eivreg (with perfect reliability) is different than regress

[Ben Highton]

Hi All,
It seems to me that using eivreg with all reliabilities=1.0 should produce identical estimates & standard errors as the same model specified with the regress command. But, it does not appear to. Here is a simple example that shows different standard errors:
sysuse auto
regress weight foreign
eivreg weight foreign
The coefficients are identical across the models, but the standard errors are different. Would someone help me understand why? Thanks!

Here's the output:

. sysuse auto
(1978 Automobile Data)

. regress price weight foreign
Source | SS df MS Number of obs = 74
-------------+---------------------------------- F(2, 71) = 35.35
Model | 316859273 2 158429637 Prob > F = 0.0000
Residual | 318206123 71 4481776.38 R-squared = 0.4989
-------------+---------------------------------- Adj R-squared = 0.4848
Total | 635065396 73 8699525.97 Root MSE = 2117

------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | 3.320737 .3958784 8.39 0.000 2.531378 4.110096
foreign | 3637.001 668.583 5.44 0.000 2303.885 4970.118
_cons | -4942.844 1345.591 -3.67 0.000 -7625.876 -2259.812
------------------------------------------------------------------------------

. eivreg price weight foreign
assumed Errors-in-variables regression
variable reliability
---------------------------- Number of obs = 74
* 1.0000 F( 2, 71) = 23.83
Prob > F = 0.0000
R-squared = 0.4989
Root MSE = 2117.02

------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | 3.320737 .4907711 6.77 0.000 2.342167 4.299307
foreign | 3637.001 629.982 5.77 0.000 2380.853 4893.15
_cons | -4942.844 1561.025 -3.17 0.002 -8055.44 -1830.248
------------------------------------------------------------------------------


Sincerely,
Ben Highton

[Phil Bromiley]

Welcome to Stata list. You will increase your chances of a helpful answer by following the FAQ on asking questions-provide Stata code in code delimiters, readable Stata output, and sample data using dataex. We don't necessarily need the entire model and data – just enough to replicate the problem.

You need to work through the detailed calculations specification to see why it gives a different estimate. Have you checked the citations the documentation gives for the calculation of the covariance matrix? They might explain why it doesn't collapse to the conventional regression with reliability set to one.

[paulvonhippel]

The point estimates are the same, but the standard errors are different. I think this must be an example of eivreg returning biased standard errors as described in this paper:

Lockwood, J. R., & McCaffrey, D. F. (2020). Recommendations about estimating errors-in-variables regression in Stata. The Stata Journal, 20(1), 116-130. https://journals.sagepub.com/doi/pdf...36867X20909692