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Folie 1

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Implementing Restricted Least Squares in Linear Models Dr. John P. Haisken-DeNew jhaiskendenew_at_rwi-essen.de 1a. Background 1b. Background 2a. RLS – PowerPoint PPT presentation

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Title: Folie 1


1

Implementing Restricted Least Squaresin Linear
Models Dr. John P. Haisken-DeNewjhaiskendenew_at_r
wi-essen.de
2
1a. Background
  • Inter-Industry Wage Differentials- Why do
    secretaries in the steel industry make more money
    than otherwise observably identical secretaries
    in the services industry?- Calculating wage
    differentials Wages in steel gt services ?-
    Dummy Variables 0 or 1
  • Starting PointKrueger/Summers (1988)
    Efficiency Wages and the Inter-Industry Wage
    Structure, Econometrica, 56, p 259-93.- Would
    like to interpret differentials as deviations
    from a weighted average- Remove arbitrary
    selection of reference category - Excellent
    seminal paper, however technical problems -
    Attempt to implement Restricted Least Squares
    (RLS) but.. - Incorrect standard errors
    t-values systematically biased downward -
    Incorrect overall inference Variation
    systematically biased downward

3
1b. Background
  • Technical Contribution (in Handout)Haisken-DeNew
    /Schmidt (1997) Inter-Industry and
    Inter-Regional Differentials Mechanics and
    Interpretation, Review of Economics and
    Statistics, 79(3), p. 517-21.- How to implement
    Restricted Least Squares (RLS) correctly- How
    to implement RLS after any linear model (OLS, FE,
    RE)- RLS was implemented in GAUSS, LIMDEP and
    Stata (crudely)
  • Now RLS is implemented in Stata in a flexible Ado
    lthds97.adogt- What does the syntax look like?

4
2a. RLS lthds97.adogt - One Dummy Set
  • Run a linear regressionreg/xtreg depvar
    indepvars
  • Standard Syntax (only ONE dummy set)hds97
    indepvars , options
  • options description
  • refname( string ) a string containing the
    name of the "reference" categoryrealname(
    string ) a string containing a descriptive
    name for the set of dummy variablesweight(
    varname ) a string containing the name of the
    weighting variable

5
2b. RLS lthds97.adogt - Many Dummy Sets
  • Run a linear regressionreg/xtreg depvar x
    Xvar_1 Zvar_1 Zvar_2 Dvar_ XXLvar_
  • Advanced Syntax (MANY dummy variable sets)
  • global hds97_1 Xvar_1 Xvar_ref
    descriptive_name_for_Xglobal hds97_2 Zvar_1
    Zvar_2 Zvar_ref descriptive_name_for_Zglobal
    hds97_3 Dvar_ Dvar_ref
    descriptive_name_for_D ...global
    hds97_50 XXLvar_ XXLvar_ref
    descriptive_name_for_XXL (up to
    50 globals/constraints can be set)
  • Xvar_1 is a regressor used in regress or
    xtreg previously
  • Xvar_ref is a text name for the
    reference category
  • descriptive_name is a descriptive text name of
    the dummy set
  • hds97 , weight(wgt_var_name)

6
2c. RLS lthds97.adogt
  • Output created by lthds97.adogt(A) Original
    Regression (OLS, RE, FE etc) repeated(B) Each
    Dummy Variable Group using RLS is calculated -
    From k-1 Dummy Variables k Coefficients
    reported(C) Weighted Standard Deviation
    (Sampling Corrected) of RLS Betas - Measure of
    overall variation (D) F-Tests of Joint
    Significance - Are the dummy variables as a
    group significant(E) Sample Shares of each
    Dummy - What were the sample shares used to
    create the weighted average - From the weighted
    average, the deviations are calculated (see B)

7
3. Illustrative Example (in Handout)
  • American Current Population Survey (CPS)- Use
    freely available January 2004 CPS sample-
    http//www.nber.org/morg/annual/morg04.dta
  • Run simple wage regression (age 18-65)- log
    hourly wages f (age, gender, race, marital
    status, state)
  • Dummy Indicators- gender male, female- race
    white, black, other- marital status married,
    divorced, separated, single- states AK, AL WY
  • Selecting arbitrary dummy variable as reference-
    Which one? Makes no difference in the
    calculation, just in interpretation
  • With RLS, interpret the dummy variables as
    deviations from a weighted average as opposed to
    an arbitrary reference category
  • If logged wages, then interpretation -point
    deviations from average
  • Use lthds97.adogt to implement RLS

8
3. Sample Regression Output (in Handout)
  • . regress lhw age genderm raceb raceo msmar msdiv
    mssep Source SS df MS
    Number of obs 8417--------------
    ----------------------------- F( 7,
    8409) 181.36 Model 242.712792 7
    34.673256 Prob gt F 0.0000
    Residual 1607.68867 8409 .191186665
    R-squared 0.1312------------------------
    ------------------- Adj R-squared
    0.1304 Total 1850.40146 8416
    .219867093 Root MSE
    .43725-------------------------------------------
    ----------------------------------- lhw
    Coef. Std. Err. t Pgtt 95
    Conf. Interval---------------------------------
    --------------------------------------------
    age .00861 .0004585 18.78 0.000
    .0077112 .0095088 genderm .1737988
    .0095849 18.13 0.000 .1550101
    .1925876 raceb -.0730053
    .0162526 -4.49 0.000 -.1048645
    -.0411462 raceo -.0131488 .0193254
    -0.68 0.496 -.0510315 .0247338
    msmar .1365145 .0125807 10.85 0.000
    .1118532 .1611758 msdiv .1014927
    .0180303 5.63 0.000 .0661489
    .1368365 mssep .0237369 .0341694
    0.69 0.487 -.0432435 .0907174
    _cons 6.5783 .016593 396.45 0.000
    6.545774 6.610826----------------------------
    --------------------------------------------------
  • . global hds97_1 genderm genderf
    gender. global hds97_2 raceb raceo racew
    race. global hds97_3 msmar msdiv
    mssep mssgl marital. hds97

description
Name of reference
9
3a. Gender (2-Way)
10
3b. Race (3-Way)
11
3c. Marital Status (4-Way)
12
3d. State of Residence (51-Way) RefHi
13
3d. State of Residence (51-Way) RefLo
14
3d. State of Residence (51-Way)
15
4. Conclusions
  • RLS Interpretation of Dummy Variables- Even
    with a small dimension, RLS intuitive
    interpretation- Remove arbitrariness of
    reference category- Allow for importance
    weighting of each category
  • Easily Implemented with lthds97.adogt- Can be used
    after regress or xtreg and coefficients
    calculated- Useful additional statistics
    calculated
  • Flexible use- Transform a single set of dummy
    variables- Transform up to 50 sets of dummy
    variables at once
  • Areas of Application- Wage Differentials by
    Region, Industry, Occupation, Education,
    Marital Status, Race, etc
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