inferringincomeriskfromeconomicchoices · 2014. 5. 17. · inferringincomeriskfromeconomicchoices:...
TRANSCRIPT
Inferring Income Risk from Economic Choices:An Indirect Inference Approach
Fatih Guvenen Anthony Smith
Minnesota and NBER Yale University
July 29, 2009
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 1 / 42
Goals of this Paper:
1 Substantive Question:I To shed light on the nature of labor income risk...
I by exploiting the information contained in the joint dynamics ofhouseholds’ labor earnings and consumption choice decisions.
2 Methodology:I To better understand how “indirect inference” can be used to extract
information from individuals’ economic choices.
Main substantive conclusion: Typical calibrations of incompletemarkets models significantly overstate uninsurable income risk.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 2 / 42
Goals of this Paper:
1 Substantive Question:I To shed light on the nature of labor income risk...
I by exploiting the information contained in the joint dynamics ofhouseholds’ labor earnings and consumption choice decisions.
2 Methodology:I To better understand how “indirect inference” can be used to extract
information from individuals’ economic choices.
Main substantive conclusion: Typical calibrations of incompletemarkets models significantly overstate uninsurable income risk.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 2 / 42
Goals of this Paper:
1 Substantive Question:I To shed light on the nature of labor income risk...
I by exploiting the information contained in the joint dynamics ofhouseholds’ labor earnings and consumption choice decisions.
2 Methodology:I To better understand how “indirect inference” can be used to extract
information from individuals’ economic choices.
Main substantive conclusion: Typical calibrations of incompletemarkets models significantly overstate uninsurable income risk.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 2 / 42
A Stochastic Process for Labor Income
y it : log labor earnings of household i at age t.
y it =
[a0 +a1t +a2t2 +a3Educ + ...
]︸ ︷︷ ︸common life-cycle component
+[α
i + βi t]︸ ︷︷ ︸
profile heterogeneity
+[z it + ε
it]︸ ︷︷ ︸
stochastic component
where z it = ρz i
t−1 + η it , and η i
t ,εit ∼ iid
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 3 / 42
A Stochastic Process for Labor Income
y it : log labor earnings of household i at age t.
y it =
[a0 +a1t +a2t2 +a3Educ + ...
]︸ ︷︷ ︸common life-cycle component
+[α
i + βi t]︸ ︷︷ ︸
profile heterogeneity
+[z it + ε
it]︸ ︷︷ ︸
stochastic component
where z it = ρz i
t−1 + η it , and η i
t ,εit ∼ iid
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 3 / 42
A Stochastic Process for Labor Income
y it : log labor earnings of household i at age t.
y it =
[a0 +a1t +a2t2 +a3Educ + ...
]︸ ︷︷ ︸common life-cycle component
+[α
i + βi t]︸ ︷︷ ︸
profile heterogeneity
+[z it + ε
it]︸ ︷︷ ︸
stochastic component
where z it = ρz i
t−1 + η it , and η i
t ,εit ∼ iid
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 3 / 42
A Stochastic Process for Labor Income
y it : log labor earnings of household i at age t.
y it =
[a0 +a1t +a2t2 +a3Educ + ...
]︸ ︷︷ ︸common life-cycle component
+[α
i + βi t]︸ ︷︷ ︸
profile heterogeneity
+[z it + ε
it]︸ ︷︷ ︸
stochastic component
where z it = ρz i
t−1 + η it , and η i
t ,εit ∼ iid
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 3 / 42
Three Questions about Labor Income Risk
1 How persistent and how large are income shocks? i.e., what is ρ andσ2
η ?
2 Do individuals differ systematically in their income growth rates? i.e.,is σ2
β� 0?
3 If indeed σ2β� 0, how much do individuals know about their β i at
different points in their life-cycle?
I i.e., what fraction of heterogeneity in β i is uncertainty as opposed toknown heterogeneity?
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 4 / 42
Three Questions about Labor Income Risk
1 How persistent and how large are income shocks? i.e., what is ρ andσ2
η ?
2 Do individuals differ systematically in their income growth rates? i.e.,is σ2
β� 0?
3 If indeed σ2β� 0, how much do individuals know about their β i at
different points in their life-cycle?
I i.e., what fraction of heterogeneity in β i is uncertainty as opposed toknown heterogeneity?
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 4 / 42
Three Questions about Labor Income Risk
1 How persistent and how large are income shocks? i.e., what is ρ andσ2
η ?
2 Do individuals differ systematically in their income growth rates? i.e.,is σ2
β� 0?
3 If indeed σ2β� 0, how much do individuals know about their β i at
different points in their life-cycle?
I i.e., what fraction of heterogeneity in β i is uncertainty as opposed toknown heterogeneity?
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 4 / 42
Three Questions about Labor Income Risk
1 How persistent and how large are income shocks? i.e., what is ρ andσ2
η ?
2 Do individuals differ systematically in their income growth rates? i.e.,is σ2
β� 0?
3 If indeed σ2β� 0, how much do individuals know about their β i at
different points in their life-cycle?
I i.e., what fraction of heterogeneity in β i is uncertainty as opposed toknown heterogeneity?
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 4 / 42
Outline of the Talk
1 Brief review of existing evidence on labor income risk
2 A life-cycle model of consumption-savings choice
3 Indirect Inference methodology
4 Identification with Consumption Data
5 Results (Monte Carlos and Real data)
6 Conclusions and future agenda
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 5 / 42
Outline of the Talk
1 Brief review of existing evidence on labor income risk
2 A life-cycle model of consumption-savings choice
3 Indirect Inference methodology
4 Identification with Consumption Data
5 Results (Monte Carlos and Real data)
6 Conclusions and future agenda
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 5 / 42
Outline of the Talk
1 Brief review of existing evidence on labor income risk
2 A life-cycle model of consumption-savings choice
3 Indirect Inference methodology
4 Identification with Consumption Data
5 Results (Monte Carlos and Real data)
6 Conclusions and future agenda
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 5 / 42
Outline of the Talk
1 Brief review of existing evidence on labor income risk
2 A life-cycle model of consumption-savings choice
3 Indirect Inference methodology
4 Identification with Consumption Data
5 Results (Monte Carlos and Real data)
6 Conclusions and future agenda
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 5 / 42
Outline of the Talk
1 Brief review of existing evidence on labor income risk
2 A life-cycle model of consumption-savings choice
3 Indirect Inference methodology
4 Identification with Consumption Data
5 Results (Monte Carlos and Real data)
6 Conclusions and future agenda
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 5 / 42
Outline of the Talk
1 Brief review of existing evidence on labor income risk
2 A life-cycle model of consumption-savings choice
3 Indirect Inference methodology
4 Identification with Consumption Data
5 Results (Monte Carlos and Real data)
6 Conclusions and future agenda
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 5 / 42
Existing Evidence from Labor Income Data
1 HIP Process (“Heterogenous Income Profiles”):I Early studies estimated the full model and found:
σ2β� 0 and 0.5≤ ρ ≤0.8
I See Hause (1977), Lillard and Weiss (1979), Baker (1997), Haider (2001),Guvenen (2005)
2 RIP Process (“Restricted Income Profiles”):
I MaCurdy (1982) suggested a test for β i≡ 0 and could not reject it.
I Then he and the following literature:F imposed β i≡ 0 and estimated 0.95≤ ρ ≤ 1.0.
I See Abowd and Card (1989), Topel (1991), Moffitt and Gottschalk (1995),Hubbard, Skinner and Zeldes (1994), Storesletten et al. (2004), etc.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 6 / 42
Existing Evidence from Labor Income Data
1 HIP Process (“Heterogenous Income Profiles”):I Early studies estimated the full model and found:
σ2β� 0 and 0.5≤ ρ ≤0.8
I See Hause (1977), Lillard and Weiss (1979), Baker (1997), Haider (2001),Guvenen (2005)
2 RIP Process (“Restricted Income Profiles”):
I MaCurdy (1982) suggested a test for β i≡ 0 and could not reject it.
I Then he and the following literature:F imposed β i≡ 0 and estimated 0.95≤ ρ ≤ 1.0.
I See Abowd and Card (1989), Topel (1991), Moffitt and Gottschalk (1995),Hubbard, Skinner and Zeldes (1994), Storesletten et al. (2004), etc.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 6 / 42
Existing Evidence from Labor Income Data
1 HIP Process (“Heterogenous Income Profiles”):I Early studies estimated the full model and found:
σ2β� 0 and 0.5≤ ρ ≤0.8
I See Hause (1977), Lillard and Weiss (1979), Baker (1997), Haider (2001),Guvenen (2005)
2 RIP Process (“Restricted Income Profiles”):
I MaCurdy (1982) suggested a test for β i≡ 0 and could not reject it.
I Then he and the following literature:F imposed β i≡ 0 and estimated 0.95≤ ρ ≤ 1.0.
I See Abowd and Card (1989), Topel (1991), Moffitt and Gottschalk (1995),Hubbard, Skinner and Zeldes (1994), Storesletten et al. (2004), etc.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 6 / 42
Existing Evidence from Labor Income Data
1 HIP Process (“Heterogenous Income Profiles”):I Early studies estimated the full model and found:
σ2β� 0 and 0.5≤ ρ ≤0.8
I See Hause (1977), Lillard and Weiss (1979), Baker (1997), Haider (2001),Guvenen (2005)
2 RIP Process (“Restricted Income Profiles”):
I MaCurdy (1982) suggested a test for β i≡ 0 and could not reject it.
I Then he and the following literature:F imposed β i≡ 0 and estimated 0.95≤ ρ ≤ 1.0.
I See Abowd and Card (1989), Topel (1991), Moffitt and Gottschalk (1995),Hubbard, Skinner and Zeldes (1994), Storesletten et al. (2004), etc.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 6 / 42
Existing Evidence from Labor Income Data
1 HIP Process (“Heterogenous Income Profiles”):I Early studies estimated the full model and found:
σ2β� 0 and 0.5≤ ρ ≤0.8
I See Hause (1977), Lillard and Weiss (1979), Baker (1997), Haider (2001),Guvenen (2005)
2 RIP Process (“Restricted Income Profiles”):
I MaCurdy (1982) suggested a test for β i≡ 0 and could not reject it.
I Then he and the following literature:F imposed β i≡ 0 and estimated 0.95≤ ρ ≤ 1.0.
I See Abowd and Card (1989), Topel (1991), Moffitt and Gottschalk (1995),Hubbard, Skinner and Zeldes (1994), Storesletten et al. (2004), etc.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 6 / 42
Existing Evidence from Labor Income Data
1 HIP Process (“Heterogenous Income Profiles”):I Early studies estimated the full model and found:
σ2β� 0 and 0.5≤ ρ ≤0.8
I See Hause (1977), Lillard and Weiss (1979), Baker (1997), Haider (2001),Guvenen (2005)
2 RIP Process (“Restricted Income Profiles”):
I MaCurdy (1982) suggested a test for β i≡ 0 and could not reject it.
I Then he and the following literature:F imposed β i≡ 0 and estimated 0.95≤ ρ ≤ 1.0.
I See Abowd and Card (1989), Topel (1991), Moffitt and Gottschalk (1995),Hubbard, Skinner and Zeldes (1994), Storesletten et al. (2004), etc.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 6 / 42
This Paper
Studies the joint dynamics of consumption and labor income to learn moreabout labor income risk.
Two Difficulties
First, GMM requires strong assumptions.
I “Indirect inference” circumvents many of these difficulties.
Second, long US panel on consumption does not exist.
I We construct a panel of imputed consumption (1968-1992) bycombining CEX and PSID.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 7 / 42
This Paper
Studies the joint dynamics of consumption and labor income to learn moreabout labor income risk.
Two Difficulties
First, GMM requires strong assumptions.
I “Indirect inference” circumvents many of these difficulties.
Second, long US panel on consumption does not exist.
I We construct a panel of imputed consumption (1968-1992) bycombining CEX and PSID.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 7 / 42
This Paper
Studies the joint dynamics of consumption and labor income to learn moreabout labor income risk.
Two Difficulties
First, GMM requires strong assumptions.
I “Indirect inference” circumvents many of these difficulties.
Second, long US panel on consumption does not exist.
I We construct a panel of imputed consumption (1968-1992) bycombining CEX and PSID.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 7 / 42
This Paper
Studies the joint dynamics of consumption and labor income to learn moreabout labor income risk.
Two Difficulties
First, GMM requires strong assumptions.
I “Indirect inference” circumvents many of these difficulties.
Second, long US panel on consumption does not exist.
I We construct a panel of imputed consumption (1968-1992) bycombining CEX and PSID.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 7 / 42
This Paper
Studies the joint dynamics of consumption and labor income to learn moreabout labor income risk.
Two Difficulties
First, GMM requires strong assumptions.
I “Indirect inference” circumvents many of these difficulties.
Second, long US panel on consumption does not exist.
I We construct a panel of imputed consumption (1968-1992) bycombining CEX and PSID.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 7 / 42
This Paper
Studies the joint dynamics of consumption and labor income to learn moreabout labor income risk.
Two Difficulties
First, GMM requires strong assumptions.
I “Indirect inference” circumvents many of these difficulties.
Second, long US panel on consumption does not exist.
I We construct a panel of imputed consumption (1968-1992) bycombining CEX and PSID.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 7 / 42
The Model
Households work for R years. Spend S years in retirement.
Only choice is consumption-savings (inelastic labor supply).
CRRA utility function
Households face the unrestricted labor income process above.
A risk-free asset: Borrowing subject to potentially binding borrowingconstraints.
After retirement: Pension system mimicking the U.S. Social Securitysystem.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 8 / 42
The Model
Households work for R years. Spend S years in retirement.
Only choice is consumption-savings (inelastic labor supply).
CRRA utility function
Households face the unrestricted labor income process above.
A risk-free asset: Borrowing subject to potentially binding borrowingconstraints.
After retirement: Pension system mimicking the U.S. Social Securitysystem.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 8 / 42
The Model
Households work for R years. Spend S years in retirement.
Only choice is consumption-savings (inelastic labor supply).
CRRA utility function
Households face the unrestricted labor income process above.
A risk-free asset: Borrowing subject to potentially binding borrowingconstraints.
After retirement: Pension system mimicking the U.S. Social Securitysystem.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 8 / 42
The Model
Households work for R years. Spend S years in retirement.
Only choice is consumption-savings (inelastic labor supply).
CRRA utility function
Households face the unrestricted labor income process above.
A risk-free asset: Borrowing subject to potentially binding borrowingconstraints.
After retirement: Pension system mimicking the U.S. Social Securitysystem.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 8 / 42
The Model
Households work for R years. Spend S years in retirement.
Only choice is consumption-savings (inelastic labor supply).
CRRA utility function
Households face the unrestricted labor income process above.
A risk-free asset: Borrowing subject to potentially binding borrowingconstraints.
After retirement: Pension system mimicking the U.S. Social Securitysystem.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 8 / 42
The Model
Households work for R years. Spend S years in retirement.
Only choice is consumption-savings (inelastic labor supply).
CRRA utility function
Households face the unrestricted labor income process above.
A risk-free asset: Borrowing subject to potentially binding borrowingconstraints.
After retirement: Pension system mimicking the U.S. Social Securitysystem.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 8 / 42
Information Structure
Recall: y it = α i + β i t + z i
t + ε it
At t = 0, each individual observes a signal about her own β i .
In each t > 0, individuals observe (α i ,y it ,ε
it) but must learn about(
β i ,z it).
Individuals use the Kalman filter to update their beliefs about(β i ,z i
t)
as new observatios on labor income arrive.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 9 / 42
Information Structure
Recall: y it = α i + β i t + z i
t + ε it
At t = 0, each individual observes a signal about her own β i .
In each t > 0, individuals observe (α i ,y it ,ε
it) but must learn about(
β i ,z it).
Individuals use the Kalman filter to update their beliefs about(β i ,z i
t)
as new observatios on labor income arrive.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 9 / 42
Information Structure
Recall: y it = α i + β i t + z i
t + ε it
At t = 0, each individual observes a signal about her own β i .
In each t > 0, individuals observe (α i ,y it ,ε
it) but must learn about(
β i ,z it).
Individuals use the Kalman filter to update their beliefs about(β i ,z i
t)
as new observatios on labor income arrive.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 9 / 42
Information Structure
Recall: y it = α i + β i t + z i
t + ε it
At t = 0, each individual observes a signal about her own β i .
In each t > 0, individuals observe (α i ,y it ,ε
it) but must learn about(
β i ,z it).
Individuals use the Kalman filter to update their beliefs about(β i ,z i
t)
as new observatios on labor income arrive.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 9 / 42
Prior and Posterior Beliefs
Priors: Bivariate Normal distribution with mean (β i1|0, z
i1|0) and
covariance matrix P1|0 =
[σ2
β ,0 00 σ2
z ,0
]Express the prior standard deviation as: σβ ,0 = λσβ . Then:
If λ = 0 → σβ ,0 = 0 and β i1|0 = β i (No prior uncertainty)
If λ = 1 → σβ ,0 = σβ and β i1|0 = β (Full prior uncertainty)
For realistic parameter values learning about β i is very slow (Guvenen2007).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 10 / 42
Prior and Posterior Beliefs
Priors: Bivariate Normal distribution with mean (β i1|0, z
i1|0) and
covariance matrix P1|0 =
[σ2
β ,0 00 σ2
z ,0
]Express the prior standard deviation as: σβ ,0 = λσβ . Then:
If λ = 0 → σβ ,0 = 0 and β i1|0 = β i (No prior uncertainty)
If λ = 1 → σβ ,0 = σβ and β i1|0 = β (Full prior uncertainty)
For realistic parameter values learning about β i is very slow (Guvenen2007).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 10 / 42
Prior and Posterior Beliefs
Priors: Bivariate Normal distribution with mean (β i1|0, z
i1|0) and
covariance matrix P1|0 =
[σ2
β ,0 00 σ2
z ,0
]Express the prior standard deviation as: σβ ,0 = λσβ . Then:
If λ = 0 → σβ ,0 = 0 and β i1|0 = β i (No prior uncertainty)
If λ = 1 → σβ ,0 = σβ and β i1|0 = β (Full prior uncertainty)
For realistic parameter values learning about β i is very slow (Guvenen2007).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 10 / 42
Prior and Posterior Beliefs
Priors: Bivariate Normal distribution with mean (β i1|0, z
i1|0) and
covariance matrix P1|0 =
[σ2
β ,0 00 σ2
z ,0
]Express the prior standard deviation as: σβ ,0 = λσβ . Then:
If λ = 0 → σβ ,0 = 0 and β i1|0 = β i (No prior uncertainty)
If λ = 1 → σβ ,0 = σβ and β i1|0 = β (Full prior uncertainty)
For realistic parameter values learning about β i is very slow (Guvenen2007).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 10 / 42
Prior and Posterior Beliefs
Priors: Bivariate Normal distribution with mean (β i1|0, z
i1|0) and
covariance matrix P1|0 =
[σ2
β ,0 00 σ2
z ,0
]Express the prior standard deviation as: σβ ,0 = λσβ . Then:
If λ = 0 → σβ ,0 = 0 and β i1|0 = β i (No prior uncertainty)
If λ = 1 → σβ ,0 = σβ and β i1|0 = β (Full prior uncertainty)
For realistic parameter values learning about β i is very slow (Guvenen2007).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 10 / 42
Dynamic Programming Problem
Worker (t = 1, ..,R−1)
Vt(ωt , βt , zt) = maxCt ,at+1
{U(Ct) + δEt
[Vt+1(ωt+1, βt+1, zt+1)
]}s.t. (1)
Ct +at+1 = ωt (2)ωt = (1+ r)at +Yt (3)
at+1 ≥ a,and Kalman recursions
Retiree (t = R, ..,T )
Vt(ωt ,Y ) = maxCt ,at+1
[U(Ct) + δVt+1(ωt+1,Y )] (4)
s.t Y = Φ(YR) , and eq.(2,3)
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 11 / 42
Dynamic Programming Problem
Worker (t = 1, ..,R−1)
Vt(ωt , βt , zt) = maxCt ,at+1
{U(Ct) + δEt
[Vt+1(ωt+1, βt+1, zt+1)
]}s.t. (1)
Ct +at+1 = ωt (2)ωt = (1+ r)at +Yt (3)
at+1 ≥ a,and Kalman recursions
Retiree (t = R, ..,T )
Vt(ωt ,Y ) = maxCt ,at+1
[U(Ct) + δVt+1(ωt+1,Y )] (4)
s.t Y = Φ(YR) , and eq.(2,3)
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 11 / 42
Estimation via Indirect Inference
Hallmark of indirect inference: Think in terms of an auxiliary modelthat can be viewed as a reduced form of the structural model.
Specifically, pick an auxiliary model that is:I easy to estimate
I rich enough to provide a good descriptive statistical model of the data.
Mimicking structural equations works well.
Thinking in terms of dynamic relationships often lead to someconditional moment conditions that are not straightforward to seeotherwise.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 12 / 42
Estimation via Indirect Inference
Hallmark of indirect inference: Think in terms of an auxiliary modelthat can be viewed as a reduced form of the structural model.
Specifically, pick an auxiliary model that is:I easy to estimate
I rich enough to provide a good descriptive statistical model of the data.
Mimicking structural equations works well.
Thinking in terms of dynamic relationships often lead to someconditional moment conditions that are not straightforward to seeotherwise.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 12 / 42
Estimation via Indirect Inference
Hallmark of indirect inference: Think in terms of an auxiliary modelthat can be viewed as a reduced form of the structural model.
Specifically, pick an auxiliary model that is:I easy to estimate
I rich enough to provide a good descriptive statistical model of the data.
Mimicking structural equations works well.
Thinking in terms of dynamic relationships often lead to someconditional moment conditions that are not straightforward to seeotherwise.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 12 / 42
Estimation via Indirect Inference
Hallmark of indirect inference: Think in terms of an auxiliary modelthat can be viewed as a reduced form of the structural model.
Specifically, pick an auxiliary model that is:I easy to estimate
I rich enough to provide a good descriptive statistical model of the data.
Mimicking structural equations works well.
Thinking in terms of dynamic relationships often lead to someconditional moment conditions that are not straightforward to seeotherwise.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 12 / 42
Estimation via Indirect Inference
Hallmark of indirect inference: Think in terms of an auxiliary modelthat can be viewed as a reduced form of the structural model.
Specifically, pick an auxiliary model that is:I easy to estimate
I rich enough to provide a good descriptive statistical model of the data.
Mimicking structural equations works well.
Thinking in terms of dynamic relationships often lead to someconditional moment conditions that are not straightforward to seeotherwise.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 12 / 42
Estimation via Indirect Inference
Hallmark of indirect inference: Think in terms of an auxiliary modelthat can be viewed as a reduced form of the structural model.
Specifically, pick an auxiliary model that is:I easy to estimate
I rich enough to provide a good descriptive statistical model of the data.
Mimicking structural equations works well.
Thinking in terms of dynamic relationships often lead to someconditional moment conditions that are not straightforward to seeotherwise.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 12 / 42
Why Indirect Inference?
The standard method since Hall and Mishkin (1982) is to derive structuralequations explicitly and estimate them.
For example, with (i) quadratic utility, (ii) no borrowing constraint,(iii) no retirement, and (iv) persistent plus transitory shocks, we have:
∆Ct = φtηt + ψtεt
φ � 0, ψt ∼ 0
Suppose εt ≡ 0:
∆Ct = φtηt = φt∆Yt
Response of consumption growth to income growth reveals persistenceof income shocks.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 13 / 42
Why Indirect Inference?
The standard method since Hall and Mishkin (1982) is to derive structuralequations explicitly and estimate them.
For example, with (i) quadratic utility, (ii) no borrowing constraint,(iii) no retirement, and (iv) persistent plus transitory shocks, we have:
∆Ct = φtηt + ψtεt
φ � 0, ψt ∼ 0
Suppose εt ≡ 0:
∆Ct = φtηt = φt∆Yt
Response of consumption growth to income growth reveals persistenceof income shocks.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 13 / 42
Why Indirect Inference?
The standard method since Hall and Mishkin (1982) is to derive structuralequations explicitly and estimate them.
For example, with (i) quadratic utility, (ii) no borrowing constraint,(iii) no retirement, and (iv) persistent plus transitory shocks, we have:
∆Ct = φtηt + ψtεt
φ � 0, ψt ∼ 0
Suppose εt ≡ 0:
∆Ct = φtηt = φt∆Yt
Response of consumption growth to income growth reveals persistenceof income shocks.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 13 / 42
Why Indirect Inference?
The standard method since Hall and Mishkin (1982) is to derive structuralequations explicitly and estimate them.
For example, with (i) quadratic utility, (ii) no borrowing constraint,(iii) no retirement, and (iv) persistent plus transitory shocks, we have:
∆Ct = φtηt + ψtεt
φ � 0, ψt ∼ 0
Suppose εt ≡ 0:
∆Ct = φtηt = φt∆Yt
Response of consumption growth to income growth reveals persistenceof income shocks.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 13 / 42
An Example
0 5 10 15 20 25 30 35 40−1
0
1
2
3
4
5
Age
Labor Income Consumption
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 14 / 42
An Example: Binding Constraints
0 5 10 15 20 25 30 35 40−1
0
1
2
3
4
5
Age
Labor Income ConsumptionAssets
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 15 / 42
IDENTIFICATION
Identification
Simplifying assumptions for intuition:(i) quadratic utility, (ii) no borrowing constraints, (iii) εt ≡ 0, and (iv)yt : level of income.
1 Optimal consumption choice:
HIP: ∆Ct = Πt ×(y it −(
αi + β
it−1t + ρ z i
t−1
))︸ ︷︷ ︸
ξ it
2 If σ2β≡ 0, learning disappears → we get (certainty equivalent)
permanent income model:
RIP: ∆Ct = Ψt ×ηt
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 17 / 42
Identification
Simplifying assumptions for intuition:(i) quadratic utility, (ii) no borrowing constraints, (iii) εt ≡ 0, and (iv)yt : level of income.
1 Optimal consumption choice:
HIP: ∆Ct = Πt ×(y it −(
αi + β
it−1t + ρ z i
t−1
))︸ ︷︷ ︸
ξ it
2 If σ2β≡ 0, learning disappears → we get (certainty equivalent)
permanent income model:
RIP: ∆Ct = Ψt ×ηt
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 17 / 42
Identification
Simplifying assumptions for intuition:(i) quadratic utility, (ii) no borrowing constraints, (iii) εt ≡ 0, and (iv)yt : level of income.
1 Optimal consumption choice:
HIP: ∆Ct = Πt ×(y it −(
αi + β
it−1t + ρ z i
t−1
))︸ ︷︷ ︸
ξ it
2 If σ2β≡ 0, learning disappears → we get (certainty equivalent)
permanent income model:
RIP: ∆Ct = Ψt ×ηt
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 17 / 42
1. Identification from Consumption Changes
1 2 3 4 5 6 7 8
0.5
1
1.5
2
2.5
3
3.5
Age
Lab
or E
arni
ngs
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 18 / 42
1. Identification from Consumption Changes
1 2 3 4 5 6 7 8
0.5
1
1.5
2
2.5
3
3.5
Age
Lab
or E
arni
ngs
RIP:
∆C1=∆C2
} η>0
}η>0
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 18 / 42
1. Identification from Consumption Changes
1 2 3 4 5 6 7 8
0.5
1
1.5
2
2.5
3
3.5
Age
Lab
or E
arni
ngs
η>0}
} η>0
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 18 / 42
1. Identification from Consumption Changes
1 2 3 4 5 6 7 8
0.5
1
1.5
2
2.5
3
3.5
Age
Lab
or E
arni
ngs
}
}
}ξ1<0
η>0
η=ξ2>0
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 18 / 42
1. Identification from Consumption Changes
1 2 3 4 5 6 7 8
0.5
1
1.5
2
2.5
3
3.5
Age
Lab
or E
arni
ngs
HIP: ∆C1<0 ∆C2>0
}
} η>0
ξ1<0
η=ξ2>0}
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 18 / 42
1. Identification from Consumption Changes
1 2 3 4 5 6 7 8
0.5
1
1.5
2
2.5
3
3.5
Age
Lab
or E
arni
ngs
RIP: ∆C1=∆C
2>0
HIP: ∆C1<0, ∆C
2>0
} η=ξ2>0
}
} ξ1<0
η>0
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 18 / 42
2. Identification from Consumption Levels
1 2 3 4 5 6 7 8 9 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Age
Lab
or E
arni
ngs
Agent 1: Actual IncomeAgent 2: Actual Income
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 19 / 42
2. Identification from Consumption Levels
1 2 3 4 5 6 7 8 9 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Age
Lab
or E
arni
ngs
Agent 1: Actual IncomeAgent 2: Actual Income
Forecast Income Paths under RIP
RIP:
Ct=31 =Y
t=3=C
t=32
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 19 / 42
2. Identification from Consumption Levels
1 2 3 4 5 6 7 8 9 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Age
Lab
or E
arni
ngs
Agent 1: Actual IncomeAgent 2: Actual Income
Forecast Income Paths under RIP
HIP:
Ct=31 >C
t=32
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 19 / 42
2. Identification from Consumption Levels
1 2 3 4 5 6 7 8 9 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Age
Lab
or E
arni
ngs
Agent 1: Actual IncomeAgent 2: Actual Income
Forecast Income Paths under HIP
HIP:
Ct=31 >C
t=32
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 19 / 42
Determining the Prior Information in HIP
1 2 3 4 5 6 7 8 9 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Age
Lab
or E
arni
ngs
Forecast Income Paths under HIP with λ=1
Forecast Income underHIP with λ<1
If λ=1: Ct=31 =C
t=32
If λ<1: Ct=31 >C
t=32
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 20 / 42
A Feasible Auxiliary Model:
∆Ct = Πt ×(Y i
t −(
α + βit−1t + ρ z i
t−1
))︸ ︷︷ ︸
ξt
(5)
This regression is not feasible, so approximate with
ct = a0 +a1yt−1 +a2yt−2 +a3yt+1 +a4yt+2
+a5y1,t−3 +a6y t+3,T +a7∆y1,t−3 +a8∆y t+3,T
+a9ct−1 +a10ct−2 +a11ct+1 +a12ct+2 + error
where ct ≡ log (Ct) .
Add a second regression where yt is the dependent variable. Use thesame income regressors above.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 21 / 42
A Feasible Auxiliary Model:
∆Ct = Πt ×(Y i
t −(
α + βit−1t + ρ z i
t−1
))︸ ︷︷ ︸
ξt
(5)
This regression is not feasible, so approximate with
ct = a0 +a1yt−1 +a2yt−2 +a3yt+1 +a4yt+2
+a5y1,t−3 +a6y t+3,T +a7∆y1,t−3 +a8∆y t+3,T
+a9ct−1 +a10ct−2 +a11ct+1 +a12ct+2 + error
where ct ≡ log (Ct) .
Add a second regression where yt is the dependent variable. Use thesame income regressors above.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 21 / 42
A Feasible Auxiliary Model:
∆Ct = Πt ×(Y i
t −(
α + βit−1t + ρ z i
t−1
))︸ ︷︷ ︸
ξt
(5)
This regression is not feasible, so approximate with
ct = a0 +a1yt−1 +a2yt−2 +a3yt+1 +a4yt+2
+a5y1,t−3 +a6y t+3,T +a7∆y1,t−3 +a8∆y t+3,T
+a9ct−1 +a10ct−2 +a11ct+1 +a12ct+2 + error
where ct ≡ log (Ct) .
Add a second regression where yt is the dependent variable. Use thesame income regressors above.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 21 / 42
Monte Carlo Results
RRA = 2
Annual net interest rate is: r = 4%
T = 41, S = 15. Social security system mimicking the U.S.
Use the observed structure of missing data.
2200 individuals with approximately 12 observations per individual.
Starting values assigned randomly 20% away from truth.
Each run takes approximately 3 hours.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 22 / 42
Monte Carlo Results
RRA = 2
Annual net interest rate is: r = 4%
T = 41, S = 15. Social security system mimicking the U.S.
Use the observed structure of missing data.
2200 individuals with approximately 12 observations per individual.
Starting values assigned randomly 20% away from truth.
Each run takes approximately 3 hours.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 22 / 42
Monte Carlo Results
RRA = 2
Annual net interest rate is: r = 4%
T = 41, S = 15. Social security system mimicking the U.S.
Use the observed structure of missing data.
2200 individuals with approximately 12 observations per individual.
Starting values assigned randomly 20% away from truth.
Each run takes approximately 3 hours.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 22 / 42
Monte Carlo Results
RRA = 2
Annual net interest rate is: r = 4%
T = 41, S = 15. Social security system mimicking the U.S.
Use the observed structure of missing data.
2200 individuals with approximately 12 observations per individual.
Starting values assigned randomly 20% away from truth.
Each run takes approximately 3 hours.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 22 / 42
Monte Carlo Results
RRA = 2
Annual net interest rate is: r = 4%
T = 41, S = 15. Social security system mimicking the U.S.
Use the observed structure of missing data.
2200 individuals with approximately 12 observations per individual.
Starting values assigned randomly 20% away from truth.
Each run takes approximately 3 hours.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 22 / 42
Monte Carlo Results
RRA = 2
Annual net interest rate is: r = 4%
T = 41, S = 15. Social security system mimicking the U.S.
Use the observed structure of missing data.
2200 individuals with approximately 12 observations per individual.
Starting values assigned randomly 20% away from truth.
Each run takes approximately 3 hours.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 22 / 42
Monte Carlo Results
RRA = 2
Annual net interest rate is: r = 4%
T = 41, S = 15. Social security system mimicking the U.S.
Use the observed structure of missing data.
2200 individuals with approximately 12 observations per individual.
Starting values assigned randomly 20% away from truth.
Each run takes approximately 3 hours.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 22 / 42
Monte Carlo Results
True value Mean estimate Std. dev.ρ 0.670 0.669 0.034ση 0.190 0.191 0.009σε 0.150 0.150 0.015σβ (×100) 2.650 2.652 0.121σα 0.490 0.493 0.031λ 0.500 0.504 0.054σuy 0.200 0.199 0.003σuc 0.200 0.199 0.008Note: Statistics are based on 150 replications
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 23 / 42
Results
PSID data, 1968-1993.
Labor income data: household non-financial after tax income(adjusted for family size and demographics)
Consumption data: imputed (adjusted for family size anddemographics)
Measurement error:I yobs
t = yt +uyt , uy
t is i.i.d over time.
I cobst = ct +mc +uc
t , mc is an individual fixed effect, uct is i.i.d over
time.
Also estimate δ , γ (RRA coefficient), and a (borrowing constraint).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 24 / 42
Results
PSID data, 1968-1993.
Labor income data: household non-financial after tax income(adjusted for family size and demographics)
Consumption data: imputed (adjusted for family size anddemographics)
Measurement error:I yobs
t = yt +uyt , uy
t is i.i.d over time.
I cobst = ct +mc +uc
t , mc is an individual fixed effect, uct is i.i.d over
time.
Also estimate δ , γ (RRA coefficient), and a (borrowing constraint).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 24 / 42
Results
PSID data, 1968-1993.
Labor income data: household non-financial after tax income(adjusted for family size and demographics)
Consumption data: imputed (adjusted for family size anddemographics)
Measurement error:I yobs
t = yt +uyt , uy
t is i.i.d over time.
I cobst = ct +mc +uc
t , mc is an individual fixed effect, uct is i.i.d over
time.
Also estimate δ , γ (RRA coefficient), and a (borrowing constraint).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 24 / 42
Results
PSID data, 1968-1993.
Labor income data: household non-financial after tax income(adjusted for family size and demographics)
Consumption data: imputed (adjusted for family size anddemographics)
Measurement error:I yobs
t = yt +uyt , uy
t is i.i.d over time.
I cobst = ct +mc +uc
t , mc is an individual fixed effect, uct is i.i.d over
time.
Also estimate δ , γ (RRA coefficient), and a (borrowing constraint).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 24 / 42
Results
PSID data, 1968-1993.
Labor income data: household non-financial after tax income(adjusted for family size and demographics)
Consumption data: imputed (adjusted for family size anddemographics)
Measurement error:I yobs
t = yt +uyt , uy
t is i.i.d over time.
I cobst = ct +mc +uc
t , mc is an individual fixed effect, uct is i.i.d over
time.
Also estimate δ , γ (RRA coefficient), and a (borrowing constraint).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 24 / 42
Results
PSID data, 1968-1993.
Labor income data: household non-financial after tax income(adjusted for family size and demographics)
Consumption data: imputed (adjusted for family size anddemographics)
Measurement error:I yobs
t = yt +uyt , uy
t is i.i.d over time.
I cobst = ct +mc +uc
t , mc is an individual fixed effect, uct is i.i.d over
time.
Also estimate δ , γ (RRA coefficient), and a (borrowing constraint).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 24 / 42
Results
PSID data, 1968-1993.
Labor income data: household non-financial after tax income(adjusted for family size and demographics)
Consumption data: imputed (adjusted for family size anddemographics)
Measurement error:I yobs
t = yt +uyt , uy
t is i.i.d over time.
I cobst = ct +mc +uc
t , mc is an individual fixed effect, uct is i.i.d over
time.
Also estimate δ , γ (RRA coefficient), and a (borrowing constraint).
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 24 / 42
Estimation of the Full Model
Parameter Estimate Std Error Descriptionρ 0.756 0.029 Persistenceση 0.189 0.005 Std. dev. of perm. shockσε 0.019 0.027 Std. dev. of transit. shockσβ (×100) 1.785 0.392 Growth rate heterogeneityσα 0.383 0.029 Level heterogeneitycorαβ −0.178 0.074 Correlationλ 0.191 0.124 Prior uncertaintyσuy 0.145 0.010 IID meas. error in incomeσuc 0.355 0.002 IID meas. error in cons.σuc 0.434 0.009 Fixed meas. error in cons.δ 0.958 0.003 Time discount factorγ 2.0* — RRA coefficienta -0.25* — Borrowing limit
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 25 / 42
Estimation of the Full Model
Parameter Estimate Std Error Descriptionρ 0.756 0.029 Persistenceση 0.189 0.005 Std. dev. of perm. shockσε 0.019 0.027 Std. dev. of transit. shockσβ (×100) 1.785 0.392 Growth rate heterogeneityσα 0.383 0.029 Level heterogeneitycorαβ −0.178 0.074 Correlationλ 0.191 0.124 Prior uncertaintyσuy 0.145 0.010 IID meas. error in incomeσuc 0.355 0.002 IID meas. error in cons.σuc 0.434 0.009 Fixed meas. error in cons.δ 0.958 0.003 Time discount factorγ 2.0* — RRA coefficienta -0.25* — Borrowing limit
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 25 / 42
Estimation of the Full Model
Parameter Estimate Std Error Descriptionρ 0.756 0.029 Persistenceση 0.189 0.005 Std. dev. of perm. shockσε 0.019 0.027 Std. dev. of transit. shockσβ (×100) 1.785 0.392 Growth rate heterogeneityσα 0.383 0.029 Level heterogeneitycorαβ −0.178 0.074 Correlationλ 0.191 0.124 Prior uncertaintyσuy 0.145 0.010 IID meas. error in incomeσuc 0.355 0.002 IID meas. error in cons.σuc 0.434 0.009 Fixed meas. error in cons.δ 0.958 0.003 Time discount factorγ 2.0* — RRA coefficienta -0.25* — Borrowing limit
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 25 / 42
Estimation of the Full Model
Parameter Estimate Std Error Descriptionρ 0.756 0.029 Persistenceση 0.189 0.005 Std. dev. of perm. shockσε 0.019 0.027 Std. dev. of transit. shockσβ (×100) 1.785 0.392 Growth rate heterogeneityσα 0.383 0.029 Level heterogeneitycorαβ −0.178 0.074 Correlationλ 0.191 0.124 Prior uncertaintyσuy 0.145 0.010 IID meas. error in incomeσuc 0.355 0.002 IID meas. error in cons.σuc 0.434 0.009 Fixed meas. error in cons.δ 0.958 0.003 Time discount factorγ 2.0* — RRA coefficienta -0.25* — Borrowing limit
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 25 / 42
Estimation of the Full Model
Parameter Estimate Std Error Descriptionρ 0.756 0.029 Persistenceση 0.189 0.005 Std. dev. of perm. shockσε 0.019 0.027 Std. dev. of transit. shockσβ (×100) 1.785 0.392 Growth rate heterogeneityσα 0.383 0.029 Level heterogeneitycorαβ −0.178 0.074 Correlationλ 0.191 0.124 Prior uncertaintyσuy 0.145 0.010 IID meas. error in incomeσuc 0.355 0.002 IID meas. error in cons.σuc 0.434 0.009 Fixed meas. error in cons.δ 0.958 0.003 Time discount factorγ 2.0* — RRA coefficienta -0.25* — Borrowing limit
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 25 / 42
Quantifying Life Cycle Income Risk
30 35 40 45 50 55 60
0.1
0.3
0.5
0.7
0.9
Age
With
in−
Coh
ort V
aria
nce
of L
og In
com
e
Var(log(Income))US Data
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 26 / 42
Quantifying Life Cycle Income Risk
30 35 40 45 50 55 60
0.1
0.3
0.5
0.7
0.9
Age
With
in−
Coh
ort V
aria
nce
of L
og In
com
e
Var(log(Income))Estimated Model
Var(log(Income))US Data
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 26 / 42
Quantifying Life Cycle Income Risk
30 35 40 45 50 55 60
0.1
0.3
0.5
0.7
0.9
Age
With
in−
Coh
ort V
aria
nce
of L
og In
com
e
Forecast Variance(This paper)
Var(log(Income))Estimated Model
Var(log(Income))US Data
Conclusion 1: About 1/2 of cross-sectional income dispersion at retirementrepresents risk—the rest is known heterogeneity.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 26 / 42
Quantifying Life Cycle Income Risk
30 35 40 45 50 55 60
0.1
0.3
0.5
0.7
0.9
Age
With
in−
Coh
ort V
aria
nce
of L
og In
com
e
Forecast Variance(This paper)
Var(log(Income))Estimated Model
Var(log(Income))US Data
Forecast Variance(Existing Literature)
Conclusion 2: Typical estimates in the literature overstate labor income risksignificantly.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 26 / 42
Within-Cohort Evolution of Inequality
25 30 35 40 45 50 55 600.1
0.2
0.3
0.4
0.5
0.6
Age
With
in−
Coh
ort V
aria
nce
of L
og In
com
e an
d C
onsu
mpt
ion
(Mod
el N
orm
aliz
ed to
Mat
ch U
S D
ata
at a
ge 3
0)
Var(log(Income)), US Data
Var(log(Income)), Model
Var(log(Consumption)), Model
Var(log(Consumption)), US Data
Var(log(Consumption)), US Data, Smoothed
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 27 / 42
Life Cycle Profile of Consumption
25 30 35 40 45 50 55 60 650.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Age
Mea
n L
og C
onsu
mpt
ion
Prof
ile (
Nor
mal
ized
to 1
at A
ge 3
0)
US DataUS Data, SmoothedModel
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 28 / 42
Conclusions and Future Directions
Monte Carlo results suggest that the indirect inference method worksvery well.
Estimates indicate
I (a) modest persistence of shocks, (b) large heterogeneity in incomegrowth rates, and (c) significant information about future incomegrowth rate (from 75 to 90% of total variance).
Implies: Typical calibrations of incomplete markets modelssubstantially overstate uninsurable income risk.
Next steps: (a) time-varying shock variances, (b) partial insurance.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 29 / 42
Conclusions and Future Directions
Monte Carlo results suggest that the indirect inference method worksvery well.
Estimates indicate
I (a) modest persistence of shocks, (b) large heterogeneity in incomegrowth rates, and (c) significant information about future incomegrowth rate (from 75 to 90% of total variance).
Implies: Typical calibrations of incomplete markets modelssubstantially overstate uninsurable income risk.
Next steps: (a) time-varying shock variances, (b) partial insurance.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 29 / 42
Conclusions and Future Directions
Monte Carlo results suggest that the indirect inference method worksvery well.
Estimates indicate
I (a) modest persistence of shocks, (b) large heterogeneity in incomegrowth rates, and (c) significant information about future incomegrowth rate (from 75 to 90% of total variance).
Implies: Typical calibrations of incomplete markets modelssubstantially overstate uninsurable income risk.
Next steps: (a) time-varying shock variances, (b) partial insurance.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 29 / 42
Conclusions and Future Directions
Monte Carlo results suggest that the indirect inference method worksvery well.
Estimates indicate
I (a) modest persistence of shocks, (b) large heterogeneity in incomegrowth rates, and (c) significant information about future incomegrowth rate (from 75 to 90% of total variance).
Implies: Typical calibrations of incomplete markets modelssubstantially overstate uninsurable income risk.
Next steps: (a) time-varying shock variances, (b) partial insurance.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 29 / 42
Conclusions and Future Directions
Monte Carlo results suggest that the indirect inference method worksvery well.
Estimates indicate
I (a) modest persistence of shocks, (b) large heterogeneity in incomegrowth rates, and (c) significant information about future incomegrowth rate (from 75 to 90% of total variance).
Implies: Typical calibrations of incomplete markets modelssubstantially overstate uninsurable income risk.
Next steps: (a) time-varying shock variances, (b) partial insurance.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 29 / 42
Imputation of Consumption in PSID
PSID tracks food consumption only. CEX measures non-durableexpenditures but its panel structure is very limited.
Blundell, et al (2006) develop a structural procedure to imputeconsumption in PSID (1980-1992).
We modify and extend this methodology to construct a panel ofconsumption for PSID covering 1968-1992.
In particular, we also make use of CEX 1972-73 and use additionalregressors.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 30 / 42
Imputation of Consumption in PSID
PSID tracks food consumption only. CEX measures non-durableexpenditures but its panel structure is very limited.
Blundell, et al (2006) develop a structural procedure to imputeconsumption in PSID (1980-1992).
We modify and extend this methodology to construct a panel ofconsumption for PSID covering 1968-1992.
In particular, we also make use of CEX 1972-73 and use additionalregressors.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 30 / 42
Imputation of Consumption in PSID
PSID tracks food consumption only. CEX measures non-durableexpenditures but its panel structure is very limited.
Blundell, et al (2006) develop a structural procedure to imputeconsumption in PSID (1980-1992).
We modify and extend this methodology to construct a panel ofconsumption for PSID covering 1968-1992.
In particular, we also make use of CEX 1972-73 and use additionalregressors.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 30 / 42
Imputation of Consumption in PSID
PSID tracks food consumption only. CEX measures non-durableexpenditures but its panel structure is very limited.
Blundell, et al (2006) develop a structural procedure to imputeconsumption in PSID (1980-1992).
We modify and extend this methodology to construct a panel ofconsumption for PSID covering 1968-1992.
In particular, we also make use of CEX 1972-73 and use additionalregressors.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 30 / 42
Imputation of Consumption in PSID Results
1965 1970 1975 1980 1985 1990 1995−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
Year
Cro
ss−
Sec
tiona
l Var
ianc
e of
Cos
umpt
ion
(Dev
iatio
n fr
om 1
980)
PSID Imputed: 1968−1992CE Non−Durable Consumption: 1980−92
CE Non−Durable, Kernel Smoothed
PSID Imputed, Kernel Smoothed
PSID Food Expenditures
PSID Food, Kernel Smoothed
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 31 / 42
Imputation of Consumption in PSID Results
25 30 35 40 45 50 55 60 65−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
Age
(With
in−
Coh
ort)
Cro
ss−
Sec
tiona
l Var
ianc
e of
Log
Con
sum
ptio
n
PSID Imputed ConsumptionCE Non−Durable Consumption
CE Kernel Smoothed
PSID Kernel Smoothed
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 32 / 42
Imputation of Consumption in PSID Results
25 30 35 40 45 50 55 60 650.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
Age
Ave
rage
Non
−D
urab
le C
onsu
mpt
ion
(Nor
mal
ized
to 1
at A
ge 3
0)
PSID Imputed ConsumptionCE Non−Durable ConsumptionCE Kernel SmoothedPSID Kernel Smoothed
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 33 / 42
Imputation of Consumption in PSID Results
Imputed=.996*Actual+.277+error
R squared=.67
68
1012
Impu
ted
6 8 10 12Actual
Regression Line 45 degree line
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 34 / 42
Ignoring profile heterogeneity biases ρ upward
yhit − yh
it =(
αi + β
ih+ εhit
)−(
αi + βh
)=(
βi −β
)h+ ε
hit
Under the (incorrect) assumption that β i ≡ β , a consistent estimatorof ρ is:
ρ =h (h−1)σ2
β
(h−1)2σ2β
+ σ2ε
−→ 1 for large h
If σ2β
= 0.0004, and σ2ε = 0.03, h = 20, yields ρ = 0.87.
If h = 30 ⇒ ρ = 0.95, when in fact true persistence is zero.If there is a population of individuals uniformly distributed from 25 to65 years of age, ρ = 0.91
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 35 / 42
A comparison to the existing literature
Body Math: MaCurdy (1982) rejected HIP by testing a simple proposition:If individuals differ systematically in the slope of their income profiles thenincome growth rates should be positively autocorrelated at higher lags.
cov(∆yhi ,∆yh+k
i ) = σ2β−[
ρk−1(1−ρ
1+ ρ
)σ2η
], k = 2, ...
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 36 / 42
Two concerns about the test:1 Low power against the alternative of HIP (even without AR(1) income
shocks):cov(∆yh
i ,∆yh+ki ) = σ
2β
= .00038≈ 0
2 With AR(1) income shocks:
cov(∆yhi ,∆yh+k
i ) = .00038−[.0033∗0.82k−1
]< 0,
for k < 12
⇒ Even with HIP autocovariances should be slightly negative andalways close to zero.
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 37 / 42
Group ρ σ2α σ2
βcorrαβ σ2
η σ2ε
A .988 .058 — — .015 .061(.024) (.011) (.007) (.010)
A .821 .022 .00038 −.23 .029 .047(.030) (.074) (.00008) (.43) (.008) (.007)
C .979 .031 — — .0099 .047(.055) (.021) (.013) (.020)
C .805 .023 .00049 −.70 .025 .032(.061) (.112) (.00014) (1.22) (.015) (.017)
H .972 .053 — — .011 .052(.023) (.015) (.007) (.008)
H .829 .038 .00020 −.25 .022 .034(.029) (.081) (.00009) (.59) (.008) (.007)
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 38 / 42
LagSample 0 1 2 3 4 5
Autocovariance(1) Data .0476 −.0176 .00058 −.00166 −.00014 −.00067
(.0019) (.0014) (.0008) (.0007) (.0008) (.0007)(2) Data .1215 −.0385 −.0031 −.0023 −.0025 −.00004
(.0023) (.0011) (.0010) (.0008) (.0007) (.0008)(3) Model .0840 −.0329 −.0014 −.0011 −.0007 −.0007
(.0013) (.0010) (.0008) (.0009) (.0008) (.0007)
Autocorrelation(4) Data 1.00 −.394 .013 −.039 −.003 −.016(5) Data 1.00 −.317 −.026 −.019 −.021 −.001(6) Model 1.00 −.391 −.016 −.012 −.009 −.009
(.000) (.008) (.009) (.010) (.008) (.009)
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 39 / 42
Imputation of Consumption in PSID: Results
25 30 35 40 45 50 55 60 650.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
Age
Ave
rage
Lab
or In
com
e
CEX all years (before−tax)PSID (before−tax)CEX drop<80PSID (After−tax)
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 40 / 42
Imputation of Consumption in PSID: Results
30 35 40 45 50 55 60 65−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Age
(With
in−
Coh
ort)
Cro
ss−
sect
iona
l Var
ianc
e of
Log
Inco
me
PSID (before−tax income)PSID (after−tax income)CEX all yearsCEX drop<80
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 41 / 42
Change in Precision of Beliefs about β i
Missing in the file
Guvenen and Smith (2009) Inferring Income Risk from Choices July 29, 2009 42 / 42