Econometric essays on model selection and inference using combined testing and shrinkage estimation

This thesis develops and applies advanced estimation techniques that combine multiple identification principles or leverage statistical evidence across observational units to enhance variable selection and inference for parametric models. Emphasis is placed on shrinkage estimation. The analysis focuses on longitudinal data, especially on distinguishing unit roots from mean-reverting time series. Chapter 2 introduces information-enriched weighting of the regressor used for unit root inference in adaptive Lasso estimation of autoregressions. By incorporating additional evidence on the stochastic order of the data, the approach improves model selection performance. The asymptotic properties of this modified Lasso estimator are derived, with particular attention to the stochastic properties of the Lasso solution path. The theoretical results of Chapter 2 underpin a novel, tuning-free significance testing principle based on the Lasso path, proposed in Chapter 3. This method bridges adaptively ℓ1 -penalised model selection with unit root testing in autoregressions. Chapter 4 addresses the challenges of heteroskedastic and autocorrelated empirical processes by proposing a sieve wild bootstrap algorithm that makes the inference procedures from Chapter 3 robust, ensuring accurate size under a general class of error processes. Chapter 5 contributes to the panel unit root literature by introducing an autoregressive wild bootstrap algorithm for meta-analytical unit root tests, enabling robust inference under time-varying volatility and dynamic cross-dependence. Chapter 6 applies Bayesian hierarchical models that leverage information from data-rich observational units to improve inference for units with sparse information via shrinkage. The developed methods are applied to a range of empirical questions with economic, environmental, and societal relevance. These include modelling inflation rates, testing for trends in house price dynamics, analysing convergence in environmental indicators such as groundwater levels and CO₂ emissions, as well as estimating penalty conversion abilities in professional football.