Statistical methods for causality analysis and non-regular inference problems

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In this program, I intend to pursue research on a wide array of topics relevant to statistical inference for models useful in economics and finance.******The topics considered include the following ones.******A. Causality analysis in both static and non-dynamic models, with the view of distinguishing between total, direct and indirect effects, as well short-run and long-run effects.***B. Inference on models with missing explanatory variables***C. Inference for various “non-regular” problems, where usual asymptotic distributional theory is not applicable, including problems where identification or usual rank assumptions may fail.***D. Volatility analysis in financial data.***E. Goodness-of-fit tests in the presence of serial dependence.******From finite-sample and asymptotic methods will be used, with an emphasis on bound approaches and simulation-based inference.***Inference on “causality” from observed data is a central issue in many statistical studies, especially if the results are meant to be used for decision making. This problem can be quite challenging when data come from observational studies, in contrast with experimental studies, because interactions between explanatory variables cannot be controlled. Indeed, this difficulty is common in economic and financial data, but also in other areas where non-experimental data are used (e.g., sociology, epidemiology). “Feedbacks” and delayed effects may be present and should be taken into account when drawing conclusions. In particular, it is important to distinguish between direct, indirect and total effects. ***I intend to pursue research on these problems in the context of both static and dynamic models. For non-dynamic setups, both regression and simultaneous equation models will be considered. In the regression case, the general objective consists in allowing for interaction between explanatory variables, in view of testing and measuring direct, indirect and total effects. This work will involve developing both formal mathematical concepts and the relevant statistical theory, to analyze total, direct and indirect effects. For this purpose, I argue that studying inference on regression with missing or mismeasured explanatory variables constitute a useful intermediate statistical problem. Both finite-sample and asymptotic bounds will be proposed in this context. This approach will also be carried to linear and nonlinear structural equation models, popular in econometrics. ***Time series data provide information on dynamic interactions along with time delays. In dynamic models, which are widely used in macroeconomics and finance, the notion of causality at different horizons (Dufour and Renault, 1998, Econometrica) will be extended with the view of measuring direct and indirect “impulse response coefficients”. Both linear multivariate time series models and nonlinear ones will be considered.*****