Household Resilience and Recovery

Income Dynamics in the SIPP

Kristina Bishop

Introduction

  • Households face income shocks

    • Income loss is difficult to offset.

    • Long recovery from income loss widens the income inequality gap.

Motivation

  • 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

  1. How long does it take for households to return to their pre-shock level of income?
  2. 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

  1. Model the income process with measurement error
  2. Simulate corrected income values
  3. Introduce a shock into the initial period
  4. 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

  • Data measured imprecisely: recall, misinformation, survey methods
  • Income contains non-classical measurement error
  • Measurement error is mean-reverting and serially correlated (Bound and Krueger, 1991; Cristia and Schwabish, 2007)

Measurement Error

Model

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

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

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

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

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

Estimation

Model of observed total household income:

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

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

Estimating equation using Two-step GMM

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

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

Estimation

Generalized Method of Moments (GMM)

  • Coefficient estimates: \(\gamma\), \(\beta\), and \(d_t\)
  • Residuals \(\Delta \tau_{it}\) form moment conditions to estimate \(\sigma^{2}_{v}, \sigma^{2}_{u}, \text{ and } \sigma^{2}_{\epsilon}\)

Shock Simulation

  • Simulate paths of \(y^{*}\) using parameter and variance distributions

  • Introduce a negative income shock at t=2 and trace out the income 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

Limitations

  • Study is an empirical exercise on shock recovery
  • Simulating shocks, not using actual shocks
  • Suspect external validity but avoids small samples and endogeneity of shocks
  • Complimentary approach to actual shocks

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, 2008, 2014

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

Variables

  • Outcome: Total real household income

  • Time-varying covariate: Household size

  • Demographic characteristics:

    • Race

    • Education

    • Marital status

    • Metro status

Results

Main Sample

Recovery Speed

Measurement error

Shock size

Proportion

Income Loss

Economic Environment

Heterogeneity Results

Race

Education

Marital Status

Metro

Decomposition

Race

Hypotheses

What explains group differences?

  • Parameters and income persistence
  • Random Errors
  • Observable characteristics
                    5%  50%  95%
Baseline             1 1.33 1.71
Gamma                1 1.33 1.71
Beta                 1 1.33 1.71
Time Trend Variance  1 1.00 1.43
Equation Error       1 1.33 1.86
Time Trend           1 1.33 1.86
Household Size       1 1.33 1.71
Initial Income       1 1.33 1.71

Conclusion

Results summary

  • Measurement error corrections bound the observed income estimates
  • Households recover longer for 25% shock than 10% shock
  • Economic environment shows similar results

Heterogeneity Summary

  • Whites recover faster than black household heads
  • High school education recovers faster than college education
  • Married household heads recover faster than single
  • Metro area household heads recover faster than non-metro

Future Work

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

Conclusion

  • Model income shock recovery speed
  • Income dynamics with measurement error
  • Policy relevant characteristics for heterogeneity in recovery speed
  • Mechanism: shocks are the driving factor
  • Accounts for measurement error in unbiased recovery speed distribution