We extend the local-to-zero analysis of models with weak instruments to models with estimated instruments and regressors and with higher-order dependence between instruments and disturbances. This framework is applicable to linear models with expectation variables that are estimated nonparametrically, such as the risk-return tradeoff in finance and the effect of inflation uncertainty on real economic activity. Our simulation evidence suggests that Lagrange multiplier confidence intervals have better coverage in these models. We apply these methods to excess returns on the S&P 500 index, yen-dollar spot returns, and excess holding yields between 6-month and 3-month Treasury bills.

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