## Marginal Effects in Tobit Models

proc qlim data = data.sme; model y = x1 - x7; endogenous y ~ censored(lb = 0 ub = 1); output out = out1 marginal; run; /* Standard Approx Parameter Estimate Error t Value Pr > |t| Intercept -2.204123 0.118473 -18.60 <.0001 x1 -0.015086 0.008345 -1.81 0.0707 x2 0.376830 0.048772 7.73 <.0001 x3 0.141672 0.008032 17.64 <.0001 x4 -0.813496 0.133564 -6.09 <.0001 x5 0.000036437 0.000320 0.11 0.9094 x6 -0.001152 0.000704 -1.64 0.1016 x7 -0.392152 0.060902 -6.44 <.0001 _Sigma 0.497938 0.012319 40.42 <.0001 */ proc means data = out1 mean; var meff_x:; run; /* Auto Calculation: Variable Label Mean ------------------------------------------------------ Meff_x1 Marginal effect of x1 on y -0.0036988 Meff_x2 Marginal effect of x2 on y 0.0923919 Meff_x3 Marginal effect of x3 on y 0.0347354 Meff_x4 Marginal effect of x4 on y -0.1994545 Meff_x5 Marginal effect of x5 on y 8.9337756E-6 Meff_x6 Marginal effect of x6 on y -0.000282493 Meff_x7 Marginal effect of x7 on y -0.0961485 */ data one; set data.sme; _xb_ = -2.204123 + x1 * -0.015086 + x2 * 0.376830 + x3 * 0.141672 + x4 * -0.813496 + x5 * 0.000036437 + x6 * -0.001152 + x7 * -0.392152; _phi_lb = probnorm((0 - _xb_) / 0.497938); _phi_ub = probnorm((1 - _xb_) / 0.497938); _pdf_lb = pdf('normal', (0 - _xb_) / 0.497938); _pdf_ub = pdf('normal', (1 - _xb_) / 0.497938); _imr = (_pdf_lb - _pdf_ub) / (_phi_ub - _phi_lb); _margin_x1 = (_phi_ub - _phi_lb) * -0.015086; _margin_x2 = (_phi_ub - _phi_lb) * 0.376830; _margin_x3 = (_phi_ub - _phi_lb) * 0.141672; _margin_x4 = (_phi_ub - _phi_lb) * -0.813496; _margin_x5 = (_phi_ub - _phi_lb) * 0.000036437; _margin_x6 = (_phi_ub - _phi_lb) * -0.001152; _margin_x7 = (_phi_ub - _phi_lb) * -0.392152; run; proc means data = one mean; var _margin_x:; run; /* Manual Calculation: Variable Mean -------------------------- _margin_x1 -0.0036988 _margin_x2 0.0923924 _margin_x3 0.0347356 _margin_x4 -0.1994555 _margin_x5 8.9337391E-6 _margin_x6 -0.000282451 _margin_x7 -0.0961491 */

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