Household Resilience and Recovery

Income Dynamics in the SIPP

Kristina Bishop

Introduction

Motivation

Income loss is difficult to offset.
Long recovery from income loss widens the income inequality gap.

Policy can be designed more effectively to aid recovery:
- Who recovers slower?
- How long does it take for them to recover?
- How much income to give?
- Is income aid the right policy?

Research Questions

How long does it take for households to return to their pre-shock level of income?
What characteristics are common of households who recover quickly from income shocks?

Contribution

Provide an empirical model to estimate the speed of recovery from shocks
Account for measurement error in self-reported income (Lee et al. 2009)
Assess heterogeneity in recovery time across household types

Methods

Empirical Strategy

Model the income process with measurement error
Simulate corrected income values
Introduce a shock into the initial period
Recovery times across households and periods

Income Process

\[\begin{align*} %y^{*}_{it} &= \alpha_{i} + \gamma_{1} y^{*}_{it-1} + \gamma_{2} (y^{*}_{it-1})^{2} + X_{it} \beta + \delta_{it} + \tilde{\lambda} m_{it} + \epsilon_{it} \quad t = 2, \ldots, T \\%\label{eq:true} y^{*}_{it} &= \gamma y^{*}_{it-1}+ X_{it} \beta + \alpha_{i} + \delta_{it} + \epsilon_{it} \quad t = 2, \ldots, T \\ \delta_{it} &= \delta_{it-1} + u_{it} + d_{t} \nonumber \end{align*}\]

\(y^{*}_{it}\): measure of true income of household \(i\) at \(t\)

\(\alpha_{i}\): household fixed effect

\(X_{it}\): time-varying household characteristics

\(\delta_{it}\): household-specific stochastic time trend

\(u_{it}\): time-varying shock with permanent effect on income

\(d_{t}\): average time effect across households

\(\epsilon_{it}\): random shock

Measurement Error

Recall error
Intentional mis-information
Imprecise collection methods or difficulty in measurement

Measurement Error

Income contains non-classical measurement error
Measurement error is mean-reverting and serially correlated (Bound and Krueger, 1991; Cristia and Schwabish, 2007)
Persons face recall error when interviewed every four months about monthly income

Measurement Error

Model

\[\begin{align*} y_{it} &= y^{*}_{it} + \eta_{it} \\ \eta_{it} &= e_{i} + v_{it} \end{align*}\]

\(y_{it}\): observed, actual income

\(y^{*}_{it}\): unobserved, true income

\(\eta_{it}\): measurement error

\(e_{i}\): time-invariant component

\(v_{it}\): time-varying component

Estimation

Model of observed total household income:

\[\begin{align*} y_{it} &= \alpha_{i} + \gamma y_{it-1} + X_{it} \beta + \delta_{it} + \tilde{\lambda}m_{it} + \tau_{it} \quad t = 2, \ldots, T \\ \tau_{it} &= (1 - \gamma_{1})e_{i} + v_{it} - \gamma_{1} v_{it-1} + \epsilon_{it} %\nonumber \end{align*}\]

First difference the model: \(\Delta y_{it} = y_{it} - y_{it-1}\)

Estimating equation using Two-step GMM

\[\begin{align*} \Delta y_{it} &= \gamma_{1} \Delta y_{it-1} + \Delta X_{it} \beta + \lambda + \Delta \tau_{it} \quad {t = 3, \ldots, T} \\ %\label{eq:delta_yit} \Delta \tau_{it} &= u_{it} + \Delta v_{it} - \gamma \Delta v_{it-1} %nonumber + \Delta \epsilon_{it}, %\nonumber \end{align*}\]

Instruments (Arellano and Bond, 1991): \(y_{i,t-s}\) for \(s=3, \ldots, 8\)

Estimation

Generalized Method of Moments (GMM) using lagged values of dependent variable as instruments (Arellano and Bond, 1991)
Estimators are consistent and asymptotically normal (Holtz-Eakin et al., 1988)
Coefficient estimates: \(\gamma\), \(\beta\), and \(d_t\)
Residuals \(\Delta \tau_{it}\) form moment conditions: \(E[(\Delta \tau_{it})^{2}]\), \(E[\Delta \tau_{it} \Delta \tau_{it-1}]\), and \(E[\Delta \tau_{it} \Delta \tau_{it-1}]\)
Estimate variances: \(\sigma^{2}_{v}, \sigma^{2}_{u}, \text{ and } \sigma^{2}_{\epsilon}\)

Shock Simulation

Simulate paths of \(y^{*}\) using distribution of parameter and variance estimates
Introduce a negative income shock at t=2 and trace out the recovery path
Recovery time: how long to return to \(y_{i1}\) after shock in t = 2
Repeat the process by splitting the sample by demographic characteristics
Compare estimates across different data periods

Data

Survey of Income and Program Participation (SIPP)

Multistage-stratified sample of US population
Rotating panels of 14,000 - 37,000 households last 2.5-4 years
Explore changes across economic environment with cohorts –
- 2004 cohort: Feb 2004 - Jan 2008
- 2008 cohort: May 2008 - Nov 2013
- 2014 cohort: Jan 2013 - Dec 201

Sample Selection

Households with head age 25-55, not currently enrolled full-time in school nor on active duty
Aggregate data to every four months due to seam bias I Individuals are interviewed every four months;
Different individuals interviewed every month
Final 2008 sample includes: 39,959 households over 16 four-month period

Variables

Outcomes: Total real household income
Time-varying covariate: Household size
Split-sample characteristics:
- Race
- Education
- Marital status
- Metro status

Limitations

Empirical exercise on shock recovery
Simulating shocks, not using actual shocks
Suspects external validity but avoids small samples and endogeneity of shocks
Complimentary approach to actual shocks

Results

Conclusion

Heterogeneity Summary

Whites recover faster than black household heads
High school education recovers faster than college education
Married and single household heads recover at similar rates
Metro area household heads reover faster than non-metro

Results summary

Accounting for measurement error corrects for biased estimates
Households recover longer for 25% shock than 10% shock
Economic environment shows similar results
..
Group differences likely due to parameter estimates and initial income

Conclusion

Model income shock recovery speed
Income dynamics with measurement error
Policy relevant characteristics for heterogeneity in recovery speed
Mechanism:

Future Work

Connect income resiliency to intergenerational measures
Mechanisms of heterogeneity results
Non-linear model for income