This paper investigates whether there is a non-linear relationship between income and the private transfers received by households in developing countries. If private transfers are unresponsive to household income, expansion of public social security and other transfer programs is unlikely to crowd out private transfers, contrary to concerns first raised by Barro and Becker. There is little existing evidence for crowding out effects in the literature, but this may be because they have been obscured by methods that ignore non-linearities. If donors switch from altruistic motivations to exchange motivations as recipient income increases, a sharp non-linear relationship between private transfers and income may result. In fact, threshold regression techniques find such non-linearity in the Philippines and after accounting for these there is evidence of serious crowding out, with 30 to 80 percent of private transfers potentially displaced for low-income households [Cox, Hansen and Jimenez 2004, 'How Responsiveare Private Transfers to Income?' Journal of Public Economics]. To see if these non-linear effects occur more widely, semiparametric and threshold regression methods are used to model private transfers in four developing countries - China, Indonesia, Papua New Guinea and Vietnam. The results of our paper suggest that non-linear crowding-out effects are not important features of transfer behaviour in these countries. The transfer derivatives under a variety of assumptions only range between 0 and -0.08. If our results are valid, expansions of public social security to cover the poorest households need not be stymied by offsetting private responses.