"If we knew what it was we were doing, it would not be called research, would it?" ~Albert Einstein
Research Award
Paul W. Boltz Fellowship, University of Illinois at Urbana Champaign, 2021. Awarded to "attract, motivate, and reward graduate students in economics who show exceptional promise for careers in academia or business."
Research Projects
1.Specification Testing under General Nesting Spatial Model, Job Market paper [Draft ]
Abstract: Three decades ago Anselin et al. (1996) was unceremoniously published in the Regional Science and Urban Economics (RSUE) journal that literally changed the landscape of testing spatial regression models. By our last count, it has been cited by around 2,500 papers in applied spatial econometrics out of which more than 1,000 papers have explicitly used it's testing tool as the principal model selection technique. The crux of the paper was to identify the source of spatial dependence: lag and/or error. Since then much water has flown through the field of spatial econometrics. Over the last 28 years another source of dependence, namely the Durbin specification that takes account of the exogenous interaction effects among the cross-sectional units (locations) has become very popular in the econometrics literature. Elhorst (2017) pointed out that conducting statistical tests while ignoring the Durbin term may spuriously lead to strong evidence in favor of interaction effects among the dependent variable or among the error terms. He further cautioned that the tests in Anselin et al. (1996) or the analogous ones developed for the spatial panel set up in Elhorst (2010) may not be very helpful in finding the right model as they do not account for the exogenous interaction effects. In this paper, we generalize Anselin et al. (1996) by including the Durbin specification and attempt to identify the three main sources of spatial dependence, namely, lag, error and Durbin. Additionally, we propose non-nested tests to select between two competing spatial models, both of which take account of the exogenous interaction effect. This work can also be viewed as an extension of Koley and Bera (2023) that took account of lag and Durbin terms, but did not consider the spatial error dependence. We believe that the diagnostic checks and the non-nested model selection methodology suggested in this paper will be useful additions to the toolbox of spatial econometricians.
2. To Use, or Not to Use the Spatial Durbin Model?-- that is the Question, Spatial Economic Analysis [pdf]
Abstract: Spatial Durbin model (SDM) is one of the most widely used models in spatial econometrics. It originated as a generalization of the spatial error model (SEM) under a non-linear parametric restriction [see Anselin (1988, pp.110-111). This restriction should be tested to select an appropriate model between SDM and SEM. Perhaps, due to the complexity of executing a test for a non-linear hypothesis, this restriction is rarely tested in practice, though see Burridge (1981), Mur and Angulo (2006) and LeSage and Pace (2009, p.164). This paper considers an alternative linear hypothesis to test the suitability of the SDM. To achieve this, we first use Rao's score (RS) testing principle and then Bera and Yoon (1993) methodology to robustify the original RS tests. The robust tests that require only ordinary least squares (OLS) estimation are able to identify the specific source(s) of departure(s) from the baseline simple linear regression model. An extensive Monte Carlo study provides evidence that our suggested tests posses excellent finite sample properties, both in terms of size and power. Our empirical illustrations with two real data sets attest that the tests developed in this paper could be very useful in judging the suitability of the SDM for the spatial data in hand.
3. Testing for Spatial Dependence in a Spatial Autoregressive (SAR) Model in the Presence of Endogenous Regressors , Journal of Spatial Econometrics 3(1), 2022. [pdf]
Abstract: Spatial modeling is one of the growing areas of research in economics in recent years. However, these models are not tested enough. Even if tests are performed, they are done in a piece-wise fashion. Another age-long problem in economic modeling is endogeneity of one or more variables. Endogeneity is caused due to a number of reasons one of which is simultaneous modeling of economic variables. This paper considers specification testing in the context of a spatial autoregresive (SAR) model with an endogenous regressor. First, we construct standard Rao's score (RS) tests for null hypothesis of the absence of spatial autocorrelation and endogeneity. These standard RS tests are invalid in the presence of local misspecification of the models under the alternative hypotheses. Therefore, in our next step, we develop adjusted tests using the technique of Bera and Yoon (1993), that are robust to local misspecification. These adjusted (or robustified) tests are simple to calculate and easy to implement. With a Monte Carlo study we investigate the finite sample performance of all the proposed tests, and the results confirm that the robust tests perform better compared to their non-robust counterparts both in terms of size and power.
4. A History of the Delta Method and Some New Results, Sankhya B, the Indian journal of Statistics, 2023. [pdf]
Abstract: Use of the delta method in statistics and econometrics is ubiquitous. Its mention can be found in almost all advanced statistics and econometrics textbooks but mostly without any reference. It appears that nobody knows for certain when the first paper on the topic was published or how the idea was first conceived. A seemingly unrelated method to find the asymptotic variance of a statistic involving one or more nuisance parameters was given by Pierce (1982). In the first part of the paper a comprehensive review of the delta method is presented with the objective of unearthing its history. In the second part a comparative analytic study of the delta method with the Pierce method is presented.