Suppose a wealth index is computed using information on a set of 14 assets that a household possesses. The index is generated using principal components, as the 14 individual asset variables are highly collinear. A OLS regression of education expenditures (in Rupees per household) on the wealth index yields a coefficient of 0.4.
It is harder to interpret coefficients principal components in terms of original regressors. But can I interpret wealth index as its own ie can I say - increase in wealth index by a score of 1 will increase education expenditure by 0.4?
Is there any alternative formulation of doing this exercise that may be preferred?