How can you address measurement error in causal inference?

1 Use instrumental variables

One way to deal with measurement error is to use instrumental variables (IVs). These are variables that are correlated with the true explanatory variable, but not with the measurement error or the outcome. For example, if you want to estimate the effect of smoking on health, but you only have self-reported data on smoking, which may be inaccurate, you can use the price of cigarettes as an IV. The price of cigarettes affects the amount of smoking, but not the health outcome directly, nor the reporting error. By using IVs, you can isolate the variation in the true explanatory variable that is relevant for the outcome, and avoid the bias from measurement error.

2 Use latent variable models

Another way to deal with measurement error is to use latent variable models. These are models that assume that there is an unobserved or hidden variable that affects both the observed variable and the outcome. For example, if you want to estimate the effect of ability on test scores, but you only have data on test scores, which may be noisy or imperfect, you can use a latent variable model that assumes that there is an underlying ability factor that influences both test scores and the outcome. By using latent variable models, you can account for the measurement error in the observed variable and estimate the effect of the hidden variable on the outcome.

3 Use multiple indicators

A third way to deal with measurement error is to use multiple indicators. These are different measures of the same concept or phenomenon that are expected to have similar effects on the outcome. For example, if you want to estimate the effect of democracy on economic growth, but you only have data on a single indicator of democracy, such as electoral freedom, which may be incomplete or subjective, you can use multiple indicators of democracy, such as civil liberties, political rights, or accountability. By using multiple indicators, you can reduce the measurement error in each indicator and improve the reliability and validity of your measure of democracy.

4 Use validation data

A fourth way to deal with measurement error is to use validation data. These are data from external sources that can verify or correct the accuracy of your observed or measured data. For example, if you want to estimate the effect of calorie intake on weight, but you only have data on self-reported calorie intake, which may be biased or inaccurate, you can use validation data from objective sources, such as food diaries, receipts, or sensors. By using validation data, you can adjust or calibrate your observed or measured data and reduce the measurement error in your explanatory variable.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?