Beschreibung:
<jats:title>Abstract</jats:title><jats:p>The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/obes12144-math-0001.png" xlink:title="urn:x-wiley:03059049:media:obes12144:obes12144-math-0001" />‐norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/obes12144-math-0002.png" xlink:title="urn:x-wiley:03059049:media:obes12144:obes12144-math-0002" />‐norm regularization with a regularized parameter <jats:italic>O</jats:italic>(<jats:italic>n</jats:italic>) allows us to obtain the Rothenberg (1984) type of higher‐order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter <jats:italic>O</jats:italic>(<jats:italic>n</jats:italic>), which is used as a standardized factor in the higher‐order approximation. We also show that the proposed <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/obes12144-math-0003.png" xlink:title="urn:x-wiley:03059049:media:obes12144:obes12144-math-0003" />‐norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.</jats:p>