Resilience and Recovery

Household Income Dynamics in the SIPP

Kristina Bishop

Introduction

  • Income inequality is an economic concern

  • Income inequality depends on factors such as:

    • Distribution of shocks

    • Effect of 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 composition

  • 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

Figure 1: Main Sample Recovery Speed Distribution with Measurement Error. Shock size is 10% on 2008 data. Recovery time is measured in the number of four-month periods.

Shock size

Figure 2: Main Sample Recovery Speed Distribution with Varying Shock Size on Upper Bound of the Projection Error. Recovery time is measured in the number of four-month periods.

Income Loss

Figure 3: Aggregate Income Loss for 10% shock size and upper bound of the projection error on the 2008 data. The graph is divided by households who recover or not.

Economic Environment

Figure 4: Main Sample: Recovery speed distribution for 2004 and 2008 SIPP Data Release. Shock size is 10% and the upper bound of measurement error is used. Recovery time is measured in the number of four-month periods.

Heterogeneity Results

Race

Figure 5: Recovery Speed Distribution by Race for 10% shock with the lower bound on measurement error. Recovery time is measured in the number of four-month periods.

Education

Figure 6: Recovery Speed Distribution by Education for 10% and the lower bound on measurement error. Recovery time is measured in the number of four-month periods.

Marital Status

Figure 7: Recovery Speed Distribution by Marital Status for a 10% shock and the lower bound on measurement error. Recovery time is measured in the number of four-month periods.

Metro

Figure 8: Recovery Speed Distribution by Metro Status for a 10% shock and the lower bound on measurement error. Recovery time is measured in the number of four-month periods.

Decomposition

Race

Hypotheses

What explains group differences?

  • Parameters and income persistence
  • Random Errors
  • Observable characteristics

Demographic Decomposition

Table 1: Proportion Recovered. Estimates are constructed for the first group by random sampling each column’s other group. For example, cell (1,1) shows that for blacks when using gamma randomly sampled from the white distribution, they have no change in the proportion recovered.
Demographic.Baseline Gamma Beta Time.Trend.Variance Equation.Error Time.Trend Household.Size Initial.Income
Black | White 1.00 1 1.40 1.60 1.00 1.00 1
College | High School 1.06 1 1.06 1.06 0.44 1.06 1
Single | Married 0.69 1 1.31 1.31 0.54 1.00 1
Metro | Non-metro 0.35 1 1.00 1.00 0.35 1.00 1

Conclusion

Results summary

  • Measurement error corrections provide unbiased recovery speed estimates
  • Households recover longer for 25% shock than 10% shock
  • Economic environment shows difference in proportion recovered, though likely due to sample size

Heterogeneity Summary

  • Black household heads recover faster than white household heads
  • High school education recovers faster than college education
  • Married household heads recover faster than single
  • Non-Metro area household heads recover faster than metro

Future Work

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

Conclusion

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

Appendix

Table 2: 2008 Empirical Recovery times.
2008
Proportion small shocks 0.57
Proportion medium shocks 0.03
Proportion large shocks 0.03
Proportion any shocks 0.64
Proportion recover first small shock 0.18
Proportion recover first medium shock 0.11
Proportion recover first large shock 0.16
Proportion recover first shock 0.18
Recovery time (months) first small shock 1.23
Recovery time (months) first medium shock 3.13
Recovery time (months) first large shock 2.52
Recovery time (months) first shock 1.18
Number of small shocks 8.48
Number medium shocks 0.49
Number large shocks 0.48
Number any shocks 9.45