Stability of the Internal Structure of Consumption Expenditure

Let y 1, …, y 14 denote an exhaustive 14-category breakdown of expenditures in one of the BLS Quarterly Expenditure Surveys (as given in Table A.2), and let $$ {y}_i={\alpha}_i+{\displaystyle \sum_{j\ne i}{\beta}_{ij}{y}_j+{u}_i}\kern1em i,j=1,\dots, 14 $$ represent the least-squares regression equation of expenditures in the ith category on expenditures in the other 13 categories. Let ξ i = (α i , β j , j ≠ i) denote the resulting vector of estimates. Equation (2.1) has been estimated for each of the 14 categories for each of 40 BLS Quarterly Consumer Expenditure Surveys from 1996Q1 through 2005Q4. The columns in Table 1.1 contain the ξ i vectors for the BLS survey for 1999Q4. The primary purpose of this chapter is to investigate the stability of the ξ i over the 40 quarters of surveys.