SIMULATION
Consistency Simulation
Simulate OLS under exogeneity and watch estimates concentrate as n grows.
Module 5
OLS Asymptotics and Large-Sample Inference
Learn how OLS behaves as sample size grows, why consistency matters, how large-sample inference works without normal errors, and how to use simulations and Python to understand asymptotic normality, asymptotic standard errors, LM tests, and asymptotic efficiency.
16 lessons6 to 9 hoursAdvanced Intermediate
Skills
Distinguish finite-sample properties from asymptotic properties.Explain why consistency and probability limits matter for OLS.Diagnose inconsistency from endogeneity and omitted variables.Use large-sample normal approximations for t tests, F tests, confidence intervals, and LM tests.Explain why more data help precision but do not fix bad identification or heteroskedasticity.Use Python simulations and real data to study asymptotic normality, skewness, standard-error shrinkage, and LM tests.
Progress tracking
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Module resources
16 quiz checks11 datasets10 notebooks
Lessons
1Finite-Sample versus Asymptotic ThinkingWhat changes when we think about very large samples?Open lesson2What Consistency MeansWhat does it mean for an estimator to get the right answer eventually?Open lesson3Probability Limits and the Law of Large NumbersWhy do sample averages become population information?Open lesson4Consistency of OLSWhen is OLS consistent?Open lesson5Zero Conditional Mean versus Zero CorrelationIs being uncorrelated with the error enough?Open lesson6Inconsistency and Asymptotic BiasWhy can more data make a bad estimator confidently wrong?Open lesson7Omitted Variable InconsistencyWhy does leaving out a relevant correlated variable not wash out?Open lesson8Large-Sample Inference without Normal ErrorsHow can inference work when errors are not normal?Open lesson9When Large Samples Are Not MagicWhat problems are not solved by collecting more rows?Open lesson10Asymptotic Standard ErrorsWhy do standard errors shrink with sample size?Open lesson11Histograms, Normality, and TransformationsCan a log transformation make inference easier?Open lesson12Skewness and Nonnormality DiagnosticsHow do we measure asymmetry?Open lesson13Large-Sample t and F TestsWhy do large-sample tests look familiar?Open lesson14The Lagrange Multiplier TestHow can a restricted model test omitted regressors?Open lesson15Asymptotic Efficiency of OLSIs every consistent estimator equally good?Open lesson16Module 5 Applied ProjectDo large samples save regression inference?Open lesson
Notebook labs
SIMULATION
OLS Inconsistency from Endogeneity
Show estimates converging to the wrong target when x and u are correlated.
SIMULATION
Omitted-Variable Inconsistency
Compare true and omitted models as sample size grows.
SIMULATION
Asymptotic Normality
Show coefficient distributions becoming approximately normal under several error distributions.
401K
Nonnormal Errors and Large-Sample Inference
Use 401K to discuss bounded, nonnormal outcomes and approximate inference.
GPA2
Standard Errors Shrink with n
Estimate growing GPA2 subsamples and compare standard errors.
WAGE1
Histograms, Skewness, and Transformations
Compare WAGE1 residual histograms for wage and log(wage).
CRIME1
LM Test with CRIME1
Compute the n-R-squared LM statistic and compare it with exclusion-test logic.
SIMULATION
Asymptotic Efficiency Simulation
Compare OLS with an alternative consistent estimator in simulation.
WAGE1
Applied Asymptotics Project
Plan a complete large-sample inference workflow with simulations, diagnostics, and limitations.