Introduction to Econometrics

Höfundur: Christopher Dougherty (Útgáfa: 5)
Introduction to Econometrics

Kaup valmöguleikar

Introduction to Econometrics provides students with clear and simple mathematics notation and step-by-step explanations of mathematical proofs, to give them a thorough understanding of the subject. Extensive exercises throughout build confidence by encouraging students to apply econometric techniques. Retaining its student-friendly approach, Introduction to Econometrics has a comprehensive revision guide to all the essential statistical concepts needed to study econometrics, additional Monte Carlo simulations, new summaries, and non-technical introductions to more advanced topics at the end of chapters.

Nánar um bókina

Útgefandi
Oxford University Press Academic UK
ISBN
9780192655783
Print ISBN
9780199676828
Format
Page Fidelity (PDF)
Útgáfa
5
Höfundar
Christopher Dougherty
Tungumál
English
Útgefið
2016-04-21
Prent takmörkun á líftíma
100
Flokkar
Hagfræði

Kaflar

  • Preface
  • Contents
  • Introduction
  • Why study econometrics?
  • Aim of this text
  • Mathematics and statistics prerequisites for studying econometrics
  • Additional resources
  • Econometrics software
  • Review: Random Variables, Sampling, Estimation, and Inference
  • R.1 The need for a solid understanding of statistical theory
  • R.2 Discrete random variables and expectations
  • Discrete random variables
  • Expected values of discrete random variables
  • Expected values of functions of discrete random variables
  • Expected value rules
  • Population variance of a discrete random variable
  • Fixed and random components of a random variable
  • R.3 Continuous random variables
  • Probability density
  • R.4 Population covariance, covariance and variance rules, and correlation
  • Covariance
  • Independence of random variables
  • Covariance rules
  • Variance rules
  • Correlation
  • R.5 Samples, the double structure of a sampled random variable, and estimators
  • Sampling
  • Estimators
  • R.6 Unbiasedness and efficiency
  • Unbiasedness
  • Efficiency
  • Conflicts between unbiasedness and minimum variance
  • R.7 Estimators of variance, covariance, and correlation
  • R.8 The normal distribution
  • R.9 Hypothesis testing
  • Formulation of a null hypothesis and development of its implications
  • Compatibility, freakiness, and the significance level
  • R.10 Type II error and the power of a test
  • R.11 t tests
  • The reject/fail-to-reject terminology
  • R.12 Confidence intervals
  • R.13 One-sided tests
  • H0:μ=μ0, H1:μ=μ1
  • Generalizing from H0:μ=μ0, H1:μ=μ1 to H0:μ=μ0, H1:μ>μ0
  • H0:μ=μ0, H1:μ<μ0
  • One-sided t tests
  • Important special case: H0:μ=0
  • Anomalous results
  • Justification of the use of a one-sided test
  • R.14 Probability limits and consistency
  • Probability limits
  • Why is consistency of interest?
  • Simulations
  • R.15 Convergence in distribution and central limit theorems
  • Limiting distributions
  • Key terms
  • Appendix R.1 Unbiased estimators of the population covariance and variance
  • Appendix R.2 Density functions of transformed random variables
  • 1 Simple Regression Analysis
  • 1.1 The simple linear model
  • 1.2 Least squares regression with one explanatory variable
  • 1.3 Derivation of the regression coefficients
  • Least squares regression with one explanatory variable: the general case
  • Two decompositions of the dependent variable
  • Regression model without an intercept
  • 1.4 Interpretation of a regression equation
  • Changes in the units of measurement
  • 1.5 Two important results relating to OLS regressions
  • The mean value of the residuals is zero
  • The sample correlation between the observations on X and the residuals is zero
  • 1.6 Goodness of fit: R2
  • Example of how R2 is calculated
  • Alternative interpretation of R2
  • Key terms
  • 2 Properties of the Regression Coefficients and Hypothesis Testing
  • 2.1 Types of data and regression model
  • 2.2 Assumptions for regression models with nonstochastic regressors
  • 2.3 The random components and unbiasedness of the OLS regression coefficients
  • The random components of the OLS regression coefficients
  • The unbiasedness of the OLS regression coefficients
  • Normal distribution of the regression coefficients
  • 2.4 A Monte Carlo experiment
  • 2.5 Precision of the regression coefficients
  • Variances of the regression coefficients
  • Standard errors of the regression coefficients
  • The Gauss–Markov theorem
  • 2.6 Testing hypotheses relating to the regression coefficients
  • 0.1 percent tests
  • One-sided tests
  • Confidence intervals
  • 2.7 The F test of goodness of fit
  • Relationship between the F test of goodness of fit and the t test on the slope coefficient in simple
  • Key terms
  • Appendix 2.1 The Gauss–Markov theorem
  • 3 Multiple Regression Analysis
  • 3.1 Illustration: a model with two explanatory variables
  • 3.2 Derivation of the multiple regression coefficients
  • The general model
  • Interpretation of the multiple regression coefficients
  • 3.3 Properties of the multiple regression coefficients
  • Unbiasedness
  • Efficiency
  • Precision of the multiple regression coefficients
  • t tests and confidence intervals
  • 3.4 Multicollinearity
  • Multicollinearity in models with more than two explanatory variables
  • Examples of multicollinearity
  • What can you do about multicollinearity?
  • 3.5 Goodness of fit: R2
  • F tests
  • Further analysis of variance
  • Relationship between F statistic and t statistic
  • 3.6 Prediction
  • Properties of least squares predictors
  • Key terms
  • 4 Nonlinear Models and Transformations of Variables
  • 4.1 Linearity and nonlinearity
  • 4.2 Logarithmic transformations
  • Logarithmic models
  • Semilogarithmic models
  • The disturbance term
  • Comparing linear and logarithmic specifications
  • 4.3 Models with quadratic and interactive variables
  • Quadratic variables
  • Higher-order polynomials
  • Interactive explanatory variables
  • Ramsey’s RESET test of functional misspecification
  • 4.4 Nonlinear regression
  • Key terms
  • 5 Dummy Variables
  • 5.1 Illustration of the use of a dummy variable
  • Standard errors and hypothesis testing
  • 5.2 Extension to more than two categories and to multiple sets of dummy variables
  • Joint explanatory power of a group of dummy variables
  • Change of reference category
  • The dummy variable trap
  • Multiple sets of dummy variables
  • 5.3 Slope dummy variables
  • Joint explanatory power of the intercept and slope dummy variables
  • 5.4 The Chow test
  • Relationship between the Chow test and the F test of the explanatory power of a set of dummy variabl
  • Key terms
  • 6 Specification of Regression Variables
  • 6.1 Model specification
  • 6.2 The effect of omitting a variable that ought to be included
  • The problem of bias
  • Invalidation of the statistical tests
  • R2 in the presence of omitted variable bias
  • 6.3 The effect of including a variable that ought not to be included
  • 6.4 Proxy variables
  • Unintentional proxies
  • 6.5 Testing a linear restriction
  • F test of a linear restriction
  • The reparameterization of a regression model
  • t test of a linear restriction
  • Multiple restrictions
  • Zero restrictions
  • Key terms
  • 7 Heteroskedasticity
  • 7.1 Heteroskedasticity and its implications
  • Possible causes of heteroskedasticity
  • 7.2 Detection of heteroskedasticity
  • The Goldfeld–Quandt test
  • The White test
  • 7.3 Remedies for heteroskedasticity
  • Weighted least squares
  • Mathematical misspecification
  • Robust standard errors
  • How serious are the consequences of heteroskedasticity?
  • Key terms
  • 8 Stochastic Regressors and Measurement Errors
  • 8.1 Assumptions for models with stochastic regressors
  • 8.2 Finite sample properties of the OLS regression estimators
  • Unbiasedness of the OLS regression estimators
  • Precision and efficiency
  • 8.3 Asymptotic properties of the OLS regression estimators
  • Consistency
  • Asymptotic normality of the OLS regression estimators
  • 8.4 The consequences of measurement errors
  • Measurement errors in the explanatory variable(s)
  • Measurement errors in the dependent variable
  • Imperfect proxy variables
  • Example: Friedman’s permanent income hypothesis
  • 8.5 Instrumental variables
  • Asymptotic distribution of the IV estimator
  • Multiple instruments
  • The Durbin–Wu–Hausman specification test
  • Key terms
  • 9 Simultaneous Equations Estimation
  • 9.1 Simultaneous equations models: structural and reduced form equations
  • 9.2 Simultaneous equations bias
  • A Monte Carlo experiment
  • 9.3 Instrumental variables estimation
  • Underidentification
  • Exact identification
  • Overidentification
  • Two-stage least squares
  • The order condition for identification
  • Unobserved heterogeneity
  • Durbin–Wu–Hausman test
  • Key terms
  • 10 Binary Choice and Limited Dependent Variable Models, and Maximum Likelihood Estimation
  • 10.1 The linear probability model
  • 10.2 Logit analysis
  • Generalization to more than one explanatory variable
  • Goodness of fit and statistical tests
  • 10.3 Probit analysis
  • 10.4 Censored regressions: tobit analysis
  • 10.5 Sample selection bias
  • 10.6 An introduction to maximum likelihood estimation
  • Generalization to a sample of n observations
  • Generalization to the case where σ is unknown
  • Application to the simple regression model
  • Goodness of fit and statistical tests
  • Key terms
  • Appendix 10.1 Comparing linear and logarithmic specifications
  • 11 Models Using Time Series Data
  • 11.1 Assumptions for regressions with time series data
  • 11.2 Static models
  • 11.3 Models with lagged explanatory variables
  • Estimating long-run effects
  • 11.4 Models with a lagged dependent variable
  • The partial adjustment model
  • The error correction model
  • The adaptive expectations model
  • More general autoregressive models
  • 11.5 Assumption C.7 and the properties of estimators in autoregressive models
  • Consistency
  • Limiting distributions
  • t tests in an autoregressive model
  • 11.6 Simultaneous equations models
  • 11.7 Alternative dynamic representations of time series processes
  • Time series analysis
  • Vector autoregressions
  • Key terms
  • 12 Autocorrelation
  • 12.1 Definition and consequences of autocorrelation
  • Consequences of autocorrelation
  • Autocorrelation with a lagged dependent variable
  • 12.2 Detection of autocorrelation
  • The Breusch–Godfrey test
  • The Durbin–Watson test
  • 12.3 Fitting a model subject to AR(1) autocorrelation
  • Issues
  • Inference
  • The common factor test
  • 12.4 Apparent autocorrelation
  • 12.5 Model specification: specific-to-general versus general-to-specific
  • Comparison of alternative models
  • The general-to-specific approach to model specification
  • Key terms
  • Appendix 12.1 Demonstration that the Durbin–Watson d statistic approximates 2 − 2r in large samp
  • 13 Introduction to Nonstationary Time Series
  • 13.1 Stationarity and nonstationarity
  • Stationary time series
  • Nonstationary time series
  • Deterministic trend
  • Difference-stationarity and trend-stationarity
  • 13.2 Spurious regressions
  • Spurious regressions with variables possessing deterministic trends
  • Spurious regressions with variables that are random walks
  • 13.3 Graphical techniques for detecting nonstationarity
  • 13.4 Tests of nonstationarity: the augmented Dickey–Fuller t test
  • Untrended process
  • Trended process
  • 13.5 Tests of nonstationarity: other tests
  • The Dickey–Fuller test using the scaled estimator of the slope coefficient
  • The Dickey–Fuller F test
  • Power of the tests
  • Further tests
  • Tests of deterministic trends
  • Further complications
  • 13.6 Cointegration
  • 13.7 Fitting models with nonstationary time series
  • Detrending
  • Differencing
  • Error correction models
  • Key terms
  • 14 Introduction to Panel Data Models
  • 14.1 Reasons for interest in panel data sets
  • 14.2 Fixed effects regressions
  • Within-groups fixed effects
  • First differences fixed effects
  • Least squares dummy variable fixed effects
  • 14.3 Random effects regressions
  • Assessing the appropriateness of fixed effects and random effects estimation
  • Random effects or OLS?
  • A note on the random effects and fixed effects terminology
  • 14.4 Differences in differences
  • Key terms
  • APPENDIX A Statistical tables
  • APPENDIX B Data sets
  • Bibliography
  • Author Index
  • Subject Index