As far as I can tell, the two programs in the code below are identical. In the first program, I just assign the parameter to a scalar. In the second program, I store this scalar for each observation in a temporary variable.
Mathematically, that should be the same, yet the second program produces "numerical derivatives are approximate" and "flat or discontinuous region encountered".
Why cannot the derivatives be computed properly in the second approach?
clear
set obs 10000
set seed 42
gen x = runiform() * 10
gen eps = rnormal()
gen y = 2 + .3 * x + eps
capture program drop testScalar
program testScalar
syntax varlist [if], at(name)
scalar b0 = `at'[1,1]
scalar b1 = `at'[1,2]
replace `varlist' = y - b0 - b1* x
end
capture program drop testTempvar
program testTempvar
syntax varlist [if], at(name)
tempvar tmp
scalar b0 = `at'[1,1]
scalar b1 = `at'[1,2]
gen `tmp' = b1
replace `varlist' = y - b0 - `tmp'* x
end
gmm testScalar, nequations(1) nparameters(2) instr(x) winitial(identity) onestep
gmm testTempvar, nequations(1) nparameters(2) instr(x) winitial(identity) onestep
Output:
. gmm testScalar, nequations(1) nparameters(2) instr(x) winitial(identity) onestep
(10,000 real changes made)
Step 1
Iteration 0: GMM criterion Q(b) = 417.93313
Iteration 1: GMM criterion Q(b) = 1.690e-23
Iteration 2: GMM criterion Q(b) = 3.568e-30
note: model is exactly identified
GMM estimation
Number of parameters = 2
Number of moments = 2
Initial weight matrix: Identity Number of obs = 10,000
------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | 2.022865 .0200156 101.06 0.000 1.983635 2.062095
/b2 | .2981147 .003465 86.04 0.000 .2913235 .3049059
------------------------------------------------------------------------------
Instruments for equation 1: x _cons
. gmm testTempvar, nequations(1) nparameters(2) instr(x) winitial(identity) onestep
(10,000 real changes made)
Step 1
Iteration 0: GMM criterion Q(b) = 417.93313
numerical derivatives are approximate
flat or discontinuous region encountered
Iteration 1: GMM criterion Q(b) = 8.073e-17
numerical derivatives are approximate
flat or discontinuous region encountered
Iteration 2: GMM criterion Q(b) = 8.073e-17 (backed up)
note: model is exactly identified
GMM estimation
Number of parameters = 2
Number of moments = 2
Initial weight matrix: Identity Number of obs = 10,000
------------------------------------------------------------------------------
| Robust
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
/b1 | 2.022865 .0201346 100.47 0.000 1.983402 2.062328
/b2 | .2981147 .0034933 85.34 0.000 .291268 .3049613
------------------------------------------------------------------------------
Instruments for equation 1: x _cons
.
In the program testTempvar you need to generate the temporary variable tmp as type double:
generate double `tmp' = b1
In other words, this is a precision problem.