A Matrix Exponential Spatial Panel Model with Heterogeneous Coefficients

We extend the heterogeneous coefficients spatial autoregressive panel model (HSAR) from Aquaro, Bailey, and Pesaran (2015) to the case of a heterogeneous coefficients matrix exponential spatial specification (HMESS). The HSAR is capable of producing parameter estimates for each region in the sample,...

Full description

Saved in:
Bibliographic Details
Published in:Geographical analysis Vol. 50; no. 4; pp. 422 - 453
Main Authors: LeSage, James, Chih, Yao‐Yu
Format: Journal Article
Language:English
Published: 01.10.2018
ISSN:0016-7363, 1538-4632
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We extend the heterogeneous coefficients spatial autoregressive panel model (HSAR) from Aquaro, Bailey, and Pesaran (2015) to the case of a heterogeneous coefficients matrix exponential spatial specification (HMESS). The HSAR is capable of producing parameter estimates for each region in the sample, that follow a spatial autoregressive process. Spatial autoregressive processes apply geometric decay of influence to higher‐order neighboring regions. The HMESS takes a similar approach as the HSAR to produce estimates for each region in the sample, but relies on a matrix exponential function to apply exponential decay to higher‐order neighbors. The MESS introduced by LeSage and Pace (2007) for the case of cross‐sectional spatial data samples has some potential computational advantages over the spatial autoregressive specification. In addition, the spatial dependence parameter in the MESS ranges from minus to plus infinity, which allows for use of normal priors assigned to this parameter in a Bayesian setting. We extend the cross‐sectional MESS to the case of a heterogeneous coefficients model, and describe Bayesian Markov Chain Monte Carlo estimation. We illustrate the HMESS model with a panel wage curve relationship using quarterly unemployment and wage rates from 261 counties centered on the Bakken shale oil region in North Dakota and Montana.
AbstractList We extend the heterogeneous coefficients spatial autoregressive panel model (HSAR) from Aquaro, Bailey, and Pesaran (2015) to the case of a heterogeneous coefficients matrix exponential spatial specification (HMESS). The HSAR is capable of producing parameter estimates for each region in the sample, that follow a spatial autoregressive process. Spatial autoregressive processes apply geometric decay of influence to higher‐order neighboring regions. The HMESS takes a similar approach as the HSAR to produce estimates for each region in the sample, but relies on a matrix exponential function to apply exponential decay to higher‐order neighbors. The MESS introduced by LeSage and Pace (2007) for the case of cross‐sectional spatial data samples has some potential computational advantages over the spatial autoregressive specification. In addition, the spatial dependence parameter in the MESS ranges from minus to plus infinity, which allows for use of normal priors assigned to this parameter in a Bayesian setting. We extend the cross‐sectional MESS to the case of a heterogeneous coefficients model, and describe Bayesian Markov Chain Monte Carlo estimation. We illustrate the HMESS model with a panel wage curve relationship using quarterly unemployment and wage rates from 261 counties centered on the Bakken shale oil region in North Dakota and Montana.
Author LeSage, James
Chih, Yao‐Yu
Author_xml – sequence: 1
  givenname: James
  surname: LeSage
  fullname: LeSage, James
  email: james.lesage@txstate.edu
  organization: Texas State University
– sequence: 2
  givenname: Yao‐Yu
  surname: Chih
  fullname: Chih, Yao‐Yu
  organization: Texas State University
BookMark eNp9kEtPwkAUhScGEwHd-Au6NinOo4_pkhCkJqAm6rq5TO_gmDpDZmqAf0-hrozxLs7ZnO_k5ozIwDqLhNwyOmHd3W8Q7IRxlvILMmSpkHGSCT4gQ0pZFuciE1dkFMInpZTnTAxJOY1W0Hqzj-b7bddlWwNN9LqFs7-AxSZaubrTnWk_ohJb9G6DFt13iGYOtTbKdFS4JpcamoA3Pz4m7w_zt1kZL58Xj7PpMlY8FzxWWoIq1LrWUmGSguQqzYEVdM0zJTgtkkRSJlNAwEQrgRpErguVaFYjl5kYE9r3Ku9C8KgrZdruW2dbD6apGK1OS1SnJarzEh1y9wvZevMF_vB3mPXhnWnw8E-yWsynTz1zBPG3ccc
CitedBy_id crossref_primary_10_1002_jae_2792
crossref_primary_10_1111_joes_12683
crossref_primary_10_1016_j_jeconom_2023_02_007
crossref_primary_10_1080_07474938_2022_2039494
crossref_primary_10_1007_s12076_020_00254_1
crossref_primary_10_1016_j_spasta_2018_10_004
Cites_doi 10.1016/j.jeconom.2009.10.035
10.3390/econometrics2040217
10.1016/j.jeconom.2006.09.007
10.1080/01621459.1996.10476677
10.1137/060659624
10.2139/ssrn.2623192
10.1007/978-3-642-40340-8
10.1016/j.econlet.2016.02.033
10.1111/j.1538-4632.2009.00758.x
10.1111/j.0950-0804.2005.00254.x
10.1177/0160017606298426
10.1111/j.1467-9787.2006.00449.x
10.1016/j.jeconom.2015.02.046
10.1016/j.regsciurbeco.2016.11.003
ContentType Journal Article
Copyright 2017 The Ohio State University
Copyright_xml – notice: 2017 The Ohio State University
DBID AAYXX
CITATION
DOI 10.1111/gean.12152
DatabaseName CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
CrossRef
DeliveryMethod fulltext_linktorsrc
Discipline Geography
EISSN 1538-4632
EndPage 453
ExternalDocumentID 10_1111_gean_12152
GEAN12152
Genre article
GroupedDBID -~X
.3N
.GA
.Y3
05W
0R~
10A
1OC
29H
31~
33P
4.4
50Y
50Z
51W
51Y
52M
52O
52Q
52S
52T
52U
52W
5GY
5HH
5LA
5VS
702
706
709
7PT
8-0
8-1
8-3
8-4
8-5
8UM
930
A04
AABNI
AAESR
AAFWJ
AAHQN
AAIKC
AAMMB
AAMNL
AAMNW
AAMZP
AAONW
AAOUF
AASGY
AAVNP
AAXRX
AAYCA
AAZKR
ABCQN
ABCUV
ABDBF
ABECW
ABEML
ABJNI
ABPVW
ABSOO
ACAHQ
ACBKW
ACCZN
ACDWB
ACGFS
ACHIS
ACHQT
ACPOU
ACSCC
ACUHS
ACXQS
ACYXD
ADBBV
ADEMA
ADEOM
ADIZJ
ADKYN
ADMGS
ADMHG
ADPSH
ADWTG
ADXAS
ADZMN
AEFGJ
AEGXH
AEHYH
AEIGN
AEIMD
AERNI
AEUYR
AEYWJ
AFBPY
AFEBI
AFFPM
AFGKR
AFKFF
AFWVQ
AFZJQ
AGHNM
AGXDD
AHBTC
AI.
AIDQK
AIDYY
AIHXW
AIURR
ALAGY
ALMA_UNASSIGNED_HOLDINGS
ALUQN
ALVPJ
AMBIC
AMBMR
AMYDB
ANBFE
ASTYK
AZBYB
AZVAB
BAFTC
BFHJK
BMXJE
BNVMJ
BQESF
BROTX
BRXPI
BY8
CAG
COF
CS3
D-C
D-D
D0S
DCZOG
DPXWK
DR2
DRFUL
DRSSH
DU5
EAD
EAP
EBS
EJD
EMK
ESX
F00
F01
F5P
FOMLG
G-S
G.N
G50
GODZA
H13
HGLYW
HVGLF
HZI
HZ~
H~9
IAO
ICJ
IEA
IOF
ITC
J0M
K48
LATKE
LC2
LC4
LEEKS
LH4
LITHE
LOXES
LP6
LP7
LPU
LUTES
LW6
LYRES
MEWTI
MK4
MRFUL
MRSSH
MSFUL
MSSSH
MUA
MUP
MUS
MVM
MXFUL
MXSSH
N04
N06
N9A
NF~
O66
O9-
OHT
OIG
OK1
P2P
P2W
P2Y
P4C
PAQYV
Q.N
Q11
QB0
R.K
RC9
ROL
RWL
RX1
RXW
SUPJJ
TAE
TN5
TUS
UB1
UHB
ULY
V8K
VH1
W8V
W99
WBKPD
WH7
WIH
WII
WMRSR
WOHZO
WQZ
WSUWO
WXSBR
XG1
XOL
YZZ
ZCG
ZY4
ZZTAW
~02
~IA
~KM
~WP
AAYXX
ABUFD
CITATION
O8X
ID FETCH-LOGICAL-c2732-cf8ac9cbdf8ce45a82c57a190b26c32094480185aeae4fc3efa37f9c4f1de2863
IEDL.DBID DRFUL
ISICitedReferencesCount 6
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000448171100005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0016-7363
IngestDate Sat Nov 29 04:13:22 EST 2025
Tue Nov 18 22:39:06 EST 2025
Wed Aug 20 07:26:25 EDT 2025
IsPeerReviewed true
IsScholarly true
Issue 4
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c2732-cf8ac9cbdf8ce45a82c57a190b26c32094480185aeae4fc3efa37f9c4f1de2863
PageCount 32
ParticipantIDs crossref_citationtrail_10_1111_gean_12152
crossref_primary_10_1111_gean_12152
wiley_primary_10_1111_gean_12152_GEAN12152
PublicationCentury 2000
PublicationDate October 2018
2018-10-00
PublicationDateYYYYMMDD 2018-10-01
PublicationDate_xml – month: 10
  year: 2018
  text: October 2018
PublicationDecade 2010
PublicationTitle Geographical analysis
PublicationYear 2018
References 2017; 62
2005; 19
2009; 41
2014; 2
2006; 46
2007; 140
2015; 188
2010; 157
2009
2017
1994
2015
2014
2008; 30
1996; 91
2007; 30
2016; 142
Blanchflower D. G. (e_1_2_8_3_1) 1994
e_1_2_8_17_1
LeSage J. P. (e_1_2_8_11_1) 2017
e_1_2_8_18_1
e_1_2_8_19_1
e_1_2_8_14_1
e_1_2_8_16_1
LeSage J. P. (e_1_2_8_13_1) 2009
e_1_2_8_2_1
e_1_2_8_5_1
e_1_2_8_4_1
e_1_2_8_7_1
e_1_2_8_6_1
e_1_2_8_9_1
e_1_2_8_8_1
LeSage J. P. (e_1_2_8_15_1) 2017
e_1_2_8_10_1
e_1_2_8_12_1
References_xml – year: 2009
– volume: 30
  start-page: 261
  issue: 1
  year: 2008
  end-page: 75
  article-title: The Sinkhorn–Knopp Algorithm: Convergence and Applications
  publication-title: SIAM Journal on Matrix Analysis and Applications
– volume: 142
  start-page: 1
  year: 2016
  end-page: 5
  article-title: Interpreting Heterogeneous Coefficient Spatial Autoregressive Panel Models
  publication-title: Economics Letters
– year: 2017
  article-title: Spatial Econometric Monte Carlo Studies: Raising the Bar
  publication-title: Empirical Economics.
– volume: 2
  start-page: 217
  issue: 4
  year: 2014
  end-page: 49
  article-title: The Biggest Myth in Spatial Econometrics
  publication-title: Econometrics
– volume: 46
  start-page: 507
  issue: 3
  year: 2006
  end-page: 15
  article-title: Estimation Problems in Models with Spatial Weight in Matrices Which have Blocks of Equal Elements
  publication-title: Journal of Regional Science
– volume: 140
  start-page: 190
  issue: 1
  year: 2007
  end-page: 214
  article-title: A Matrix Exponential Spatial Specification
  publication-title: Journal of Econometrics
– volume: 19
  start-page: 421
  issue: 3
  year: 2005
  end-page: 50
  article-title: The Last Word on the Wage Curve?
  publication-title: Journal of Economic Surveys
– volume: 157
  start-page: 34
  issue: 1
  year: 2010
  end-page: 52
  article-title: GMM Estimation of Spatial Autoregressive Models with Unknown Heteroskedasticity
  publication-title: Journal of Econometrics
– volume: 188
  start-page: 1
  issue: 1
  year: 2015
  end-page: 21
  article-title: Large Sample Properties of the Matrix Exponential Spatial Specification with an Application to FDI
  publication-title: Journal of Econometrics
– volume: 91
  start-page: 198
  issue: 433
  year: 1996
  end-page: 210
  article-title: The Matrix‐Logarithmic Covariance Model
  publication-title: Journal of the American Statistical Association
– volume: 62
  start-page: 46
  year: 2017
  end-page: 55
  article-title: A Bayesian Heterogeneous Coefficients Spatial Autoregressive Panel Data Model of Retail Fuel Duopoly Pricing
  publication-title: Regional Science and Urban Economics
– year: 2017
  article-title: A Bayesian Spatial Panel Model with Heterogeneous Coefficients
  publication-title: Regional Science and Urban Economics.
– year: 1994
– year: 2014
– year: 2015
– volume: 41
  start-page: 307
  issue: 3
  year: 2009
  end-page: 32
  article-title: Estimation Bias in Spatial Models with Strongly Connected Weight Matrices
  publication-title: Geographical Analysis
– volume: 30
  start-page: 173
  issue: 2
  year: 2007
  end-page: 91
  article-title: New Evidence on the Wage Curve: A Spatial Panel Approach
  publication-title: International Regional Science Review
– ident: e_1_2_8_17_1
  doi: 10.1016/j.jeconom.2009.10.035
– ident: e_1_2_8_14_1
  doi: 10.3390/econometrics2040217
– ident: e_1_2_8_12_1
  doi: 10.1016/j.jeconom.2006.09.007
– ident: e_1_2_8_4_1
  doi: 10.1080/01621459.1996.10476677
– ident: e_1_2_8_9_1
  doi: 10.1137/060659624
– volume-title: Introduction to Spatial
  year: 2009
  ident: e_1_2_8_13_1
– ident: e_1_2_8_2_1
  doi: 10.2139/ssrn.2623192
– ident: e_1_2_8_6_1
  doi: 10.1007/978-3-642-40340-8
– ident: e_1_2_8_10_1
  doi: 10.1016/j.econlet.2016.02.033
– ident: e_1_2_8_19_1
  doi: 10.1111/j.1538-4632.2009.00758.x
– ident: e_1_2_8_18_1
  doi: 10.1111/j.0950-0804.2005.00254.x
– year: 2017
  ident: e_1_2_8_11_1
  article-title: A Bayesian Spatial Panel Model with Heterogeneous Coefficients
  publication-title: Regional Science and Urban Economics.
– ident: e_1_2_8_7_1
  doi: 10.1177/0160017606298426
– ident: e_1_2_8_8_1
  doi: 10.1111/j.1467-9787.2006.00449.x
– volume-title: The Wage Curve
  year: 1994
  ident: e_1_2_8_3_1
– ident: e_1_2_8_5_1
  doi: 10.1016/j.jeconom.2015.02.046
– year: 2017
  ident: e_1_2_8_15_1
  article-title: Spatial Econometric Monte Carlo Studies: Raising the Bar
  publication-title: Empirical Economics.
– ident: e_1_2_8_16_1
  doi: 10.1016/j.regsciurbeco.2016.11.003
SSID ssj0002713
Score 2.2042737
Snippet We extend the heterogeneous coefficients spatial autoregressive panel model (HSAR) from Aquaro, Bailey, and Pesaran (2015) to the case of a heterogeneous...
SourceID crossref
wiley
SourceType Enrichment Source
Index Database
Publisher
StartPage 422
Title A Matrix Exponential Spatial Panel Model with Heterogeneous Coefficients
URI https://onlinelibrary.wiley.com/doi/abs/10.1111%2Fgean.12152
Volume 50
WOSCitedRecordID wos000448171100005&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVWIB
  databaseName: Wiley Online Library Full Collection 2020
  customDbUrl:
  eissn: 1538-4632
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002713
  issn: 0016-7363
  databaseCode: DRFUL
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://onlinelibrary.wiley.com
  providerName: Wiley-Blackwell
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB5KK-jFt1hfLOhFYQ_ZZJtd8FJqaw9ailjoLWwmuyqUpPQh9d-7m6S1ggjiKTnMkmWYmf1mmXwfwFWsRCKVQWpMaBuUxAtozLmmnht1RB-ZLMUmwl5PDIeyX4Hb5b8wBT_E6sLNZUZer12Cq3i6luQvWqU5N4ItwDVmAzeoQu3uqTN4WFViFhbyyBbW0NBv-CU9qZvk-Vr97UBaB6j5CdPZ-d_edmG7RJakWYTCHlR0ug-bpcj568cBdJvk0RHyL0h7Mc5SNyZk7Z0msXv2lf0ocdJoI-IuZ0nXDcpkNr50Np-SVqZzsgk3d3EIg077udWlpZACRYtOGEUjFEqMEyNQB1wJhjxUFgrErIE-sx2eI5ERXGmlA4O-NsoPjcTAeIlmouEfQTW1-zoGoqXtYYTi2tPCLkJpPC0TFXNEbjiGdbheejPCkmXciV2MomW34XwT5b6pw-XKdlxwa_xodZO7-heT6L7d7OVvJ38xPoUtC38KdlvvDKqzyVyfwwa-z96mk4symD4BNfbOIA
linkProvider Wiley-Blackwell
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEF6kFfTiW6zPgF4Ucshjm91jqa0R21Ckhd7CZrKrQklKH1L_vTvJtlYQQTwlh1myDDOz3yyT7yPkJhEs5UKBrVSgG5TU8e2EUmk7OOoIHrjciE0EUcSGQ94zszn4L0zJD7G6cMPMKOo1JjheSK9l-YsUWUGOoCtw1ddxRCukev_cHnRWpdgNSn1kjWvswKt7hp8UR3m-Vn87kdYRanHEtHf_ubk9smOwpdUog2GfbMjsgGwZmfPXj0MSNqwuUvIvrNZinGc4KKTtUZUYnz2hv2qhONrIwutZK8RRmVxHmMznU6uZy4JuAicvjsig3eo3Q9tIKdig8Ylrg2ICOCSpYiB9KpgLNBAaDCRuHTxX93hII8OokEL6CjyphBcoDr5yUumyundMKpne1wmxJNddDBNUOpLpRcCVI3kqEgpAFYWgRm6X7ozB8Iyj3MUoXvYb6Ju48E2NXK9sxyW7xo9Wd4WvfzGJH1qNqHg7_YvxFdkK-91O3HmMns7ItgZDJdetc04qs8lcXpBNeJ-9TSeXJrI-AZcy0hA
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEF6kFfXiW6zPBb0o5JDHJrvH0ocVayhiobewmeyqUJLSh9R_706S1goiiKfkMEuWYWZ2ZvnyfYRcx5InQmqwtA7MgJLYnhUzpiwboY7ggiNKsYkgDPlgIHolNgf_hSn4IZYXbpgZeb3GBFejRK9k-YuSaU6OYCpw1WPCN3lZbT61-91lKXaCQh_Z9DVW4PpuyU-KUJ6v1d9OpNUONT9i2jv_3Nwu2S57S1ovgmGPrKl0n2yWMuevHwekU6ePSMk_p635KEsRKGTsUZUYnz1pvkpRHG1I8XqWdhAqk5kIU9lsQhuZyukmEHlxSPrt1nOjY5VSChaY_sSxQHMJAuJEc1Aek9wBFkjTDMSOD65jZjykkeFMKqk8Da7S0g20AE_biXK47x6RSmr2dUyoEmaK4ZIpW3GzCIS2lUhkzACYZhDUyM3CnRGUPOModzGMFvMG-ibKfVMjV0vbUcGu8aPVbe7rX0yiu1Y9zN9O_mJ8STZ6zXbUvQ8fTsmW6YUKqlv7jFSm45k6J-vwPn2bjC_KwPoEZabRiw
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Matrix+Exponential+Spatial+Panel+Model+with+Heterogeneous+Coefficients&rft.jtitle=Geographical+analysis&rft.au=LeSage%2C+James&rft.au=Chih%2C+Yao%E2%80%90Yu&rft.date=2018-10-01&rft.issn=0016-7363&rft.eissn=1538-4632&rft.volume=50&rft.issue=4&rft.spage=422&rft.epage=453&rft_id=info:doi/10.1111%2Fgean.12152&rft.externalDBID=10.1111%252Fgean.12152&rft.externalDocID=GEAN12152
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0016-7363&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0016-7363&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0016-7363&client=summon