*! version 3.0 14feb2019 Pablo Mitnik

Title

igeset -- Set estimation of intergenerational income elasticities (IGEs) with a single set of instruments

Syntax and options

igeset cvar pvar [if] [in] [weight][, options]

where cvar is the name of the children's income or log income variable, as relevant, and pvar is the name of the log parental-income variable

Required options
ige(igetype) igetype is either igee, the IGE of the expectation, or igeg, the IGE of the geometric mean

insts(varlist:varlist1) varlist1 specifies the set of instruments used to produce an estimate of the upper bound

Other options
exvars(varlist:varlist2) varlist2 specifies exogenous variables, i.e., independent variables other than log parental income

ci(citype) citype is either im, Imbens and Manki's (2004) confidence interval (the default); nr, Nevo and Rosen's (2012) confidence interval; or imnr, both confidence intervals

gmm requires that the GMM estimator be used for the estimation of the IGE of the geometric mean (the default is to use the 2SLS estimator)

igmm requires that the iterative instead of two-step GMM estimator be used; requires option gmm if option ige(igeg) has been specified

cluster(varname:varlist3) varlist3 are variables identifying sample clusters

technique() technique() specifies the optimization technique to use with the instrumental-variable estimator of the IGE of the expectation, which may be gn (the default), nr, dfp, or bfgs

level(#) confidence level; default is level(95)

show requires that the full results of estimating the individual bound estimates on which the reported set estimate is based be shown

fweights, iweights, and pweights are allowed; see weight.

Description

igeset set estimates, or "brackets," IGEs of children's income with respect to parental income. To estimate the lower bound, igeset uses an estimator assumed to be affected by attenuation bias given the parental
information available (i.e., a short-run instead of a long-run parental-income measure). To estimate the upper bound, igeset uses an instrumental-variable (IV) estimator and one (and only one) set of invalid
instruments assumed to be positively correlated with the error term of the population regression function of interest. The estimated IGE may be the IGE of the expectation or the IGE of the geometric mean
(see Mitnik and Grusky [Forthcoming] for these two IGEs).

Remarks and related commands

igeset set estimates (a) the IGE of the geometric mean, by combining a lower-bound estimate obtained with the Ordinary Least Squares estimator (see regress) and an upper-bound estimate obtained with a linear
IV estimator (gmm or 2sls, see ivregress), or (b) the IGE of the expectation, by combining a lower-bound estimate obtained with the Poisson Pseudo Maximum Likelihood estimator (see poisson) and an
upper-bound estimate obtained with the Poisson gmm additive-error IV estimator (see ivpoisson). If the option show is specified, igeset shows the full results of its estimation of the upper and lower bounds. This allows the user to confirm that igeset produces the same estimates as those obtained with
the underlying commands. igeset computes Imbens and Manski's (2004) and (optionally) Nevo and Rosen's (2012: Sec. IV) confidence intervals for the partially identified IGEs
it estimates (rather than for the identified set). See Mitnik (Forthcoming) for a detailed discussion regarding the set estimation of IGEs.

While igeset is an estimation command, the command igesetci (see igesetci, if installed) is a closely related post-estimation command that computes the confidence intervals computed by
igeset after the upper and lower bounds have already been estimated by the user, and which provides more flexibility (e.g., gives the user full control of estimators, optimization options, VCE options and so forth) but requires
more coding.

The command igeset cannot be used to estimate IGEs with multiple sets of instruments (as different from multiple instruments). The command igeintb may be used instead. It set estimates IGEs by generating multiple
estimates of the upper-bound and selecting the minimun estimate as the final estimate of the upper bound (see igeintb, if installed).

Examples

Read and describe data

.use igeset_data, clear
.de

IGE of the expectation: Three examples

.igeset c_inc p_ln_inc, insts(p_educ) ige(igee)

.igeset c_inc p_ln_inc [pw = c_wcore], insts(i.p_occ) ige(igee) ci(nr) exvars(c.p_age c.p_age#c.p_age) igmm

.igeset c_inc p_ln_inc, insts(c.p_educ c.p_educ#c.p_educ i.p_occ) ige(igee) ci(imnr) igmm tech(nr)

IGE of the geometric mean: Three examples

.igeset c_ln_inc p_ln_inc, insts(p_educ) ige(igeg)

.igeset c_ln_inc p_ln_inc [pw = c_wcore], insts(i.p_occ) ige(igeg) ci(nr) exvars(c.p_age c.p_age#c.p_age)

.igeset c_ln_inc p_ln_inc, insts(c.p_educ c.p_educ#c.p_educ i.p_occ) ige(igeg) ci(imnr) gmm igmm

Stored results

igeset stores the following in e():

Macros

e(cmd) igeset

e(ige) igeg or igee

e(ci) im, nr, or imnr

e(cvar) children's income or log income variable

e(pvar) log parental-income variable

e(insts) instruments

e(exvars) exogenous variables

e(estimator) gmm or 2sls

e(gmmestimator) twostep or igmm

e(wtype) weight type

e(wexp) weight expression

e(clustvar) name of cluster variable/s

e(technique) optimization technique used to estimate the upper bound of the igee

Scalars

e(N) number of observations

e(pe_lb) lower bound of set estimate

e(pe_ub) upper bound of set estimate

e(ci_im_lb) lower bound of IM confidence interval for partially identified IGE

e(ci_im_ub) upper bound of IM confidence interval for partially identified IGE

e(c) critival value used to construct IM confidence interval

e(ci_nr_lb) lower bound of NR confidence interval for partially identified IGE

e(ci_nr_ub) upper bound of NR confidence interval for partially identified IGE

e(k) critival value used to construct NR confidence interval

e(confidence_level) confidence level

Author

Pablo A. Mitnik, Center on Poverty and Inequality, Stanford University.

Suggested citation if using igeset in published work

igeset is not an official Stata command. It is a free contribution to the research community, produced jointly with Mitnik (Forthcoming). Citation of this paper when using igeset would be appreciated.

References

Chernozhukov, Victor, Sokbae Lee and Adam Rosen. 2013. "Intersection Bounds: Estimation and Inference." Econometrica 81(2): 667-737.

Imbens, Guido and Charles Manski. 2004. "Confidence Intervals for Partially Identified Parameters." Econometrica 72(6): 1845-1857.

Mitnik, Pablo. Forthcoming. "Intergenerational Income Elasticities, Instrumental Variable Estimation and Bracketing Strategies." Sociological Methodology.

Mitnik, Pablo and David Grusky. Forthcoming. "The Intergenerational Elasticity of What? The Case for Redefining the Workhorse Measure of Economic Mobility." Sociological Methodology.

Nevo, Aviv and Adam Rosen. 2012. "Identification with Imperfect Instruments." Review of Economics and Statistics 94(3): 659-671.

Disclaimer

igeset is provided as is, without warranty of any kind, express or implied, including but not limited to the warranties of merchantability, fitness for a particular purpose and
noninfringement.