Application of a Principal Component Analysis, (PCA), Based on the Macroeconomic Factors, Namely, Personal Consumption Expenditures, Gross Private Domestic Investment, Net Export of Goods and Services and Government Consumption Expenditures and Gross Investment that Constitute The US GDP.

Abstract

In this article, we have tested the correlation and covariance relationships that the natural logarithmic yearly returns of the macroeconomic variables in terms of personal consumption expenditures, gross private domestic investment, net export of goods and services and government consumption expenditures and gross investment, have on the US Gross domestic product, (GDP). We have applied a principal component analysis, (PCA), in EViews 6 to check the eigenvalues, the eigenvectors loadings of the correlation matrix and the covariance matrix. The aim by using this methodology is twofold. Firstly, to identify the degree of correlation between the variables. Secondly to reduce the dimension of variation between the variables by eliminating the factors. We have found though the correlation matrix that most of the correlation coefficients of the macroeconomic variables are greater than 0.5 and they show very strong positive linear correlation. There is also linear weak negative and positive correlation between the macro variables. In terms of dimensionality reduction, we have found that factors 1 and 2 have an eigenvalues greater than 1. Specifically, factor 1 has a value of 3.14 and factor 2 has a value of 1.09. Thus, the factors that we will retain are two. Concerning, eigenvalues figures, we have found that the proportion for factor 1 is 62.73% and for factor 2 is 21.74% of the total variance. The first two components namely account for 84.47% of the total variation. Most of the residuals of the common covariance matrix are positive, which mean that the variables increase together. The orthonormal loadings biplot shows that the first component has the highest proportion of total variation, which is 62.7% and positive loadings for all five variables. The second component has a value of 21.7% of total variation. It has a positive variable loadings for government consumption expenditures and gross investment, (GCEGI) and negative variable loadings for gross private domestic investment, (GPDI), and net export of goods and services, (NEGS). The total dataset includes annual data starting from 1980 to 2012 and total to 33 observations. The total data of the logarithmic yearly returns account to 32 observations. The data was obtained from the US Bureau of Economic Analysis, (BEA).