The weak-instruments problem in factor models
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This study considers the instrumental variable estimation of factor models. Specifically, we investigate the weak-instruments problem, which is not well investigated in the literature, in detail. We show that the signal-to-noise ratios, which are defined by the variance ratios of the common components to the errors, of the scaling variable and the instruments mainly determine the strength of instruments in a confirmatory factor model, while the structure of the factor loading is closely related to the strength of instruments in an explanatory factor model. By Monte Carlo simulation, we confirm that the simulation results are consistent with the theoretical implications, and Stock and Yogo test is useful in practice in detecting the weak instruments.
The author is grateful to two reviewers for helpful comments. The author also acknowledges the financial support from the Grant-in-Aid for Scientific Research (KAKENHI 25780153, 15H01943, 16H03606, 17KK0070) provided by the JSPS.
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