IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i11p1276-d567401.html
   My bibliography  Save this article

A Review of Software for Spatial Econometrics in R

Author

Listed:
  • Roger Bivand

    (Department of Economics, Norwegian School of Economics, 5045 Bergen, Norway
    These authors contributed equally to this work.)

  • Giovanni Millo

    (Generali Investments, 34132 Trieste, Italy
    These authors contributed equally to this work.)

  • Gianfranco Piras

    (Department of Economics, School of Arts and Sciences, The Catholic University of America, Washington, DC 20064, USA
    Department of Economics, University ‘Gabriele d’Annunzio’, 66100 Chieti-Pescara, Italy
    These authors contributed equally to this work.)

Abstract

The software for spatial econometrics available in the R system for statistical computing is reviewed. The methods are illustrated in a historical perspective, highlighting the main lines of development and employing historically relevant datasets in the examples. Estimators and tests for spatial cross-sectional and panel models based either on maximum likelihood or on generalized moments methods are presented. The paper is concluded reviewing some current active lines of research in spatial econometric software methods.

Suggested Citation

  • Roger Bivand & Giovanni Millo & Gianfranco Piras, 2021. "A Review of Software for Spatial Econometrics in R," Mathematics, MDPI, vol. 9(11), pages 1-40, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1276-:d:567401
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/11/1276/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/11/1276/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2008. "Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large," Journal of Econometrics, Elsevier, vol. 146(1), pages 118-134, September.
    2. Roberto Patuelli & Norbert Schanne & Daniel A. Griffith & Peter Nijkamp, 2012. "Persistence Of Regional Unemployment: Application Of A Spatial Filtering Approach To Local Labor Markets In Germany," Journal of Regional Science, Wiley Blackwell, vol. 52(2), pages 300-323, May.
    3. Jan Mutl & Michael Pfaffermayr, 2011. "The Hausman test in a Cliff and Ord panel model," Econometrics Journal, Royal Economic Society, vol. 14, pages 48-76, February.
    4. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    5. Suesse, Thomas, 2018. "Marginal maximum likelihood estimation of SAR models with missing data," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 98-110.
    6. Roger Bivand, 2002. "Spatial econometrics functions in R: Classes and methods," Journal of Geographical Systems, Springer, vol. 4(4), pages 405-421, December.
    7. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    8. M. Hashem Pesaran, 2021. "General diagnostic tests for cross-sectional dependence in panels," Empirical Economics, Springer, vol. 60(1), pages 13-50, January.
    9. Baltagi, Badi H. & Liu, Long, 2011. "Instrumental variable estimation of a spatial autoregressive panel model with random effects," Economics Letters, Elsevier, vol. 111(2), pages 135-137, May.
    10. Kelejian, Harry H. & Prucha, Ingmar R., 2004. "Estimation of simultaneous systems of spatially interrelated cross sectional equations," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 27-50.
    11. Manfred M. Fischer & Arthur Getis (ed.), 2010. "Handbook of Applied Spatial Analysis," Springer Books, Springer, number 978-3-642-03647-7, November.
    12. Anselin, Luc & Bera, Anil K. & Florax, Raymond & Yoon, Mann J., 1996. "Simple diagnostic tests for spatial dependence," Regional Science and Urban Economics, Elsevier, vol. 26(1), pages 77-104, February.
    13. Guanpeng Dong & Jing Ma & Richard Harris & Gwilym Pryce, 2016. "Spatial Random Slope Multilevel Modeling Using Multivariate Conditional Autoregressive Models: A Case Study of Subjective Travel Satisfaction in Beijing," Annals of the American Association of Geographers, Taylor & Francis Journals, vol. 106(1), pages 19-35, January.
    14. Baltagi, Badi H. & Egger, Peter & Pfaffermayr, Michael, 2007. "Estimating models of complex FDI: Are there third-country effects?," Journal of Econometrics, Elsevier, vol. 140(1), pages 260-281, September.
    15. Baltagi, Badi H. & Heun Song, Seuck & Cheol Jung, Byoung & Koh, Won, 2007. "Testing for serial correlation, spatial autocorrelation and random effects using panel data," Journal of Econometrics, Elsevier, vol. 140(1), pages 5-51, September.
    16. Kelley Pace, R. & LeSage, James P., 2008. "A spatial Hausman test," Economics Letters, Elsevier, vol. 101(3), pages 282-284, December.
    17. Michel Goulard & Thibault Laurent & Christine Thomas-Agnan, 2017. "About predictions in spatial autoregressive models: optimal and almost optimal strategies," Spatial Economic Analysis, Taylor & Francis Journals, vol. 12(2-3), pages 304-325, July.
    18. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2021. "Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 18-44, January.
    19. Luc Anselin & Nancy Lozano-Gracia, 2009. "Errors in variables and spatial effects in hedonic house price models of ambient air quality," Studies in Empirical Economics, in: Giuseppe Arbia & Badi H. Baltagi (ed.), Spatial Econometrics, pages 5-34, Springer.
    20. Harry Kelejian & Gianfranco Piras, 2020. "Spillover effects in spatial models: Generalizations and extensions," Journal of Regional Science, Wiley Blackwell, vol. 60(3), pages 425-442, June.
    21. Umlauf, Nikolaus & Adler, Daniel & Kneib, Thomas & Lang, Stefan & Zeileis, Achim, 2015. "Structured Additive Regression Models: An R Interface to BayesX," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i21).
    22. Badi H. Baltagi, 2021. "Simultaneous Equations with Error Components," Springer Texts in Business and Economics, in: Econometric Analysis of Panel Data, edition 6, chapter 0, pages 157-186, Springer.
    23. Millo, Giovanni, 2014. "Maximum likelihood estimation of spatially and serially correlated panels with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 914-933.
    24. Millo, Giovanni & Piras, Gianfranco, 2012. "splm: Spatial Panel Data Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i01).
    25. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    26. Patrick Sevestre & Laszlo Matyas, 2008. "The Econometrics of Panel Data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00279977, HAL.
    27. Wagner Martin & Zeileis Achim, 2019. "Heterogeneity and Spatial Dependence of Regional Growth in the EU: A Recursive Partitioning Approach," German Economic Review, De Gruyter, vol. 20(1), pages 67-82, February.
    28. Debarsy, Nicolas & Ertur, Cem, 2010. "Testing for spatial autocorrelation in a fixed effects panel data model," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 453-470, November.
    29. Gianfranco Piras, 2013. "Efficient GMM Estimation of a Cliff and Ord Panel Data Model with Random Effects," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 370-388, September.
    30. Elhorst, J. Paul & Lacombe, Donald J. & Piras, Gianfranco, 2012. "On model specification and parameter space definitions in higher order spatial econometric models," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 211-220.
    31. Federico Belotti & Gordon Hughes & Andrea Piano Mortari, 2017. "Spatial panel-data models using Stata," Stata Journal, StataCorp LP, vol. 17(1), pages 139-180, March.
    32. Giovanni Millo & Gaetano Carmeci, 2011. "Non-life insurance consumption in Italy: a sub-regional panel data analysis," Journal of Geographical Systems, Springer, vol. 13(3), pages 273-298, September.
    33. Klier, Thomas & McMillen, Daniel P, 2008. "Clustering of Auto Supplier Plants in the United States," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 460-471.
    34. Cornwell, Christopher & Trumbull, William N, 1994. "Estimating the Economic Model of Crime with Panel Data," The Review of Economics and Statistics, MIT Press, vol. 76(2), pages 360-366, May.
    35. Pesaran, M. Hashem & Smith, Ron, 1995. "Estimating long-run relationships from dynamic heterogeneous panels," Journal of Econometrics, Elsevier, vol. 68(1), pages 79-113, July.
    36. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2013. "A Generalized Spatial Panel Data Model with Random Effects," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 650-685, August.
    37. Giovanni Millo & Giacomo Pasini, 2010. "Does Social Capital Reduce Moral Hazard? A Network Model for Non-Life Insurance Demand," Fiscal Studies, Institute for Fiscal Studies, vol. 31(3), pages 341-372, September.
    38. Elhorst, J. Paul, 2008. "Serial and spatial error correlation," Economics Letters, Elsevier, vol. 100(3), pages 422-424, September.
    39. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    40. Croissant, Yves & Millo, Giovanni, 2008. "Panel Data Econometrics in R: The plm Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i02).
    41. Lee, Lung-fei & Yu, Jihai, 2010. "A Spatial Dynamic Panel Data Model With Both Time And Individual Fixed Effects," Econometric Theory, Cambridge University Press, vol. 26(2), pages 564-597, April.
    42. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    43. David M. Drukker & Ingmar Prucha & Rafal Raciborski, 2013. "A command for estimating spatial-autoregressive models with spatial-autoregressive disturbances and additional endogenous variables," Stata Journal, StataCorp LP, vol. 13(2), pages 287-301, June.
    44. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    45. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    46. Bivand, Roger & Piras, Gianfranco, 2015. "Comparing Implementations of Estimation Methods for Spatial Econometrics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i18).
    47. Thomas Suesse, 2018. "Estimation of spatial autoregressive models with measurement error for large data sets," Computational Statistics, Springer, vol. 33(4), pages 1627-1648, December.
    48. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
    49. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    50. Croissant, Yves & Millo, Giovanni, 2008. "Panel Data Econometrics in R: The plm Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i02).
    51. Baltagi, Badi H. & Song, Seuck Heun & Koh, Won, 2003. "Testing panel data regression models with spatial error correlation," Journal of Econometrics, Elsevier, vol. 117(1), pages 123-150, November.
    52. Baltagi, Badi H. & Liu, Long, 2008. "Testing for random effects and spatial lag dependence in panel data models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3304-3306, December.
    53. Roger Bivand & Albrecht Gebhardt, 2000. "Implementing functions for spatial statistical analysis using the language," Journal of Geographical Systems, Springer, vol. 2(3), pages 307-317, September.
    54. David M. Drukker & Hua Peng & Ingmar Prucha & Rafal Raciborski, 2013. "Creating and managing spatial-weighting matrices with the spmat command," Stata Journal, StataCorp LP, vol. 13(2), pages 242-286, June.
    55. Lung‐fei Lee & Jihai Yu, 2012. "Spatial Panels: Random Components Versus Fixed Effects," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(4), pages 1369-1412, November.
    56. James P. LeSage, 2014. "What Regional Scientists Need to Know about Spatial Econometrics," The Review of Regional Studies, Southern Regional Science Association, vol. 44(1), pages 13-32, Spring.
    57. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1, July-Dece.
    58. J. Paul Elhorst, 2014. "Dynamic Spatial Panels: Models, Methods and Inferences," SpringerBriefs in Regional Science, in: Spatial Econometrics, edition 127, chapter 0, pages 95-119, Springer.
    59. Helene Roth & Stefan Lang & Helga Wagner, 2015. "Random intercept selection in structured additive regression models," Working Papers 2015-02, Faculty of Economics and Statistics, Universität Innsbruck.
    60. Viliam Druska & William C. Horrace, 2004. "Generalized Moments Estimation for Spatial Panel Data: Indonesian Rice Farming," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(1), pages 185-198.
    61. Daniel P. McMillen, 2003. "Spatial Autocorrelation Or Model Misspecification?," International Regional Science Review, , vol. 26(2), pages 208-217, April.
    62. Guanpeng Dong & Richard Harris & Kelvyn Jones & Jianhui Yu, 2015. "Multilevel Modelling with Spatial Interaction Effects with Application to an Emerging Land Market in Beijing, China," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-18, June.
    63. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    64. Daniel A. Griffith, 2003. "Spatial Autocorrelation and Spatial Filtering," Advances in Spatial Science, Springer, number 978-3-540-24806-4, Fall.
    65. Li, Hongfei & Calder, Catherine A. & Cressie, Noel, 2012. "One-step estimation of spatial dependence parameters: Properties and extensions of the APLE statistic," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 68-84.
    66. J. Paul Elhorst, 2003. "Specification and Estimation of Spatial Panel Data Models," International Regional Science Review, , vol. 26(3), pages 244-268, July.
    67. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    68. David M. Drukker & Ingmar Prucha & Rafal Raciborski, 2013. "Maximum likelihood and generalized spatial two-stage least-squares estimators for a spatial-autoregressive model with spatial-autoregressive disturbances," Stata Journal, StataCorp LP, vol. 13(2), pages 221-241, June.
    69. J. Elhorst, 2010. "Applied Spatial Econometrics: Raising the Bar," Spatial Economic Analysis, Taylor & Francis Journals, vol. 5(1), pages 9-28.
    70. Harry Kelejian & George Tavlas & George Hondroyiannis, 2006. "A Spatial Modelling Approach to Contagion Among Emerging Economies," Open Economies Review, Springer, vol. 17(4), pages 423-441, December.
    71. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    72. Tony Smith & Ka Lee, 2012. "The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach," Journal of Geographical Systems, Springer, vol. 14(1), pages 91-124, January.
    73. Piras, Gianfranco, 2010. "sphet: Spatial Models with Heteroskedastic Innovations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i01).
    74. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    75. Daniel P. McMillen, 2013. "Quantile Regression for Spatial Data," SpringerBriefs in Regional Science, Springer, edition 127, number 978-3-642-31815-3, March.
    76. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gianfranco Piras & Mauricio Sarrias, 2023. "Heterogeneous spatial models in R: spatial regimes models," Journal of Spatial Econometrics, Springer, vol. 4(1), pages 1-32, December.
    2. Kozo Kiyota, 2023. "Spatially uneven pace of deindustrialisation within a country," The World Economy, Wiley Blackwell, vol. 46(7), pages 2187-2230, July.
    3. Charlotte J. Alster & Allycia Laar & Jordan P. Goodrich & Vickery L. Arcus & Julie R. Deslippe & Alexis J. Marshall & Louis A. Schipper, 2023. "Quantifying thermal adaptation of soil microbial respiration," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    4. Chalermpong, Saksith & Ratanawaraha, Apiwat & Anuchitchanchai, Ornicha, 2023. "Motorcycle taxis' varying degrees of complementarity and substitution with public transit in Bangkok," Journal of Transport Geography, Elsevier, vol. 108(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Millo, Giovanni, 2014. "Maximum likelihood estimation of spatially and serially correlated panels with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 914-933.
    2. Debarsy, Nicolas & Ertur, Cem, 2010. "Testing for spatial autocorrelation in a fixed effects panel data model," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 453-470, November.
    3. Álvarez, Inmaculada C. & Barbero, Javier & Zofío, José L., 2017. "A Panel Data Toolbox for MATLAB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i06).
    4. Harry H. Kelejian & Gianfranco Piras, 2013. "A J-Test for Panel Models with Fixed Effects, Spatial and Time," Working Papers Working Paper 2013-03, Regional Research Institute, West Virginia University.
    5. repec:rri:wpaper:201303 is not listed on IDEAS
    6. Su, Liangjun & Yang, Zhenlin, 2015. "QML estimation of dynamic panel data models with spatial errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 230-258.
    7. Harry H. Kelejian & Gianfranco Piras, 2016. "A J test for dynamic panel model with fixed effects, and nonparametric spatial and time dependence," Empirical Economics, Springer, vol. 51(4), pages 1581-1605, December.
    8. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
    9. Bivand, Roger & Piras, Gianfranco, 2015. "Comparing Implementations of Estimation Methods for Spatial Econometrics," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i18).
    10. Luc Anselin, 2010. "Thirty years of spatial econometrics," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 3-25, March.
    11. Gianfranco Piras, 2013. "Efficient GMM Estimation of a Cliff and Ord Panel Data Model with Random Effects," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 370-388, September.
    12. Harald Badinger & Peter Egger, 2015. "Fixed Effects and Random Effects Estimation of Higher-order Spatial Autoregressive Models with Spatial Autoregressive and Heteroscedastic Disturbances," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(1), pages 11-35, March.
    13. Herrera Gómez, Marcos, 2017. "Fundamentos de Econometría Espacial Aplicada [Fundamentals of Applied Spatial Econometrics]," MPRA Paper 80871, University Library of Munich, Germany.
    14. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2021. "Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 18-44, January.
    15. J. Paul Elhorst, 2014. "Dynamic Spatial Panels: Models, Methods and Inferences," SpringerBriefs in Regional Science, in: Spatial Econometrics, edition 127, chapter 0, pages 95-119, Springer.
    16. Lina Lu, 2017. "Simultaneous Spatial Panel Data Models with Common Shocks," Supervisory Research and Analysis Working Papers RPA 17-3, Federal Reserve Bank of Boston.
    17. Giuseppe Arbia, 2011. "A Lustrum of SEA: Recent Research Trends Following the Creation of the Spatial Econometrics Association (2007--2011)," Spatial Economic Analysis, Taylor & Francis Journals, vol. 6(4), pages 377-395, July.
    18. Millo, Giovanni & Piras, Gianfranco, 2012. "splm: Spatial Panel Data Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 47(i01).
    19. Zhang, Yuanqing & Sun, Yanqing, 2015. "Estimation of partially specified dynamic spatial panel data models with fixed-effects," Regional Science and Urban Economics, Elsevier, vol. 51(C), pages 37-46.
    20. Pesaran, M. Hashem & Tosetti, Elisa, 2011. "Large panels with common factors and spatial correlation," Journal of Econometrics, Elsevier, vol. 161(2), pages 182-202, April.
    21. repec:asg:wpaper:1013 is not listed on IDEAS
    22. Giovanni Millo, 2022. "The generalized spatial random effects model in R," Journal of Spatial Econometrics, Springer, vol. 3(1), pages 1-18, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1276-:d:567401. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.