Nonclassical Measurement Error Research Articles

The effects of tobacco 21 laws on smoking and vaping: Evidence from panel data and biomarkers

We use data from the Population Assessment of Tobacco Use and Health (PATH), a longitudinal data set including self-reported and biomarker measures of tobacco use, to examine the effects of state-level tobacco 21 (T21) laws on smoking and vaping. T21 laws reduce self-reported cigarette smoking among 18-to-20 year olds, concentrated in males. Initial non-users who “age-out” of treatment are less likely to subsequently initiate self-reported smoking or vaping. Treated smokers are less likely to buy their own cigarettes and more likely to buy cigarettes in a different state. Biomarker results are mixed, and we find some evidence of a reduction in nicotine exposure but less evidence for a reduction in exposure to tobacco. Finally, we test for non-classical measurement error. T21 laws reduce the probability that clinically identified likely cigarette smokers self-report as smokers, which may increase the apparent effect of T21 laws on cigarette smoking as measured by self-reports.

Non-classical measurement error in instrumental variables estimation: An application to the medical care costs of obesity.

Estimates of the impact of body mass index and obesity on health and labor market outcomes often use instrumental variables estimation (IV) to mitigate bias due to endogeneity. When these studies rely on survey data that include self- or proxy-reported height and weight, there is non-classical measurement error due to the tendency of individuals to under-report their own weight. Mean reverting errors in weight do not cause IV to be asymptotically biased per se, but may result in bias if instruments are correlated with additive error in weight. We demonstrate the conditions under which IV is biased when there is non-classical measurement error and derive bounds for this bias conditional on instrument strength and the severity of mean-reverting error. We show that improvements in instrument relevance alone cannot eliminate IV bias, but reducing the correlation between weight and reporting error mitigates the bias. A solution we consider is regression calibration (RC) of endogenous variables with external validation data. In simulations, we find IV estimation paired with RC can produce consistent estimates when correctly specified. Even when RC fails to match the covariance structure of reporting error, there is still a reduction in asymptotic bias.

A formal model accounting for measurement reliability shows attenuated effect of higher education on intelligence in longitudinal data.

The effect of higher education on intelligence has been examined using longitudinal data. Typically, these studies reveal a positive effect, approximately 1 IQ point per year of higher education, particularly when pre-education intelligence is considered as a covariate in the analyses. However, such covariate adjustment is known to yield positively biased results if the covariate has measurement errors and is correlated with the predictor. Simultaneously, a negative bias may emerge if the intelligence measure after higher education has non-classical measurement errors as in data from the 1970 British Cohort Study that were used in a previous study of the effect of higher education. In response, we have devised an estimation method that used iterated simulations to account for both classical measurement errors in the covariate and non-classical errors in the dependent variable. Upon applying this method in a reanalysis of the data from the 1970 British Cohort Study, we find that the estimated effect of higher education diminishes to 0.4 IQ points per year. Additionally, our findings suggest that the impact of higher education is somewhat more pronounced in the initial 2 years of higher education, aligning with the notion of diminishing marginal cognitive benefits.

Powerful t-tests in the presence of nonclassical measurement error

. This article proposes a powerful alternative to the t-test of the null hypothesis that a coefficient in a linear regression is equal to zero when a regressor is mismeasured. We assume there are two contaminated measurements of the regressor of interest. We allow the two measurement errors to be nonclassical in the sense that they may both be correlated with the true regressor, they may be correlated with each other, and we do not require any location normalizations on the measurement errors. We propose a new maximal t-statistic that is formed from the regression of the outcome onto a maximally weighted linear combination of the two measurements. The critical values of the test are easily computed via a multiplier bootstrap. In simulations, we show that this new test can be significantly more powerful than t-statistics based on OLS or IV estimates. Finally, we apply the proposed test to a study of returns to education based on twin data from the UK. With our maximal t-test, we can discover statistically significant returns to education when standard t-tests do not.

Using Digitized Newspapers to Address Measurement Error in Historical Data

This paper shows how to remove attenuation bias in regression analyses due to measurement error in historical data for a given variable of interest by using a secondary measure that can be easily generated from digitized newspapers. We provide three methods for using this secondary variable to deal with non-classical measurement error in a binary treatment: set identification, bias reduction via sample restriction, and a parametric bias correction. We demonstrate the usefulness of our methods by replicating four recent economic history papers. Relative to the initial analyses, our results yield markedly larger coefficient estimates.

Attenuating measurement errors in agricultural productivity analysis by combining objective and self-reported survey data

This paper exploits unique survey data from Mali to validate an alternative approach to estimate the relationship between crop yields and inputs. The estimation relies on predicted objective crop yields that stem from a machine learning model trained on a random subsample of surveyed plots, for which crop cutting and self-reported sorghum yield estimates are both available. The analysis demonstrates that it is possible to predict sorghum yields with attenuated non-classical measurement error, resulting in a less-biased assessment of the relationship between yields and agricultural inputs. The external validity of the findings based on the data from a sub-national survey experiment is verified using the data from a nationally representative agricultural survey. The discussion expands on the implications of the findings for the design of future surveys where objective data collection could be limited to a subsample to save costs, with the intention to apply the suggested machine learning approach.

Is older age more unequal than we think? Estimates from the Survey of Income and Program Participation linked to administrative records

Despite increased scholarly and policy interest in income inequality, our knowledge of inequality in later life is relatively limited. One challenge to studying inequality in older age groups is that income sources that are important in later life, including pensions and retirement accounts, may be poorly captured by household income surveys. In this study, we investigate income inequality among the older population in the United States, focusing on how measurement error affects retirement income estimates and its impact on summary measures of inequality. We use a rich dataset that links respondents in the Survey of Income and Program Participation with restricted-use administrative records from the Social Security Administration and Internal Revenue Service. We find systematic, nonclassical measurement error in survey-reported retirement income, particularly from pensions and retirement accounts. Due to these patterns of measurement error, income inequality estimates are considerably higher using administrative records instead of survey-reported data. Additional analyses show the effects of measurement error when estimating between- and within-group inequality across racial-ethnic and education groups. The downward bias associated with measuring income inequality among older Americans could worsen in the future given the shift from defined-benefit to defined-contribution retirement plans.

Revisiting the size–productivity relationship with imperfect measures of production and plot size

AbstractMonitoring smallholder agricultural productivity growth, one of the targets of the Sustainable Development Goals, rests on accurate measures of crop production and land area. Existing methods and protocols for measuring smallholder production and plot size are prone to various sources and forms of mismeasurement. Inaccuracies in production and land area measurement are likely to distort descriptive and predictive inferences. We examine the sensitivity of empirical assessments of the relationship between agricultural productivity and land area to alternative measurement protocols. We implement six production and six land area measurement protocols, and show that most of these protocols differ systematically in their accuracy. We find that an apparent inverse size–productivity relationship in our data is fully explained by measurement error in both production and plot size. Moreover, we show that some of the previously used “gold standard” measures are themselves prone to nonclassical measurement error, and hence can generate spurious inverse size–productivity findings. Our results also show that slight improvements in the precision of objective measures significantly reduce the inferential bias associated with the size–productivity relationship.

Nonclassical measurement error and farmers’ response to information treatment

This paper reports on a randomized experiment conducted among Malawian agricultural households to study nonclassical measurement error (NCME) in self-reported plot area, and farmers' responses to new information — the objective plot area measure — subsequently provided to them. Farmers' pre-treatment self-reported plot areas exhibit considerable NCME. Most of the measurement error follows a regression-to-mean pattern with respect to plot area, and another 18 percent arises from asymmetric rounding to half acre increments. Randomized provision of GPS-based measures of true plot area generates four important findings. First, most treated farmers’ self-reports exhibit no reduction in NCME after the provision of true plot area measures. Second, farmers update asymmetrically in response to information, with upward corrections being far more common than downward ones even though most plot sizes were initially overestimated. Third, the magnitude of updating varies by true plot area, as well as the magnitude and direction of initial NCME. Fourth, the information treatment affects self-reported information about non-land inputs such as fertilizer and labor, indicating that the effects of measurement error and updating spillover across variables. NCME clearly carries implications for survey data collection methods, econometric inference, and the design of information-based interventions. It might also reflect behavioral anomalies that may matter for farm management practices, input allocation, agricultural productivity, and the design of effective interventions.

Remotely Incorrect? Accounting for Nonclassical Measurement Error in Satellite Data on Deforestation

Remotely Incorrect? Accounting for Nonclassical Measurement Error in Satellite Data on Deforestation

Statistical Capacity Matters: The Long-Term Effects of Africa’s Slave Trade on Development Reflected by Nighttime Light Intensity

Abstract Empirical research depends on reliable data. Yet, in many countries, statistical agencies do not have the capacity to collect high-quality data on economic development. This is especially the case in Africa, where the capacity to collect such data is affected by the same historical factors that explain economic development—in particular, the slave trade. We hypothesise that the impact of the slave trade on economic development in Africa is biased because cross-country heterogeneity in statistical capacity related to the slave trade creates a non-classical measurement error in gross domestic product (GDP) per capita. Our empirical evidence supports this view. When replacing GDP per capita by nighttime light intensity per capita—an indicator of economic development unrelated to statistical capacity—the impact of the slave trade on economic development drops by a factor of 2–4 depending on model specification and estimation methodology (OLS, IV and high-dimensional sparse models). Various robustness tests further corroborate our main hypothesis.

On the timing of relevant weather conditions in agriculture

AbstractA growing literature is analyzing the effects of weather on agricultural outcomes. In these studies, constructing weather variables requires researchers to define a “season,” a period over which weather conditions are considered relevant to the outcome. We explore the consequences of assuming an incorrect season in such analyses. We show in simulations that imposing an incorrect season introduces nonclassical measurement error in weather regressors, bias in unknown directions. We propose an approach to recover the “true” underlying season and apply it to a US state‐level panel of agricultural Total Factor Productivity. We find that accounting for seasonality can lead to substantially different estimates.

Panel Regression Models with Non-Classical Measurement Errors: An Application to Investment Equations

Panel Regression Models with Non-Classical Measurement Errors: An Application to Investment Equations

The implications of self-reported body weight and height for measurement error in BMI

We designed an experiment to explore the extent of measurement error in body mass index (BMI), when based on self-reported body weight and height. We find that there is a systematic age gradient in the reporting error in BMI, while there is limited evidence of systematic associations with gender, education and income. This is reassuring evidence for the use of self-reported BMI in studies that use it as an outcome, for example, to analyse socioeconomic gradients in obesity. However, our results suggest a complex structure of non-classical measurement error in BMI, depending on both individuals’ and within-household peers’ true BMI. This may bias studies that use BMI based on self-reported data as a regressor. We also observe non-classical reporting error in height and weight — taller people seem to report their height more accurately, while a nonlinear relationship is evident for weight, with a sharper increase in reporting errors for those of greater weight. Common methods to mitigate reporting error in BMI using predictions from corrective equations do not fully eliminate reporting heterogeneity associated with individual and within-household true BMI. Overall, the presence of non-classical error in BMI highlights the importance of collecting measured body weight and height data in large social science datasets.

A simple test of completeness in a class of nonparametric specification

This paper provides a test for completeness in a class of nonparametric specification with an additive and independent error term. It is known that such a nonparametric location family of functions is complete if and only if the characteristic function of the error term has no zeros on the real line. Because a zero of the error characteristic function implies that of an observed marginal distribution, we propose a simple test for zeros of characteristic function of the observed distribution, in which rejection of the null hypothesis implies the completeness. This test is applicable to many popular settings, such as nonparametric regression models with instrumental variables, and nonclassical measurement error models. We describe the asymptotic behavior of the tests under the null and alternative hypotheses and investigate the finite sample properties of the proposed test through a Monte Carlo study. We illustrate our method empirically by estimating a measurement error model using the CPS/SSR 1978 exact match file.

Identification of nonparametric monotonic regression models with continuous nonclassical measurement errors

This paper provides sufficient conditions for identification of a nonparametric regression model with an unobserved continuous regressor subject to nonclassical measurement error. The measurement error may be directly correlated with the latent regressor in the model. Our identification strategy does not require the availability of additional data information, such as a secondary measurement, an instrumental variable, or an auxiliary sample. Our main assumptions for nonparametric identification include monotonicity of the regression function, independence of the regression error, and completeness of the measurement error distribution. We also propose a sieve maximum likelihood estimator and investigate its finite sample property through Monte Carlo simulations.

Analyzing Subjective Well-Being Data with Misclassification

We use novel nonparametric techniques to test for the presence of nonclassical measurement error in reported life satisfaction (LS) and study the potential effects from ignoring it. Our dataset comes from Wave 3 of the UK Understanding Society that is surveyed from 35,000 British households. Our test finds evidence of measurement error in reported LS for the entire dataset as well as for 26 out of 32 socioeconomic subgroups in the sample. We estimate the joint distribution of reported and latent LS nonparametrically in order to understand the mis-reporting behavior. We show this distribution can then be used to estimate parametric models of latent LS. We find measurement error bias is not severe enough to distort the main drivers of LS. But there is an important difference that is policy relevant. We find women tend to over-report their latent LS relative to men. This may help explain the gender puzzle that questions why women are reportedly happier than men despite being worse off in objective outcomes such as income and employment.

Land Measurement Bias: Comparisons from Global Positioning System, Self-Reports, and Remote Sensing Data

We investigate the reliability of land measurement modes on non-classical measurement error and empirical relationships. In our multi-country survey experiment, we find significant differences between GPS and remotely sensed data only in Viet Nam, where plot sizes are small relative to the other countries. The magnitude of farmers’ self-reporting bias relative to GPS measures is nonlinear, with the largest magnitude of self-reporting bias of 130% of a standard deviation (2.2-hectare bias) in the Lao People’s Democratic Republic relative to Viet Nam, which has 13.3% of a standard deviation (.008-hectare bias). In all countries except Viet Nam, the inverse land size–productivity relationship is upwardly biased for lower land area self-reported measures relative to GPS measures. In Viet Nam, the intensive margin of organic fertilizer use is negatively biased (30.4 percentage points) by self-reported measurement error. We conclude by considering sources of measurement error in implementation and costs.

Accounting for Skewed or One-Sided Measurement Error in the Dependent Variable

AbstractWhile classical measurement error in the dependent variable in a linear regression framework results only in a loss of precision, nonclassical measurement error can lead to estimates, which are biased and inference which lacks power. Here, we consider a particular type of nonclassical measurement error: skewed errors. Unfortunately, skewed measurement error is likely to be a relatively common feature of many outcomes of interest in political science research. This study highlights the bias that can result even from relatively “small” amounts of skewed measurement error, particularly, if the measurement error is heteroskedastic. We also assess potential solutions to this problem, focusing on the stochastic frontier model and Nonlinear Least Squares. Simulations and three replications highlight the importance of thinking carefully about skewed measurement error as well as appropriate solutions.

The Implications of Self-Reported Body Weight and Height for Measurement Error in BMI

We designed an experiment to explore the extent of measurement error in body mass index (BMI), when based on self-reported body weight and height. We find that there is a systematic age gradient in the reporting error in BMI, while there is limited evidence of systematic associations with gender, education and income. This is reassuring evidence for the use of self-reported BMI in studies that use it as an outcome, for example, to analyse socioeconomic gradients in obesity. However, our results suggest a complex structure of non-classical measurement error in BMI, depending on both individuals' and within-household peers' true BMI. This may bias studies that use BMI based on self-reported data as a regressor. Common methods to mitigate reporting error in BMI using predictions from corrective equations do not fully eliminate reporting heterogeneity associated with individual and within-household true BMI. Overall, the presence of non-classical error in BMI highlights the importance of collecting measured body weight and height data in large social science datasets.