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Introduction into STATA III: Graphs and Regressions. Prof. Dr. Herbert Brücker University of Bamberg Seminar “Migration and the Labour Market” June 27, 2013. 1GRAPHS Present your data graphically

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Introduction into stata iii graphs and regressions

Introduction into STATA III:

Graphs and Regressions

Prof. Dr. Herbert Brücker

University of Bamberg

Seminar “Migration and the Labour Market”

June 27, 2013


Introduction into stata iii graphs and regressions

  • 1GRAPHS

  • Present your data graphically

  • It is usually helpful if you present the main information /vairables in your data set graphically

  • There are many graphical commands, use the Graphicsmenue

  • the simplest way is to show the development of your variable(s) over time

  • Syntax:

    • graph twoway line [variable1] [variable2] if …

    • graph twoway line wqjt year if ed==1 & ex == 1

  • This produces a two-dimensional variable with the wage on the vertical and the year on the horizontal axis for education group 1 and experience group 1


Introduction into stata iii graphs and regressions

  • Making a graph


Introduction into stata iii graphs and regressions

  • Graph of mean wage in education 1 and experience 1 group


Introduction into stata iii graphs and regressions

  • Graph of migration rate in edu 1 and exp 1 group


Introduction into stata iii graphs and regressions

  • GRAPHS: Two Y-axes

  • Two axes: It might be useful to display two variables in different y-axes with different scales (e.g. wages and migration rates)

  • Syntax:

    • graph (twoway line [variable1] [variable2], yaxis(1)) (twoway line [variable3] [variable2], yaxis(2)) if …

    • graph (twoway line wqjt year, yaxis(1)) (twoway line mqjt year, yaxis(2)) if ed==1 & ex == 1

  • This produces a two-dimensional graph with the wage on the first vertical axis (y1) and the migration rate on the second vertical axis (y2)


Introduction into stata iii graphs and regressions

  • GRAPHS: Scatter plots (I/II)

  • Scatter plots display the relations between two variables

  • Syntax:

    • graph twoway scatter [variable1] [variable2] if …

    • graph twoway scatter wqjtmqjt if ed==1

  • This produces a two-dimensional scatter plot which shows the relation between the two variables


Introduction into stata iii graphs and regressions

  • GRAPHS: Scatter plots (II/II)

  • You can also add a linear fitted line:

  • Syntax:

    • graph twoway scatter [variable1] [variable2] if …|| lfit [variable1] [variable2] if …

    • graph twoway scatter wqjtmqjt if ed==1|| lfitwqjtmqjt if ed==1


Introduction into stata iii graphs and regressions

  • 2Running regressions

  • The standard OLS regression command in STATA is

  • Syntax

    • regress depvar [list of indepvar ] [if], [options]

    • e.g. regress ln_wijtmijt $D_i $D_j $D_t


Introduction into stata iii graphs and regressions

The multivariate linear regression model

The general econometric model:

γi indicates the dependent (or: endogenous) variable

x1i,ki exogenous variable, explaining the independent variable

β0 constantorthe y-axisintercept (if x = 0)

β1,2,k regressioncoefficientorparameterofregression

εi residual, disturbanceterm


Introduction into stata iii graphs and regressions

  • Running a regression model

Globals !

Regressioncommand

Dependentvariable

Independentvariables


Introduction into stata iii graphs and regressions

  • Running a Regression: Output


Introduction into stata iii graphs and regressions

  • How to interpret the output of a regression

variance of model

degreesoffreedom

1. Observations2. fit of the model

3. F-Test 4. R-squared5. adjusted R-squared

6. Root Mean

Standard Error

β1

95% confidenceinterval

β0

analysis of significance levels


Introduction into stata iii graphs and regressions

  • Recall the Borjas (2003)-Modell

  • yijt = βmijt + si + xj + tt + (si ∙ xj) + (si ∙ tt) + (xj ∙ tt) + εijt

  • This model in STATA Syntax:

  • regress ln_wqjtmqjt $Di $Dj $Dt $Dij $Dit $Djt

  • where

  • ln_wqjt: dependent variable (log wage)

  • mqjt: migration share in educatipn-experience cell

  • $Di: global for education dummies

  • $Dj: global for experience dummies

  • $Dt: global for time dummies

  • $Dij: global for interaction education-experience dummies

  • $Dit: global for education-time interaction dummies

  • $Djt: global for experience-time interaction dummies


Introduction into stata iii graphs and regressions

  • What is a global?

  • A global defines a vector of variables

  • Defining a global:

  • STATA Syntax:

  • global [global name] [variable1] [variable2] …[variablex]

  • global Di Ded1 Ded2 Ded3

  • Using a global e.g. in a regression:

  • regress [depvariable] [other variable] [$global name]

  • regress ln_wqjtmqjt $Di

  • This is equivalent to:

  • regress ln_wqjtmqjt Ded1 Ded2 Ded3

  • Thus, globals are useful shortcuts for lists (vectors) of variables.


Introduction into stata iii graphs and regressions

  • An alternative to the Borjas (2003) model:

  • yijkt = βmijt + γk (zk∙ mijt) + si + xj + zk + tt + (si ∙ xj) + (si ∙ zk) + (xj ∙ zk) + (si ∙ tt) + (xj ∙ tt) + (zk ∙ tt) + εijt

  • where

  • zkis a dummy for foreigners (1 if foreigner, 0 if native)

  • γk is a coefficient, whichcapturesthe different impact on foreigners,

  • k (k= 0, 1) is a subscriptfornationality

  • Idea: theslopecoefficientγk issignificantly different fromzero, ifnatives andimmigrantsareimperfectsubstitutes in thelabourmarket.

  • Problem: Wehavetoreorganizethedataset such thatitdeliversthe wage andunemploymentrates etc. forforeignersand natives.


Introduction into stata iii graphs and regressions

  • 3Panel Models

  • Very often you use panel models, i.e. models which have a group and time series dimension

  • There exist special estimators for this, e.g. fixed or random effects models

    • A fixed effects model is a model where you have a fixed (constant) effect for each individual/group. This is equivalent to a dummy variable for each group

  • A random effects model is a model where you have a random effect for each individual group, which is based on assumptions on the distribution of individual effects


Introduction into stata iii graphs and regressions

  • Panel Models

  • Preparing data for Panel Models:

  • For running panel models STATA needs to identify the group(individual) and time series dimension

  • Therefore you need an index for each group and an index for each time period

  • Then use the tsset command to organize you dataset as a panel data set

  • Syntax:

    • tsset index year

  • where index is the group/individual index and year the time index


Introduction into stata iii graphs and regressions

  • Preparation: Running the tsset command


Introduction into stata iii graphs and regressions

  • Running Regressions: Panel Models

  • Then you can use panel estimators, e.g. the xtreg estimator

  • Syntax

    • xtregressdepvar [list of indepvar ] [if], [options]

    • xtregressln_wijtm_ijt, fe

  • i.e. in the example we run a simple fixed effects panel regression model which is equivalent to include a dummy variable for each group (in this case education-experience group)


Introduction into stata iii graphs and regressions

  • Running a Panel Regression: command


Introduction into stata iii graphs and regressions

  • Running a Panel Regression: Output


Introduction into stata iii graphs and regressions

  • Running Regressions: Panel Models

  • There are other features of panel estimators which are helpful

  • Heteroscedasticity:

    • Heteroscedasticity: the variance is not constant, but varies across groups

    • xtpcse , p(h) corrects for heteroscedastic standard errors

    • xtgls , p(h) corrects coefficient and standard errors for panel heteroscedasticity, but may produce biased results depending on the group and time dimension of the panel

    • Note: p(h) after the comma is a so-called “option” in the STATA syntax


Introduction into stata iii graphs and regressions

  • Heteroscedasticity within a group

Y

x


Introduction into stata iii graphs and regressions

  • Heteroscedasticity in panel models across groups

Y

x


Introduction into stata iii graphs and regressions

  • Running Regressions: Panel Models

  • Contemporary correlation across cross-sections

    • Contemporary correlation: the error terms are contemporarily correlated across cross-sections, e.g. due to macroeconomic disturbances

    • xtgls , p(c) corrects for contemporary correlation and panel heteroscedasticity, but may produce biased results depending on the group and time dimension of the panel.


Introduction into stata iii graphs and regressions

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