Linear regression with an estimated regressor: applications to aggregate indicators of economic development

Meng, Lingsheng; Wu, Binzhen; Zhan, Zhaoguo

doi:10.1007/s00181-015-0941-z

Cited by 8 publications

(10 citation statements)

References 28 publications

(64 reference statements)

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“…Our simulation again shows that ForestIV outperforms LatentIV in bias correction. Third, in the generated regressors literature, Meng et al (2016) have proposed a method to explicitly adjust coefficient estimates to account for biases due to measurement error in linear regressions, deriving from mis-measured, nonparametrically generated regressors. Once more, our simulation shows that ForestIV outperforms this method in bias correction.…”

Section: Simulation Experimentsmentioning

confidence: 99%

“…The authors assume that the functional relationship underlying the generated regressor is inconsistent across observations, and thus the generated regressor can be viewed as nonparametric. Meng et al (2016) derive an explicit formula for the magnitude of bias, as a function of the first two moments of the measurement error (e.g., mean and variance), which allows the biased estimates to be adjusted accordingly. In our setting, the moment statistics of measurement/prediction error can be readily estimated using the testing data, where prediction errors are directly observed.…”

Section: G Benchmarking Forestiv With Three Alternative Approachesmentioning

confidence: 99%

“…Finally, we benchmark ForestIV against the regression adjustment approach developed by Meng et al (2016) for measurement error in nonparametrically generated regressors. We apply the formula in (Meng et al, 2016, p.305) to obtain the adjusted coefficient and standard error on lnCnt.…”

Section: G5 Benchmarking With Generated Regressor Adjustmentmentioning

confidence: 99%

“…In addition to the above simulation experiments, we conduct benchmarking analyses to compare the relative correction performance of ForestIV with those of three other approaches from the existing literature: Simulation-Extrapolation (SIMEX, Cook and Stefanski, 1994), Latent Instrumental Variables (LatentIV, Ebbes et al, 2005), and regression adjustment for nonparametrically generated regressors (Meng et al, 2016). First, SIMEX is an alternative correction approach that has previously been demonstrated to perform well in the same problem context.…”

Section: Simulation Experimentsmentioning

confidence: 99%

“…The above having been said, some recent work in the generated regressors literature has proposed methods to correct for bias in generated regressors in the presence of distributional information about that bias (e.g., Meng et al, 2016). Accordingly, as part of our benchmarking analyses, we seek to compare the relative performance of our method with that approach (Meng et al, 2016).…”

Section: A3 the Generated Regressors Literaturementioning

confidence: 99%

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Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem

et al. 2019

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Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to "mine" variables of interest from available data, followed by the inclusion of those variables into an econometric framework, with the objective of estimating causal effects. Recent work highlights that, because the predictions from machine learning models are inevitably imperfect, econometric analyses based on the predicted variables are likely to suffer from bias due to measurement error. We propose a novel approach to mitigate these biases, leveraging the ensemble learning technique known as the random forest. We propose employing random forest not just for prediction, but also for generating instrumental variables to address the measurement error embedded in the prediction. The random forest algorithm performs best when comprised of a set of trees that are individually accurate in their predictions, yet which also make "different" mistakes, i.e., have weakly correlated prediction errors. A key observation is that these properties are closely related to the relevance and exclusion requirements of valid instrumental variables. We design a data-driven procedure to select tuples of individual trees from a random forest, in which one tree serves as the endogenous covariate and the other trees serve as its instruments. Simulation experiments demonstrate the efficacy of the proposed approach in mitigating estimation biases, and its superior performance over three alternative methods for bias correction.

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Section: Simulation Experimentsmentioning

confidence: 99%

Section: G Benchmarking Forestiv With Three Alternative Approachesmentioning

confidence: 99%

Section: G5 Benchmarking With Generated Regressor Adjustmentmentioning

confidence: 99%