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Saving Behavior Across the Wealth Distribution: The Importance of Capital Gains Andreas Fagereng Martin Holm Benjamin Moll Gisle Natvik SF Fed, 31 October 2019 Question Do wealthier households save larger share of income than poorer ones?

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Saving Behavior Across the Wealth Distribution: The Importance of Capital Gains

Andreas Fagereng Martin Holm Benjamin Moll Gisle Natvik

SF Fed, 31 October 2019

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Question

Do wealthier households save larger share of income than poorer ones? Two reasons to care:

  • 1. Interesting in its own right
  • In both academia and media, frequent statements that

“wealthier households have higher saving rates”

  • Is this actually true?
  • 2. Informative about theory
  • Many theories of household wealth accumulation:

saving rate = saving

income ≈ independent of wealth

  • What does saving behavior look like in the data?

1

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What We Do

  • Use Norwegian administrative data on income & wealth to examine

saving behavior across the wealth distribution

2

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Our Findings

  • 1. Q: Do rich save larger share of income than poor? A: “No and Yes”

Answer depends on whether saving includes capital gains: (a) saving rates net of capital gains (“net” or “active saving”) No, rich people don’t have higher saving rates in traditional sense. But, yes, they still accumulate more wealth through capital gains.

3

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Our Findings

  • 1. Q: Do rich save larger share of income than poor? A: “No and Yes”

Answer depends on whether saving includes capital gains: (a) saving rates net of capital gains (“net” or “active saving”) (b) saving rates including capital gains (“gross saving”) No, rich people don’t have higher saving rates in traditional sense. But, yes, they still accumulate more wealth through capital gains.

3

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Our Findings

  • 1. Q: Do rich save larger share of income than poor? A: “No and Yes”

Answer depends on whether saving includes capital gains: (a) saving rates net of capital gains (“net” or “active saving”) test

10 20 30 40

Median Saving Rate in %

20 40 60 80 100

Wealth Percentile

Net

No, rich people don’t have higher saving rates in traditional sense. But, yes, they still accumulate more wealth through capital gains.

3

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Our Findings

  • 1. Q: Do rich save larger share of income than poor? A: “No and Yes”

Answer depends on whether saving includes capital gains: (a) saving rates net of capital gains (“net” or “active saving”) (b) saving rates including capital gains (“gross saving”)

10 20 30 40

Median Saving Rate in %

20 40 60 80 100

Wealth Percentile

Net Gross (Systematic Component)

No, rich people don’t have higher saving rates in traditional sense. But, yes, they still accumulate more wealth through capital gains.

3

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Our Findings

  • 1. Q: Do rich save larger share of income than poor? A: “No and Yes”

Answer depends on whether saving includes capital gains: (a) saving rates net of capital gains (“net” or “active saving”) (b) saving rates including capital gains (“gross saving”)

10 20 30 40

Median Saving Rate in %

20 40 60 80 100

Wealth Percentile

Net Gross (Systematic Component)

No, rich people don’t have higher saving rates in traditional sense. But, yes, they still accumulate more wealth through capital gains.

3

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Our Findings

  • 1. Q: Do rich save larger share of income than poor? A: “No and Yes”

Answer depends on whether saving includes capital gains: (a) saving rates net of capital gains (“net” or “active saving”) (b) saving rates including capital gains (“gross saving”)

10 20 30 40

Median Saving Rate in %

20 40 60 80 100

Wealth Percentile

Net Gross (Systematic Component)

Rich people hold assets that experience persistent capital gains, do not sell these to consume ⇒ “saving by holding”

3

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Our Findings: “Saving by Holding” – Back-of-Envelope

10 20 30 40

Median Saving Rate in %

20 40 60 80 100

Wealth Percentile

Net Gross (Systematic Component)

Back-of-envelope example to clarify:

  • assume net saving rate = 10%, capital gains on all assets = 2%
  • Paul: income (excluding cap gains) = $100,000, assets = $0

Richie: income (excluding cap gains) = $100,000, assets = $1,000,000

  • gross savings are $10,000 and $10,000 + $20,000 = $30,000
  • gross saving rates are 10% and

30,000 100,000+20,000 = 25%

4

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To be clear: statement is about how saving rates vary with wealth and not income

10 20 30 40

Median Saving Rate in %

20 40 60 80 100

Wealth Percentile

Net Gross (Systematic Component)

(a) Saving rates and wealth

10 20 30 40

Median Saving Rate in %

20 40 60 80 100

Income Percentile

Net Gross (Systematic Component)

(b) Saving rates and income

5

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Our Findings

  • 2. Macro implication: “saving by holding” explains up to 80% of

increase in wealth-to-income ratio since 1995

  • 3. Implications for theory: patterns ̸= canonical models of hh saving

which predict ≈ flat gross saving rate Potential explanations:

  • 1. Demand-driven asset price changes
  • 2. Multiple assets + portfolio adjustment frictions
  • 3. ... (a few others – see paper)

6

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The Simplest Consumption-Saving Model

  • Households solve:

max

{c(t)}t≥0

∫ ∞ e−ρt c(t)1−γ 1 − γ dt s.t. ˙ a = w + ra − c, a ≥ −w/r

  • Saving policy function:

˙ a = s(a) = r − ρ γ (w r + a )

  • Constant saving rate out of income

s y = s w + ra = r − ρ γr

20 40 60 80 100 Wealth Percentile 10 20 30 40 Saving Rate in %

7

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Changing Asset Prices (in partial equilibrium)

  • Two sources of returns: dividends + capital gains

r = θ + ˙ p p, ˙ p p = µ + ε, µ = “persistent”, ε = “transitory”

  • Mapping to previous slide: wealth a := pk where k = quantity
  • Saving responses depend on type of capital gains:

20 40 60 80 100 Wealth Percentile 10 20 30 40 Saving Rate in %

Saving rate net of capital gains Gross saving rate

(a) Only persistent: µ > 0, ε = 0

20 40 60 80 100 Wealth Percentile 10 20 30 40 Saving Rate in %

Saving rate net of capital gains Gross saving rate, average year Gross saving rate, good year Gross saving rate, bad year

(b) Both: µ > 0, ε ≶ 0

  • 1. net saving rate decreasing with wealth (if µ > 0)
  • 2. systematic component of gross saving rate independent of wealth 8
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Extensions

(a) Housing not just an asset, but also consumption good:

  • collapses to one-asset model with flat saving rate

details

(b) Labor income risk and borrowing constraints:

  • flat saving rate conditional on labor income

(c) More realistic life cycle:

  • flat saving rate conditional on age and income

(d) Discount rate heterogeneity:

  • flat saving rate conditional on discount rate

Overall: ≈ constant saving rate conditional on observables (age, ...)

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Data

  • Norwegian population tax record data with supplements
  • Panel, 2005 to 2015 (11 years)
  • ≈ 3.3M persons per year
  • Tax records include (third-party reported):
  • asset holdings by broad asset class (e.g. deposits, housing)
  • income (labor, business, capital, and transfers)

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Portfolio Shares

20 40 60 80 100 Mean Portfolio Share in % of Total Assets 20 40 60 80 100 Wealth Percentile Safe Assets Housing Debt Public Equity Private Business Vehicles

Notes: Wealth = assets − liabilities, pensions: not today (in appendix) 12th pctile = 0 net worth

11

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Portfolio Shares

20 40 60 80 100 Mean Portfolio Share in % of Total Assets 20 40 60 80 100 Wealth Percentile Safe Assets Housing Debt Public Equity Private Business Vehicles

Notes: Wealth = assets − liabilities, pensions: not today (in appendix) 12th pctile = 0 net worth

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Portfolio Shares

20 40 60 80 100 Mean Portfolio Share in % of Total Assets 20 40 60 80 100 Wealth Percentile Safe Assets Housing Debt Public Equity Private Business Vehicles

Notes: Wealth = assets − liabilities, pensions: not today (in appendix) 12th pctile = 0 net worth

11

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Net, Gross and “Recurrent” Saving

  • Three ways of writing consumption + saving = income

c + p ˙ k

  • net saving

= w + θpk

  • net income

(1) c + p ˙ k + ˙ pk

  • gross saving

= w + (θ + ˙ p/p)pk

  • Haig-Simons income

(2) c + (˙ k/k + µ)pk

  • “recurrent saving”

= w + (θ + µ)pk

  • “recurrent income”

, µ := ˙ p/p (3)

  • Implementation:
  • 1. Separate gross saving into net saving and capital gains

(use housing transaction data and shareholder registry)

  • 2. Estimate persistent capital gains (µ)

(mean of realized capital gains as long as series go back)

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Median Saving Rates

10 20 30 40 Median Saving Rate in % 20 40 60 80 100 Wealth Percentile Net Gross Recurrent 13

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Controlling for Age, Earnings ...

within-group percentiles

10 20 30 40 Median Net Saving Rate in % 20 40 60 80 100 Wealth Percentile Age 20−29 Age 30−49 Age 50−59 Age 60−75

(a) Age, net saving rate

10 20 30 40 Median Recurrent Saving Rate in % 20 40 60 80 100 Wealth Percentile Age 20−29 Age 30−49 Age 50−59 Age 60−75

(b) Age, recurrent saving rate

10 20 30 40 Median Net Saving Rate in % 20 40 60 80 100 Wealth Percentile 1st Income Quintile 2nd Income Quintile 3rd Income Quintile 4th Income Quintile 5th Income Quintile

(c) Earnings, net saving rate

10 20 30 40 Median Recurrent Saving Rate in % 20 40 60 80 100 Wealth Percentile 1st Income Quintile 2nd Income Quintile 3rd Income Quintile 4th Income Quintile 5th Income Quintile

(d) Earnings, recurrent saving rate

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Saving Rates by Year

10 20 30 40 Median Net Saving Rate in % 20 40 60 80 100 Wealth Percentile Average

(a) Net saving rates across years

−20 20 40 60 80 Median Gross Saving Rate in % 20 40 60 80 100 Wealth Percentile Average

(b) Gross saving rates across years

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Zooming in on right tail of wealth distribution

20 40 60 80 100 Mean Portfolio Share in % of Total Assets P0−P10 P10−P20 P20−P30 P30−P40 P40−P50 P50−P60 P60−P70 P70−P80 P80−P90 P90−P95 P95−P97.5 P97.5−P99 P99−P99.5 P99.5−P99.9 Top 0.1% Wealth Rank Safe Assets Housing Debt Public Equity Private Business Vehicles

(a) Mean portfolio shares

10 20 30 40 50 60 Median Saving Rate in % P0−P10 P10−P20 P20−P30 P30−P40 P40−P50 P50−P60 P60−P70 P70−P80 P80−P90 P90−P95 P95−P97.5 P97.5−P99 P99−P99.5 P99.5−P99.9 Top 0.1% Wealth Rank Net Gross Recurrent

(b) Saving rates

10 20 30 Median Assets to Disposable Income 1 2 3 4 Median Capital Gains in % P0−P10 P10−P20 P20−P30 P30−P40 P40−P50 P50−P60 P60−P70 P70−P80 P80−P90 P90−P95 P95−P97.5 P97.5−P99 P99−P99.5 P99.5−P99.9 Top 0.1% Wealth Rank Persistent Capital Gains (left) Assets to Disposable Income (right)

(c) Capital gains, asset-to-income

−40 −30 −20 −10 10 20 30 40 Median Saving Rate in % P0−P10 P10−P20 P20−P30 P30−P40 P40−P50 P50−P60 P60−P70 P70−P80 P80−P90 P90−P95 P95−P97.5 P97.5−P99 P99−P99.5 P99.5−P99.9 Top 0.1% Wealth Rank Recurrent Net Gross

(d) Saving rates in 2008

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Is this exclusively a story about housing? No

Question: what if “take out” housing?

  • similar patterns for net and gross saving rates?
  • how do households treat capital gains on other assets?

Challenge: Norwegians hold few other assets with capital gains

portfolios

Solution: restrict to households with stocks > 25% of financial wealth

Alternative exercise: drop all home owners

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Is this exclusively a story about housing? No

5 10 15 20 25 30 35 Median Financial Saving Rate in % 20 40 60 80 100 Financial Wealth Percentile Net Gross Recurrent

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Is this exclusively a story about housing? No

5 10 15 20 25 30 35 Median Financial Saving Rate in % 20 40 60 80 100 Financial Wealth Percentile Net Gross Recurrent

  • Caveat: cannot use shareholder registry for stock fund holdings,

use aggregate index ⇒ net saving biased if Cov(ai, ˙ pi) ̸= 0.

  • Not just about housing. But smaller capital gains for other assets. 19
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Macro Implications

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Importance for Aggregate Wealth

Counterfactuals: what if recurrent saving rates were flat as in the models?

2 3 4 5 6 7 8 Wealth−to−Income Ratio 1995 2000 2005 2010 2015 Year

20

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Importance for Aggregate Wealth

Counterfactuals: what if recurrent saving rates were flat as in the models?

NOR US SWE UK 2 3 4 5 6 7 8 Wealth−to−Income Ratio 1995 2000 2005 2010 2015 Year

Source: WID.world

20

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Importance for Aggregate Wealth

Counterfactuals: what if recurrent saving rates were flat as in the models?

3 4 5 6 7 8 Wealth−to−Income Ratio 1995 2000 2005 2010 2015 Year Data No Saving by Holding No Capital Gains

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Importance for Aggregate Wealth

Counterfactuals: what if recurrent saving rates were flat as in the models?

3 4 5 6 7 8 Wealth−to−Income Ratio 1995 2000 2005 2010 2015 Year Data No Saving by Holding No Capital Gains

“Saving by holding” explains up to 80% of increase in wealth-to-income

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What Explains Our Results?

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What Explains Our Results?

Reduced form of all our explanations gross saving = sd(net income) + sc(cap gains) sd ≪ sc ≈ 100% Potential explanations

  • 1. demand-driven asset price changes
  • 2. multiple assets + portfolio adjustment “frictions”

21

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What Explains Our Results?

long version

Reduced form of all our explanations gross saving = sd(net income) + sc(cap gains) sd ≪ sc ≈ 100% Potential explanations

  • 1. demand-driven asset price changes
  • same as benchmark model but with time-varying discount rate
  • two sources of capital gains:

(a) dividend growth (“supply”) (b) discount rates (“demand”)

  • if only (b): consume constant

dividend stream but not cap gains

10 20 30 40 50 60 70 80 90 100 Wealth Percentile 5 10 15 20 25 30 35 40 Saving Rate in % Recurrent Net

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What Explains Our Results?

Reduced form of all our explanations gross saving = sd(net income) + sc(cap gains) sd ≪ sc ≈ 100% Potential explanations

  • 1. demand-driven asset price changes
  • 2. multiple assets + portfolio adjustment “frictions”
  • two assets: ‘consumption asset,’ ‘investment asset’ (e.g. housing)
  • investment asset experiences capital gains but is costly to liquidate

23

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What Explains Our Results?

Reduced form of all our explanations gross saving = sd(net income) + sc(cap gains) sd ≪ sc ≈ 100% Potential explanations (see paper for 3.-5.)

  • 1. demand-driven asset price changes
  • 2. multiple assets + portfolio adjustment “frictions”
  • 3. non-homothetic preferences
  • 4. misperceptions about asset price process
  • 5. inattention and behavioral explanations

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Conclusions

We provide evidence on how saving rates vary across wealth distribution using population tax records from Norway

  • 1. Capital gains are key to relation between saving and wealth
  • rich people don’t have higher saving rates in traditional sense

(net saving rates ≈ flat across wealth distribution)

  • but they still accumulate more wealth through capital gains

(gross saving rates increasing with wealth)

  • 2. Saving by holding explains ≈ 80% of wealth-to-income increase
  • 3. Joint pattern for net & gross saving rates ̸= canonical models
  • demand-driven asset price changes
  • multiple assets + portfolio adjustment frictions

Theories of wealth accumulation need to include changing asset prices!

24

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Q&A Slides

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Portfolio Shares with Public Pensions

20 40 60 80 100 Mean Portfolio Share in % of Total Assets 20 40 60 80 100 Wealth Percentile (incl. Pensions) Safe Assets Housing Debt Public Equity Private Business Vehicles Public Pensions

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Saving Rates with Public Pensions

10 20 30 40 50 60 Median Saving Rate in % 20 40 60 80 100 Wealth Percentile (excl. Pensions) Net Gross Recurrent

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Saving Rates with Public Pensions

10 20 30 40 50 60 Median Saving Rate in % 20 40 60 80 100 Wealth Percentile (incl. Pensions) Net Gross Recurrent

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Dispersion in Saving Rates

−40 −30 −20 −10 10 20 30 40 50 60 Net Saving Rate in % 20 40 60 80 100 Wealth Percentile Median 25th percentile 75th percentile

(a) Net saving rate

−30 −20 −10 10 20 30 40 50 60 70 Recurrent Saving Rate in % 20 40 60 80 100 Wealth Percentile Median 25th percentile 75th percentile

(b) Recurrent saving rate

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Controlling for the usual suspects

Median regression with controls xit = age, earnings, education

sit yit = φ1 +

100

∑

p=2

φpDit,p + f (xit) + µt + εit

10 20 30 40 Median Saving Rate in % 20 40 60 80 100 Wealth Percentile Net Recurrent

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Education Controls

10 20 30 40 Median Net Saving Rate in % 20 40 60 80 100 Wealth Percentile No High School High School College

(a) Education, net saving rate

10 20 30 40 Median Recurrent Saving Rate in % 20 40 60 80 100 Wealth Percentile No High School High School College

(b) Education, recurrent saving rate

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Controlling for Age, Earnings ...

back

10 20 30 40 Median Net Saving Rate in % 20 40 60 80 100 Wealth Percentile Age 20−29 Age 30−49 Age 50−59 Age 60−75

(a) Age, net saving rate

10 20 30 40 Median Recurrent Saving Rate in % 20 40 60 80 100 Wealth Percentile Age 20−29 Age 30−49 Age 50−59 Age 60−75

(b) Age, recurrent saving rate

−10 10 20 30 40 Median Net Saving Rate in % 20 40 60 80 100 Wealth Percentile 1st Income Quintile 2nd Income Quintile 3rd Income Quintile 4th Income Quintile 5th Income Quintile

(c) Earnings, net saving rate

−10 10 20 30 40 Median Recurrent Saving Rate in % 20 40 60 80 100 Wealth Percentile 1st Income Quintile 2nd Income Quintile 3rd Income Quintile 4th Income Quintile 5th Income Quintile

(d) Earnings, recurrent saving rate

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Simply High Saving Rate ⇒ High Wealth?

10 20 30 40 Median Recurrent Saving Rate in % 20 40 60 80 100 Wealth Percentile Baseline 2nd Past SR Decile 4th Past SR Decile 7th Past SR Decile 9th Past SR Decile

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Saving as Fraction of Wealth (Bach-Calvet-Sodini)

10 20 30 40 50 60 70 Median Saving/Wealth in % 20 40 60 80 100 Wealth Percentile Net Gross Recurrent

(a) Saving rates as fraction of wealth

10 20 30 40 50 60 70 80 90 100 Median (Imputed Consumption)/Wealth in % 20 40 60 80 100 Wealth Percentile

(b) Imputed cons as fraction of wealth

˙ a = r − ρ γ (w r + a ) , c = ( r − r − ρ γ ) (w r + a ) ˙ a a = ρ − r γ ( w ra + 1 ) , c a = ( r − r − ρ γ ) ( w ra + 1 )

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Average Capital Gains and Asset-to-Income Ratio

5 10 15 20 Median Assets to Disposable Income 1 2 3 4 5 6 Median Capital Gains in % 20 40 60 80 100 Wealth Percentile Total Capital Gains (left) Persistent Capital Gains (left) Assets to Disposable Income (right)

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Saving Rates with Time Averaging

  • Concern: medians of year-to-year saving rates may get it wrong if

expenditure is “lumpy”

  • Our solution: time-average saving rates within individuals

10 20 30 40 Time−averaged Saving Rate in % (2006−2015) 20 40 60 80 100 Wealth Percentile (2005) Recurrent Recurrent, mean Gross Net

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Housing (in partial equilibrium)

back

Housing differs from other assets:

  • 1. not just an asset, but also a consumption good
  • 2. indivisibilities, transaction costs

Common intuition: (1) by itself ⇒ should save ˙ p > 0

  • p ↑ means housing more expensive = bad for you

We show: intuition ignores intertemporal substitution in housing

  • ˙

p > 0 ⇒ buy bigger house now, then sell off over time

  • collapses to one-asset model with ≈ constant gross saving rate

Takeaway: housing is different, but due to (2), not (1)

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  • 1. Demand-driven Asset Price Changes

back

max

{ct}t≥0

∫ ∞ e−

∫ t

0 ρsds c1−γ

t

1 − γ dt s.t. ct + pt ˙ kt = w + Θtkt Now endogenize asset price. Viewing return rt as primitive: pt = ∫ ∞

t

e−

∫ s

t rτdτΘsds

Case I: capital gains due dividend growth (“supply-driven”)

  • equivalent to earlier model: consume out of persistent capital gains

Case II: capital gains due to time-varying returns (“demand-driven”)

  • if ρt = rt, then consume constant

dividend stream but not cap gains ct = w + Θkt, pt ˙ kt = 0

10 20 30 40 50 60 70 80 90 100 Wealth Percentile 5 10 15 20 25 30 35 40 Saving Rate in % Recurrent Net

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  • 2. Multiple Assets + Portfolio Adjustment “Frictions”
  • Two assets: consumption asset b and investment asset k

˙ b = w + r bb + θpk − pd − c ˙ k = d, ˙ p p = µ + ε

  • + some reason for d = 0 most of the time

20 40 60 80 100 Wealth Percentile 2 4 6 8 10 12 14 16 18 20 Saving Rate in % Net Recurrent

(a) Saving Rates

20 40 60 80 100 Wealth Percentile 10 20 30 40 50 60 70 80 90 100 Portfolio Share in % of Total Assets Investment Asset Consumption Asset Debt

(b) Portfolio Shares