Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model
In this paper, the spatial dynamic panel data (SDPD) model is extended to the single-index spatial dynamic panel data (Si-SDPD) model by introducing a nonlinear connection function to reflect the interaction between explanatory variables. The Si-SDPD model not only retains the advantages of the para...
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| Format: | Article |
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MDPI AG
2023-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/13/2947 |
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| author | Mengqi Zhang Boping Tian |
| author_facet | Mengqi Zhang Boping Tian |
| author_sort | Mengqi Zhang |
| collection | DOAJ |
| description | In this paper, the spatial dynamic panel data (SDPD) model is extended to the single-index spatial dynamic panel data (Si-SDPD) model by introducing a nonlinear connection function to reflect the interaction between explanatory variables. The Si-SDPD model not only retains the advantages of the parametric SDPD model in dealing with spatial and temporal interaction effects and spatio-temporal dependencies, but also solves the limitations of the parametric SDPD model that may lead to missed bias. It reduces the data dimension of non-parametric models and enhances the practicability and explanatory power of parametric models. Since the parts of the model to be estimated contain unknown functions, we propose a new estimation method, a profile maximum likelihood (PML) method, to solve the problem of incidental parameters in the estimation. Under the assumption that the spatial coefficients are known, we preliminarily estimate the unknown function by carrying out local polynomial estimation, so as to transform the model into the parametric form for solving purposes. We then solve the dynamic panel parametric model via quasi-maximum likelihood (QML) estimation. We derive the asymptotic properties of profile maximum likelihood estimators (PMLEs) and find that, under certain regularity conditions, both parametric and non-parametric estimators are consistent. Monte Carlo results show that PMLEs have good finite sample performance. |
| first_indexed | 2024-03-11T01:35:04Z |
| format | Article |
| id | doaj.art-47445ef084aa4c78be9390b4ebed9f72 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T01:35:04Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-47445ef084aa4c78be9390b4ebed9f722023-11-18T17:03:37ZengMDPI AGMathematics2227-73902023-07-011113294710.3390/math11132947Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data ModelMengqi Zhang0Boping Tian1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaIn this paper, the spatial dynamic panel data (SDPD) model is extended to the single-index spatial dynamic panel data (Si-SDPD) model by introducing a nonlinear connection function to reflect the interaction between explanatory variables. The Si-SDPD model not only retains the advantages of the parametric SDPD model in dealing with spatial and temporal interaction effects and spatio-temporal dependencies, but also solves the limitations of the parametric SDPD model that may lead to missed bias. It reduces the data dimension of non-parametric models and enhances the practicability and explanatory power of parametric models. Since the parts of the model to be estimated contain unknown functions, we propose a new estimation method, a profile maximum likelihood (PML) method, to solve the problem of incidental parameters in the estimation. Under the assumption that the spatial coefficients are known, we preliminarily estimate the unknown function by carrying out local polynomial estimation, so as to transform the model into the parametric form for solving purposes. We then solve the dynamic panel parametric model via quasi-maximum likelihood (QML) estimation. We derive the asymptotic properties of profile maximum likelihood estimators (PMLEs) and find that, under certain regularity conditions, both parametric and non-parametric estimators are consistent. Monte Carlo results show that PMLEs have good finite sample performance.https://www.mdpi.com/2227-7390/11/13/2947profile maximum likelihoodnonparametric estimationspatial dynamic panel datasingle-index panel model |
| spellingShingle | Mengqi Zhang Boping Tian Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model Mathematics profile maximum likelihood nonparametric estimation spatial dynamic panel data single-index panel model |
| title | Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model |
| title_full | Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model |
| title_fullStr | Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model |
| title_full_unstemmed | Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model |
| title_short | Profile Maximum Likelihood Estimation of Single-Index Spatial Dynamic Panel Data Model |
| title_sort | profile maximum likelihood estimation of single index spatial dynamic panel data model |
| topic | profile maximum likelihood nonparametric estimation spatial dynamic panel data single-index panel model |
| url | https://www.mdpi.com/2227-7390/11/13/2947 |
| work_keys_str_mv | AT mengqizhang profilemaximumlikelihoodestimationofsingleindexspatialdynamicpaneldatamodel AT bopingtian profilemaximumlikelihoodestimationofsingleindexspatialdynamicpaneldatamodel |