Introduction to Econometrics: Theory and practice

Explore the five stages of the econometric process—data collection, model formulation, estimation, evaluation, and policy analysis—and build robust models using primary, scanner, and official statistics data.

Explore simple linear regression to link an independent predictor and a dependent variable, and derive ordinary least squares estimates for beta naught and beta one to fit the regression line.

Derive the alternate ols estimators in deviation form, showing how beta1 equals the sum of deviation products over the sum of squared x deviations, and beta0 from the means.

Derive the variance of the error term; show beta1 hat variance equals sigma^2 over sum x^2 and beta0 hat variance equals sigma^2 (1/n + xbar^2 / sum x^2).

Explore the R-squared concept (coefficient of determination) and its formulas, including explained and residual sum of squares, total sum of squares, and the role of adjusted R-squared in model fit.

Learn hypothesis testing in simple linear regression, comparing null and alternative hypotheses, compute the t statistic, and make decisions using the significance level and p value.

Explore how normal distribution properties, skewness and kurtosis, and the Jarque-Bera test assess the normality of the error term.

Derive the variances of beta1 hat, beta2 hat, and beta0 hat in a multiple regression, using the blue property, fixed x values, and sigma squared, and compute their covariances.

learn to perform a t-test for individual coefficients in multiple regression, form null and alternative hypotheses, compute the t statistic, set a significance level, and compare with the critical value.

Explore the F-test for overall significance in linear regression, comparing restricted and unrestricted models, and interpreting the F statistic derived from residual sums of squares.

Learn how the Chow test detects structural breaks by comparing pooled and split regressions using an F statistic, with residual sums of squares guiding the decision.

Explore multicollinearity in the classical linear regression model, distinguishing perfect and imperfect forms, and examine causes from data collection limits, model constraints, polynomial terms, and overdetermined model.

Explore the consequences of multicollinearity: perfect multicollinearity makes beta estimates indeterminate, while imperfect multicollinearity inflates variances, lowers t-stats, and can produce high r-squared.

Detect multicollinearity by R-squared and t tests, correlations among independent variables, auxiliary regressions with Klein's rule, and VIF above ten indicating high multicollinearity.

Drop a less theoretical variable to reduce multicollinearity, combine cross-sectional and time series data, collect data, transform variables, or use principal component analysis, or do nothing if theory supports it.

Explore autocorrelation in regression errors and the first-order coefficient rho that signals relation to the immediately preceding error term. See how time-series dependence and trends create systematic error patterns.

Apply the durbin-watson and breusch-godfrey tests to detect autocorrelation, interpret residuals and hypotheses, and use critical values to decide on autocorrelation.

Explore heteroskedasticity and its causes in econometric analysis, distinguishing homoskedasticity, residual variance, and the impact of changing variance with X, outliers, omitted variables, incorrect functional form, and skewness.

explain the consequences of heteroscedasticity, showing unbiased but less efficient parameters, increased variance of beta hat one, and resulting insignificant t and f statistics due to nonconstant error variance.

Learn to detect heteroscedasticity using graphical residual plots and formal tests (Park, Goldfeld-Quandt, Breusch-Pagan), including OLS steps, log transformations, and 5% significance.