Identification, estimation and inference of nonlinear dynamic causal effects in macroeconometrics

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This research proposal studies the identification and estimation of nonlinear impulse response functions (IRFs). While structural linear vector autoregressive (VAR) models are often used to compute IRFs, linear models are too simple to properly describe the complex data generating processes that characterize the relationship among macroeconomic variables. For instance, they do not accommodate the possibility that the IRF is asymmetric, depending on the sign of the shock. In order to capture nonlinearities, we need to move beyond the standard linear VAR model and consider nonlinear variations of this model. The existing literature has considered two main classes of models: (i) linear models that include regressors that are censored or otherwise nonlinearly transformed, and (ii) nonlinear VAR models, which include models with state dependence where the effect of a shock, for example, may depend on whether the economy is in recession or not. A popular example is the smooth transition VAR model, where the parameters are allowed to change from one regime to the next. My goal in this research project is to propose new estimation and inference methods for nonlinear impulse response functions derived from these structural dynamic models. I will first derive closed-form expressions for the IRFs implied by the class of models in (i). The effect of a structural shock on a target variable will be measured by the difference between two sample paths for this variable: a perturbed path where the economy is subject to a shock and a benchmark path without the shock. In linear models, this difference is constant and identifies the linear IRF. In models with nonlinearities, it depends on the current and future values of the shock sequence. I will consider both an unconditional IRF (which integrates out these shocks) and a conditional IRF, where the expectation is conditional on a given history of the process. The second goal will be to propose a new plug-in estimator of the IRF, based on the sample analogue of the closed-form expression obtained for the IRF. Finally, I will propose bootstrap confidence intervals for the IRF, based on the newly proposed plug-in estimator. For a nonlinear VAR model, no closed-form expression exists unless we assume strong conditions on the conditional distribution of the error terms. Therefore, Monte Carlo Integration (MCI) methods are appealing in this context. These amount to a bootstrap-based estimator of the IRF, based on resampling from the estimated structural model. My first goal will be to show the consistency of the MCI estimator, a result that is lacking in the literature. The second goal is to extend the applicability of the bootstrap for inference on the nonlinear IRF based on the MCI estimator. This will require a double bootstrap and I will explore fast versions of this method. Finally, in the third part of this proposal, I will consider variations of the popular local projection approach to estimating nonlinear IRFs.