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?

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
    --------------------------------------------