Econometrics Lecture 8: Threats to Identification

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Questions and Answers

What solution should be used if an omitted variable can be measured?

Include it as an additional regressor in multiple regression (correct)

Use instrumental variables regression

Exclude the variable entirely

Use panel data

If conditional mean independence holds, what should you do?

Run a randomized controlled experiment

Include the adequate control variables (correct)

Exclude all controls

Use an interaction term

What method is appropriate for dealing with functional form mis-specification for a continuous dependent variable?

Apply nonlinear specifications like logarithms or interactions (correct)

Use probit analysis

Use simple linear regression

Eliminate all interaction terms

What is one reason economic data may have measurement error?

Data entry errors (D) Signup and view all the answers

In cases where the omitted variable cannot be adequately controlled, what method should be used?

Use instrumental variables regression (B) Signup and view all the answers

Which of the following is a potential issue with surveys that can lead to measurement error?

Recollection errors (A) Signup and view all the answers

What approach should be taken when working with a binary dependent variable?

Use logit or probit analysis (D) Signup and view all the answers

What is the primary concern with the errors-in-variables problem in regression analysis?

Bias in the estimation of causal effects (D) Signup and view all the answers

Which of the following is a threat to the internal validity of a multiple regression study?

Omitted variables (D) Signup and view all the answers

What does the external validity requirement for prediction emphasize?

Data must be from the same distribution as out-of-sample observations (B) Signup and view all the answers

What can be said about the regression coefficients in a prediction model?

They can exist without direct causal interpretations (D) Signup and view all the answers

Which condition is important for using Ordinary Least Squares (OLS) in prediction?

Number of regressors should be small relative to observations (D) Signup and view all the answers

Which of the following is NOT considered a threat to internal validity in multiple regressions?

High correlation between true and observed values (C) Signup and view all the answers

When should special estimators beyond OLS be used?

When the number of regressors is large relative to observations (B) Signup and view all the answers

Which statement accurately describes simultaneous causality's impact on internal validity?

It can lead to biased and inconsistent estimates (B) Signup and view all the answers

Which of the following is an example of heteroskedasticity?

Variance of errors increases with an increase in predictors (D) Signup and view all the answers

What is a key factor that could lead to omitted variable bias in a regression study?

The omitted variable must be a determinant of the dependent variable. (D) Signup and view all the answers

Which of the following statements correctly describes internal validity?

It assesses whether unbiased causal inferences can be made for a population. (C) Signup and view all the answers

What does sample selection bias typically refer to in regression studies?

The error introduced by selecting a non-representative sample. (B) Signup and view all the answers

Which of the following is NOT one of the five threats to internal validity of regression studies?

Measurement error bias (C) Signup and view all the answers

When does omitted variable bias occur?

When factors affecting the dependent variable are ignored. (D) Signup and view all the answers

Which of the following factors contributes to the failure of conditional mean independence?

Correlating the error term with the variables of interest. (D) Signup and view all the answers

What term is used to describe a study that compares multiple related studies on the same topic?

Meta-analysis (B) Signup and view all the answers

What is necessary for a variable Z to cause omitted variable bias in a study?

Z must correlate with both the dependent and independent variables. (A) Signup and view all the answers

What does it indicate when data are missing at random?

The standard errors are larger than if there were no missing data. (B) Signup and view all the answers

Which case of missing data does NOT introduce bias?

Data missing at random. (C), Data missing based on an unrelated independent variable. (D) Signup and view all the answers

What is sample selection bias?

Bias introduced by a non-random selection process relating to the dependent variable. (C) Signup and view all the answers

How could sample selection bias be avoided?

By ensuring that the sample selection process is unrelated to the outcome variable. (A) Signup and view all the answers

What consequence did the Literary Gazette face in their polling error?

Their sample included wealthier individuals who predominantly supported Landon. (A) Signup and view all the answers

If data are missing based on the value of one or more independent variables, this situation is described as:

Data missing conditionally. (C) Signup and view all the answers

Which of the following is an example of data being missing not at random?

Not observing data from a specific demographic group. (C) Signup and view all the answers

In which scenario will standard errors be larger due to missing data?

When data are missing at random. (B) Signup and view all the answers

What does a polynomial regression include as regressors?

The independent variable X, its squared term X^2, and its cubic term X^3 (C) Signup and view all the answers

What can the inclusion of interaction terms in a regression allow for?

Understanding how the effect of one variable affects another variable's slope or intercept (D) Signup and view all the answers

What does internal validity refer to in regression studies?

The accuracy of statistical inferences for the specific population studied (D) Signup and view all the answers

How can small changes in logarithms be interpreted in regression analysis?

As percentage changes in a variable (A) Signup and view all the answers

Which factor contributes to external validity in regression analysis?

The legal and policy environments of the studied population (A) Signup and view all the answers

What is the effect of mis-measuring the variable X in the regression model?

It causes a biased estimator for β1. (A) Signup and view all the answers

Under the classical measurement error model, how does the bias of β̂1 behave in relation to zero?

It is biased towards zero. (A) Signup and view all the answers

What is a common pitfall when using observational data in multiple regression?

The failure to account for confounding factors that can introduce bias (A) Signup and view all the answers

What is the covariance formula for cov(X̃i, ũi) when assuming X̃i = Xi + vi?

cov(X̃i, ũi) = β1 cov(Xi + vi, -vi) (C) Signup and view all the answers

What is the main consideration when assessing threats to external validity?

The generalization of class size results across different states (C) Signup and view all the answers

What is indicated if the marginal effect of X on Y is not constant in regression analysis?

A linear regression model is likely misspecified (D) Signup and view all the answers

If the variance of the measurement error vi is extremely large, what happens to β̂1?

β̂1 will approximate zero. (B) Signup and view all the answers

What is the expected correlation between the true variable Xi and the random error vi?

ρXi,vi = 0 (B) Signup and view all the answers

When analyzing the mis-measured variable X̃i, which covariance term is often assumed to be zero?

cov(X̃i, ui) (B) Signup and view all the answers

Which component is not included in the formula for var(X̃i)?

cov(Xi, vi) (A) Signup and view all the answers

What happens to cov(X̃i, ũi) in relation to the true parameter β1 when there is measurement error?

It creates a negative bias affecting the estimation. (B) Signup and view all the answers

Study Notes

Lecture 8: Threats to Identification

Lecture 8, 25117 - Econometrics, Universitat Pompeu Fabra, November 13th, 2024.

What We Learned in the Last Lesson

A linear regression is misspecified if the marginal effect of X on Y is not constant.
Multiple OLS framework can be expanded to introduce non-linearities.
The effect of a change in the independent variable(s) can be calculated by evaluating the regression function at various values.
Polynomial regression incorporates powers of X as regressors (e.g., quadratic, cubic).
Small changes in logarithms represent proportional or percentage changes.
Regressions involving logarithms estimate proportional changes and elasticities.
Interaction terms are products of two variables.
Interaction terms allow regression slopes or intercepts to depend on the value of another variable.

Classic Pitfalls to Regression Analysis

Internal validity: Statistical inferences about causal effects are valid for the study population.
External validity: Statistical inferences can be generalized from the study population and setting to other populations and settings. Setting refers to legal, policy, and physical environment and related factors.

External Validity

Assessing external validity requires detailed substantive knowledge and judgment.
Generalizing results from one case requires considering differences in time, space, and setting, and considering legal and institutional requirements.
A meta-analysis examines many related studies on a given topic.

A Meta-Analysis – Lane (2016)

A visual representation showing frequency of findings in relation to conditional effect size; comparing findings of discrimination vs neutral vs favouritism.

A Meta-Analysis – Hahn-Holbrook et al. (2018)

A visual representation displaying prevalence of postpartum depression across various countries.

Internal Validity

Five threats to the internal validity of regression studies: omitted variable bias, wrong functional form, errors-in-variables bias, sample selection bias, and simultaneous causality.
These threats imply that the expected value of the error term given the independent variables (E[u|X]) is not zero. This means OLS estimates are biased and inconsistent.

Omitted Variable Bias (Revision)

Omitted variable bias occurs when an important variable affecting Y is omitted from the regression model.
The omitted variable must be correlated with the regressor X to cause bias.

Solutions to OVB

Measure the omitted variable and add it as a regressor in multiple regression.
Use controls to account for omitted variables, if conditional mean independence plausibly holds.
Use instrumental variables regression, panel data, or a randomized controlled experiment if variables can't be adequately controlled.

Wrong Functional Form (Revision)

Functional form misspecification occurs when the relationship between the variables is not correctly modelled (e.g., omitting an interaction term).
Correcting this involves using appropriate non-linear specifications (e.g., logarithms, interaction terms) for continuous dependent variables, or probit/logit methods for binary dependent variables

Errors-in-Variables

Errors in variables occur when the independent variable is mis-measured.
The errors in measurements can affect the slope estimate of the regression, often biasing it towards zero.

Classical Measurement Error

The measurement model assumes that the observed variable is equal to the true variable plus random noise.
The bias from this error is towards zero.

Missing Data

Missing data can sometimes introduce bias, but not always.
Data can be missing at random (not related to the dependent or independent variable).
Data might be missing based on a variable's value (or a combination of values).
Case 1 (random missing data) and 2 (missing data based on x) causes no bias, but may increase the variability of estimates.
Case 3 (missing data based in part on y or u) introduces "sample selection" bias.

Sample Selection Bias

Sample selection bias occurs when the sample selection process is influenced by the independent or dependent variable.
The selection process often relates to the outcome of interest.

Simultaneity Bias

Simultaneity bias arises when there is a causal link between Y and X. This makes the independent variable (X) correlated with the error term of the regression. X might be causing Y, but also, Y might be causing X – meaning a bidirectional relationship.

Inconsistent Standard Errors

Inconsistent standard errors can affect the validity of a regression study; even with reliable OLS estimators.
Heteroskedasticity and correlation of errors across observations are major issues. Corrections for these are typically needed when conducting hypothesis tests.

Internal Validity Checklist for Multiple Variable Regressions

Provides an organized way to examine internal validity. This list identifies potential threats to internal validity in a regression analysis.

What About Prediction?

Prediction and causal effect estimations have different objectives.
Data for the model must come from the same distribution as the out-of-sample prediction.
Predictors should explain variation in Y, not necessarily cause Y.
Estimator should provide reliable out-of-sample predictions.

Material I

Lists relevant textbooks and a specific paper related to meta-analysis.

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Description

This quiz covers the key concepts discussed in Lecture 8 of Econometrics at Universitat Pompeu Fabra. It addresses issues related to linear regression, multiple OLS frameworks, and the incorporation of non-linearities. Test your understanding of internal validity and classic pitfalls in regression analysis.