Granger Causality Test to Study Causal Relationships Finance Essay

SME, self-employed and business ownership are used interchangeably in our context. There are many definitions for SME and according to SPRING Singapore; an SME refers to enterprises with fixed asset investment of lesser than S$15 million for manufacturing sector and less than 200 employees for non-manufacturing sectors.

There is little published information on business ownership and SMEs in Singapore. The only statistics on the rate of start-ups of business and companies are available in the Yearbook of Statistics (Tan, 2002). As such, we use the number of business formed and the number of companies formed to proxy business ownership and self employment. We also generate a series, named 'STARTUPS' using the sum of companies and businesses.

STARTUPS = FORM_BUS + FORM_COMP

Annual time series of formation of businesses and formation of companies from 1990 to 2009 are obtained from the Singapore Yearbook of Statistics. Business refers to a business firm, operating either as a sole-proprietorship or a partnership. It may be set up by individuals or companies. A company refers to a business entity registered under the Companies Act, Chapter 50. It has a legal personality (i.e. it has the right to own properties, it has perpetual succession and it can sue or be sued in its own name). It usually has the words 'Pte Ltd' or 'Ltd' as part of its name.

Annual average unemployment rates, annual GDP and per capita GDP of these 20 years are also obtained from Department of Statistics, Singapore.

4.2 Methodology

In regression model, existence of relationship between variables does not prove causality. In this paper we will use the Granger Causality test (Geweke, 1982, 1984; Geweke, Meese, & Dent, 1983; C.W.J. Granger, 1969) to study causal relationships. The Granger Causality test is a statistical hypothesis test used to determine if one series can be used to forecast another. Unlike the classical linear regression model which shows only 'correlation', this test can reveal causality. The Granger Causality test is more preferred to Sims Causality Test as the Sims test uses more regressors, leading to a bigger loss of degree of freedom (Sims, 1980). The Vector Autoregression (VAR) model is usually used in Granger Causality due to its simplicity.

4.2.1 Unit Root Test

Granger causality tests are only strictly valid for stationary series [1] and should therefore be preceded by a check of the order of integration of the variables, i.e. whether the data generating processes show a unit root or not. Many economic time series are not stationary at the levels (Nelson & Plosser, 1982). As a first step, we used the Dickey Fuller (DF) unit root test (Dickey & Fuller, 1979). If a series is non stationary in their level forms but is stationary in its first differenced form, we say the series is integrated of order 1. As the Granger Causality test follows the result of this unit root test, it is important to correctly determine this step. Hence we also performed an alternative unit root test, the Philips Perron test which is a generalized ADF test allowing autocorrelated residuals (Phillips & Perron, 1988).

4.2.2 Cointegration Test

Before performing Granger Causality Test on the series, cointegration tests are first carried out to test if there exist long run relationships between the variables. If two series are cointegrated, it means that at any point in time the two variables may drift apart, but there will always be a tendency for them to retain a reasonable proximity to each other. Following Granger and Lin (1995), two integrated series cannot cause each other in the long run unless they are cointegrated, in which case the Granger Causality will have to be tested using Vector Error Correction model (VECM). Cointegration test are only carried out on pairs of series that are non-stationary and are both integrated of the same order.

In this paper, we will perform the Engel-Granger cointegration test (Engle & Granger, 1987). A linear combination of two variables, Yt and Xt can be estimated from the following regression:

Yt= AŽA²1 + AŽA²2Xt + et

Taking the residuals:

êt = Yt - 1 - 2Xt

If êt is stationary, then the variables Yt and Xt are said to be cointegrated. Unit root test on this residual is carried out to check the order of integration. It is also noted that because êt is residual we do not include a constant nor a time trend when performing the unit root test. Engle and Granger (1987) also point out that the critical values are different from that of Fuller (1976).

4.2.3 Constructing VAR Equations

In Audretsch, Carrie and Thurik (2001), the following VAR equations are estimated using panel data of OECD countries from 1974 to 1998.

Ut - Ut-L = AŽA± + j (Et-jL - Et-(j+1)L) + j (Ut-jL-Ut-(j+1)L) + A‰”º1t (1)

Et - Et-L = AŽAº + j (Ut-jL - Ut-(j+1)L) + j (Et-jL-Et-(j+1)L) + A‰”º2t (2)

where

U = unemployment rate,

E = entrepreneurship represented by self-employment rate

A‰”º = random error such that A‰”º A¢”°Ë† N (0, A¢Ë†‘)

L = time span in the number of years

J = number of time lags included.

In (1), the lagged endogenous unemployment variables are added into the equation to correct for autocorrelation of unemployment growth over time. A negative coefficient AŽA² is found, showing a clear 'Schumpeter' effect of entrepreneurship reducing unemployment. Coefficient c is also negative, suggesting cyclical effect related to influence of policy measure.

Similarly, we would like to examine these equations in the context of Singapore. For these OECD countries, Audretsch et al (2001) use a L=4 time span. On the other hand, Golpe & van Stel (2007) use a L=2 time span in estimating this relationship in Spain. These time span is used as the impact of self employment on unemployment rate is not instantaneous; it requires a few year for firms to grow and if likely to contribute to the economy. In view of unemployment, it is also likely that people take time to make mental preparation before deciding to be self-employed.

Before constructing the model, we will first determine the suitable length of time span, L for Singapore. We start by constructing simple VAR models with J=1 lag for each proxy of business ownership (start-ups, formation of business and formation of companies) to determine the optimal L. We estimate the following equations and select the best model using model selection criterion.

Table 1: Estimating VAR models of J=1

L

Equation

1

Ut - Ut-1 = AŽA± + AŽA² (Et-1 - Et-2) + c (Ut-1 - Ut-2) + A‰”º1t

Et - Et-1 = AŽAº + AŽA³ (Ut-1 - Ut-2) + AŽA¼ (Et-1-Et-2) + A‰”º2t

2

Ut - Ut-2 = AŽA± + AŽA² (Et-2 - Et-4) + c (Ut-2 - Ut-4) + A‰”º1t

Et - Et-2 = AŽAº + AŽA³ (Ut-2 - Ut-4) + AŽA¼ (Et-2-Et-4) + A‰”º2t

3

Ut - Ut-3 = AŽA± + AŽA² (Et-3 - Et-6) + c (Ut-3 - Ut-6) + A‰”º1t

Et - Et-3 = AŽAº + AŽA³ (Ut-3 - Ut-6) + AŽA¼ (Et-3-Et-6) + A‰”º2t

4

Ut - Ut-4 = AŽA± + AŽA² (Et-4 - Et-8) + c (Ut-4 - Ut-8) + A‰”º1t

Et - Et-4 = AŽAº + AŽA³ (Ut-4 - Ut-8) + AŽA¼ (Et-4-Et-8) + A‰”º2t

As the VAR model is only valid for stationary series, we confirmed the stationarity of all Ut - Ut-L and Et - Et-L series of these model by performing unit root test. Detailed results of both the ADF test and PP test can be found in Table 3A and 3B (Appendix A).

After determining the optimal L*, we construct equation (1) and (2) with variation in J=1,2 and 3 to choose the best number of lagged terms to be included in the model to describe this causal relationship. Granger causality test is then run on these models.

Similarly, we construct VAR model as in equation (1) and (2) to investigate the causal relationship between Singapore's business start-ups and economic growth. 'U' is replaced with Y to represent annual GDP. 'U' in equation (1) and (2) is then replaced with X, representing GDP Per Capita.

Statistical package, EViews 6.0 which has built in unit root test will be used to carry out the analysis. Representation of all series in EVIEWS is shown in Table 2 of Appendix A.

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