Bài 8: Mô hình Tobit

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 prices, when controlled by government  working hours, stays zero for unemployed  loan, remains zero for rejected application... Example: non-censored/truncated variable..[r] (1)THE TOBIT MODEL (2)Censored & Truncated data  Sometimes we can’t observe values lower or beyond a certain level, for example:  dividend, which remains zero until profit reaches a certain level (3)Censored & Truncated data  y is censored if:  we can observe all values of y, but  only in a certain interval, values beyond the interval are recorded as a constant (example: 0)  y >= k : censored from below  y <= k : censored from above  y is truncated if we can only observe it in the (4)(5)(6)(7)(8)(9)(10)(11)OLS, censored/truncated variable and the Tobit model  OLS with censored/truncated dependent variables (12)The Tobit model  Tobit model  Notes:  We can observe y*, but can’t observe y  y is the latent variable * y x if a y b y a if y a b if y b            (13)Estimation of the Tobit model  Log-likelihood function (d is dummy: = censored)  2    2   2 1 log log log 2 1 1 2 N N i i i i i i i y X X L   dd  (14)Case study: credit card balance  Dependent variable: balance of credit card (USD)  Explanatory variables:  interest charged (%)  age (year) (15)Credit card balance and interest 0 10 00 00 20 00 00 30 00 00 40 00 00 ba la nce 5 10 15 20 25 30 (16)Tobit model in Stata right-censored observations 1886 uncensored observations Obs summary: 1018 left-censored observations at balance<=0 (17)Hypotheses testing Prob > F = 0.0000 F( 3, 2900) = 118.33 ( 3) [model]edu = 0 ( 2) [model]male = 0 ( 1) [model]age = 0 test age male edu Prob > F = 0.0000 F( 1, 2900) = 18.21 ( 1) [model]interest = 0 (18)Marginal effects of Tobit model Three types of marginal effects after Tobit:  Type 1: the betas indicate how latent variable y change when regressors x changes.  Type 2: indicates how y* changes when x changes, provided that y* is within the boundaries.  Type 3: indicates how the observed variable y* changes when x changes. y x      * *  | (19)Marginal effects (Type 2) at average edu -694.8761 115.1101 -6.04 0.000 -920.4877 -469.2645 male 2610.969 709.4244 3.68 0.000 1220.523 4001.415 age -371.4221 21.45434 -17.31 0.000 -413.4718 -329.3723 interest -277.4943 65.10832 -4.26 0.000 -405.1043 -149.8844 dy/dx Std Err z P>|z| [95% Conf Interval] Delta-method dy/dx w.r.t : interest age male edu Expression : E(balance|balance>0), predict(e(0,.)) Model VCE : OIM (20)Marginal effects (Type 2) at specific value edu -763.6603 134.754 -5.67 0.000 -1027.773 -499.5474 male 2869.423 781.2861 3.67 0.000 1338.13 4400.716 age -408.1883 24.24905 -16.83 0.000 -455.7156 -360.6611 interest -304.9629 73.5335 -4.15 0.000 -449.0859 -160.8398 dy/dx Std Err z P>|z| [95% Conf Interval] Delta-method edu = 12 at : interest = 12 dy/dx w.r.t : interest age male edu Expression : E(balance|balance>0), predict(e(0,.)) Model VCE : OIM (21)Marginal effects (Type 3) at average edu -870.875 144.0877 -6.04 0.000 -1153.282 -588.4684 male 3272.278 889.0664 3.68 0.000 1529.74 5014.816 age -465.4963 26.79131 -17.37 0.000 -518.0063 -412.9863 interest -347.7784 81.54693 -4.26 0.000 -507.6074 -187.9493 dy/dx Std Err z P>|z| [95% Conf Interval] Delta-method dy/dx w.r.t : interest age male edu Expression : E(balance*|balance>0), predict(ystar(0,.)) Model VCE : OIM (22)Marginal effects (Type 3) at specific value edu -1001.511 181.137 -5.53 0.000 -1356.533 -646.4891 male 3763.137 1025.247 3.67 0.000 1753.69 5772.585 age -535.3232 31.84395 -16.81 0.000 -597.7362 -472.9102 interest -399.947 97.54245 -4.10 0.000 -591.1267 -208.7673 dy/dx Std Err z P>|z| [95% Conf Interval] Delta-method edu = 12 at : interest = 12 dy/dx w.r.t : interest age male edu Expression : E(balance*|balance>0), predict(ystar(0,.)) Model VCE : OIM (23)Applications of Tobit model Mayer & Walker (1996) An Empirical Analysis of the Choice of Payment Method in Corporate Acquisitions Quarterly J of Bus and Econ 35 (3): 48-65  Sample: 261 acquisitions 1979-90 Fortune 500  Dependent variable: % cash financing the acquisition  independent variables:  preference of manager on control (24)Applications of Tobit model Min&Kim (2003) Modeling Credit Card Borrowing Southern Economic Journal 70(1): 128-43.  Data: US Survey of Consumer Finance 1998, 2904 inds  dependent variable: individual credit card balance  independent variables:  interest rate charged  income  liquid assets  taste (25)Applications of Tobit model Amuedo-Dorantes (2006) Money Transfer among Banked and Unbanked Mexican Immigrants Southern Economic J 73(2): 374-401.  Data: 2928 Mexican immigrants in the US  dependent variable: remittances  independent variable:
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