Step 2: Develop the level 1 model

Using SPSS Mixed

Add individual level explanatory variables, edyears, age, agesqr and female, to the null model. Compare the results with the OLS model.

SPSS menus

In the main menu, select Analyze, Mixed models, Linear. In the first dialogue box, enter firmno under Subjects and press continue. In the following box, define wage as the dependent variable and edyears, age, agesqr, and female as covariates.

Press Fixed and define the ‘fixed effects’, i.e. the fixed regression coefficients.

The rest is similar to the dialogue boxes for the null model.

SPSS syntax

Pressing Paste produces the following syntax:

MIXED wage WITH edyears age agesqr female
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=edyears age agesqr female | SSTYPE(3)
/METHOD=ML
/PRINT=SOLUTION
/RANDOM=INTERCEPT | SUBJECT(firmno) COVTYPE(VC).

SPSS output

Table 4.4. Estimates of Fixed Effectsa

Table 4.5. Estimates of Covariance Parametersa

Using Stata xtmixed

. xtmixed wage edyears age agesqr female || firmno: , variance

Table 4.6.

Comparison with OLS model

The fixed regression coefficients differ from the OLS estimates, but not substantially so. Returns on education are slightly lower (4.49 vs. 4.56) and the female disadvantage is smaller (-15.37 vs. 17.39). The fixed coefficients are interpreted in the same way as for OLS regression. The standard errors of the coefficients seem to be surprisingly similar. This is probably due to the high number of firms (880).

Questions:

  1. Calculate the pseudo R squares for the two levels.
  2. How much of the between-firm variation in wages can be explained by compositional factors?

Answers:
  1. Explained variance at level 1: (643.936 - 476.334)/643.936 = 0.260. Explained variance at level 2: (260.893 - 116.291)/260.893 = 0.554.
  2. About 55 per cent.
Go to next page >>