Essays on inference in weakly identified models in macroeconomics and finance

This dissertation is concerned with the implications of weak identification in macroeconomics and finance: the risks of making spurious inferences, strategies for valid inference, and their economic implications. In the first essay I show that the standard estimation and t-test in the GARCH(1,1) model are spurious when the GARCH effect is weakly identified, implying strong and significant persistence of volatility when in fact there is little. This spurious inference is partly attributed to the severely under-estimated standard error for the estimated GARCH effect. A strategy for valid inference is suggested and seems to give robust results for this case. In my second essay I derive an analytical asymptotic variance matrix for the GARCH(1,1) Maximum Likelihood Estimator and show that the Zero-Information-Limit Condition (ZILC) of Nelson and Startz (2007) holds, accounting for spuriously large t-statistics. In the third essay I propose a general approach to valid inference in weakly identified models based on a common linear approximation and show that this general test strategy succeeds in obtaining a correct size in the presence of weak identification. In the fourth essay I apply this valid test to evaluate a recent resolution of the equity premium puzzle based on a high level of persistence in consumption growth. My results find little empirical evidence in support of this resolution.