Featured White Papers
Content provided in partnership with
Business Services Industry
An analysis of causal flow between social development and economic growth: the social developement index
American Journal of Economics and Sociology, The, July, 1996 by Krishna Mazumdar
Since the objective of this study is to have a composite representation of all the important variables, only the first principal component is considered. The exact procedure followed for obtaining the first principal component is as follows: the characteristic vector corresponding to the largest characteristic root of the correlation matrix of the eight constituents is rescaled to make the sum of its elements equal to one, and the principal component is obtained as a weighted sum of the eight constituents with rescaled elements of the characteristic vector as the weights.
This study attempts to throw light on the causal relation between social development and economic development for the sample as a whole, representing the entire world as well as for three different income groups. Therefore each sample country is viewed from two points of view: as a member of a particular income-group and as a member of the world as a whole. Therefore, there are four sets of weights for each variable at each time as varying with sample: entire world, high income countries, middle income countries, and low income countries. As a result for each time, there are two social development indices for each country of the sample, one as a member of the world as a whole and as a member of the particular income group.
VI
Methodology
The lag-lead relation between social development and economic growth may be found by simple test of causality. In this respect the Granger (1969) causality test is used. The concept of causality in the Granger sense is based on the basic assumptions: (i) Future cannot cause the past. It is the past and present which cause the future and (ii) Detection of causality is only possible between two stochastic variables.
Granger proposed for a pair of linear covariance-stationary time series x and y: x causes y if the past values of x can be used to predict y more correctly than simply using the past values of y. Formally, x is said to cause y if and only if [Mathematical Expression Omitted] where [[Sigma].sup.2] represents the variance of forecast error and i and j = 1,2,3, . . . n.
To test causality and its direction between economic growth and social development in the Granger sense, the following equations are specified:
[X.sub.1t] = [A.sub.1] + [summation of] [B.sub.i][X.sub.[1.sub.(t-i)]] where i=1 to n + [summation of] [C.sub.j][X.sub.[2.sub.(t-i)]] where j=1 to m + [E.sub.1t] [1]
[X.sub.2t] = [A.sub.2] + [summation of] [P.sub.i][X.sub.[1.sub.(t-i)]] where i=1 to k + [summation of] [Q.sub.j][X.sub.[2.sub.(t-i)]] where j=1 to l + [E.sub.2t] [2]
where [X.sub.1] and [X.sub.2] are the variables across which causal ordering are to be investigated (here [X.sub.1] denotes Social Development Index and [X.sub.2] denotes Per Capita Real Gross Domestic Product, i and j are the time lags, B, C, P, Q are the coefficients and [E.sub.1t], and [E.sub.2t] are serially independent random vector with mean zero and finite covariance matrix. The causality tests to be performed can be represented simply in terms of the following hypotheses. The hypothesis that there is no causal flow from [X.sub.1] to [X.sub.2] and [X.sub.2] to [X.sub.1] is equivalent to postulate:
