Microeconometrics Using Stata

v:i Contents
1.5 Scalars and matrices 1 5
1.5.1 Scalars . 1 5
1 .5.2 Matrices 15
1.6 Using results from Stata commands . 16
1 .6.1 Using results from the r-class command summarize 16
1.6.2 Using results from the e-class command regress 17
1.7 Global and local macros 19
1.7.1 Global macros 19
1.7.2 Local m acros 20
1 .7.3 Scalar or macro? 21
1.8 Looping commands . . . . 22
1 .8.1 The foreach loop 23
1.8.2 The forvalues loop 23
1.8.3 The while loop 24
1.8.4 The continue command 0 24
1. 9 Some useful commands 0 24
1 . 10 Template do-file . . . . 0 25
1.11 User-written commands ')_􀟒;:>
1. 12 Stata resources 26
1 .13 Exercises 0 0 . . 26
2 Data management and graphics 29
2.1 Introduction . 29
2.2 Types of data 29
2.201 Text or ASCII data 0 30
2.2.2 Internal numeric data . 30
2.2.3 String data . . . . . . 31
2.2.4 Formats for· displaying num eric data 31
2.3 Inputting data . . . . . . . 32
2.3.1 General principles 0 32
2.3.2 Inputting data already in Stata format 33
Contents vii
2.3.3 Inputting data from the keyboard . 34
2.3.4 Inputting nontext data . . . . . . . 34
2.3.5 Inputting text data from a spreadsheet 35
2.3.6 Inputting text data in free format . 36
2.3.7 Inputting text data in fixed format 36
·2.3.8 Dictionary files 37
2.3.9 Common pitfalls 37
2.4 Data management ... 38
2.4. 1 PSID example . 38
2.4.2 Naming and labeling variables 41
2.4.3 Viewing data . . . . . . . . . 42
2.4.4 Using original documentation 43
2.4.5 Missing values . . . . . 43
2.4.6 Imputing missing data 45
2. 4. 7 Transforming data (generate, replace, egen, recode) 45
The generate and replace commands 46
The egen command . . 46
The recode command . 47
The by prefix . . . 47
Indicator variables 47
Set of indicator variables 48
Interactions 49
Demeaning . 50
2.4.8 S aving data 51
2.4.9 Selecting the sample 51
2.5 Manipulating datasets . . . . 53
2.5.1 Ordering observations and variables . 53
2.5.2 Preserving and restoring a dataset 53
2.5.3 Wide and long forms for a dataset 54
viii Contents
2.5.4 Merging datasets . . 54
2.5.5 Appending datasets . 56
2.6 Graphical display of data . . 57
2. 6.1 Stata graph commands 57
Example graph commands 57
Saving and exporting graphs . 58
Learning how to use graph commands 59
2.6.2 Box-and-whisker plot 60
2.6.3 Histogram . . . . . 61
2.6.4 Kernel density plot 62
2.6.5 Twoway scatterplots and fitted lines 64
2.6.6 Lowess, kernel, local linear, and nearest-neighbor regression 65
2.6.7 Multiple scatterplots 67
2.7 Stata resources 68
2.8 Exercises . . . . 68
3 Linear regression basics 71
3.1 Introduction . . . . . 71
3.2 Data and data summary 71
3.2.1 Data description 71
3.2.2 Variable description . 72
3.2.3 Summary statistics 73
3.2.4 More-detailed summary statistics 74
3. 2.5 Tables for data 75
3.2.6 Statistical tests 78
3.2.7 Data plots . . . 78
3.3 Regression in levels and logs . 79
3.3.1 Basic regression theory 79
3.3.2 OLS regression and matrix algebra 80
3.3.3 Properties of the OLS estimator . . 81
3.3.4 Heteroskedasticity-robust standard errors 82
Contents
Cluster-robust standard errors
Regression in logs
3.4 Basic regression analysis
Correlations . .
The regress command
Hypothesis tests . . . .
Tables of output from several regressions
Even better tables or" regression output
3.5 Specification analysis . . . . . . . . . . . . . . .
Specification tests and model diagnostics . ·
Residual diagnostic plots .
Influential observations
Specification tests . . .
Test of omitted variables
Test of the Box-Cox model
Test of the functional form of the conditional mean
Heteroskedasticity test
Omnibus test . . . . .
3.5.5 Tests have power in more than one direction
3.6 Prediction . . . . . . . . . . .
3.6.1. In-sample prediction
3.6.2 Marginal effects 0 . .
3.6.3 Prediction in logs: The retransformation problem
306.4 Prediction exercise
3.7 Sampling weights
Weights
Weighted mean
Weighted regression 0
3.7.4 Weighted prediction and MEs
3.8 OLS usirig Mata . . o o • • • • • • • •
4
3.9 Stata resources
3.10 Exercises .
Simulation
4.1 Introduction .
4.2 Pseudorandom-number generators: Introduction
Uniform random-number generation
Draws from normal . . . . . . . . . .
Draws from t, chi-squared, F, gamma, and beta
Draws from binomial, Poisson, and negative binomial .
Independent (but not identically distributed) draws from
Contents
binomial . . . . . . . . . . . . . . . . . . . . . . 118
Independent (but not identically distributed) draws from
Poisson . . . . . . . 119
Histograms and density plots 120
4.3 Distribution of t he sample mean
Stata program . . . . . .
The simulate command .
Central limit theorem simulation
The postfile command . . . . . .
Alternative central limit theorem simulation
4.4 Pseudorandom-number generators: Further details
Inverse-probability transformation .
Direct transformation .
Other methods . . . .
Draws from truncated normal
Draws from multivariate normal .
Direct draws from multivariate normal
'I\:an.sformation using Cholesky decomposition
Draws using Markov chain Monte Carlo method .
4.5 Computing integrals
4.5.1 Quadrature
Contents
5
Monte Carlo integration . . . . . . . . . .
Monte Carlo integration using different S .
4.6 Simulation for regression: Introduction . . . . . .
4.6.1 Simulation example: OLS with x2 errors
Interpreting simulation output .
Unbiasedness of estimator
Standard errors
t statistic
Test size
Number of simulations
Variations . . . . . . .
Different sample size and number of simulations .
Test power . . . . . . . . . .
Different error distributions
Estimator inconsistency . .
Simulation with endogenous regressors
4. 7 Stata resources
4.8 Exercises . .
GLS regression
5.1
5.2
Introduction .
GLS .1:1. .nd FGLS regression
5.2. 1 GLS for heteroskedastic errors .
5.2.2 GLS a.nd FGLS . . . . . . . . .
Weighted least squares and robust standard errors
Leading examples . . .
5.3 Modeling heteroskedastic data .
5.3.1 Simulated dataset .
5.3.2 OLS estimation . .
5.3.3 Detecting heteroskedasticity
5.3.4 FGLS estimation . . . . . .
5.3.5 WLS estimation . .
System of linear regressions
5.4.1 SUR model . . . .
The sureg command
Application to two categories of expenditures
Robust standard errors . . . . . . .
5.4.5 Testing cross-equation constraints .
5.4.6 Imposing cross-equation constraints .
Survey data: Weighting, clustering, and stratification .
5.5.1 Survey design . . . . . .
5.5.2 Survey mean estimation
5.5.3 Survey linear regression
5 .6 Stata resources
5.7 Exercises . . . .
Linear instrumental-variables regression
6.1 Introduction .
6.2 IV estimation
6.2.1 Ba8ic IV theory
6.2.2 Model setup .
IV estimators: IV, 2SLS, and GMM
Instrument validity and relevance
Robust standard-error estimates .
6.3 IV example . . . . . . . . . . . .
6.3.1 The ivregress command
Medical expenditures with one endogenous regressor
Available instruments . . . . . . . . . . . . .
IV estimation of an exactly identified model
IV estimation of an overidentified model
Testing for regressor endogeneity .
Tests of overidentifying restrictions
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