------------------------------------------------------------------------------- help for gmmcovearn (update August 2010) -------------------------------------------------------------------------------
Title
GMM estimator for covariance structure of earnings
Syntax gmmcovearn earningsvar [if] [in], required options [other options]
required_opts Description ------------------------------------------------------------------------- modeln specifies the type of model to be estimated. The default is modeln(1)
AR, no heterogeneity: modeln(1) ARMA, no heterogeneity: modeln(2) AR, random growth: modeln(3) ARMA, random growth: modeln(4) AR, random walk: modeln(5) ARMA, random walk: modeln(6) AR, combined random growth and random walk: mod > eln(7) ARMA, combined random growth and random walk: m > odeln(8)
All models include time factor loadings on the > permanent and transitory components.
yearn specifies the number of years used for the analysis
other_opts Description ------------------------------------------------------------------------- expvar specifies the name of the experience variable to be used for models that allow for heterogeneity in the life-cycle earnings profile ( modeln(3) to modeln(8)). firstyr specifies the numeric year indicator attached to the first wave of earnings. The default value is 1. earningsvar and expvar are assumed to be indexed in consecutive integers from firstyr to (firstyr + yearn -1). cohortn specifies the number of cohorts used for the analysis. The default is 1. cohortvar specifies the name of the cohort indicator variable. The default is cohort firstcohort specifies the numeric indicator of the first cohort. The default value is 1. Cohorts are assumed to be coded in consecutive integers from firstcohort to (firstcohort + cohortn -1). [e.g. In a model with four cohorts cohortvar could contain values such as 1 to 4 or 1994 to 1997. However values such as 1960, 1970, 1980 and 1990 would have to be recoded before being used.] stvalue specifies the starting values for the estimation. For T years of data and C cohorts, values are entered in the following order, separated by commas: sigalpha, rho, sigv1, sige, l2-lT, p2-pT, q2-qC, s2-sC, sigbeta, covalphabeta, sigw, theta. The user should specify starting values only for the parameters estimated in the chosen model.The default values for the l’s, p’s, q’s and s’s are 1; for sigalpha and rho they are 0.5; for sigv1 and sige they are 0.1; for sigbeta, covalphabeta and sigw they are 0; and for theta it is -0.5. newdataname allows the user to create a dataset called newdataname containing the sample moments used in the estimation and the number of observations used in calculating each of these moments. If a heterogeneous model is specified the dataset will also contain the average of expvar and the average of squared expvar. graph 1 if the user wants a graphical display of the estimated variance decomposition, 0 otherwise. The default value is 0.
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Description
gmmcovearn provides GMM estimates of the parameters of the covariance structure of earnings using the earnings variable specified in earningsvar.
The general earnings dynamics model (modeln(8)) for individual i, belonging to cohort c, with x years of experience, at time t, y_icxt, is specified as
y_icxt=q_c*p_t*(alpha_ix)+s_c*l_t*v_it
alpha_ix=alpha_i(x-1)+b_i+w_ix
And
v_it=rho*v_i(t-1)+theta*e_i(t-1)+e_it
The parameters estimated are sigalpha, rho, sig > v1, sige, l2-lT, p2-pT, q2-qC, s2-sC, sigbeta, covalphabeta, sig > w, theta.
The model is described in more detail in Doris > et al (2010a).
The command makes use of an additional program nlgmmcovearn that must be downloaded along with gmmcovearn. A detailed analysis of this approach to estimating the covariance structure of earnings can be found in Doris et al (2010b).
The program requires that the data be in wide format. It must contain an earnings (or earnings residual) variable. If using a model with heterogeneous profiles, it must also include a labour market experience variable. If using a model with cohort effects, it must also include a cohort indicator variable.
The Identity matrix is used as the GMM weighting matrix and standard errors are adjusted for unbalanced data using the approach reported in Haider(2001)
Examples Example 1: NLS Earnings Data In this example we make use of the NLS panel data set used in Wooldridge (2002) and available for download from within Stata. The dataset provides an unbalanced panel of data on earnings, schooling, and demographic information for 530 individuals from the National Longitudinal Survey for the years 1981-1987.
. use http://www.stata.com/data/jwooldridge/eacsap/nls81_87.dta
Since the data is in long format we must first reshape it prior to using gmmcovearn.
. keep id year exper lwage
. reshape wide lwage exper, i(id) j(year)
We estimate a earnings covariance structure model on log wages without heterogeneous profiles and an AR(1) model for the transitory component as follows:
. gmmcovearn lwage, yearn(7) modeln(1) cohortn(1) firstyr(81) (obs = 28)
Iteration 0: residual SS = .1643298 Iteration 1: residual SS = .05161 Iteration 2: residual SS = .0017779 Iteration 3: residual SS = .0016158 Iteration 4: residual SS = .001615 Iteration 5: residual SS = .001615 Iteration 6: residual SS = .001615 Iteration 7: residual SS = .001615 Iteration 8: residual SS = .001615 Iteration 9: residual SS = .001615
Source | SS df MS -------------+------------------------------ Number of obs = 28 Model | .796840451 16 .049802528 R-squared = 0.9980 Residual | .001614961 12 .00013458 Adj R-squared = 0.9953 -------------+------------------------------ Root MSE = .0116009 Total | .798455413 28 .028516265 Res. dev. = -193.8376
------------------------------------------------------------------------------ moment | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /sigalpha | .0683058 .0088071 7.76 0.000 .0491168 .0874948 /rho | .3130349 .0608686 5.14 0.000 .1804137 .4456561 /sigv1 | .201089 .0144893 13.88 0.000 .1695194 .2326586 /sige | .0588356 .0375667 1.57 0.143 -.0230152 .1406864 /l2 | 1.209775 .3380594 3.58 0.004 .4732069 1.946343 /l3 | 1.497133 .496198 3.02 0.011 .4160105 2.578256 /l4 | 1.142064 .3835471 2.98 0.012 .3063868 1.977742 /l5 | 1.317238 .4160183 3.17 0.008 .4108118 2.223664 /l6 | 1.438042 .464473 3.10 0.009 .4260424 2.450042 /l7 | 1.706241 .5657103 3.02 0.011 .4736643 2.938818 /p2 | .9159306 .0803285 11.40 0.000 .7409098 1.090951 /p3 | 1.112308 .0998032 11.15 0.000 .894856 1.329761 /p4 | 1.307378 .1214745 10.76 0.000 1.042708 1.572048 /p5 | 1.449588 .1411007 10.27 0.000 1.142156 1.75702 /p6 | 1.466273 .1388268 10.56 0.000 1.163796 1.768751 /p7 | 1.470464 .1267276 11.60 0.000 1.194348 1.74658 ------------------------------------------------------------------------------ coefficients and corrected standard errors below ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- sigalpha | .0683058 .024722 2.76 0.006 .0198516 .1167599 rho | .3130349 .077011 4.06 0.000 .1620961 .4639736 sigv1 | .201089 .0402344 5.00 0.000 .122231 .279947 sige | .0588356 .0456725 1.29 0.198 -.0306809 .1483521 l2 | 1.209775 .4187484 2.89 0.004 .3890433 2.030507 l3 | 1.497133 .6406559 2.34 0.019 .2414706 2.752796 l4 | 1.142064 .4497494 2.54 0.011 .2605716 2.023557 l5 | 1.317238 .5380952 2.45 0.014 .2625906 2.371885 l6 | 1.438042 .5672408 2.54 0.011 .3262706 2.549814 l7 | 1.706241 .6850775 2.49 0.013 .3635139 3.048968 p2 | .9159306 .1452523 6.31 0.000 .6312413 1.20062 p3 | 1.112308 .2170894 5.12 0.000 .6868211 1.537796 p4 | 1.307378 .237724 5.50 0.000 .8414475 1.773308 p5 | 1.449588 .2657075 5.46 0.000 .9288111 1.970366 p6 | 1.466273 .270121 5.43 0.000 .9368458 1.995701 p7 | 1.470464 .3122724 4.71 0.000 .8584214 2.082507 -------------+----------------------------------------------------------------
Hypothesis tests can be carried out using test after running the gmmcovearn command. For example a test that the permanent factor loadings, the p_t’s, are constant over time can be carried out using a Wald test as follows:
. test _b[p2]=_b[p3]=_b[p4]=_b[p5]=_b[p6]=_b[p7]=1
( 1) p2 - p3 = 0 ( 2) p2 - p4 = 0 ( 3) p2 - p5 = 0 ( 4) p2 - p6 = 0 ( 5) p2 - p7 = 0 ( 6) p2 = 1
chi2( 6) = 12.14 Prob > chi2 = 0.0588
In this example we reject constant permanent factor loadings at the 10% significance level.
Example 2: German Earnings Data To illustrate the use of gmmcovearn for a more complicated model including cohort effects we use data taken from the eight waves of the European Community Household Panel for Germany. This data set has earnings for 8 years denoted yi1994 to yi2001, a potential experience variable denoted potexp1994 to potexp2001 and 4 cohorts labeled 1 to 4. To estimate a random growth model of the covariance structure with these data we type:
gmmcovearn yi, yearn(8) modeln(3) cohortn(4) expvar(potexp) firstyr(1994)
Iteration 0: residual SS = .4483834 Iteration 1: residual SS = .0186083 Iteration 2: residual SS = .0086681 Iteration 3: residual SS = .0070441 Iteration 4: residual SS = .0070062 Iteration 5: residual SS = .0070061 Iteration 6: residual SS = .0070061 Iteration 7: residual SS = .0070061 Iteration 8: residual SS = .0070061
Source | SS df MS -------------+------------------------------ Number of obs = 144 Model | 2.16612446 26 .083312479 R-squared = 0.9968 Residual | .007006143 118 .000059374 Adj R-squared = 0.9961 -------------+------------------------------ Root MSE = .0077055 Total | 2.17313061 144 .015091185 Res. dev. = -1021.378
------------------------------------------------------------------------------ moment | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- /sigalpha | .4386704 .0605217 7.25 0.000 .318821 .5585198 /rho | .3417541 .0361788 9.45 0.000 .2701102 .4133979 /sigv1 | .0742456 .0062163 11.94 0.000 .0619355 .0865556 /sige | .0301694 .0112735 2.68 0.009 .0078448 .0524939 /l2 | 1.498371 .2427683 6.17 0.000 1.017624 1.979118 /l3 | 1.312379 .2569202 5.11 0.000 .8036072 1.821151 /l4 | 1.162531 .2301328 5.05 0.000 .7068056 1.618257 /l5 | 1.193413 .2324563 5.13 0.000 .7330861 1.65374 /l6 | 1.297056 .2507765 5.17 0.000 .8004506 1.793662 /l7 | 1.279366 .2507241 5.10 0.000 .7828636 1.775868 /l8 | 1.428739 .2791012 5.12 0.000 .8760424 1.981435 /p2 | .9842998 .0222086 44.32 0.000 .9403208 1.028279 /p3 | 1.07534 .0254406 42.27 0.000 1.024961 1.125719 /p4 | 1.08418 .0279634 38.77 0.000 1.028804 1.139555 /p5 | 1.148706 .0318299 36.09 0.000 1.085674 1.211738 /p6 | 1.168077 .033754 34.61 0.000 1.101235 1.234919 /p7 | 1.205651 .0364914 33.04 0.000 1.133388 1.277914 /p8 | 1.219382 .0372949 32.70 0.000 1.145528 1.293236 /q2 | .989772 .0419597 23.59 0.000 .9066803 1.072864 /q3 | .7322496 .0536754 13.64 0.000 .6259578 .8385415 /q4 | .4866869 .0387748 12.55 0.000 .4099022 .5634715 /s2 | .6293472 .0447309 14.07 0.000 .5407679 .7179265 /s3 | .8336288 .0377501 22.08 0.000 .7588734 .9083842 /s4 | 1.214287 .0390211 31.12 0.000 1.137014 1.291559 /sigbeta | .0003872 .0000489 7.92 0.000 .0002904 .0004841 /covalphab~a | -.012158 .001729 -7.03 0.000 -.0155819 -.0087341 ------------------------------------------------------------------------------ coefficients and corrected standard errors below ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- sigalpha | .4386704 .1706614 2.57 0.010 .1041801 .7731606 rho | .3417541 .0361377 9.46 0.000 .2709254 .4125827 sigv1 | .0742456 .0118533 6.26 0.000 .0510135 .0974776 sige | .0301694 .0104324 2.89 0.004 .0097223 .0506164 l2 | 1.498371 .2208264 6.79 0.000 1.065559 1.931183 l3 | 1.312379 .2312379 5.68 0.000 .8591613 1.765597 l4 | 1.162531 .1944341 5.98 0.000 .7814474 1.543615 l5 | 1.193413 .1942618 6.14 0.000 .8126667 1.574159 l6 | 1.297056 .2167269 5.98 0.000 .8722795 1.721833 l7 | 1.279366 .2119609 6.04 0.000 .8639299 1.694801 l8 | 1.428739 .2584156 5.53 0.000 .9222535 1.935224 p2 | .9842998 .0313717 31.38 0.000 .9228123 1.045787 p3 | 1.07534 .0433522 24.80 0.000 .9903711 1.160309 p4 | 1.08418 .050535 21.45 0.000 .9851328 1.183226 p5 | 1.148706 .0694794 16.53 0.000 1.012529 1.284883 p6 | 1.168077 .0789378 14.80 0.000 1.013362 1.322793 p7 | 1.205651 .0887034 13.59 0.000 1.031796 1.379507 p8 | 1.219382 .0922591 13.22 0.000 1.038558 1.400207 q2 | .989772 .111584 8.87 0.000 .7710713 1.208473 q3 | .7322496 .1311763 5.58 0.000 .4751487 .9893505 q4 | .4866869 .1032265 4.71 0.000 .2843667 .689007 s2 | .6293472 .0628975 10.01 0.000 .5060703 .7526241 s3 | .8336288 .0684399 12.18 0.000 .6994891 .9677684 s4 | 1.214287 .0917179 13.24 0.000 1.034523 1.394051 sigbeta | .0003872 .0001758 2.20 0.028 .0000426 .0007319 covalphabeta | -.012158 .005614 -2.17 0.030 -.0231613 -.0011547 ------------------------------------------------------------------------------
Saved results
gmmcovearn saves the following in e():
Scalars e(nummomnent) number of moment conditions used in estimation
Vectors and Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(momentc) sample moments for earnings variable for cohort c, c=1 to cohortn e(permc) predicted permanent component of earnings variance for cohort c, c=1.. cohortn e(tempc) predicted transitory component of earnings variance for cohortc, c=1.. cohortn
References
Doris, A, D. O’Neill and O.Sweetman (2010a) “GMMCOVEARN: A Stata Module for GMM Estimation of the Covariance Structure of Earnings.,” NUIM Economics Working paper No.212-10.
Doris, A, D. O’Neill and O.Sweetman (2010b) “Identification of the Covariance Structure of Earnings using the GMM Estimator,” IZA Working paper No. 4952.
Haider, S. (2001), “Earnings Instability and Earnings Inequality of Males in the United States: 1967-1991’, Journal of Labor Economics, Vol. 19(4), pp. 799-836.
Wooldridge, J. (2002), Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambdridge, Massachusetts.
Authors
Aedin Doris, Donal O’Neill and Olive Sweetman, Economics, NUI Maynooth, Ireland.