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It is not easy. If you think it is really hard, please do not choose my question.ECON 3338 Final exam
17 December, 2020, from 8:30 am to 11:30 am AST (duration: 3 hrs)
Wooldridge: Chapters 1 – 9, Math Refresher A – C. Review lectures, notes on
Brightspace, assignments, midterm, and tutorials.
Fundamentals of probability (Math Refresher B)
Concepts: discrete and continuous random variables; probability density function;
cumulative distribution function; joint, marginal, and conditional distributions;
independence; law of iterated expectations; Bernoulli random variable; standardized
random variable.
Know how to compute (and interpret) the expected value, variance, standard
deviation, skewness, kurtosis, covariance, and correlation coefficient when the exact
distribution is given; how to obtain marginal and conditional distributions from joint
distributions; how to compute conditional moments; how to verify independence of
random variables; know the difference between independent and uncorrelated random
variables; know the rules for computing expected values and variances of linear
combinations of random variables; know how to work with N0, 1 and t tables.
Fundamentals of mathematical statistics (Math Refresher C)
Concepts: population, random sampling, estimator, bias, unbiasedness,
consistency, efficiency, mean squared error, law of large numbers, central limit
theorem, null and alternative hypotheses, two-sided and one-sided alternatives, Type I
and Type II errors, significance level, power of a test, critical value, critical/rejection
region, acceptance region, statistical significance, p-value.
Know how to compute sample mean, sample variance, sample covariance and
correlation; to derive expected value and variance of a sample mean; to know the
difference in meaning (and formulas) between sample mean and population mean,
sample variance and population variance; the difference between an estimator and an
estimate. Know how to compute confidence intervals for the population mean, how to
interpret confidence intervals, what distribution to use, how to test hypotheses about
population mean with known and unknown variance, how to set up the null and
alternative hypotheses, to construct test-statistics and find critical values, compute
p-values, how to interpret test-statistics and p-values.
Chapter 1
Concepts: cross-sectional data, time series, panel data, pooled cross section,
experimental and nonexperimental data, data frequency, ceteris paribus, causal effect.
Chapter 2
Concepts: regression, dependent and independent variables, population
regression function, sample regression line, scatter plot, error/disturbance term
(explain its presence in the model), residuals, fitted value, ordinary least squares,
assumptions of the classical linear regression model, normal equations, point
estimators, interval estimators, homoskedasticity, heteroskedasticity, SST, SSR, SSE,
standard error of the regression, standard error of the OLS estimators, goodness of fit,
coefficient of determination R2, regression through the origin, regression on a
constant, Gauss-Markov assumptions.
Know how to apply the least squares approach (formulate the objective function;
minimize it by solving the first-order conditions); how to derive expectation and
variance of the OLS coefficients for the models with one unknown coefficient; know
how to prove such statements as ∑Xi − X2  ∑Xi
2 − nX2
; how to compute and
interpret R2 knowing SSR, SSE, or SST; how to interpret regression coefficients in a
standard model, log-log model (constant elasticity model), semilog models (log-linear
and linear-log); know statistical properties of the OLS estimators; know how to prove
the decomposition of SST.
Chapter 3
Concepts: least squares method, normal equations, assumptions of the classical
linear regression model (be ready to explain their importance), homoskedasticity,
heteroskedasticity, SSR, SST, SSE, population regression function, sample
regression function, partial effect, standard error of the regression, Gauss-Markov
theorem, BLUE, goodness of fit, coefficient of determination, partial effect, regression
through the origin, omitted variable bias, endogenous regressor, multicollinearity,
perfect collinearity.
Know how to apply the least squares approach in the multivariate case: formulate
the objective function and derive the first-order conditions (do not solve the first-order
conditions); know how to interpret the regression coefficients, including the models
with quadratic terms and log transformations.; discuss the consequences of omitting
relevant regressors and including irrelevant regressors; know statistical properties of
the OLS estimators in a multivariate regression with normally distributed errors; how to
compute and interpret R2 knowing SSR, SSE, SST. Explain what happens to OLS
estimators in the presence of (i) perfect collinearity and (ii) less-than-perfect
multicollinearity.
Chapter 4
Concepts: classical linear model, exclusion restrictions, t statistic, F statistic, joint
hypotheses testing, joint (in)significance, test for overall significance (goodness-of-fit
test); restricted and unrestricted models.
Know how to compute confidence intervals for regression coefficients, how to
interpret confidence intervals, what distribution to use, how to test hypotheses about
individual regression coefficients, how to set up the null and alternative hypotheses, to
find test statistics and critical values, compute p-values, how to interpret test statistics
and p-values, how to work with N0, 1 table, t −table and F-table; how to test
regression coefficients for significance, how to test the model for goodness of fit. Know
how to construct the F-statistic using SSR or R2 for restricted and unrestricted
regressions; how to test one linear restriction using t-statistic, how to test several
linear restrictions using F-statistic.
Chapter 5
Asymptotic properties (consistency and normality) of the OLS estimators (even
when errors are not normally distributed); assumptions required for consistency and
asymptotic normality.
Chapter 6
Concepts: scaling and units of measurement, adjusted R2, interaction terms,
prediction error, beta coefficients.
Know how coefficients, standard errors and R2 change when the data are reported
using different scale (units of measurement); know how to interpret the coefficients in
a polynomial regression (with regressors X,X2, etc.), log-log model (constant elasticity
model), semilog model, regression with interaction terms; how and when to use R2
and adjusted R2 to select the best model.
Chapter 7 (skip 7.6a)
Concepts: dummy variables, omitted category (base group), dummy variable trap,
perfect collinearity, Chow test (test for a structural break), linear probability model.
Know how to replace a categorical variable with a set of dummy variables; how to
interpret coefficients for the dummy variables (including the model with log dependent
variable); how to interpret interaction terms with dummy variables; how to test for a
structural break using subsamples or dummy variables; know how to interpret fitted
values in the linear probability model, know why error terms in the linear probability
model are heteroskedastic.
Chapter 8
Concepts: Breusch-Pagan test for heteroskedasticity, White test for
heteroskedasticity, heteroskedasticity-robust standard errors, weighted least squares
estimation.
Discuss the consequences of heteroskedasticity for OLS estimators and
hypothesis testing; explain how to work with OLS estimators and how to test
hypotheses about regression coefficients in the case of heteroskedasticity; know
procedures for Breusch-Pagan and White tests for heteroskedasticity
Chapter 9 (skip 9.2c, 9.3, 9.5, 9.6)
Concepts: functional form misspecification, regression specification error test
(RESET), proxy variable, measurement error.
Know how to implement and interpret the RESET test; know its purpose.
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