Consumption Heterogeneity: Micro Drivers and Macro Implications - - PowerPoint PPT Presentation

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Consumption Heterogeneity: Micro Drivers and Macro Implications

Edmund Crawley & Andreas Kuchler Norges Bank, Danmarks Nationalbank and Deutsche Bundesbank conference on Heterogeneous households, firms and financial intermediaries September 28, 2018

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Is Heterogeneity Important for Macroeconomics?

Theory: Consumption heterogeneity is potentially very important for macroeconomic dynamics e.g. Recent HANK models Macroeconomic events can redistribute wealth between High and Low MPC households, affecting aggregate consumption

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Is Heterogeneity Important for Macroeconomics?

Theory: Consumption heterogeneity is potentially very important for macroeconomic dynamics e.g. Recent HANK models Macroeconomic events can redistribute wealth between High and Low MPC households, affecting aggregate consumption Empirics: Testing and quantifying these effects often boils down to measuring the distribution of MPC along some dimension of redistribution Ability to do so is limited by: Methods to measure MPCs Consumption data Household balance sheet data

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What does this paper do?

Two Empirical Contributions 1 Method: New methodology to measure MPCs out of transitory and permanent income shocks

Builds on Blundell, Pistaferri, and Preston (2008) Correctly accounts for the Time Aggregation Problem

2 Data: Panel data covering all Danish households 2004-2015

Large sample size reveals clear, systemic heterogeneity Detailed household balance sheets allow us to infer implications for monetary policy transmission

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What does this paper do?

Two Empirical Contributions 1 Method: New methodology to measure MPCs out of transitory and permanent income shocks

Builds on Blundell, Pistaferri, and Preston (2008) Correctly accounts for the Time Aggregation Problem

2 Data: Panel data covering all Danish households 2004-2015

Large sample size reveals clear, systemic heterogeneity Detailed household balance sheets allow us to infer implications for monetary policy transmission

We also test to what extent a buffer-stock model can fit the

• bserved distribution of MPC with liquid wealth

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What does this paper find?

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What does this paper find?

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What does this paper find?

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What does this paper find?

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What has the Empirical MPC literature Found?

General consensus: MPCs are large (≈ 0.5 including durables) For both expected and unexpected transitory shocks

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

What has the Empirical MPC literature Found?

General consensus: MPCs are large (≈ 0.5 including durables) For both expected and unexpected transitory shocks Few studies have enough power to say much about the distribution

• f MPCs in the population

Jappelli and Pistaferri (2014) Italian Survey Data Fuster, Kaplan, and Zafar (2018) NY Fed Survey Fagereng, Holm, and Natvik (2016) Norway Lottery Data Gelman (2016) Financial App Data Liquid assets and income are key predictors of transitory MPC Our method and data can uncover detailed heterogeneity - Many potential applications

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

How Are Consumption Responses Typically Measured?

Three methods: 1 (Natural) Experiments - stimulus checks, lotteries etc

Few true experiments, especially for permanent shocks Data limitations

2 Ask people

Unclear how to interpret

3 Make identifying restrictions on income and consumption dynamics

Empirical methods (until now!) have been flawed

We develop a robust method based on 3

Relation to BPP

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Identification: Income

Income flow consists of: Permanent Income (random walk) Transitory Income (persistence < 2 years) ¯ yT = T

T−1

ptdt + T

T−1

t

t−2

f (t − s)dqsdt = ⇒ Var(∆N ¯ yT) = (N − 1 3)σ2

p + 2σ2 ˜ q for N ≥ 3

Details on income process

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Identification: Consumption

Assumptions on Consumption Permanent: Consumption permanently moves by fraction φ of the income shock Transitory: Persistence < 2 years ct = φpt + t

t−2

g(t − s)dqs = ⇒ Cov(∆N ¯ cT, ∆N ¯ yT) = φ(N − 1 3)σ2

p + 2ψσ2 ˜ q

where ψ = Cov(˜

c,˜ q) Var(˜ q) , the regression coefficient of ‘transitory’

consumption on transitory income

Consumption identification

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Full Identification

We use GMM on the equations: Var(∆N ¯ yT) = (N − 1 3)σ2

p + 2σ2 ˜ q

Cov(∆N ¯ cT, ∆N ¯ yT) = φ(N − 1 3)σ2

p + 2ψσ2 ˜ q

with N = 3, 4, 5 (and T = 2007, .., 2015) to identify the four unknowns: σ2

p: Permanent shock variance

σ2

˜ q: (Time aggregated) transitory shock variance

φ: MPX out of permanent income shocks ψ: MPX out of transitory income shocks Marginal Propensity to eXpend (includes durables)

Methodology intuition

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Data

What we need: Panel Data on Income and Expenditure Household Balance Sheet Data (detail on nominal assets)

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Data

What we need: Panel Data on Income and Expenditure Household Balance Sheet Data (detail on nominal assets) Income: Starting point: Register based micro data for all Danish households made available by Statistics Denmark

We use after-tax income for the household head, based on third-party reported tax data Restrict sample to heads aged 30-55

We divide through by permanent income (mean income over all observed years) and take the residual after controlling for age, education, marital status etc. (along with interactions of these)

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Data: Expenditure

We impute expenditure from the budget constraint Ct ≡ Yt − St = Yt − Pt − ∆NW Deposit and brokerage accounts all third party reported Works well for households with simple financial lives Main issue: Capital gains and losses

Exclude households where methodology will not work well (eg business owners) Exclude housing wealth and years with housing transactions Capital gains for stocks based on a diversified index

Noisy, but perhaps better than surveys (Abildgren, Kuchler, Rasmussen, and Sorensen (2018)) Huge sample size advantage: sample covers 7.6 million

• bservations over 2004-2015

On measurement error

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Results by Liquid Wealth

Permanent and Transitory Variance by Liquid Wealth Quantile

Shock Variance

0.000 0.002 0.004 0.006

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , > $ 3 , σp

2 Permanent Var

σq

2 Transitory Var

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , > $ 3 , φ Permanent MPX ψ Transitory MPX

MPX by Net Wealth

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Monetary Policy: Auclert’s Decomposition

How does Monetary Policy Affect Aggregate Consumption? Intertemporal Substitution Aggregate Income Representative Agent Channels

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Monetary Policy: Auclert’s Decomposition

How does Monetary Policy Affect Aggregate Consumption? Intertemporal Substitution Aggregate Income Representative Agent Channels Dominates in Rep. Agent NK models Large in Spender-Saver, or TANK models

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Monetary Policy: Auclert’s Decomposition

How does Monetary Policy Affect Aggregate Consumption? Intertemporal Substitution Aggregate Income Representative Agent Channels Fisher (Inflationary debt relief) Earnings Heterogeneity Interest Rate Exposure Redistribution Channels

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Monetary Policy: Auclert’s Decomposition

How does Monetary Policy Affect Aggregate Consumption? Intertemporal Substitution Aggregate Income Representative Agent Channels Fisher (Inflationary debt relief) Earnings Heterogeneity Interest Rate Exposure Redistribution Channels How can we empirically measure the size of the redistribution channels? Need to know the distribution of MPCs along the relevant dimension of redistribution

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Interest Rate Exposure: Auclert’s Experiment

Real interest rate increases 1 pp. for 1 year Hold constant income and inflation How does the subsequent redistribution impact aggregate consumption? Dimension of Redistribution: Unhedged Interest Rate Exposure

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Interest Rate Exposure: Dimension of Redistribution

Define Unhedged Interest Rate Exposure for household i as the total savings the household will invest at this year’s interest rate: UREi = Yi − Ci + Ai − Li Where Yi = Total after tax income Ci = Total Expenditure, including interest payments Ai = Maturing assets Li = Maturing liabilities Following a change in the interest rate dR, the size of the Interest Rate Exposure channel on household i’s expenditure is: dci = MPCiUREi dR R

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Interest Rate Exposure: Aggregation

Aggregate to find size of channel: dci = MPCiUREi dR R = ⇒ dC C = EI

• MPCi

UREi EI(ci) dR R Define sufficient statistic: ER = EI

• MPCi

UREi EI(ci)

• =

⇒ Need to know the distribution of MPCi with UREi We can do that!

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Interest Rate Exposure: MPX Distribution

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX Medium MPX High MPX Low MPX

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Interest Rate Exposure: MPX Distribution

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX Medium MPX High MPX Low MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX Home Ownership Homeowners Renters Homeowners

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Interest Rate Exposure: MPX Distribution

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX Medium MPX High MPX Low MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX Home Ownership Homeowners Renters Homeowners

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX

MPX by URE Decile

URE/Mean Expenditure MPX

0.0 0.2 0.4 0.6 0.8 1.0

− 6 . 8 2 − 2 . 4 8 − 1 . 5 7 − . 9 9 − . 5 7 − . 2 7 − . 6 . 1 . 4 8 2 . 2 3 ψ Transitory MPX Home Ownership Liquid Assets (Right Axis)

$ 0 $ 20,000 $ 40,000 $ 60,000

Wealthy Hand−to−Mouth Poor Hand−to−Mouth Wealthy

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Interest Rate Exposure: Out of Sample

Total URE sums to zero - this is not true for our household sample

• 61bn USD

MPX URE ER component Estimation Sample See Distribution

• 61
• 0.29

Young 0.5

• 15
• 0.06

Old 0.5 6 0.02 Pension Funds 0.1 37 0.03 Government 0.0

• 23

0.00 Non-financial Corp. 0.1

• 13
• 0.01

Financial Sector 0.1 61 0.05 Rest of World 0.0 9 0.00 Total

• 0.26

Notes: URE numbers are in billions of 2015 USD.

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

All Five Transmission Channels

dC C =

Aggregate Income Channel

MdY Y

Earnings Heterogeity Channel

• +γEY

dY Y

Fisher Channel

−EP dP P +ER dR R

Interest Rate Exposure Channel

−σS dR R

• Intertemporal Substitution Channel

M 0.52 EY

• 0.03

EP

• 0.75

ER

• 0.26

S 0.49

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

All Five Transmission Channels

dC C =

Aggregate Income Channel

MdY Y

Earnings Heterogeity Channel

• +γEY

dY Y

Fisher Channel

−EP dP P +ER dR R

Interest Rate Exposure Channel

−σS dR R

• Intertemporal Substitution Channel

M 0.52 EY

• 0.03

EP

• 0.75

ER

• 0.26

S 0.49 Compare ER to σS: σ in the range of 0.1 to 0.5 (maybe) σS ≈ 0.05 − 0.25

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Aim of Modeling Exercise

Can we calibrate a standard Buffer-Stock saving model to fit the distribution of MPC with liquid wealth?

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , > $ 3 , φ Permanent MPX ψ Transitory MPX

Key features: High overall Transitory MPC Decreasing with liquid wealth

Model details

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Taste Shock Model: Results

Permanent MPX by Liquid Wealth Quantile: Model vs Data

Liquid Wealth Quintile MPX

0.0 0.2 0.4 0.6 0.8 1.0 1.2

1 2 3 4 5 Data Model

Transitory MPX by Liquid Wealth Quantile: Model vs Data

Liquid Wealth Quintile MPX

0.0 0.2 0.4 0.6 0.8 1.0 1.2

1 2 3 4 5 Data Model

Motivation Empirical Strategy Data Liquid Wealth Monetary Policy Model Conclusion

Conclusion

We have designed a new method to estimate consumption responses to income shocks It appears to work well, both in theory and practice We can use it to show that heterogeneity plays a key role in monetary policy transmission Thank you!

MPC vs MPX Appendix

Durables

We have data on value of household cars Construct expenditure excluding car purchases and sales C nocar

T

= CT − ∆CarValue Construct proxy for non durable consumption (Cars ≈ 42.1% durable expenditure) C nondurable

T

= CT − 1 0.421∆CarValue

MPC vs MPX Appendix

Durables

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , + All Expenditure φ Permanent MPX ψ Transitory MPX

MPC vs MPX Appendix

Durables

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , + All Expenditure φ Permanent MPX ψ Transitory MPX

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0 MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , +

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , + All Expenditure Excluding Cars φ Permanent MPX ψ Transitory MPX

MPC vs MPX Appendix

Durables

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , + All Expenditure φ Permanent MPX ψ Transitory MPX

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0 MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , +

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , + All Expenditure Excluding Cars φ Permanent MPX ψ Transitory MPX

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0 MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0 MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , +

MPX by Liquid Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

$ − 2 , $ 2 , − 6 , $ 6 , − 1 2 , $ 1 2 , − 3 , $ 3 , + All Expenditure Excluding Cars Non−durable Proxy φ Permanent MPX ψ Transitory MPX

MPC vs MPX Appendix

Methodology Intuition and Suggestive Findings

Exploit increasing importance of permanent shocks as the time

• ver which growth is measured increases
• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

Complete Markets

∆Nci = αN + βN∆Nyi + εi

MPC vs MPX Appendix

Methodology Intuition and Suggestive Findings

Exploit increasing importance of permanent shocks as the time

• ver which growth is measured increases
• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

Complete Markets

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow

∆Nci = αN + βN∆Nyi + εi

MPC vs MPX Appendix

Methodology Intuition and Suggestive Findings

Exploit increasing importance of permanent shocks as the time

• ver which growth is measured increases
• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

Complete Markets

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow Buffer−Stock Relatively more transitory variance Relatively more permanent variance

∆Nci = αN + βN∆Nyi + εi

MPC vs MPX Appendix

Methodology Intuition and Suggestive Findings

Exploit increasing importance of permanent shocks as the time

• ver which growth is measured increases
• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

Complete Markets

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow Buffer−Stock Relatively more transitory variance Relatively more permanent variance

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow Buffer−Stock Data Relatively more transitory variance Relatively more permanent variance

∆Nci = αN + βN∆Nyi + εi

MPC vs MPX Appendix

Methodology Intuition and Suggestive Findings

Exploit increasing importance of permanent shocks as the time

• ver which growth is measured increases
• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

Complete Markets

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow Buffer−Stock Relatively more transitory variance Relatively more permanent variance

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow Buffer−Stock Data Relatively more transitory variance Relatively more permanent variance

• 2

4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 Regressing Consumption Growth on Income Growth

N, Years of Growth βN, Regression Coefficient

• Complete Markets

Solow Buffer−Stock Data Relatively more transitory variance Relatively more permanent variance Least Liquid Most liquid

∆Nci = αN + βN∆Nyi + εi

MPC vs MPX Appendix

Aside: Why Not Blundell, Pistaferri and Preston 2008?

Common Assumptions Income yt is made up of: Permanent Income (random walk) Transitory Income (uncorrelated over time) Key to BPP Identification ∆yt+1 is a valid instrument for transitory shocks in year t Negatively correlated with transitory shocks in year t Uncorrelated with permanent shocks in year t

MPC vs MPX Appendix

Aside: Why Not Blundell, Pistaferri and Preston 2008?

Common Assumptions Income yt is made up of: Permanent Income (random walk) Transitory Income (uncorrelated over time) Key to BPP Identification ∆yt+1 is a valid instrument for transitory shocks in year t Negatively correlated with transitory shocks in year t Uncorrelated with permanent shocks in year t Fails due to the Time Aggregation Problem

Time aggregation problem

MPC vs MPX Appendix

Time Aggregation Problem (Crawley 2018)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time Aggregation

Time Income

0.0 0.5 1.0

Income Flow

MPC vs MPX Appendix

Time Aggregation Problem (Crawley 2018)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time Aggregation

Time Income

0.0 0.5 1.0

Income Flow

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time Aggregation

Time Income

0.0 0.5 1.0

Income Flow Observed Income

MPC vs MPX Appendix

Time Aggregation Problem (Crawley 2018)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time Aggregation

Time Income

0.0 0.5 1.0

Income Flow

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time Aggregation

Time Income

0.0 0.5 1.0

Income Flow Observed Income

Observed permanent income growth is positively autocorrelated BPP misinterprets positive permanent income shocks as negative transitory shocks = ⇒ Thinks negative transitory shocks result in consumption increasing

MPC vs MPX Appendix

Time Aggregation Problem (Crawley 2018)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time Aggregation

Time Income

0.0 0.5 1.0

Income Flow

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Time Aggregation

Time Income

0.0 0.5 1.0

Income Flow Observed Income

Observed permanent income growth is positively autocorrelated BPP misinterprets positive permanent income shocks as negative transitory shocks = ⇒ Thinks negative transitory shocks result in consumption increasing If the Permanent Income Hypothesis holds, BPP will estimate the MPC to be -0.6

MPC vs MPX Appendix

Identification Restrictions: Income

Income flow consists of: Permanent Income (random walk) Transitory Income (persistence < 2 years)

1 2 3 4 5 0.0 0.4 0.8 1.2 Generic Transitory Impulse Response, f(t)

Time Income

yt = pt + t

t−2

f (t − s)dqs Permanent income flow Transitory income flow

MPC vs MPX Appendix

Identification Restrictions: Income

Income flow consists of: Permanent Income (random walk) Transitory Income (persistence < 2 years)

1 2 3 4 5 0.0 0.4 0.8 1.2 Generic Transitory Impulse Response, f(t)

Time Income

¯ yT = T

T−1

ytdt = T

T−1

ptdt + T

T−1

t

t−2

f (t − s)dqsdt Observed Income Time Aggregation

MPC vs MPX Appendix

Identification Restrictions: Income

¯ yT = T

T−1

ptdt + T

T−1

t

t−2

f (t − s)dqsdt ∆N ¯ yT = ¯ yT − ¯ yT−N = T

T−1

(pt − pT−1)dt − T−N

T−N−1

(pt − pT−N)dt + (pT−1 − pT−N) + T

T−1

t

t−2

f (t − s)dqsdt − T−N

T−N−1

t

t−2

f (t − s)dqsdt

Independent increments Var = ( 1

3 + 1 3 +N−1)σ2 p

MPC vs MPX Appendix

Identification Restrictions: Income

¯ yT = T

T−1

ptdt + T

T−1

t

t−2

f (t − s)dqsdt ∆N ¯ yT = ¯ yT − ¯ yT−N = T

T−1

(pt − pT−1)dt − T−N

T−N−1

(pt − pT−N)dt + (pT−1 − pT−N) + T

T−1

t

t−2

f (t − s)dqsdt − T−N

T−N−1

t

t−2

f (t − s)dqsdt

Independent increments Var = ( 1

3 + 1 3 +N−1)σ2 p

Independent if N ≥ 3

MPC vs MPX Appendix

Identification Restrictions: Income

¯ yT = T

T−1

ptdt + T

T−1

t

t−2

f (t − s)dqsdt ∆N ¯ yT = ¯ yT − ¯ yT−N = T

T−1

(pt − pT−1)dt − T−N

T−N−1

(pt − pT−N)dt + (pT−1 − pT−N) + T

T−1

t

t−2

f (t − s)dqsdt − T−N

T−N−1

t

t−2

f (t − s)dqsdt = ⇒ Var(∆N ¯ yT) = (N − 1 3)σ2

p + 2σ2 ˜ q for N ≥ 3

Independent increments Var = ( 1

3 + 1 3 +N−1)σ2 p

Independent if N ≥ 3

MPC vs MPX Appendix

Identification Restrictions: Consumption

Assumptions on Consumption Permanent: Consumption permanently moves by fraction φ of the income shock Transitory: Persistence < 2 years

Evidence

1 2 3 4 5 0.0 0.4 0.8 1.2 Generic Transitory Impulse Responses, f(t) and g(t)

Time Income/Consumption

Income f(t) Consumption g(t)

MPC vs MPX Appendix

Identification Restrictions: Consumption

Assumptions on Consumption Permanent: Consumption permanently moves by fraction φ of the income shock Transitory: Persistence < 2 years

Evidence

1 2 3 4 5 0.0 0.4 0.8 1.2 Generic Transitory Impulse Responses, f(t) and g(t)

Time Income/Consumption

Income f(t) Consumption g(t)

1 2 3 4 5 0.0 0.4 0.8 1.2 Generic Transitory Impulse Responses, f(t) and g(t)

Time Income/Consumption

Income f(t) Consumption g(t) BPP Random Walk

This is a key difference between what we assume and BPP

MPC vs MPX Appendix

Identification Restrictions: Consumption

Consumption flow is given by: ct = φpt + t

t−2

g(t − s)dqs = ⇒ Cov(∆N ¯ cT, ∆N ¯ yT) = φ(N − 1 3)σ2

p + 2ψσ2 ˜ q

where ψ = Cov(˜

c,˜ q) Var(˜ q) , the regression coefficient of ‘transitory’

consumption on transitory income

MPC vs MPX Appendix

Identification Restrictions: Consumption

Consumption flow is given by: ct = φpt + t

t−2

g(t − s)dqs = ⇒ Cov(∆N ¯ cT, ∆N ¯ yT) = φ(N − 1 3)σ2

p + 2ψσ2 ˜ q

where ψ = Cov(˜

c,˜ q) Var(˜ q) , the regression coefficient of ‘transitory’

consumption on transitory income φ: MPX out of permanent income shocks ψ: MPX out of transitory income shocks Marginal Propensity to eXpend (includes durables)

MPC vs MPX Appendix

Evidence of Consumption Decay Within 2 Years

From Fagereng, Holm, and Natvik (2016) From Gelman (2016)

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MPC vs MPX Appendix

Data: When is Measurement Error a Problem?

Our method has the same measurement error issues as the regressions: ∆Nci = αN + βN∆Nyi + εi That is: 1 Measurement error in ∆Nyi leads to attenuation bias 2 Measurement error in ∆Nci should be uncorrelated with ∆Nyi When might 2 fail? When a proportion of assets are held off balance sheet When returns are correlated with changes in income (e.g. own stock in the company you work for) When insurance is provided by friends and family

MPC vs MPX Appendix

MPX by Net Wealth

Permanent and Transitory Variance by Net Wealth Quantile

Shock Variance

0.000 0.001 0.002 0.003 0.004 0.005 0.006

< − 2 , $ − 2 , − 3 , $ 3 , − 6 2 , $ 6 2 , − 1 8 2 , > $ 1 8 2 , σp

2 Permanent Var

σq

2 Transitory Var

MPX by Net Wealth Quantile

MPX

0.0 0.2 0.4 0.6 0.8 1.0

< − 2 , $ − 2 , − 3 , $ 3 , − 6 2 , $ 6 2 , − 1 8 2 , > $ 1 8 2 , φ Permanent MPX ψ Transitory MPX

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