# research

## 2024

- Locally robust inference for non-Gaussian linear simultaneous equations models
*Adam Lee*, and Geert Mesters*Journal of Econometrics*, 2024All parameters in linear simultaneous equations models can be identified (up to permutation and sign) if the underlying structural shocks are independent and at most one of them is Gaussian. Unfortunately, existing inference methods that exploit such identifying assumptions suffer from size distortions when the true distributions of the shocks are close to Gaussian. To address this weak non-Gaussian problem we develop a locally robust semi-parametric inference method which is simple to implement, improves coverage and retains good power properties. The finite sample properties of the methodology are illustrated in a large simulation study and an empirical study for the returns to schooling.

- Locally Robust Inference for Non-Gaussian SVAR models
*Quantitative Economics*, 2024All parameters in structural vector autoregressive (SVAR) models are locally identified when the structural shocks are independent and follow non-Gaussian distributions. Unfortunately, standard inference methods that exploit such features of the data for identification fail to yield correct coverage for structural functions of the model parameters when deviations from Gaussianity are small. To this extent, we propose a locally robust semi-parametric approach to conduct hypothesis tests and construct confidence sets for structural functions in SVAR models. The methodology fully exploits non-Gaussianity when it is present, but yields correct size / coverage for local-to-Gaussian densities. Empirically we revisit two macroeconomic SVAR studies where we document mixed results. For the oil price model of Kilian and Murphy (2012) we find that non-Gaussianity can robustly identify reasonable confidence sets, whereas for the labour supply-demand model of Baumeister and Hamilton (2015) this is not the case. Moreover, these exercises highlight the importance of using weak identification robust methods to assess estimation uncertainty when using non-Gaussianity for identification.

- Working PaperLocally Regular and Efficient Tests in Non-Regular Semiparametric Models
*Adam Lee*2024This paper considers hypothesis testing in semiparametric models which may be non-regular. I show that C(α) style tests are locally regular under mild conditions, including in cases where locally regular estimators do not exist, such as models which are weakly identified. I characterise the appropriate limit experiment in which to study local (asymptotic) optimality of tests in the non-regular case, permitting the generalisation of classical power bounds to this case. I give conditions under which these power bounds are attained by the proposed C(α) style tests. The application of the theory to a single index model and an instrumental variables model is worked out in detail.

- Working PaperRobust Estimation and Inference for Time-varying Unconditional Volatility2024Submitted
We derive a unified and general framework for estimation and inference in a large class of parametric models of time-varying unconditional volatility of financial return, both univariate and multivariate. A large number of well-known and widely used specifications, for many of which asymptotic results have not been specifically established, are contained in the class. Our framework is based on the multivariate equation-by-equation version of the Gaussian Quasi Maximum Likelihood Estimator (QMLE). An attractive property of the estimator is its ease of implementation, since the equation-by-equation nature reduces the curse of dimensionality associated with multivariate methods. Another attractive property is that the exact specification of the conditional volatility dynamics need not be known or estimated. Nevertheless, a model of conditional volatility can be estimated in a second step. In particular, we show that the (scaled) GARCH(1,1) specification is well-defined under both correct and incorrect specification within our framework. Due to the assumptions we rely upon, our results extend directly to the Multiplicative Error Model (MEM) interpretation of volatility models. So our results can also be applied to other non-negative processes like volume, duration, realised volatility, dividends, unemployment and so on. Finally, three numerical applications illustrate our results.