Nonparametric instrumental variable derivative estimation

Estimation of firm‐level productivity in the presence of exports: Evidence from China's manufacturing

“…In this paper, we adopt an alternative Landweber–Fridman regularization technique, with its primary appeal being that it is iterative, thereby not requiring direct inversion of a large‐dimensional matrix , which is of particular importance to us given large values that n takes in our application. Recent applications of the Landweber–Fridman regularization include Centorrino (), Centorrino et al (), Florens et al (), and Centorrino et al ().The sample analogue of the identifying equation (Equation ) is which defines the estimator of ψ as a solution of this large‐dimensional system of equation. In light of the ill‐posed inverse problem, the system in Equation is expected to be almost singular in the finite sample, which is why we are to regularize it.To obtain consistent estimates of r , and to be used in Equation , we employ series regressions.…”

“…Effectively, c controls the size of an iterative step with the larger values resulting in fewer but coarser iterations and, in contrast, values close to 0 yielding small iterative updates, which, however, may require an impractically long computational time. Following Florens et al (), we set c =0.5 to balance computational speed and precision. Also, to improve over the mean squared error of in the finite sample, we follow Centorrino et al's advice and update L n and J n for the estimation of operators and at each iteration.…”

“…In this paper, we adopt an alternative Landweber–Fridman regularization technique, with its primary appeal being that it is iterative, thereby not requiring direct inversion of a large‐dimensional matrix , which is of particular importance to us given large values that n takes in our application. Recent applications of the Landweber–Fridman regularization include Centorrino (), Centorrino et al (), Florens et al (), and Centorrino et al ().…”

Additive Nonparametric Instrumental Regressions: A Guide to Implementation

“…However, Florens and Racine (2012) have shown that smoothing parameters for T and T * could be updated at every iteration step in equation 15and that this procedure seems to improve over the mean squared error of the estimator in finite samples. 7 Therefore, we proceed as follows: (i) From our estimators of the r, T and T * , discussed above, we construct the initial conditionφ 0 = cT * r .…”

“…Tuning of the latter parameter constitutes an additional layer of complication, and it has to be tackled with the appropriate methods. Data-driven techniques for the choice of regularization parameter in the framework of nonparametric instrumental regressions are presented in: Breunig and Johannes (2015), Centorrino (2015), Chen and Christensen (2015), Fève and Florens (2010), Florens and Racine (2012), Horowitz (2014a) and Liu and Tao (2014). 2 These works, however, focus on a specific regularization scheme and there is not, to the best of our knowledge, a paper which gives empirical researchers a broad picture about regularization frameworks that can be used in the context of nonparametric instrumental regressions.…”