Modeling Macroeconomic Variables Using Principal Component Analysis and Multiple Linear Regression: The Case of Ghana's Economy

摘要

The paper sought to model the relationship between GDP and 29 macroeconomic variables in Ghana using the Principal Component Analysis and multiple linear regression. Economic data with 583 data points were collected from January, 1990 through to May, 2018. The KMO statistics was 0.750 and the Bartlett's Test of sphericity statistic obtained for the data was 24807.231 of p-value 0.000. The variables were found to be powerfully correlated with reference to the correlation matrix. Principal Component Analysis was performed to reduce the factors (using orthogonal varimax technique to produce uncorrelated factor structures to help allocate appropriately loadings to factors) to a minimum without compromising the variability of the original data. Seven factors were retained (explained 74% of the overall variation) after using multiple extraction approaches of Scree test, Kaiser Criterion and parallel analysis to avoid over- and under-extraction errors. Regression analysis was performed where component scores were used to develop a relationship with the uncorrelated components and GDP. The component 2 (Closed Economy without Government Activities) explicitly contained seven indicators consisting of consumer price index-Food, Consumer price index-Nonfood, Consumer Price index (overall), Monetary Policy Rate, 91-Days Treasury Bill, 182-Days Treasury Bill, crude oil, and Core Inflation (Adjusted for Energy and Utility). Component 2 was significant and positively related with GDP (B = 0.6, p0.01). Again, Component 5 (Closed Economy with Government activities) explicitly contained two indicators such as Tax-Equivalent Rate on 28-Days Treasury Bill and Tax-Equivalent Rate on 56-DaysTreasury Bill. Component 5 had a positive and significant impact on GDP (B = 0.386, p0.01). However, component 4 (monetary economy; B = -3.927, p0.01), component 6 (B = -0.577, p0.01) and component 7 (B = -0.256, p0.01) were negatively related with GDP but were statistically significant. The R-squared value of 0.304 shows that the regression model explains about 30% of the variance. It was recommended for future researchers to consider increasing the number of macroeconomic variables to increase the predictive power of the model.