The fictitious negative correlation may cancel out a real positive correlation, making it look as though expenditure has no effect on achievement. The problem with this argument is that it proves too much. If we substitute the employer's utility function for the government's, it implies that employers typically invest more money training their less able employees. If we substitute the parent's utility function, it implies that poor but aspiring parents scrimp to provide additional education to their least able children. If we substitute the utility function of the political structure controlling state higher education, it implies that the state universities admit from the bottom instead of the top of the distribution of graduating seniors, and specialize in remedial rather than advanced education.
Casual observation suggests, in each case, the opposite pattern.
That implies either that the marginal return is higher for expenditures on abler students or that utility functions for educational achievement exhibit increasing marginal utility in the relevant range. If this conclusion is correct, the argument Peltzman offers works in reverse. Expenditures will tend to be higher, not lower, on students with better backgrounds. Unobserved variation in background will correlate positively with both expenditure and achievement, creating the illusion of a positive correlation between expenditure and achievement. The measured correlation will then overstate the actual correlation.