Engel curves are often estimated within a linear, or at least approximately linear, system of equations. However, Engel curves are required to lie on or within the unit interval, while summing to unity. These restrictions are not easily accommodated within a linear system. Therefore, we apply the fractional multinomial logit model in our estimation of expenditure shares, because it more readily accommodates these theoretical restrictions. Within our estimation subsample from the South African Income and Expenditure Survey, we find that accounting for these restrictions within the fractional multinomial logit model provides a better fit to the data than does the standard linear system.