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Introduction into STATA III: Graphs and Regressions

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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
- 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

- Making a graph

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

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

- 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)

- 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

- 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

- 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

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

- Running a regression model

Globals !

Regressioncommand

Dependentvariable

Independentvariables

- Running a Regression: Output

- 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

- 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

- 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.

- 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.

- 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

- 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

- Preparation: Running the tsset command

- 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)

- Running a Panel Regression: command

- Running a Panel Regression: Output

- 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

- Heteroscedasticity within a group

Y

x

- Heteroscedasticity in panel models across groups

Y

x

- 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.

- Next Meeting
- July 4!
- Presentation: July 18
- Room RZ 01.02