Econometrics Lecture 8: Threats to Identification

The potential for misleading results when a key factor influencing the outcome is not included in the analysis. This happens when the omitted factor is both a determinant of the outcome and correlated with the variable of interest.

A regression model is considered internally valid when the statistical inferences about the relationships between variables accurately reflect the reality of the population being studied. Essentially, it means the researchers can trust their findings to be true.

Occurs when the relationship between variables is misrepresented because the model doesn't accurately capture the true functional connection. This can lead to inaccurate estimates of the impact of the variables.

A type of bias in regression analysis that arises from errors in measuring the variables of interest, leading to inaccurate estimates of the relationships between them.

Occurs when the selection of the study sample is biased, leading to inaccurate generalizations about the entire population. This can happen if certain groups are overrepresented or underrepresented in the sample.

This bias arises when there is a two-way causal relationship between variables, making it difficult to determine which variable is causing the other. This is a common problem when studying economic relationships, where variables influence each other simultaneously.

Occurs when the model does not correctly capture the relationship between the independent variable and the dependent variable. This can happen when crucial interaction terms are overlooked, leading to inaccurate estimations of the causal effects.

Measurement errors might creep in, leading to discrepancies between the observed data and the truly desired measurement. These errors might occur in different forms, including data entry mistakes, survey errors, or ambiguous questions.

Incorporating the omitted variable as an additional regressor in the model, if it can be measured, directly addresses the issue of omitting an important variable.

Utilizing control variables, if they adequately account for the omitted variable's influence, helps mitigate the bias. This requires that the control variables satisfy conditional mean independence.

Employing instrumental variables regression techniques is a valuable tool for tackling omitted variable bias. This method uses variables that influence the independent variable but not the dependent variable, helping uncover the true causal effect.

Using panel data, where each entity (individual) is observed over multiple time periods, often helps control for omitted variables. This approach allows for comparison of individual changes over time.

When possible, conducting a randomized controlled experiment is the gold standard for isolating causal effects. Randomly assigning individuals to treatment and control groups ensures that the independent variable is distributed independently of any confounding factors.

The error term in the regression equation is affected by the measurement error in the independent variable, leading to a biased estimate of the coefficient.

The actual regression equation is different from the one thought to be run because of measurement error in the independent variable.

The covariance between the measured X variable (X̃) and the combined error term (ũ) is not zero because of the measurement error, leading to bias.

The classical measurement error model assumes that the measured X variable is equal to the true X plus a random noise term that is uncorrelated with the true X and the error term in the regression equation.

In the classical measurement error model, the coefficient estimated from the regression equation is biased towards zero due to the random noise in the measured X.

The estimate of the coefficient is biased towards zero because the variance of the measured X variable is inflated by the variance of the random noise.

The bias in the coefficient estimate is proportional to the ratio of the noise variance to the true X variable variance.

If the noise variance is large compared to the true X variable variance, the coefficient estimate will be close to zero, even in large samples. This is because the measured X variable will become less informative about the true X.

The assumption that the error term in a regression model is uncorrelated with the independent variables. If this assumption is violated, the estimated coefficients will be biased and inconsistent, meaning they don't accurately reflect the true relationship between the variables.

A statistical problem in regression analysis where the variance of the error term is not constant across different values of the independent variables. This can lead to inaccurate standard errors and hypothesis tests for the regression coefficients.

Occurs when the error term in a time-series regression model is correlated across different time periods. This violates the assumption of independent errors, making the standard errors of the regression coefficients unreliable.

A type of bias introduced when the data used to estimate a prediction model comes from a different distribution than the data for which the prediction will be made.

Data is missing based on the value of one or more independent variables (X's).

Data is missing based on the value of the dependent variable (Y) or any other unobserved factors (u).

The standard errors of estimated coefficients are wider than they would be if there were no missing data, but the coefficients themselves remain unbiased.

A type of sample selection bias where individuals are chosen for a study based on their characteristics, which are correlated with the outcome of interest.

A situation where the sample is not representative of the population because the selection process is related to the outcome being studied.

To reduce sample selection bias, try avoiding selection processes that are related to the variable you're interested in.

Methods to correct for sample selection bias are available, but won't be covered in current lecture.

The functional form of the regression is incorrect, meaning the marginal effect of X on Y is not constant.

A regression model that includes powers of X as regressors.

A polynomial regression that includes X and X^2, allowing for a curved relationship between variables.

A polynomial regression that includes X, X^2, and X^3, allowing for more complex, S-shaped relationships.

A change in the logarithm of a variable can be interpreted as a percentage change in the variable.

When included as regressors, these terms allow the regression slope and/or intercept of one variable to depend on the value of another variable.