I am using a 2step heckman regression model and I want to evaluate that probit looks okay and that the model converges and that there are no "red" flags.

One of the estimators that I get is the inverse Mills ration (I am using R). Is this supposed to be statistically significant or not?

> summary( heckit( lfp ~ age + I( age^2 ) + faminc + kids + educ,
+                  wage ~ exper + I( exper^2 ) + educ + city, Mroz87 ) )
--------------------------------------------
Tobit 2 model (sample selection model)
2-step Heckman / heckit estimation
753 observations (325 censored and 428 observed)
14 free parameters (df = 740)
Probit selection equation:
                Estimate   Std. Error t value  Pr(>|t|)    
(Intercept) -4.156806923  1.402085958  -2.965  0.003127 ** 
age          0.185395096  0.065966659   2.810  0.005078 ** 
I(age^2)    -0.002425897  0.000773540  -3.136  0.001780 ** 
faminc       0.000004580  0.000004206   1.089  0.276544    
kidsTRUE    -0.448986740  0.130911496  -3.430  0.000638 ***
educ         0.098182281  0.022984120   4.272 0.0000219 ***
Outcome equation:
              Estimate Std. Error t value  Pr(>|t|)    
(Intercept) -0.9712003  2.0593505  -0.472     0.637    
exper        0.0210610  0.0624646   0.337     0.736    
I(exper^2)   0.0001371  0.0018782   0.073     0.942    
educ         0.4170174  0.1002497   4.160 0.0000356 ***
city         0.4438379  0.3158984   1.405     0.160    
Multiple R-Squared:0.1264,  Adjusted R-Squared:0.116
   Error terms:
              Estimate Std. Error t value Pr(>|t|)
invMillsRatio   -1.098      1.266  -0.867    0.386
sigma            3.200         NA      NA       NA
rho             -0.343         NA      NA       NA
--------------------------------------------

I am using a two-step Heckman regression model and I want to evaluate if probit looks okay, that the model converges, and that there are no "red" flags.

One of the estimators that I get is the inverse Mills ratio. Is this supposed to be statistically significant or not?

summary(heckit(lfp ~ age + I( age^2 ) + faminc + kids + educ,
               wage ~ exper + I( exper^2 ) + educ + city, Mroz87 ) ) 

--------------------------------------------
Tobit 2 model (sample selection model)
2-step Heckman / heckit estimation
753 observations (325 censored and 428 observed)
14 free parameters (df = 740) 

Probit selection equation:
                Estimate   Std. Error t value  Pr(>|t|)    
(Intercept) -4.156806923  1.402085958  -2.965  0.003127 ** 
age          0.185395096  0.065966659   2.810  0.005078 ** 
I(age^2)    -0.002425897  0.000773540  -3.136  0.001780 ** 
faminc       0.000004580  0.000004206   1.089  0.276544    
kidsTRUE    -0.448986740  0.130911496  -3.430  0.000638 ***
educ         0.098182281  0.022984120   4.272 0.0000219 *** 

Outcome equation:
              Estimate Std. Error t value  Pr(>|t|)    
(Intercept) -0.9712003  2.0593505  -0.472     0.637    
exper        0.0210610  0.0624646   0.337     0.736    
I(exper^2)   0.0001371  0.0018782   0.073     0.942    
educ         0.4170174  0.1002497   4.160 0.0000356 ***
city         0.4438379  0.3158984   1.405     0.160     

Multiple R-Squared:0.1264,  Adjusted R-Squared:0.116
 
Error terms:
              Estimate Std. Error t value Pr(>|t|)
invMillsRatio   -1.098      1.266  -0.867    0.386
sigma            3.200         NA      NA       NA
rho             -0.343         NA      NA       NA
--------------------------------------------

I am using an example from the book:

> summary( heckit( lfp ~ age + I( age^2 ) + faminc + kids + educ,
+                  wage ~ exper + I( exper^2 ) + educ + city, Mroz87 ) )
--------------------------------------------
Tobit 2 model (sample selection model)
2-step Heckman / heckit estimation
753 observations (325 censored and 428 observed)
14 free parameters (df = 740)
Probit selection equation:
                Estimate   Std. Error t value  Pr(>|t|)    
(Intercept) -4.156806923  1.402085958  -2.965  0.003127 ** 
age          0.185395096  0.065966659   2.810  0.005078 ** 
I(age^2)    -0.002425897  0.000773540  -3.136  0.001780 ** 
faminc       0.000004580  0.000004206   1.089  0.276544    
kidsTRUE    -0.448986740  0.130911496  -3.430  0.000638 ***
educ         0.098182281  0.022984120   4.272 0.0000219 ***
Outcome equation:
              Estimate Std. Error t value  Pr(>|t|)    
(Intercept) -0.9712003  2.0593505  -0.472     0.637    
exper        0.0210610  0.0624646   0.337     0.736    
I(exper^2)   0.0001371  0.0018782   0.073     0.942    
educ         0.4170174  0.1002497   4.160 0.0000356 ***
city         0.4438379  0.3158984   1.405     0.160    
Multiple R-Squared:0.1264,  Adjusted R-Squared:0.116
   Error terms:
              Estimate Std. Error t value Pr(>|t|)
invMillsRatio   -1.098      1.266  -0.867    0.386
sigma            3.200         NA      NA       NA
rho             -0.343         NA      NA       NA
--------------------------------------------