Greetings,

I am using the psacalc (Oster, 2017) command to estimate delta (the ration of selection on unobservable over selection on observables) after I run a regression, for a specific value of beta.
Here is the setting:

I first run the regression without controls, and get a beta of -0.5. When I run it with controls, I get a beta of -0.39, which indicates that the selection on observables brings the estimate closer to zero.

Now, I know from an instrumental variable regression, that the actual value of my beta is negative, let's say -2.5. Given that once I correct for the selection on unobservables using IV I get a much smaller value, I would expect the delta related to a beta of -2.5 to be negative, indicating that selection on observables and unobservables move the beta in different ways. Instead, I get a positive delta of around 1.87.

The command I run is the following:

psacalc delta uni, rmax(0.7) beta(-2.5)

and this is the output.

-------------+----------------------------------------------------------------
delta | 1.87526
-------------+----------------------------------------------------------------

---- Inputs from Regressions ----
| Coeff. R-Squared
-------------+----------------------------------------------------------------
Uncontrolled | -0.52430 0.002
Controlled | -0.39779 0.111
-------------+----------------------------------------------------------------

---- Other Inputs ----
-------------+----------------------------------------------------------------
R_max | 0.700
Beta | -2.500000
Unr. Controls|
-------------+----------------------------------------------------------------


Such a value for delta is puzling me, as from the way delta is defined it should be negative instead of positive.

Has anyone got any suggestion on what might be happening?

Best regards,
Gabriele