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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 N0, 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 − X2 ∑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 N0, 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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