Abstract
The difficulties caused by the lack of stability in the parameters of an econometric model are well known: biased and inconsistent estimators, misleading tests and, in general, wrong inference. Their importance explains the attention that the literature has dedicated to the problem. The first formal test of parameter stability is that of Chow (1960), which considers only one break point, known a priori, under the assumption of constant variances. Dufour (1982) extends the discussion to the case of multiple regimes and Phillips and Ploberger (1994) and Rossi (2005) place it in a context of model selection. Simultaneously, Quandt (1960) started another line of research in which the break point is unknown and the variance can change. The CUSUM test, based on recursive residuals (Brown et al. 1975), the various methods for endogenizing the choice of the break point (as in Banerjee et al. 1992), and the extension to multiple structural changes in a system of equations (Qu and Perron 2007) are natural proposals in this line. Other more peculiar approaches include the tests for continuous parameter variation (Hansen 1996), the Markov switching regression (García and Perron 1996) and the Bayesian approaches (e.g., Salazar 1982; Zivot and Phillips and Ploberger 1994; Koop and Potter 2007).
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Notes
- 1.
For simplicity, we suppose that this capacity of interaction only depends on one factor, although the discussion can be generalized to the case of p variables.
- 2.
If ρ were zero in (11), the R2 coefficient of the corresponding OLS regression should oscillate around 0.9.
- 3.
The tables of estimated power for the cases just described have not been included for reasons of length but are available from the authors upon request.
- 4.
If the function were linear and the model were well specified, the local estimators would be unbiased, as is the case with the LWR or GWR estimation.
- 5.
An additional source of bias is that we are not using the original, global, W weighting matrix but specify the corresponding local weighting matrix, W r (m) for each local system of estimation.
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Acknowledgements
This work has been carried out with the financial support of project SEJ2006–02328/ECON of the Ministerio de Ciencia y Tecnología of the Reino de España.
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López, F., Mur, J., Angulo, A. (2010). Local Estimation of Spatial Autocorrelation Processes. In: Páez, A., Gallo, J., Buliung, R., Dall'erba, S. (eds) Progress in Spatial Analysis. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03326-1_6
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