Robust inference for the Two-Sample 2SLS estimator

Pacini, David; Windmeijer, Frank

doi:10.1016/j.econlet.2016.06.033

Cited by 46 publications

(42 citation statements)

References 11 publications

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“…However, there is a subtle but important difference between two-sample Mendelian randomization and the existing applications of TSIV in economic applications. To the best of our knowledge, with the exception of Graham et al (2016) who considered a general data combination problem including just-identified TSIV, all the TSIV estimators previously proposed in econometrics assumed that the two datasets are sampled from the same population (Angrist and Krueger, 1992, Ridder and Moffitt, 2007, Inoue and Solon, 2010, Pacini and Windmeijer, 2016. This is usually not a problem in the economic applications using timeinvariant instrumental variables (Jappelli et al, 1998) such as quarter of birth (Angrist and Krueger, 1992) and sex composition of the children in the household (Currie and Yelowitz, 2000).…”

Section: Introductionmentioning

confidence: 99%

Two-Sample Instrumental Variable Analyses Using Heterogeneous Samples

Zhao¹,

Wang²,

Spiller³

et al. 2019

Statist. Sci.

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Instrumental variable analysis is a widely used method to estimate causal effects in the presence of unmeasured confounding. When the instruments, exposure and outcome are not measured in the same sample, Angrist and Krueger (1992) suggested to use two-sample instrumental variable (TSIV) estimators that use sample moments from an instrument-exposure sample and an instrument-outcome sample. However, this method is biased if the two samples are from heterogeneous populations so that the distributions of the instruments are different. In linear structural equation models, we derive a new class of TSIV estimators that are robust to heterogeneous samples under the key assumption that the structural relations in the two samples are the same. The widely used two-sample two-stage least squares estimator belongs to this class. It is generally not asymptotically efficient, although we find that it performs similarly to the optimal TSIV estimator in most practical situations. We then attempt to relax the linearity assumption. We find that, unlike one-sample analyses, the TSIV estimator is not robust to misspecified exposure model. Additionally, to nonparametrically identify the magnitude of the causal effect, the noise in the exposure must have the same distributions in the two samples. However, this assumption is in general untestable because the exposure is not observed in one sample. Nonetheless, we may still identify the sign of the causal effect in the absence of homogeneity of the noise.

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Section: Introductionmentioning

confidence: 99%

Two-Sample Instrumental Variable Analyses Using Heterogeneous Samples

Zhao¹,

Wang²,

Spiller³

et al. 2019

Statist. Sci.

View full text Add to dashboard Cite

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“…This estimator uses an instrument for parental earnings and combines information from two surveysthe main one containing information on the child's income and a supplemental one that holds data on the parental generation. It was formally developed by Angrist and Krueger (1992) and more recently extended by Inoue and Solon (2010) and Pacini and Windmeijer (2016) to account for differences in the distributions of the instruments that may arise from heterogeneous samples, referred to as Two-Samples-Two-Stages Least Squares (TS2SLS). Only a few studies applying this methodology can identify actual parents in the supplemental dataset, 11 while the majority predict some average value of 'synthetic fathers' in an older survey of working men of the parental generation.…”

Section: Mobility In Incomementioning

confidence: 99%

“…To account for the uncertainty that arises from generating the regressor ̂, we derive robust standard errors as a function of the variances and covariances of the estimators in (5) and their linear projection in our main dataset (Pacini and Windmeijer, 2016). 14 Compare in particular three studies for the US: Solon (1992), Zimmerman (1992) and Mazumder (2005), as well as Corak and Heisz (1999) and Dunn (2007).…”

Section: Predicting Parental Incomementioning

confidence: 99%

More Educated, Less Mobile? Diverging Trends in Income and Educational Mobility in Chile and Peru

Gaentzsch

Roman

2018

SSRN Journal

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We analyse intergenerational persistence in income and education in Chile and Peru for birth cohorts of the early 1950s to 1990. Both countries have seen a structural expansion of education over this period and decreasing income inequality in recent decades. We impute non-observed parental income from repeated cross-sections and estimate persistence in the range of 0.63 to 0.67 in Peru and 0.66 to 0.76 in Chile for household heads of the birth cohorts 1977-90. The analysis of educational mobility covers household heads of birth cohorts from 1953 to 1990 and relies on retrospective information. We observe an increase in absolute mobility for younger generations, which we relate to the structural expansion of education that created room at the top. In relative terms, mobility patterns remain more stableparental education is still a strong predictor of children's educational achievement. The relationship is non-linear in both countries: persistence among very poorly and highly educated groups is strong, while individuals with parents of average education levels are more mobile. Upward mobility is stronger in Peru than in Chile: the chances to move from no formal education to higher education across one generation are 46% of the average in Peru compared to 20% in Chile. The chances of persisting in the top across generations are also slightly higher in Peru, with a factor of three times the average compared to 2.76 in Chile.

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“…13 The asymptotic variances in Equations 1 and 2 are special cases of Ridder and Moffitt (2007, Formula 179). 14 For more on the relationship between the 2SLS and two-sample GMM estimators, see Pacini and Windmeijer (2016).…”

Section: The Semiparametric Efficiency Boundmentioning

confidence: 99%

The two‐sample linear regression model with interval‐censored covariates

Pacini

2018

J of Applied Econometrics

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There are surveys that gather precise information on an outcome of interest, but measure continuous covariates by a discrete number of intervals, in which case the covariates are interval censored. For applications with a second independent dataset precisely measuring the covariates, but not the outcome, this paper introduces a semiparametrically efficient estimator for the coefficients in a linear regression model. The second sample serves to establish point identifi-cation. An empirical application investigating the relationship between income and body mass index illustrates the use of the estimator.1 For the advantages see, for example, Juster and Smith (1997). For the disadvantages see, for example, Hsiao (1983) and Rigobon and Stoker (2009). 2 See, for example, Hsiao (1983) for a linear regression model. This paper introduces an estimator, called the two-step, two-sample augmented generalized instrumental variable (2S-AGIV) estimator, drawing on the comparative advantages of the point-and set-identifying approaches. The paper has three results. The first result states that, when there is a second independent sample with continuous measurements of the covariates, the linear regression model with interval-censored covariates in the first sample point-identifies the coefficients of interest. The model implies an identifying moment restriction using indicator variables for the intervals as instrumental variables observed in both samples. Neither parametric, support, nor monotonicity restrictions on the interval-censored covariates are needed to obtain this result. The second result shows that the existing two-sample instrumental variable estimators, including the two-stage least squares (2SLS; Klevmarken, 1982) and two-sample instrumental variable (2S-GIV; Ridder & Moffitt, 2007) estimators, are consistent and asymptotically normal; however, they are not semiparametrically efficient. The 2SLS estimator is equivalent to imputing in the censored sample the truncated mean of the covariate of interest within the interval calculated from the uncensored sample. The 2S-GIV estimator is equivalent to a weighted least squares estimator on the truncated mean outcome and covariate of interest within the interval. The paper shows that the 2S-AGIV estimator is consistent, asymptotically normal, and semiparametrically efficient, which is the third result. This last property means that, in large samples, the 2S-AGIV estimator can realize in the best possible way the precision gains offered by the point-identifying approach without parametrizing the distribution of the covariates. A simulation study bears out these theoretical properties of the 2S-AGIV estimator.An empirical exercise using data from the HSE and the FRS illustrates and supports the use of the 2S-AGIV estimator. The exercise tests the unearned income effect (UIE) hypothesis, which postulates an inverted U-shaped relationship between income and body mass index (BMI; see; Lakdawalla & Philipson, 2009). This hypothesis is relevant, for instance, in assessing the eff...

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Robust inference for the Two-Sample 2SLS estimator

Cited by 46 publications

References 11 publications

Two-Sample Instrumental Variable Analyses Using Heterogeneous Samples

Two-Sample Instrumental Variable Analyses Using Heterogeneous Samples

More Educated, Less Mobile? Diverging Trends in Income and Educational Mobility in Chile and Peru

The two‐sample linear regression model with interval‐censored covariates

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