Causalidad. Aportes a la econometría espacial

Résumé

This study has approached the analysis of spatial causality for a cross-section of data. We aimed to provide an operative concept in space, suggesting a series of steps for its empirical testing. Those steps were developed based on both parametric and non-parametric approaches. In order to establish a definition of spatial causality, we analyzed different philosophical and economic thoughts so to clarify the concept. As our interest lies in spatial econometrics, where there is no control over study variables, it is natural to consider the inferential process approach as the most appropriate proposal (Granger, 1969; Sims, 1980). Under this general approach, our proposal contemplates a definition of causality that makes emphases on the concept of incremental informative content. Intuitively, it establishes that causality means that: the cause variable provides additional information about the effect variable. In a parametric context, Chapter 3, this measure of information content led us to the concepts of sample variance and forecast error. As stated by Granger (1980), a variable will be causal if it contains unique information about the effect variable. As a result, the cause variable must help us to explain, or forecast better, the effect variable (in terms of lower variance or mean absolute error). Chapter 4 considered a broader definition of information content. The key concept in this case is the term information in the sense of numerical quantity that captures the uncertainty in the result of an experiment to be conducted. This definition makes direct reference to the entropy of a given information set. The main contribution of our study was the provision of an operative concept of spatial causality and a strategy capable of detecting it empirically. Alternative procedures or tests were included in each step of the strategy. These procedures may be useful also in other fields, not only for causal analysis. With regards to the problem of selecting a weighting matrix, there is only one formal test in the literature, the J-test. This step was enriched with the Conditional Entropy procedure, capable of detecting the correct order and the number of neighbours even with non-linear relationships. We presented an alternative to the Bivariate Moran test in the form of a Lagrange Multiplier, LM(i). In a non-linear case, the non-parametric Psi(1) test performs quite well for intra- and inter-dependence. Depending on the characteristics of the spatial distribution of the data, an asymptotic or a bootstrapped version of the Psi(1) test can be used. The alternative bootstrapped version, Psi(2), also provides a second option for the detection of dependence between variables. Detection of spatial dependence leads us to the final step of the procedure, where we try to detect the direction of the information flow between the variables. We propose three alternatives: in the parametric case, a Lagrange Multiplier, LM(NC), and a Granger-like iterative predictive approach; and in the non-parametric case, the DELTA test. The predictive approach presents severe limitations and it is not capable of detecting causality in space. The performance of the LM(NC) test is acceptable under specific conditions (linearity is the most stringent). When these conditions change, the power of the test falls drastically. The DELTA non-parametric test meets the adequate conditions required to detect direction in information between spatial variables.