Biprobit convergence not achieved

[Kangkang Zhang]

Hi all,

Following Barton, Burnett, Gunny, and Miller (2024 Management Science), I’m estimating a biprobit model to separate the probability of committing and detecting restatements. I'm following their Table 3, but changed the dependent variable to be whether a restatement was filed in a certain year. I'm analyzing this in a difference-in-differences setting, therefore I have treatxpost as the variable of interest.

My code looks like this:

biprobit (restatement treatxpost treat post $alist) (rr treatxpost treat post $blist), partial nolog difficult vce(cluster gvkey)

• The first equation models the probability of a commitment (restatement), and the second models detection (rr = restatement).
• $alist contains control variables for restatements (Accruals, AltmanZ, Litigation, Loss, MTB, CFO, CFOVolatility, PPEGrowth, SalesGrowth, SalesVolatility, SharesIssued, StockReturn, StockReturnVolatility, TotalLeverage, #OperatingSegments, PerfMatchedDA).
• $blist includes all variables in $alist plus a set of exclusionary restrictions (AbRestAnnounce, AbROA, DisastrousRet, Turnover, Volatility).

The problem: For almost all variations of my code (different control variables, different fixed effects), Stata reports "convergence not achieved."

I’d like to ask:

1. Is the convergence issue fatal for interpreting the results?
2. How can I resolve this non-convergence issue?

Any insight or guidance would be greatly appreciated.

Thank you,
Kangkang

[Richard Williams]

Generic tips on convergence problems are on pp. 2-3 of

https://www3.nd.edu/~rwilliam/xsoc73994/L02.pdf

[Nick Cox]

Concise if unhelpful replies to the general questions seem possible.

1. Is the non-convergence issue fatal?

I would say so, A model whose fit does not converge is not one to cite as an example, unless in a paper on fits that don't converge unless and until you fix what's needing to be fixed.

2. How can I resolve it?

Hard to say. I guess Richard's guidance includes advice to consider whether the dataset is large enough, whether there may be quirks in the dataset that cause particular problems, and above all to try first fitting much simpler models and to complicate them gradually until you can isolate particular sources of difficulty.

[Richard Williams]

I agree on the fatal part. I actually saw a paper that got published, and once I saw the original output I realized the models had not converged. But if all you want is a publication and don’t care whether the results are correct or not, maybe non-convergence isn’t fatal!

[Jeff Wooldridge]

The biprobit in this case is only buying you, at best, a bit of efficiency. You can estimate each equation by probit and not introduce bias. biprobit can be useful for testing across equations but even then it’s not necessary.

[John Mullahy]

I concur with #2-#5.

I might add that one rationale—which may or may not be your rationale—for estimating a bivariate probit model is because conditional joint probabilities Pr(y1, y2 | x) are of interest. (Jeff's suggestion in #5 implicitly assumes that the conditional marginal probabilities are of interest.)

If so, however, then the same x variables belong in both equations since the conditioning in the joint probability is on a single x-vector.

[Vincent Narh]

I am having a similar challenge with my biprobit estimation. I am implementing an IV technique where both the outcome and endogenous variables are binary, but convergence is not achieved. Would Jeff's suggestion still apply, especially when I am relying on the assumption joint normality?