
Notes: Monte carlo experiments based on 2000 replications. Solid line:
1. | Instituto Interdisciplinario de Economía Política de Buenos Aires, (IIEP-BAIRES-UBA)-CONICET, Facultad de Ciencias Económicas, Universidad de Buenos Aires, Av. Córdoba 2122 2do piso, C1120AAQ, Ciudad Autónoma de Buenos Aires, Argentina |
2. | Banco Central de la República Argentina and Universidad Nacional de La Plata |
This paper develops a subgraph network random effects error components structure for network data to perform analysis of variance. In particular, it proposes a model for evaluating the network interdependence of nodes attributes allowing for edge and triangle specific components. The latter serve as a basal model for modeling more general network effects. Consistent estimators of the variance components and Lagrange Multiplier specification tests for evaluating the appropriate model of random components in networks structures is proposed. Monte Carlo simulations show that the tests have good performance in finite samples. The proposed tests is applied to the unsecured (Call) interbank market network in Argentina.
[1] |
D. Acemoglu, A. Ozdaglar and A. Tahbaz-Salehi,
Systemic risk and stability in financial networks, American Economic Review, 105 (2015), 564-608.
doi: 10.3386/w18727. |
[2] |
P. Angelini, A. Nobili and C. Picillo,
The interbank market after August 2007: What has changed and why?, Journal of Money, Credit and Banking, 43 (2011), 923-958.
|
[3] |
L. Anselin, A. Bera, R. Florax and M. Yoon,
Simple diagnostic tests for spatial dependence, Regional Science and Urban Economics, 26 (1996), 77-104.
doi: 10.1016/0166-0462(95)02111-6. |
[4] |
L. Bargigli, G. di Iasio, L. Infante, F. Lillo and F. Pierobon,
The multiplex structure of interbank networks, Quantitative Finance, 15 (2015), 673-691.
doi: 10.1080/14697688.2014.968356. |
[5] |
S. Battiston, M. Puliga, R. Kaushik, P. Tasca and G. Caldarelli, Debtrank: Too central to fail? Financial networks, the fed and systemic risk, Scientific Reports, 2.
doi: 10.1038/srep00541. |
[6] |
M. L. Bech, J. T. E. Chapman and R. J. Garratt, Which bank is the central bank?, Journal of Monetary Economics, 57.
doi: 10.1016/j.jmoneco.2010.01.002. |
[7] |
A. Bera and Y. Bilias,
Rao's score, Neyman's $c(\alpha)$ and Silvey's lm tests: An essay on historical developments and some new results, Journal of Statistical Planning and Inference, 97 (2001), 9-44.
doi: 10.1016/S0378-3758(00)00343-8. |
[8] |
A. Bera, G. Montes-Rojas and W. Sosa-Escudero,
General specification testing with locally misspecified models, Econometric Theory, 26 (2010), 1838-1845.
doi: 10.1017/S0266466609990818. |
[9] |
A. Bera, G. Montes-Rojas and W. Sosa-Escudero,
A new robust and most powerful test in the presence of local misspecification, Communications in Statistics - Theory and Methods, 46 (2017), 8187-8198.
doi: 10.1080/03610926.2016.1177077. |
[10] |
A. Bera and M. Yoon,
Specification testing with locally misspecified alternatives, Econometric Theory, 9 (1993), 649-658.
doi: 10.1017/S0266466600008021. |
[11] |
G. G. Booth, U. G. Gurun and H. Zhang,
Financial networks and trading in bond markets, Journal of Financial Markets, 18 (2014), 126-157.
doi: 10.1016/j.finmar.2013.08.001. |
[12] |
A. G. Chandrasekhar, Econometrics of network formation, in The Oxford Handbook of the Economics of Networks, Oxford University Press, Oxford, 2016.
![]() |
[13] |
A. de Paula, Econometrics of network models, CEMMAP Working Paper CWP52/15, (2017). |
[14] |
S. de Raco and V. Semeshenko,
Labor mobility and industrial space in Argentina, Journal of Dynamics & Games, 6 (2019), 107-118.
doi: 10.3934/jdg.2019008. |
[15] |
B. S. Graham, Network data, NBER Working Paper 26577, (2019). |
[16] |
H. H. Kelejian and I. R. Prucha,
A generalized moments estimator for the autoregressive parameter in a spatial model, International Economic Review, 40 (1999), 509-533.
doi: 10.1111/1468-2354.00027. |
[17] |
H. H. Kelejian and I. R. Prucha,
Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances, Journal of Econometrics, 157 (2010), 53-67.
doi: 10.1016/j.jeconom.2009.10.025. |
[18] |
Y. Kumagai,
Social networks and global transactions, Journal of Dynamics & Games, 6 (2019), 211-219.
doi: 10.3934/jdg. |
[19] |
S. Langfield, Z. Liu and T. Ota,
Mapping in the UK interbank system, Journal of Banking & Finance, 45 (2014), 288-303.
|
[20] |
J.-L. Molina-Borboa, S. Martinez-Jaramillo, F. Lopez-Gallo and M. van der Leij,
A multiplex network analysis of the mexican banking system: Link persistence, overlap and waiting times, Journal of Network Theory in Finance, 1 (2015), 99-138.
doi: 10.21314/JNTF.2015.006. |
[21] |
S. Poledna, J. L. Molina-Borboa, S. Martínez-Jaramillo, M. van der Leij and S. Thurner,
The multi-layer network nature of systemic risk and its implications for the costs of financial crises, Journal of Financial Stability, 20 (2015), 70-81.
doi: 10.1016/j.jfs.2015.08.001. |
[22] |
A. Temizsoy, G. Iori and G. Montes-Rojas,
The role of bank relationship in the interbank market, Journal of Economic Dynamics & Control, 59 (2015), 118-141.
doi: 10.1016/j.jedc.2015.07.008. |
[23] |
A. Temizsoy, G. Iori and G. Montes-Rojas,
Network centrality and funding rates in the e-mid interbank market, Journal of Financial Stability, 33 (2017), 346-365.
doi: 10.1016/j.jfs.2016.11.003. |
[24] |
C. Upper,
Simulation methods to assess the danger of contagion in interbank markets, Journal of Financial Stability, 7 (2011), 111-125.
doi: 10.1016/j.jfs.2010.12.001. |
show all references
[1] |
D. Acemoglu, A. Ozdaglar and A. Tahbaz-Salehi,
Systemic risk and stability in financial networks, American Economic Review, 105 (2015), 564-608.
doi: 10.3386/w18727. |
[2] |
P. Angelini, A. Nobili and C. Picillo,
The interbank market after August 2007: What has changed and why?, Journal of Money, Credit and Banking, 43 (2011), 923-958.
|
[3] |
L. Anselin, A. Bera, R. Florax and M. Yoon,
Simple diagnostic tests for spatial dependence, Regional Science and Urban Economics, 26 (1996), 77-104.
doi: 10.1016/0166-0462(95)02111-6. |
[4] |
L. Bargigli, G. di Iasio, L. Infante, F. Lillo and F. Pierobon,
The multiplex structure of interbank networks, Quantitative Finance, 15 (2015), 673-691.
doi: 10.1080/14697688.2014.968356. |
[5] |
S. Battiston, M. Puliga, R. Kaushik, P. Tasca and G. Caldarelli, Debtrank: Too central to fail? Financial networks, the fed and systemic risk, Scientific Reports, 2.
doi: 10.1038/srep00541. |
[6] |
M. L. Bech, J. T. E. Chapman and R. J. Garratt, Which bank is the central bank?, Journal of Monetary Economics, 57.
doi: 10.1016/j.jmoneco.2010.01.002. |
[7] |
A. Bera and Y. Bilias,
Rao's score, Neyman's $c(\alpha)$ and Silvey's lm tests: An essay on historical developments and some new results, Journal of Statistical Planning and Inference, 97 (2001), 9-44.
doi: 10.1016/S0378-3758(00)00343-8. |
[8] |
A. Bera, G. Montes-Rojas and W. Sosa-Escudero,
General specification testing with locally misspecified models, Econometric Theory, 26 (2010), 1838-1845.
doi: 10.1017/S0266466609990818. |
[9] |
A. Bera, G. Montes-Rojas and W. Sosa-Escudero,
A new robust and most powerful test in the presence of local misspecification, Communications in Statistics - Theory and Methods, 46 (2017), 8187-8198.
doi: 10.1080/03610926.2016.1177077. |
[10] |
A. Bera and M. Yoon,
Specification testing with locally misspecified alternatives, Econometric Theory, 9 (1993), 649-658.
doi: 10.1017/S0266466600008021. |
[11] |
G. G. Booth, U. G. Gurun and H. Zhang,
Financial networks and trading in bond markets, Journal of Financial Markets, 18 (2014), 126-157.
doi: 10.1016/j.finmar.2013.08.001. |
[12] |
A. G. Chandrasekhar, Econometrics of network formation, in The Oxford Handbook of the Economics of Networks, Oxford University Press, Oxford, 2016.
![]() |
[13] |
A. de Paula, Econometrics of network models, CEMMAP Working Paper CWP52/15, (2017). |
[14] |
S. de Raco and V. Semeshenko,
Labor mobility and industrial space in Argentina, Journal of Dynamics & Games, 6 (2019), 107-118.
doi: 10.3934/jdg.2019008. |
[15] |
B. S. Graham, Network data, NBER Working Paper 26577, (2019). |
[16] |
H. H. Kelejian and I. R. Prucha,
A generalized moments estimator for the autoregressive parameter in a spatial model, International Economic Review, 40 (1999), 509-533.
doi: 10.1111/1468-2354.00027. |
[17] |
H. H. Kelejian and I. R. Prucha,
Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances, Journal of Econometrics, 157 (2010), 53-67.
doi: 10.1016/j.jeconom.2009.10.025. |
[18] |
Y. Kumagai,
Social networks and global transactions, Journal of Dynamics & Games, 6 (2019), 211-219.
doi: 10.3934/jdg. |
[19] |
S. Langfield, Z. Liu and T. Ota,
Mapping in the UK interbank system, Journal of Banking & Finance, 45 (2014), 288-303.
|
[20] |
J.-L. Molina-Borboa, S. Martinez-Jaramillo, F. Lopez-Gallo and M. van der Leij,
A multiplex network analysis of the mexican banking system: Link persistence, overlap and waiting times, Journal of Network Theory in Finance, 1 (2015), 99-138.
doi: 10.21314/JNTF.2015.006. |
[21] |
S. Poledna, J. L. Molina-Borboa, S. Martínez-Jaramillo, M. van der Leij and S. Thurner,
The multi-layer network nature of systemic risk and its implications for the costs of financial crises, Journal of Financial Stability, 20 (2015), 70-81.
doi: 10.1016/j.jfs.2015.08.001. |
[22] |
A. Temizsoy, G. Iori and G. Montes-Rojas,
The role of bank relationship in the interbank market, Journal of Economic Dynamics & Control, 59 (2015), 118-141.
doi: 10.1016/j.jedc.2015.07.008. |
[23] |
A. Temizsoy, G. Iori and G. Montes-Rojas,
Network centrality and funding rates in the e-mid interbank market, Journal of Financial Stability, 33 (2017), 346-365.
doi: 10.1016/j.jfs.2016.11.003. |
[24] |
C. Upper,
Simulation methods to assess the danger of contagion in interbank markets, Journal of Financial Stability, 7 (2011), 111-125.
doi: 10.1016/j.jfs.2010.12.001. |
Notes: Monte carlo experiments based on 2000 replications. Solid line:
Notes: Monte carlo experiments based on 2000 replications. Solid line:
Notes: Monte carlo experiments based on 2000 replications. Solid line:
Notes: Monte carlo experiments based on 2000 replications. Solid line:
Note: P-values in log-scale. Dashed line is the 10% critical value and dotted line to the 5% critical values. Horizontal axis corresponds to joint test for edge and triangle effects (LMµ, δ). Vertical axis corresponds to Moran's Ⅰ LM tests for spatial error.
Note: P-values in log-scale. Dashed line is the 10% critical value and dotted line to the 5% critical values. Horizontal axis corresponds to tests for edge effects (LMµ). Vertical axis corresponds to tests for triangle effects (LMδ).
Note: P-values in log-scale. Dashed line is the 10% critical value and dotted line to the 5% critical values. Horizontal axis corresponds to tests for edge effects robust to triangle effects (LMµ(δ)). Vertical axis corresponds to tests for triangle effects robust to edge effects (LMδ(µ)).
N | LMµ | LMδ | LMµ,δ | LMµ(δ) | LMδ(µ) | LMδ−µ |
Erdös-Rényi random graph | ||||||
Size 1% | ||||||
100 | 0.009 | 0.016 | 0.0145 | 0.009 | 0.0165 | 0.0115 |
225 | 0.012 | 0.0115 | 0.015 | 0.013 | 0.012 | 0.009 |
400 | 0.013 | 0.012 | 0.0085 | 0.0095 | 0.0075 | 0.007 |
Size 5% | ||||||
100 | 0.043 | 0.05 | 0.0465 | 0.042 | 0.052 | 0.041 |
225 | 0.052 | 0.0485 | 0.0495 | 0.052 | 0.0495 | 0.041 |
400 | 0.047 | 0.0475 | 0.049 | 0.046 | 0.046 | 0.0435 |
Size 10% | ||||||
100 | 0.082 | 0.0885 | 0.0855 | 0.089 | 0.092 | 0.0765 |
225 | 0.1045 | 0.092 | 0.102 | 0.098 | 0.0995 | 0.0875 |
400 | 0.089 | 0.087 | 0.093 | 0.0965 | 0.099 | 0.0915 |
Spatial queen structure | ||||||
Size 1% | ||||||
100 | 0.0115 | 0.0105 | 0.0105 | 0.01 | 0.011 | 0.0115 |
225 | 0.0075 | 0.0065 | 0.012 | 0.0145 | 0.0135 | 0.014 |
400 | 0.0085 | 0.0085 | 0.0095 | 0.012 | 0.011 | 0.011 |
Size 5% | ||||||
100 | 0.0475 | 0.0515 | 0.047 | 0.048 | 0.044 | 0.046 |
225 | 0.045 | 0.039 | 0.0565 | 0.0595 | 0.052 | 0.0525 |
400 | 0.046 | 0.0465 | 0.049 | 0.0535 | 0.049 | 0.0505 |
Size 10% | ||||||
100 | 0.0965 | 0.0975 | 0.0955 | 0.094 | 0.09 | 0.097 |
225 | 0.0965 | 0.09 | 0.1 | 0.1085 | 0.1115 | 0.1125 |
400 | 0.0935 | 0.0965 | 0.098 | 0.096 | 0.0995 | 0.1015 |
Notes: Monte carlo experiments based on 2000 replications. |
N | LMµ | LMδ | LMµ,δ | LMµ(δ) | LMδ(µ) | LMδ−µ |
Erdös-Rényi random graph | ||||||
Size 1% | ||||||
100 | 0.009 | 0.016 | 0.0145 | 0.009 | 0.0165 | 0.0115 |
225 | 0.012 | 0.0115 | 0.015 | 0.013 | 0.012 | 0.009 |
400 | 0.013 | 0.012 | 0.0085 | 0.0095 | 0.0075 | 0.007 |
Size 5% | ||||||
100 | 0.043 | 0.05 | 0.0465 | 0.042 | 0.052 | 0.041 |
225 | 0.052 | 0.0485 | 0.0495 | 0.052 | 0.0495 | 0.041 |
400 | 0.047 | 0.0475 | 0.049 | 0.046 | 0.046 | 0.0435 |
Size 10% | ||||||
100 | 0.082 | 0.0885 | 0.0855 | 0.089 | 0.092 | 0.0765 |
225 | 0.1045 | 0.092 | 0.102 | 0.098 | 0.0995 | 0.0875 |
400 | 0.089 | 0.087 | 0.093 | 0.0965 | 0.099 | 0.0915 |
Spatial queen structure | ||||||
Size 1% | ||||||
100 | 0.0115 | 0.0105 | 0.0105 | 0.01 | 0.011 | 0.0115 |
225 | 0.0075 | 0.0065 | 0.012 | 0.0145 | 0.0135 | 0.014 |
400 | 0.0085 | 0.0085 | 0.0095 | 0.012 | 0.011 | 0.011 |
Size 5% | ||||||
100 | 0.0475 | 0.0515 | 0.047 | 0.048 | 0.044 | 0.046 |
225 | 0.045 | 0.039 | 0.0565 | 0.0595 | 0.052 | 0.0525 |
400 | 0.046 | 0.0465 | 0.049 | 0.0535 | 0.049 | 0.0505 |
Size 10% | ||||||
100 | 0.0965 | 0.0975 | 0.0955 | 0.094 | 0.09 | 0.097 |
225 | 0.0965 | 0.09 | 0.1 | 0.1085 | 0.1115 | 0.1125 |
400 | 0.0935 | 0.0965 | 0.098 | 0.096 | 0.0995 | 0.1015 |
Notes: Monte carlo experiments based on 2000 replications. |
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