This paper analyzes the properties of standard estimators, tests, and confidence sets (CS's) for parameters that are unidentified or weakly identified in some parts of the parameter space. The paper also introduces methods to make the tests and CS's robust to such identification problems. The results apply to a class of extremum estimators and corresponding tests and CS's that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification. This covers a class of models estimated using maximum likelihood (ML), least squares (LS), quantile, generalized method of moments, generalized empirical likelihood, minimum distance, and semi-parametric estimators. The consistency/lack-of-consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions. The asymptotic sizes (in a uniform sense) of standard and identification-robust tests and CS's are established. The results are applied to the ARMA(1, 1) time series model estimated by ML and to the nonlinear regression model estimated by LS. In companion papers, the results are applied to a number of other models.

We combine personnel records of the United States federal bureaucracy from 1997 to 2019 with administrative voter registration data to study how ideological alignment between politicians and bureaucrats affects turnover and performance. We document significant partisan cycles and turnover among political appointees. By contrast, we find no political cycles in the civil service. At any point in time, a sizable share of bureaucrats is ideologically misaligned with their political leaders. We study the performance implications of this misalignment for the case of procurement officers. Exploiting presidential transitions as a source of “within‐bureaucrat” variation in political alignment, we find that procurement contracts overseen by misaligned officers exhibit greater cost overruns and delays. We provide evidence consistent with a general “morale effect,” whereby misaligned bureaucrats are less motivated to pursue the organizational mission. Our results thus help to shed some of the first light on the costs of ideological misalignment within public organizations.

This paper shows that robust inference under weak identification is important to the evaluation of many influential macro asset pricing models, including (time‐varying) rare‐disaster risk models and long‐run risk models. Building on recent developments in the conditional inference literature, we provide a novel conditional specification test by simulating the critical value conditional on a sufficient statistic. This sufficient statistic can be intuitively interpreted as a measure capturing the macroeconomic information decoupled from the underlying content of asset pricing theories. Macro‐finance decoupling is an effective way to improve the power of the specification test when asset pricing theories are difficult to refute because of a severe imbalance in the information content about the key model parameters between macroeconomic moment restrictions and asset pricing cross‐equation restrictions. We apply the proposed conditional specification test to the evaluation of a time‐varying rare‐disaster risk model and the construction of robust model uncertainty sets.