Basics of Spatial Interdepence in Theory and Practice

Laron Williams, University of Missouri


Spatial econometric models have grown in popularity in the social sciences over the last two decades, especially as scholars grapple with estimating models that match the spatial complexity of their theories. This five-day course is designed to provide students with the tools necessary to understand and use spatial econometric models.  It prepares students to carefully theorize about these spatial processes, specify the appropriate models and more effectively test theoretical expectations about patterns of spatial interdependence.

We begin the course by exploring how prominent theories of social science (e.g., policy diffusion, party competition, civil war spillovers, etc) argue that the processes of nearby or similar units are related.  In the second day we focus on issues of model specification that are unique to these models; this includes correctly specifying the manner in which the units (i.e., individuals, states, countries, etc) are spatially related, and whether the spatial interdependence occurs among variables, the errors, or the outcome itself.  The third day emphasizes how to estimate a variety of cross-sectional spatial econometric models.  The fourth day introduces a variety of spatial econometric models to deal with spatial heterogeneity and dependence across time and space.  In the final day, we explore graphical and tabular techniques to provide meaningful quantities of interest from these models.  Students are encouraged to develop their own research questions about spatial processes and to bring their own data sets.  In the afternoon sessions, students will use Stata and R to apply the concepts discussed in the lectures to their own research questions.



This course runs January 21-25, 2019.

Teaching Fellow: Flávio Souza, Texas A&M University


Day 1: Spatial dependence in theory and practice

This introductory seminar provides an overview of the uses of spatial econometric models in the social sciences, and discusses how these models get us closer to our causal models of politically interdependent outcomes.

Day 2: Identifying neighbors

The work horse of spatial econometric models is the W matrix, which specifies the manner in which all the observations are connected.  This lecture explores the variety of options for specifying the weights matrices.  We will discuss strategies for determining the appropriate patterns of interconnectedness, whether scholars begin with a strong theoretical foundation or the desire to maximize model fit.  While most scholars focus on geographic patterns of interdependence, we discuss a range of other means of identifying how neighboring units are socially, politically and economically interdependent. 

Day 3: Specifying and estimating spatial econometric models

There are a variety of models in the broad family of spatial econometrics, and a useful categorization divides the spatially interdependent processes based on whether the spatial interdependence occurs in the observables, unobservables and/or outcomes.  Most theories provide some insight that guides this decision; a range of tests can assert whether the theory is supported.  This lecture introduces a series of tests that will detect different patterns of spatial interdependence.  Moreover, we will explore how to connect the causal relationships in one’s theory to some basic spatial econometric models including the spatial lag, spatial error and spatial-X models.  We explore a variety of techniques used to estimate a simple class of spatial econometric models including OLS, MLE and two-stage least squares.

Day 4: Spatial dependence in a time-series cross-section world

The simple class of spatial econometric models introduced in the previous day serves as a useful foundation for understanding basic spatial dependence across units.  Since these models are relatively simple, they cannot handle the additional obstacles that arise in time-series cross-sectional data.  This lecture introduces a variety of modifications to these simple models that incorporate both spatial heterogeneity and temporal dependence. 

Day 5: Visualizing and depicting spatial dependence

A recent trend in the social sciences centers on providing meaningful and easy-to-interpret quantities of interest from one’s model.  This is particularly important in spatial econometric models because outcomes are often simultaneously determined with significant feedback, and/or are spatially dependent on factors occurring in nearby units.  Due to these factors, simply providing the coefficients in a table provides little insight to readers beyond the sign and statistical significance.  This lecture demonstrates how to calculate and provide visual depictions of substantive effects from a variety of spatial econometric models.


A full-semester graduate-level course in multiple regression analysis and a background in simple mathematics and statistics (including probability distributions, random variables, and hypothesis tests).  A strong familiarity with Stata and R are helpful, though not required. This is the second course in a two-week spatial module.  It is strongly encouraged that students also take the first week’s class, “Introduction to Spatial Data” with Jonathan Phillips.



Online Applications will be received starting May, 2019.
Applications are due by October, 2019.
Notifications of acceptances will be sent by the end of October, 2019.
Applicants must pay the registration fee by November, 2019.