IntroductoryEconometrics
JeffreyM. Wooldridge Z
Chapter 1 The Nature of Econometrics and Economic Data ...................................... 1
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Part 1Z Regression Analysis with Cross-Sectional Data ........................................... 1
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Chapter 2 The Simple Regression Model ...................................................................... 1
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Chapter 3 Multiple Regression Analysis: Estimation ..................................................... 2
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Chapter 4 Multiple Regression Analysis: Inference .................................................. 4
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Chapter 5 Multiple Regression Analysis: OLS Asymptotics......................................... 5
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Chapter 6 Multiple Regression Analysis: Further Issues ............................................... 6
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Chapter7 MultipleRegression Analysis withQualitative Z Z
Information:Binaryvariables 8 Chapter 8
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Heteroskedasticity ............................................................................................ 9
Chapter 9 More on Specification and Data problems ............................................. 12
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Part 2Z Regression Analysis with Time Series Data ............................................... 14
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Chapter 10 Basic Regression analysis with Time Series Data ............................ 14
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Chapter 11 Further Issues in Using OLS with Time Series Data .......................... 16
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Chapter 12 Serial Correlation and Heteroskedasticity in Time Series Regression .. 19
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Part 3Z Advanced Topics ............................................................................................. 23
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Chapter 13 Pooling Cross Sections across Time. Simple Panel Data Methods .. 23
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Chapter 14 Advanced Panel Data Methods ............................................................... 25
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Chapter 15 Instrumental Variables Estimation and Two Stage Least Squares .... 27
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Chapter 16 Simultaneous Equations Models .............................................................. 30
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Chapter 17 Limited Dependent Variable Models and Sample Selection Corrections
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31 Chapter 18
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Advanced Time Series Topics ............................................................... 35
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Chapter 19 Carrying Out an Empirical Project ....................................................... 39
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Appendix: Some fundamentals of probability .............................................................42
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,https://www.stuvia.com/user/Smartscroll
Chapter1 The Nature of Econometrics and Economic Data Z Z Z Z Z Z
I. Thegoalof any econometricanalysisistoestimatetheparameters inthe model Z Z Z Z
and to test hypotheses about these parameters; the values
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andsigns of the parameters determine the validity of an
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economictheoryand the effects of certainpolicies.
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II. Panel data - advantages: Z Z Z
1. Having multiple observations on the same units allows us to
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Zcontrol certain unobserved characteristics ofindividuals,firms, and soon.
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Theuseof more than one observation can facilitate causal
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Zinference in situations where inferring causality would be very Z Z Z Z Z Z Z Z
hard if only a singlecross section were available.
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2. Theyoften allowustostudytheimportanceoflagsinbehaviororthe Z Z
Zresult of decisionmaking. Z Z
Part 1 Z RegressionAnalysiswithCross-Sectional
Data Chapter 2The Simple Regression Model
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I. Model: Y = b0 + b1x + u Z Z Z Z Z Z Z
1. Population regression function (PRF): E(y|x) = b0 +b1x Z Z Z Z Z Z Z Z
2. systematic part of y: b0 + b1x Z Z Z Z Z
3. unsystematic part: u Z Z
II. Sample regression function (SRF): yhat = b0hat + b1hat*x Z Z Z Z Z Z Z Z
1. PRF is something fixed, but unknown, in the population. Since
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the SRFis obtained foragivensampleofdata, anew samplewillgenerate a
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different slope andintercept.
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III. Correlation: it ispossible forutobeuncorrelated with x while Z L Z Z Z L Z Z
being correlated with functions of x, such as
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x 2. Z
E(u|x) = E(u) Cov(u, x) = 0. not vice versa.
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IV. Algebraic properties of OLS statistics Z Z Z Z
1. The sum of the OLS residuals is zero.
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2. The sample covariance between the (each) regressors and the
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residuals is zero. Consequently, thesample covariancebetweenthe fitted
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valuesand
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theresidualsis zero. Z Z Z
3. The point (x, y) is on the OLS regression line.
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4. the goodness-of-fit of the model is invariant to changes in the units of y or x.
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5. Thehomoskedasticityassumption plays no roleinshowingOLS estimatorsare L Z L L Z
unbiased.
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V. Variance
1. Var(b1) = var(u)/SSTx Z Z
a. morevariation in theunobservables (u) affectingymakesitmore Z L Z Z Z
difficultto precisely estimate b1.
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1
,https://www.stuvia.com/user/Smartscroll
b. More variability in x is preferred, since the more spread
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out is thesample of independentvariables, the easieritis totrace
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outthe relationship between E(y|x) and x. That is, the easier
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it is to estimateb1.
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2. standard error of the regression, standard error of the estimate and Z Z Z Z Z Z Z Z Z Z
1
Z
=
theroot mean squared error u2 Z Z Z
(n
Chapter3 MultipleRegression Analysis: Estimation Z Z Z
I. The power of multiple regression analysis is that is
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allows us todo in nonexperimentalenvironmentswhat
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naturalscientists areabletodoina controlled laboratory setting:
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keep other factorsfixed.
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II. Model:Y = b0 + b1x1 + b2x2 + u Z Z Z Z Z Z Z Z Z
( v y )/(
n n
b Z Z v2), where v is the OLS residuals from a simple regression of x1
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1 i1 i i1
i1
i1
on x2.Z
1. v is the part of x1 that is uncorrelated with x2, or v is x1 after the effects
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ofx2have been partialled out, or netted out. Thus, b1 measures
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the samplerelationship between y and x1 after x2 has been
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partialled out.Z Z
III. Goodness-of-fit
1. R2 =thesquared correlationcoefficientbetween theactualyandthe
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fitted values yhat.
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2. R2 neverdecreases becausethesumofsquared residualsneverincreases
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when additional regressors are added to the model.
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IV. Regression through the origin: Z Z Z Z
1. OLS residuals no longer have a zero sample average.
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2. R2 can benegative. Thismeansthatthe sample average“explains”more of
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the variation in the y than the explanatory variables.
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V. MLR Assumptions: Z
A1:linearinparameters. A2:
random sampling. Z
A3: Zero conditional mean: E(u|x1, x2, …, xk) = 0
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When A3 holds, we saythat we have Exogenous explanatoryvariables.
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Z If xj is correlated withuforany reason, thenxjissaid tobe an endogenous
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explanatory variables.
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A4: No perfect collinearity.
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A1 – A4 unbiasedness of OLS
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VI. Overspecifying the model: Z Z
2
, https://www.stuvia.com/user/Smartscroll
1. Including one or more irrelevant variables, does not affect theunbiasedness
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3
JeffreyM. Wooldridge Z
Chapter 1 The Nature of Econometrics and Economic Data ...................................... 1
Z Z Z Z Z Z Z
Part 1Z Regression Analysis with Cross-Sectional Data ........................................... 1
Z Z Z Z
Chapter 2 The Simple Regression Model ...................................................................... 1
Z Z Z Z
Chapter 3 Multiple Regression Analysis: Estimation ..................................................... 2
Z Z Z Z
Chapter 4 Multiple Regression Analysis: Inference .................................................. 4
Z Z Z Z
Chapter 5 Multiple Regression Analysis: OLS Asymptotics......................................... 5
Z Z Z Z Z
Chapter 6 Multiple Regression Analysis: Further Issues ............................................... 6
Z Z Z Z Z
Chapter7 MultipleRegression Analysis withQualitative Z Z
Information:Binaryvariables 8 Chapter 8
Z Z Z Z
Heteroskedasticity ............................................................................................ 9
Chapter 9 More on Specification and Data problems ............................................. 12
Z Z Z Z Z Z
Part 2Z Regression Analysis with Time Series Data ............................................... 14
Z Z Z Z Z
Chapter 10 Basic Regression analysis with Time Series Data ............................ 14
Z Z Z Z Z Z Z
Chapter 11 Further Issues in Using OLS with Time Series Data .......................... 16
Z Z Z Z Z Z Z Z Z
Chapter 12 Serial Correlation and Heteroskedasticity in Time Series Regression .. 19
Z Z Z Z Z Z Z Z
Part 3Z Advanced Topics ............................................................................................. 23
Z
Chapter 13 Pooling Cross Sections across Time. Simple Panel Data Methods .. 23
Z Z Z Z Z Z Z Z Z
Chapter 14 Advanced Panel Data Methods ............................................................... 25
Z Z Z Z
Chapter 15 Instrumental Variables Estimation and Two Stage Least Squares .... 27
Z Z Z Z Z Z Z Z
Chapter 16 Simultaneous Equations Models .............................................................. 30
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Chapter 17 Limited Dependent Variable Models and Sample Selection Corrections
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31 Chapter 18
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Advanced Time Series Topics ............................................................... 35
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Chapter 19 Carrying Out an Empirical Project ....................................................... 39
Z Z Z Z Z
Appendix: Some fundamentals of probability .............................................................42
Z Z Z Z
,https://www.stuvia.com/user/Smartscroll
Chapter1 The Nature of Econometrics and Economic Data Z Z Z Z Z Z
I. Thegoalof any econometricanalysisistoestimatetheparameters inthe model Z Z Z Z
and to test hypotheses about these parameters; the values
Z Z Z Z Z Z Z Z Z
andsigns of the parameters determine the validity of an
Z Z Z Z Z Z Z Z Z
economictheoryand the effects of certainpolicies.
Z Z Z Z Z Z
II. Panel data - advantages: Z Z Z
1. Having multiple observations on the same units allows us to
Z Z Z Z Z Z Z Z Z
Zcontrol certain unobserved characteristics ofindividuals,firms, and soon.
Z Z L Z L Z Z Z Z L Z
Theuseof more than one observation can facilitate causal
Z Z Z Z Z Z Z Z Z
Zinference in situations where inferring causality would be very Z Z Z Z Z Z Z Z
hard if only a singlecross section were available.
Z Z Z Z Z Z Z Z
2. Theyoften allowustostudytheimportanceoflagsinbehaviororthe Z Z
Zresult of decisionmaking. Z Z
Part 1 Z RegressionAnalysiswithCross-Sectional
Data Chapter 2The Simple Regression Model
Z Z Z Z Z Z
I. Model: Y = b0 + b1x + u Z Z Z Z Z Z Z
1. Population regression function (PRF): E(y|x) = b0 +b1x Z Z Z Z Z Z Z Z
2. systematic part of y: b0 + b1x Z Z Z Z Z
3. unsystematic part: u Z Z
II. Sample regression function (SRF): yhat = b0hat + b1hat*x Z Z Z Z Z Z Z Z
1. PRF is something fixed, but unknown, in the population. Since
Z Z Z Z Z Z Z Z Z
the SRFis obtained foragivensampleofdata, anew samplewillgenerate a
Z Z Z L Z Z Z Z
different slope andintercept.
Z Z Z
III. Correlation: it ispossible forutobeuncorrelated with x while Z L Z Z Z L Z Z
being correlated with functions of x, such as
Z Z Z Z Z Z Z Z
x 2. Z
E(u|x) = E(u) Cov(u, x) = 0. not vice versa.
Z Z Z Z Z Z Z Z Z Z
IV. Algebraic properties of OLS statistics Z Z Z Z
1. The sum of the OLS residuals is zero.
Z Z Z Z Z Z Z
2. The sample covariance between the (each) regressors and the
Z Z Z Z Z Z Z Z
residuals is zero. Consequently, thesample covariancebetweenthe fitted
Z Z Z Z Z Z Z
valuesand
Z Z
theresidualsis zero. Z Z Z
3. The point (x, y) is on the OLS regression line.
Z Z Z Z Z Z Z Z Z
4. the goodness-of-fit of the model is invariant to changes in the units of y or x.
Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z
5. Thehomoskedasticityassumption plays no roleinshowingOLS estimatorsare L Z L L Z
unbiased.
Z
V. Variance
1. Var(b1) = var(u)/SSTx Z Z
a. morevariation in theunobservables (u) affectingymakesitmore Z L Z Z Z
difficultto precisely estimate b1.
Z Z Z Z Z
1
,https://www.stuvia.com/user/Smartscroll
b. More variability in x is preferred, since the more spread
Z Z Z Z Z Z Z Z Z
out is thesample of independentvariables, the easieritis totrace
Z Z Z Z Z Z Z Z Z Z Z
outthe relationship between E(y|x) and x. That is, the easier
Z Z Z Z Z Z Z Z Z Z
it is to estimateb1.
Z Z Z Z Z
2. standard error of the regression, standard error of the estimate and Z Z Z Z Z Z Z Z Z Z
1
Z
=
theroot mean squared error u2 Z Z Z
(n
Chapter3 MultipleRegression Analysis: Estimation Z Z Z
I. The power of multiple regression analysis is that is
Z Z Z Z Z Z Z Z
allows us todo in nonexperimentalenvironmentswhat
Z Z Z Z Z Z L
naturalscientists areabletodoina controlled laboratory setting:
Z Z Z Z Z Z
keep other factorsfixed.
Z Z Z Z
II. Model:Y = b0 + b1x1 + b2x2 + u Z Z Z Z Z Z Z Z Z
( v y )/(
n n
b Z Z v2), where v is the OLS residuals from a simple regression of x1
Z Z Z Z Z Z Z Z Z Z Z Z
1 i1 i i1
i1
i1
on x2.Z
1. v is the part of x1 that is uncorrelated with x2, or v is x1 after the effects
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ofx2have been partialled out, or netted out. Thus, b1 measures
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the samplerelationship between y and x1 after x2 has been
Z Z Z Z Z Z Z Z Z
partialled out.Z Z
III. Goodness-of-fit
1. R2 =thesquared correlationcoefficientbetween theactualyandthe
Z
Z Z Z Z Z Z Z Z Z Z
fitted values yhat.
Z Z Z
2. R2 neverdecreases becausethesumofsquared residualsneverincreases
Z Z Z
when additional regressors are added to the model.
Z Z Z Z Z Z Z Z
IV. Regression through the origin: Z Z Z Z
1. OLS residuals no longer have a zero sample average.
Z Z Z Z Z Z Z Z
2. R2 can benegative. Thismeansthatthe sample average“explains”more of
Z Z Z L Z Z Z Z
the variation in the y than the explanatory variables.
Z Z Z Z Z Z Z Z Z
V. MLR Assumptions: Z
A1:linearinparameters. A2:
random sampling. Z
A3: Zero conditional mean: E(u|x1, x2, …, xk) = 0
Z Z Z Z Z Z Z Z Z
When A3 holds, we saythat we have Exogenous explanatoryvariables.
Z Z Z Z Z Z Z Z Z
Z If xj is correlated withuforany reason, thenxjissaid tobe an endogenous
Z Z Z L Z Z Z Z Z Z
explanatory variables.
Z Z
A4: No perfect collinearity.
Z Z Z
A1 – A4 unbiasedness of OLS
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VI. Overspecifying the model: Z Z
2
, https://www.stuvia.com/user/Smartscroll
1. Including one or more irrelevant variables, does not affect theunbiasedness
Z Z Z Z Z Z Z Z Z Z
3
