This paper examines how different econometric models, each with distinct functional form
assumptions, influence estimates of the Supplemental Nutrition Assistance Program (SNAP)
effect on food insecurity. To address potential endogeneity in SNAP participation, we employ
a range of instrumental variables methods, including two-stage least squares, control function
approaches, and (recursive) bivariate probit models, analyzing SNAP’s impact under various
linear and nonlinear specifications in both the first-stage reduced form and second-stage structural
equations. Using data from the 1996-2008 panels of the Survey of Income and Program
Participation (SIPP), our findings reveal that the magnitude and direction of SNAP’s effect on
food insecurity vary across model specifications, with estimates ranging from null effects to reductions
of approximately 27 percentage points. Furthermore, heterogeneity analysis indicates
that SNAP’s effectiveness is more pronounced among certain subpopulations.
