# SE of tobit goes to infinity if I include time trend variable (year variable)

I'm dealing with some data that is restricted to unmarried women with two or more children to find out if a tax policy affects their annual hours of work.

But, pretty much different from my expectation, when I include a time variable (in this case, h_year (it's a list of 6 years: 2008, 2009, 2010, 2012, 2013, 2014), the standard errors of the all explanatory variables in the tobit model goes to infinity. Very weird.

So below is the code and summary statistics:

tobit_model <- censReg(yworking_hrs ~ other_income_val + fownu6 + nonwhite + a_age + age_sqrd + year_education + year_educ_sqrd + h_year + gestcen + three_kids + post_arra + three_x_arra, data = Mcps_HS, left=0)

summary(tobit_mod)


This gives me a summary table that looks like:

Call:
censReg(formula = yworking_hrs ~ other_income_val + fownu6 +
nonwhite + a_age + age_sqrd + year_education + year_educ_sqrd +
h_year + gestcen + unemp + minwage + three_kids + post_arra +
three_x_arra, left = 0, data = Mcps_HS)

Observations:
Total  Left-censored     Uncensored Right-censored
1666            548           1118              0

Coefficients:
Estimate Std. error t value Pr(> t)
(Intercept)      -6139.205        Inf       0       1
other_income_val    61.544        Inf       0       1
fownu6            -139.087        Inf       0       1
nonwhite           -99.584        Inf       0       1
a_age              103.132        Inf       0       1
age_sqrd            -1.198        Inf       0       1
year_education     -96.878        Inf       0       1
year_educ_sqrd       6.655        Inf       0       1
h_year               2.059        Inf       0       1
gestcen              3.149        Inf       0       1
unemp              -45.452        Inf       0       1
minwage            215.183        Inf       0       1
three_kids        -189.103        Inf       0       1
post_arra          -73.396        Inf       0       1
three_x_arra        51.153        Inf       0       1
logSigma             7.167        Inf       0       1

Newton-Raphson maximisation, 8 iterations
Return code 2: successive function values within tolerance limit
Log-likelihood: -10113.75 on 16 Df



By contrast, if I exclude h_year, then it seems it works normally.

Call:
censReg(formula = yworking_hrs ~ other_income_val + fownu6 +
nonwhite + a_age + age_sqrd + year_education + year_educ_sqrd +
gestcen + unemp + minwage + three_kids + post_arra + three_x_arra,
left = 0, data = Mcps_BH)

Observations:
Total  Left-censored     Uncensored Right-censored
9461           1680           7781              0

Coefficients:
Estimate Std. error t value  Pr(> t)
(Intercept)      -5.632e+03  1.260e+03  -4.471 7.79e-06 ***
other_income_val -1.102e+01  8.401e+00  -1.312 0.189474
fownu6           -3.152e+01  1.506e+01  -2.093 0.036392 *
nonwhite         -3.117e+01  2.464e+01  -1.265 0.205814
a_age             1.421e+02  9.495e+00  14.969  < 2e-16 ***
age_sqrd         -1.711e+00  1.361e-01 -12.574  < 2e-16 ***
year_education    5.283e+02  1.520e+02   3.477 0.000508 ***
year_educ_sqrd   -1.439e+01  4.756e+00  -3.025 0.002489 **
gestcen           6.562e-01  4.265e-01   1.539 0.123868
unemp            -2.722e+01  6.489e+00  -4.195 2.73e-05 ***
minwage          -1.269e+01  5.123e+01  -0.248 0.804385
three_kids       -6.690e+01  3.394e+01  -1.971 0.048703 *
post_arra        -1.621e+01  2.918e+01  -0.556 0.578497
three_x_arra     -7.084e+00  4.796e+01  -0.148 0.882568
logSigma          6.947e+00  8.476e-03 819.658  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Newton-Raphson maximisation, 14 iterations
Return code 2: successive function values within tolerance limit
Log-likelihood: -67075.13 on 15 Df



Can anyone help this?

Thanks!

(plus, I'm wondering what logSigma stands for. Even though I've taken Econometrics, I haven't heard about that..)