Consider Estimating a Consumption Function from a Large Cross-Section Sample

Essay

Consider estimating a consumption function from a large cross-section sample of households. Assume that households at lower income levels do not have as much discretion for consumption variation as households with high income levels. After all, if you live below the poverty line, then almost all of your income is spent on necessities, and there is little room to save. On the other hand, if your annual income was $1 million, you could save quite a bit if you were a frugal person, or spend it all, if you prefer. Sketch what the scatterplot between consumption and income would look like in such a situation. What functional form do you think could approximate the conditional variance var(u_i | Inome)?