Exact computation of GMM estimators for instrumental variable quantile regression models

Chen, Le‐Yu; Lee, Sokbae

doi:10.1002/jae.2619

Cited by 31 publications

(14 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The actual situation is that economic variables are often skewed because they are complex and volatile. Moreover, the extreme values (i.e., maximum and minimum) of economic variables often imply important information and have important impacts on the related socio‐economic phenomena (Chen & Lee, 2018). The quantile regression model does not require economic variables to follow a normal distribution and is resistant to outliers.…”

Section: Literature Reviewmentioning

confidence: 99%

Large fluctuations of China's commodity prices: Main sources and heterogeneous effects

Lin

2020

Int. J Fin Econ

View full text Add to dashboard Cite

Assuming that the economic variables obey the normal distribution, existing studies often use traditional mean models to explore commodity prices. In fact, the distribution of economic data is often skewed. When the economic data is left‐biased or right‐biased, the quantile regression can more fully characterize the distribution of economic variables, and thus obtain a comprehensive analysis result. Moreover, the coefficient estimates of the quantile regression are more robust than those in the ordinary least squares regression. Therefore, this paper uses the quantile regression method to investigate commodity price fluctuations. The results show that the money supply has a greater impact on commodity prices in the lower 10th and 10th–25th quantile groups. Among all quantile groups, the impact of international oil prices on commodity prices in the upper 90th quantile group is the highest. The effect of the exchange rate in the 25th–50th quantile group is greater than those in other quantile groups. However, the real economy has a minimal impact on the 25th–50th quantile group. Thus, the heterogeneous effects of these influencing factors should be taken into consideration when stabilizing commodity prices.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Large fluctuations of China's commodity prices: Main sources and heterogeneous effects

Lin

2020

Int. J Fin Econ

View full text Add to dashboard Cite

show abstract

“…Kaplan and Sun (2017) and de Castro, Galvao, Kaplan, and Liu (2019) have suggested using smoothed estimating equations to overcome the non‐smoothness of the IVQR estimation problem; however, the nonconvexity persists. More recently, Chen and Lee (2018) have proposed to recast the IVQR problem as a mixed‐integer quadratic programming problem that can be solved using well‐established algorithms. However, efficiently solving such a problem is still challenging even for low‐dimensional settings.…”

Section: Introductionmentioning

confidence: 99%

“…However, efficiently solving such a problem is still challenging even for low‐dimensional settings. Zhu (2018) has shown that if the

ℓ_{normal∞}

norm is used rather than the

ℓ_{2}

norm, the problem admits a reformulation as a mixed‐integer linear programming problem, which can be solved more efficiently than the quadratic program in Chen and Lee (2018). This procedure typically requires an early termination of the algorithm to ensure computational tractability which is akin to a tuning parameter choice.…”

Section: Introductionmentioning

confidence: 99%

Decentralization estimators for instrumental variable quantile regression models

Kaido

Wüthrich

2021

View full text Add to dashboard Cite

The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen (2005)) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the nonsmoothness and nonconvexity of the IVQR GMM objective function. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression subproblems which are convex and can be solved efficiently. This reformulation leads to new identification results and to fast, easy to implement, and tuning‐free estimators that do not require the availability of high‐level “black box” optimization routines.

show abstract

“…Kaplan and Sun (2017) and de Castro, Galvao, Kaplan, and Liu (2018) have suggested to use smoothed estimating equations to overcome the non-smoothness of the IVQR estimation problem, although the non-convexity remains. More recently, Chen and Lee (2018) have proposed to reformulate the IVQR problem as a mixed-integer quadratic programming problem which can be solved using well-established algorithms. However, efficiently solving such a problem is still challenging even for low-dimensional settings.…”

Section: Introductionmentioning

confidence: 99%

Decentralization estimators for instrumental variable quantile regression models

Kaido¹,

Wüthrich²

2018

View full text Add to dashboard Cite

The instrumental variable quantile regression (IVQR) model of Hansen (2005, 2006) is a flexible and powerful tool for evaluating the impact of endogenous covariates on the whole distribution of the outcome of interest. Estimation, however, is computationally burdensome because the GMM objective function is non-smooth and non-convex. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression sub-problems, which are convex and can be solved efficiently. This allows for reformulating the original estimation problem as the problem of finding the fixed point of a low dimensional map. This reformulation leads to new identification results and, most importantly, to practical, easy to implement, and computationally tractable estimators. We explore estimation algorithms based on the contraction mapping theorem and algorithms based on root-finding methods. We prove consistency and asymptotic normality of our estimators and establish the validity of a bootstrap procedure for estimating the limiting laws. Monte Carlo simulations support the estimator's enhanced computational tractability and demonstrate desirable finite sample properties.

show abstract

Exact computation of GMM estimators for instrumental variable quantile regression models

Cited by 31 publications

References 38 publications

Large fluctuations of China's commodity prices: Main sources and heterogeneous effects

Large fluctuations of China's commodity prices: Main sources and heterogeneous effects

Decentralization estimators for instrumental variable quantile regression models

Decentralization estimators for instrumental variable quantile regression models

Contact Info

Product

Resources

About