*! version 1.0 19Feb2019 Pablo Mitnik

Title

igesetci -- Computation of confidence intervals for partially identified intergenerational income elasticities (IGEs)

Syntax and options

igesetci cvar pvar, lbound(name1) ubound(name2) ige(igetype) [ci(citype) level(#)]

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

lbound(name1) name1 is the name under which estimation results for the lower-bound model were stored via estimates store

ubound(name2) name2 is the name under which estimation results for the upper-bound model were stored via estimates store

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

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

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

Description

igesetci is a post-estimation command that computes Imbens and Manski's (2004) and Nevo and Rosen's (2012: Sec. IV) confidence intervals for a partially identified parameter
(rather than for the identified set) in contexts in which the parameter in question is the IGE of the expectation or the IGE of the geometric mean (see Mitnik and Grusky [Forthcoming] for these two IGEs), and either
(a) a set estimate of the IGE of the expectation has been produced by combining a lower-bound estimate obtained with the command poisson and an upper-bound estimate obtained with the command ivpoisson
or (b) a set estimate of the IGE of the geometric mean has been produced by combining a lower-bound estimate obtained with the command regress and an upper-bound estimate obtained with the command
ivregress. See Mitnik (Forthcoming) for details regarding the set estimation of IGEs.

Remarks and related commands

While igesetci is a post-estimation command, igeset (see igeset if installed) is a closely related estimation command that both set estimates IGEs and computes the confidence intervals computed
by igesetci in one pass, but at the cost of some loss of flexibility for the user (e.g., igeset allows the user less control of optimization options, gmm options, VCE options and so forth).

The confidence intervals for a partially identified parameter computed by igesetci are valid when there is one lower-bound estimate and one upper-bound estimate, and where these estimates are
produced by estimators that are consistent and asymptotically normally distributed (see Mitnik [Forthcoming] for a brief discussion of the rationale of, and formulae for the computation of, these confidence
intervals). There are cases, however, in which the upper-bound (lower-bound) estimate is defined as the minimum (maximum) of a set of a estimates. In the estimation of IGEs, this happens when the upper-bound is estimated more than
once with different sets of instruments. The command igeintb (see igeintb if installed) both set estimates IGEs and computes appropriate confidence intervals in this context.

Examples

Read and describe data

.use igesetci_data, clear
.describe

IGE of the expectation: Three examples of set estimation followed by the computation of confidence interval/s

.poisson c_inc p_ln_inc, robust
.estimates store poi
.ivpoisson gmm c_inc (p_ln_inc = p_educ)
.estimates store ivp_educ
.igesetci c_inc p_ln_inc, lb(poi) ub(ivp_educ) ige(igee)

.poisson c_inc c.p_age c.p_age#c.p_age p_ln_inc [pw = c_wcore]
.estimates store poi
.ivpoisson gmm c_inc c.p_age c.p_age#c.p_age (p_ln_inc = i.p_occ) [pw = c_wcore]
.estimates store ivp_occ
.igesetci c_inc p_ln_inc, lb(poi) ub(ivp_occ) ige(igee) ci(nr)

.poisson c_inc p_ln_inc, robust
.estimates store poi
.ivpoisson gmm c_inc (p_ln_inc = c.p_educ c.p_educ#c.p_educ i.p_occ)
.estimates store ivp_educ_occ
.igesetci c_inc p_ln_inc, lb(poi) ub(ivp_educ_occ) ige(igee) ci(imnr)

IGE of the geometric mean: Three examples of set estimation followed by the computation of confidence interval/s

.regress c_ln_inc p_ln_inc, robust
.estimates store ols
.ivregress 2sls c_ln_inc (p_ln_inc = p_educ), robust
.estimates store iv_educ
.igesetci c_ln_inc p_ln_inc, lb(ols) ub(iv_educ) ige(igeg)

.regress c_ln_inc c.p_age c.p_age#c.p_age p_ln_inc [pw = c_wcore]
.estimates store ols
.ivregress 2sls c_ln_inc c.p_age c.p_age#c.p_age (p_ln_inc = i.p_occ) [pw = c_wcore]
.estimates store iv_occ
.igesetci c_ln_inc p_ln_inc, lb(ols) ub(iv_occ) ige(igeg) ci(nr)

.regress c_ln_inc p_ln_inc, robust
.estimates store ols
.ivregress gmm c_ln_inc (p_ln_inc = c.p_educ c.p_educ#c.p_educ i.p_occ)
.estimates store iv_educ_occ
.igesetci c_ln_inc p_ln_inc, lb(ols) ub(iv_educ_occ) ige(igeg) ci(imnr)

Stored results

igesetci stores the following in r():

Macros

r(cmd) igesetci

r(ige) igee or igeg

r(ci) type of confidence interval: im, nr, or imnr

r(model_lb) name of lower-bound model

r(model_ub) name of upper-bound model

Scalars

r(pe_lb) lower bound of set estimate

r(pe_ub) upper bound of set estimate

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

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

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

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

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

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

r(confidence_level) confidence level

Author

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

Suggested citation if using igesetci in published work

igesetci 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 igesetci would be appreciated.

References

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." The Review of Economics and Statistics 94(3): 659-671.

Disclaimer

igesetci 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.