Efficient estimation of the semiparametric spatial autoregressive model

Abstract

Efficient semiparametric and parametric estimates are developed for a spatial autoregressive model, containing nonstochastic explanatory variables and innovations suspected to be non-normal. The main stress is on the case of distribution of unknown, nonparametric, form, where series nonparametric estimates of the score function are employed in adaptive estimates of parameters of interest. These estimates are as efficient as ones based on a correct form, in particular they are more efficient than pseudo-Gaussian maximum likelihood estimates at non-Gaussian distributions. Two different adaptive estimates are considered. One entails a stringent condition on the spatial weight matrix, and is suitable only when observations have substantially many "neighbours". The other adaptive estimate relaxes this requirement, at the expense of alternative conditions and possible computational expense. A Monte Carlo study of finite sample performance is included. JEL Classifications: C13; C14; C21

On spatial processes and asymptotic inference under near-epoch dependence

“…These models have been used widely in applications. For recent contributions on estimation strategies for these models see, e.g., Robinson (2010, 2009), Kelejian and Prucha (2010, 2007, 2004), and Lee (2007, 2004). The second example is linear infinite moving average (MA(∞)) random fields.…”

“… 2 For recent contributions see, e.g., Robinson (2010, 2009), Yu, de Jong and Lee (2008), Kelejian and Prucha (2010, 2007, 2004), Lee (2007, 2004), and Chen and Conley (2001). …”

The Future of Spatial Econometrics

“…Such procedures typically require the estimation of an asymptotic variance using a procedure that accounts for the spatial dependence (e.g., Pinkse et al, 2006; Kelejian and Prucha, 2007), of which the new and attractive procedure of Bester et al (2009) is both the most ambitious and requires the strongest assumptions. One can even achieve the semiparametric efficiency bound (Robinson, 2009b) and improve the higher‐order properties of estimators in such models (Iglesias and Phillips, 2008), much like in the case of i.i.d. data, e.g., Robinson (1987) and Newey and Smith (2004), respectively.…”

Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances

“…Contributions to the theoretical econometric literature include, e.g., Baltagi and Li (2004, 2001a,b), Baltagi, Song, Jung and Koh (2007), Baltagi, Song and Koh (2003), Bao and Ullah (2007), Conley (1999), Das, Kelejian and Prucha (2003), Driscol and Kraay (1998), Kapoor, Kelejian and Prucha (2007), Kelejian and Prucha (2007a, 2004, 2002, 2001, 1999, 1998), Korniotis (2005), Lee (2007a,b, 2004, 2003, 2002), Pinkse and Slade (1998), Pinkse, Slade, and Brett (2002), Robinson (2007a,b), Su and Yang (2007). …”