funds. We expect an increase in pension assets to move in a positive direction with economic growth as previous studies have shown a relationship between financial development and growth (Davis & Hu, 2008; Hu, 2012).
Total pension asset interaction (INTPFA) is measured using aggregate assets of retirement funds in South Africa to GDP multiplied by market capitalisation to GDP. This is a variable that shows the interaction between pension asset and capital market development. It is expected that pension fund assets channelled into the economy through capital markets are likely to increase economic growth.
Stock Market (STK) is a proxy that measures Market capitalisation (as percentage of GDP) as a ratio to Gross fixed capital formation (GCFC) (as percentage of GDP). Market capitalisation of listed companies is the market value measured by number of shares times the share price. This is a proxy for capital market development and is also referred to as stock market capitalisation. GFCF formerly gross domestic fixed investment is a measure of gross domestic investment our variable for physical capital accumulate. It is measured as the outlays on additions to assets of the economy and changes to the level of inventories. Stock market is expected to have a positive impact on growth.
Population Growth (POP) is a measure of the annual population growth for the year t-1 to year t. It is a proxy for the labour force, we expect population growth to have a negative effect on long-run growth.
Number of listed companies (LST) is a measure using the number of listed companies in the stock exchange. It is expected that improved corporate governance will encourage listings and thus have a positive impact on growth.
5.6 MODEL ESTIMATION