λ and ρ parameters outside [-1;1] with spreg command

[Yann Raineau]

Hello to all,

I'm running a spatial autoregressive model with Stata and command -spreg-.
I'm confused by getting λ and ρ parameters outside [-1;1].

Weight matrix has been created with -spmat idistance- command, and I use it as both the spatial-autoregressive term and the spatial-error term (notified by dlmat and elmat options in -spreg- command).
I've tried three different normalization methods (row, spectral and minmax) and I've runned spreg with both max likelihood and GS2SLS estimators.
λ and ρ are really different out of each of these six cases. And on half cases, λ or/and ρ are outside [-1;1] (from -1.73 for rho to 2.95 for lambda).

Can someone help me understanding these results?
Many thanks in advance.

Regards,
Yann

[Aria Mac]

Hi Yann. I am having the same issue. Did you ever figure out your problem?

[Harry O'Rahilly]

Hi Aria, Yann,
Did either of you have any luck with your co-efficients outside the range?
I have the same issue myself. PSB
Best
Harry

Hello all,

I am using Stata 15.1

I have created a Spectrally Normalized Spatially Weighted Inverse-distance Cross-Sectional Matrix - using proprietary distance data - by means of spmatrix fromdata, i.e. not using methods employing a shapefile or co-ordinate variables.

The Matrix is 66x66, non-symmetric, and hollow (diagonal elements = 0).

spregress run on this Matrix with a gs2sls (generalized spatial two-stage least-squares) estimate produces an errorlag co-efficient greater than 1. [1.586804]

As discussed on page 147 of the Stata Spatial Autoregressive Models Ref Manual the errorlag co-efficient (rho [hat] )



To note, the Stata example for Spatial autoregressive models provided also appears to have an errorlag co-efficient greater than 1 [3.247298]

I have two questions please.

1. Given the steps taken below, is an errorlag co-efficient [rho hat] greater than 1 problematic?*
2. If so, is there a remedy for this?

*By which I mean the results cannot be used to reject H₀

Happy to PM matrix data/provide clarity. Regards,

Harry

PS Following spregress I have run estat impact for completeness.
PPS dataex linesize limit exceeded by matrix

. clear

. use "C:\Users\Atlan\OneDrive\PC\UCD\Matrix\STATA\2020 08 19 matrix.dta"

. spset catnumber
Sp dataset 2020 08 19 matrix.dta
data: cross sectional
spatial-unit id: _ID (equal to catnumber)
coordinates: none
linked shapefile: none

. spmatrix fromdata WmeM = stats_22050-stats_18454, normalize(spectral) idistance replace

. spmatrix export WmeM using WmeM.txt
(matrix WmeM saved in file WmeM.txt)

. save "C:\Users\Atlan\OneDrive\PC\UCD\Matrix\STATA\2020 09 02 matrix.dta", replace

file C:\Users\Atlan\OneDrive\PC\UCD\Matrix\STATA\2020 09 02 matrix.dta saved

. clear

. use "C:\Users\Atlan\OneDrive\PC\UCD\Matrix\STATA\2019 12 27 Analysis_2015_2019_5.dta"

. regress LE_1 SUMBC660sSQ

Source | SS df MS Number of obs = 66
-------------+---------------------------------- F(1, 64) = 28.13
Model | .005390905 1 .005390905 Prob > F = 0.0000
Residual | .012265551 64 .000191649 R-squared = 0.3053
-------------+---------------------------------- Adj R-squared = 0.2945
Total | .017656456 65 .000271638 Root MSE = .01384

------------------------------------------------------------------------------
LE_1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
SUMBC660sSQ | -.0001403 .0000265 -5.30 0.000 -.0001932 -.0000875
_cons | .0746009 .0035903 20.78 0.000 .0674285 .0817732
------------------------------------------------------------------------------

. spset catnumber
Sp dataset 2019 12 27 Analysis_2015_2019_5.dta
data: cross sectional
spatial-unit id: _ID (equal to catnumber)
coordinates: none
linked shapefile: none

. estat moran, errorlag(WmeM)

Moran test for spatial dependence
Ho: error is i.i.d.
Errorlags: WmeM

chi2(1) = 10.22
Prob > chi2 = 0.0014

. spregress LE_1 SUMBC660sSQ, gs2sls errorlag(WmeM) 
(66 observations)
(66 observations (places) used)
(weighting matrix defines 66 places)

Estimating rho using 2SLS residuals:

initial: GMM criterion = 6.965e-10
alternative: GMM criterion = 1.179e-10
rescale: GMM criterion = 3.067e-12
Iteration 0: GMM criterion = 3.067e-12
Iteration 1: GMM criterion = 2.534e-13

Estimating rho using GS2SLS residuals:

Iteration 0: GMM criterion = .01728762
Iteration 1: GMM criterion = .01186374
Iteration 2: GMM criterion = .01175648
Iteration 3: GMM criterion = .01175648

Spatial autoregressive model Number of obs = 66
GS2SLS estimates Wald chi2(1) = 10.00
Prob > chi2 = 0.0016
Pseudo R2 = 0.3053

--------------------------------------------------------------------------------
LE_1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
LE_1 |
SUMBC660sSQ | -.000081 .0000256 -3.16 0.002 -.0001312 -.0000308
_cons | .0679234 .0042821 15.86 0.000 .0595307 .0763162
---------------+----------------------------------------------------------------
WmeM |
e.LE_1 | 1.586804 .554908 2.86 0.004 .499204 2.674403
--------------------------------------------------------------------------------
Wald test of spatial terms: chi2(1) = 8.18 Prob > chi2 = 0.0042

. estat impact 

progress :100%

Average impacts Number of obs = 66

------------------------------------------------------------------------------
| Delta-Method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
direct |
SUMBC660sSQ | -.000081 .0000256 -3.16 0.002 -.0001312 -.0000308
-------------+----------------------------------------------------------------
indirect |
SUMBC660sSQ | 0 (omitted)
-------------+----------------------------------------------------------------
total |
SUMBC660sSQ | -.000081 .0000256 -3.16 0.002 -.0001312 -.0000308
------------------------------------------------------------------------------
.
end of do-file
.

Tags: errorlag, spatial regression, spregress, weighted_spatial_lag