Secular Stagnation, Financial Frictions, and Land Prices
Zhifeng Cai
Rutgers University
Federal Reserve Bank of Philadelphia, November 2019
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Introduction
I Many works have been done on the causes of the 2008 Great Recession
I Two main channels: house price bust and financial distress
I Much less on what drives the slow recovery after the Great Recession
I Question: What role does housing and financial frictions play in driving the
“secular stagnation” after the recession?
I This paper: presents a model where large transitory financial shocks can
generate persistent slumps in outputs, house prices, and interest rates that
resemble a secular stagnation
2 / 44
Motivation House Price GDP Structual Break
-.15
-.1
-.05
0%
dev
iatio
n fr
om tr
end
0 5 10 15 20Quarters after recessions start
The Great Recession
Previous Recessions
GDP
-.4
-.3
-.2
-.1
0.1
% d
evia
tion
from
tren
d
0 5 10 15 20Quarters after recessions start
Investment-.
15-.
1-.
050
% d
evia
tion
from
tren
d
0 5 10 15 20Quarters after recessions start
Hours
-.4
-.3
-.2
-.1
0.1
% d
evia
tion
from
tren
d
0 5 10 15 20Quarters after recessions start
House Price
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This Paper
I Key feature: Financial frictions lead to existence of multiple “regimes”
(locally stable steady states)
I Nonlinearity: Asymmetric responses to small and large negative
shocks
I large shocks → regime switch → push the economy to the bad
steady state
I The good steady state corresponds to the classic neoclassic steady
state
I The bad steady state resembles secular stagnation: low output, land
prices, and interest rates
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How?
I Models with financial frictions typically cannot generate quantitatively
strong amplification and propagation (Kocherlakota, 2000; Cordopa and
Ripoll, 2004)
I One concern is that in these class of models the asset price volatility is too
low (Quadrini, 2011)
I This paper proposes a “land consumption channel” that addresses this
I Land has not only collateral value but also consumption value
I The consumption value of land can be highly volatile if land services
(housing) and other consumption are highly complementarity
I The high volatility of land value implies that the collateral constraint
matters quantitatively
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The paper
I The paper consists of a theoretical part and a quantitative part
I First, embed the land consumption channel into a standard neoclassic
growth model
I Prove that the model exhibits multiple steady states if land services
and consumption are sufficiently complementarity
I Second, quantify the model and discipline this complementarity with
structural estimates.
I The resulting law of motion for capital is S-shaped with multiple
stationary points.
I At the bad steady state, firms are permanently constrained, leading to
secular stagnation
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How Secular Stagnation Happens
I Imagine a recession that destroys certain amount of capital
I Asset (land) prices are low, constraining firms’ ability to borrow, reducing
their investment, reinforcing low capital ⇒ Bad steady state
I Why can’t the firms accumulate financial assets or simply issue equity to
grow out of the bad steady state?
1. Due to house price bust, the households experience painful
deleveraging
2. This drives down the equilibrium interest rate, making firms unwilling
to hold financial asset
3. Low consumption and tight borrowing constraint imply households
unwilling to purchase equity
I The interaction between firm-side and household-side borrowing constraints
lead to secular stagnation
7 / 44
Related Literature
I Macro models with collateral constraints (Kiyotaki and Moore, 1997)
I Role of land prices: Iacoviello (2005), Liu, Wang, & Zha (2013)
I Working capital: Mendoza (2010), Jermann and Quadrini (2012)...
I Secular Stagnation
I Shimer (2012); Fajgelbaum, Schaal, and Taschereau-Dumouchel
(2015); Schaal and Taschereau-Dumouchel (2015, 2016); Benigno and
Fornaro(2018); Eggertsson et al.(2019)...
I Empirical estimates of IES between housing and consumption
I Hanushek and Quigley(1980), Flavin and Nakagawa(2008), Siegel
(2008), Stokey(2009), Li, Liu, Yang, and Yao(2018);...
I Empirical evidence on real-estate prices and investment/employment
I Chaney, Sraer, and Thesmar (2012); Mian and Sufi (2013);
Chodorow-Reich(2014); Adelino, Schoar, and Severino (2015);
Benmelech, Bergman, Seru (2015); Giroud and Mueller (2017)...
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Model
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Model
I Discrete time. Infinite horizon
I Two types of agents: households and firms. Households are owners of
the firms.
I Land: of fixed supply L; can be used for consumption or production.
I Both capital and land can serve as collateral for its owner (be it
household or firm)
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The Firms’ Problem
I Start with land l1t−1, capital kt−1, and intertemporal debt b1t−1.
I Hire labor n1t at rate wt and produce F (zt, kt−1, n1t, l1t)
I Simplifying assumption: capital is pre-determined but not land. Kills
land as a state variable.
I Isomorphic to the existence of a land rental market.
I Dividend dt is distributed after making investment decision it, debt
issuance decision b1t/Rt, and land allocation decision l1t:
b1t−1 + dt + it + pt (l1t − l1t−1) ≤ F (zt, kt−1, n1t, l1t)− wtn1t +b1tRt
I Next period capital is given by:
kt = (1− δ) kt−1 + it
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Financial Friction
I The modeling of financial friction follows Mendoza (2010) and
Jermann and Quadrini (2012)
I Besides issuing intertemporal debt, the firm needs to raise funds with
an intra-period loan to finance working capital.
I Working capital is required to cover cash flow mismatch between
payments to various parties (workers, etc) and production revenue
I Total (inter. + intra.) borrowing is limited by a fraction of the
collateral asset:
b1tRt
+ F (zt, kt−1, n1t, l1t) ≤ ξ1tptl1t + κtkt
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The Firms’ Problem
max{b1t,kt,l1t,it,n1t,dt} E∑∞
t=1Mtdt
b1t−1 + dt + it + pt (l1t − l1t−1) ≤ F (zt, kt−1, n1t, l1t) − wtn1t + b1tRt
b1tRt
+ F (zt, kt−1, n1t, l1t) ≤ ξ1tptl1t + κtkt
kt = (1 − δ) kt−1 + it
k0, l10, b10 given
I Constant Return to Scale Production Function:
F (z, k, n, l) = z[lγk1−γ
]αn1−α
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The Households’ Problem
I Start period t with land holding l2t−1 and debt b2t−1.
I His income include labor income wtn2t and capital income dt.
I In each period he chooses consumption and next period land and
bond holdings subject to the following budget constraint:
b2t−1 + ct + pt (l2t − l2t−1) ≤ dt + wtn2t +b2tRt
(1)
I The household can borrow with land as collateral:
b2tRt
≤ ξ2tptl2t (2)
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The households’ problem
max{b2t,l2t,ct,n2t} E∑∞
t=1 βtU (ct, n2t, l2t)
b2t−1 + ct + pt (l2t − l2t−1) ≤ dt + wtn2t + b2tRt
b2tRt
≤ ξ2tpl2t
n2t ≤ n, k0, l20, b20 given
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Preference
U(ct, n2t, l2t) =
[ω(ct − χn2t
1+1/ν
1+1/ν
)1−1/σ
+ (1 − ω) l1−1/σ2t
] 1−1/η1−1/σ
1 − 1/η
I CES form of utility function where σ captures the intratemporal
elasticity of substitution between the (composite) consumption
and land
I The composite consumption term implies no wealth effect on
labor supply (GHH preference)
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Competitive Equilibrium
DefinitionA competitive equilibrium is defined in a standard way in which the firm
and the households maximize their respective objectives given market
prices, and the markets for goods, labor, land and bonds all clear:
1. Goods: ct + it = yt
2. Labor: n1t = n2t
3. Land: l1t + l2t = L
4. Bond: b1t + b2t = 0
Lastly, the firm’s pricing kernel is equal to the household’s marginal utility:
Mt = βtUct
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Characterization
I In the absence of equity issuance friction, household borrowing
constraint binds if and only if firm borrowing constraint binds
I Suppose otherwise, firm constraint binds but not the household one
I The firm can reduce dividend payment, and the household can
increase inter-borrowing to maintain the same level of consumption
I This relaxes the firm’s borrowing constraint and yields higher output
I Thus, the two constraints must bind at the same time
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Characterization
I Thus, we can write the two borrowing constraints as one aggregate
constraint:
b1t + b2tRt
+ F (zt, kt−1, n1t, l1t) ≤ ξ2tptl2t + ξ1tptl1t + κtkt
I Or, with bond market clearing condition:
F (zt, kt−1, n1t, l1t) ≤ ξ2tptl2t + ξ1tptl1t + κtkt
I The bond distribution is irrelevant for equilibrium allocations
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Isomorphism to Representative Agent
I Given that the bond distribution is irrelevant, we can aggregate
household and firm into one single agent solving:
max{l1t,l2t,ct,nt} E∑∞
t=1 βtU (ct, nt, l2t)
ct + kt − (1− δ)kt−1+∑
i=1,2 pt (lit − lit−1) ≤ F (zt, kt, l1t, nt)
F (zt, kt, n1t, l1t) ≤ ξ2tptl2t + ξ1tptl1t + κtkt
k0, l10, l20 given
I We also don’t need to keep track of the land distribution:
consumption and production take place using ex post land holdings
I The only endogenous state variable is capital accumulation
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Steady-State Interest Rate
I The steady-state interest rate is pinned down by:
1
R= β +
λ
R
where λ is the multiplier on the collateral constraint
I Accumulating financial assets not only increases future consumption,
but also relaxes future borrowing constraint
Proposition
The steady-state interest rate is decreasing in the tightness of the collateral
constraint (measured by λ)
R =1− λβ
(3)
I If constraint binds, the gross interest rate could be less than 1
depending on how tight the collateral constraint is.
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Steady State Multiplicity
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Strategy
I Given any land price p, solve the representative agent problem at
steady state, and obtain the steady-state land demand (sum of
residential l1 and commercial l2 land demand)
L(p) = l1(p) + l2(p)
I Look for p such that the land market clears:
L(p) = L
I Goal: show that the L(.) function is nonmonotonic with financial
frictions
23 / 44
Land Consumption Channel
I Absence frictions, the model collapses to a standard growth model,
thus land demand L is monotonically decreasing in price p
I In the presence of financial frictions, land demand could be increasing
in price p. This nonmonotonicity comes from residential land demand:
1− ωω
(c
l2
) 1σ
︸ ︷︷ ︸Consumption benefit (MRS)
+ ξ2pλ︸︷︷︸Collateral benefit
− (1− β)p︸ ︷︷ ︸User cost
= 0
I When land price p ⇑, output increases, (composite) consumption c ⇑,
demand for residential land l2 ⇑, the magnitude depends on
substitution parameter σ
24 / 44
Theorem
Suppose σ (substitution in utility) and γ (land share in production)
are sufficiently small. Then for some combination of loan-to-value
ratios, there exists:
1. a unique unconstrained steady state, in which the collateral
constraint is slack and
2. at least two constrained steady states, in which the collateral
constraints are binding.
25 / 44
Graphic Illustration
Frictionless steady state A
Household demand is upward-sloping𝑙2′ 𝑝𝑠𝑠 > 0 (Lemma 3.1)
Aggregate land demand function is upward-sloping 𝐿′ 𝑝𝑠𝑠 = 𝑙1
′ 𝑝𝑠𝑠 +𝑙2′ 𝑝𝑠𝑠 > 0
Land demand 𝐿 → +∞as land price 𝑝 → 0
C B
Frictionless land demand is downward-sloping (Proposition 3.3)
𝑝1
𝐿 𝑝1 > 0
𝑝2
𝐿 𝑝2 < 0
𝑝3
𝐿 𝑝3 > 0
Figure 1: Graphical Illustration of Theorem 1
26 / 44
Remark on Interest Rate
I The interest rates of constrained steady states are lower than the
interest rate of the unconstrained steady state, due to the binding
collateral constraint.
I Transitions from good to bad steady state would entail a decline of
the interest rate
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Quantitative Analysis
28 / 44
Calibration
Table 1: Calibration
Parameters Value Source
Discount factor β 0.99 Quarterly modelIntertemporal elasticity η 0.5 StandardDisutility of working χ 2.41 Steady state labor equal to .33Frisch Elasticity ν 4 Macro StudiesPref. weight ω 0.27 Land value/GDP= 1.06Depreciation δ 2.5% StandardCapital share α 0.35 StandardLand share αγ 0.03 Share of commer./res. land=.5Intratemporal Elasticity σ 0.487 Micro estimates (Li et al. 2016)Aggregate land stock l 1 Normalization
29 / 44
Calibration
Elasticity of Substitution between Housing and Consumption σ
I Most micro estimates between 0.13 and 0.6
I Hanushek and Quigley(1980), Flavin and Nakagawa(2008),
Siegel (2008), Stokey(2009), Li, Liu, Yang, and Yao(2016)
I Set η = 0.487 as in the structural estimation of Li, Liu, Yang, and
Yao(2016)
Loan-to-value Ratio ξ, κ
I Constraint occasionally binding ⇒ cannot estimate using steady state
targets
I Set it so that constraint only binds in big recessions
I Set ξ = κ = 0.03: Constraint binds with about 6% drop in
output
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Dynamics: Multiple Steady States
Current Capital 𝐾𝑡
Futu
re C
apit
al
450 𝑙𝑖𝑛𝑒
Good Steady State(unconstrained)
Bad Steady State(constrained)
Frictionless Model Model with Collateral Constraint
Middle Unstable Steady State
Region Converging to bad steady state Region Converging to good steady state
Constrained Region Unconstrained Region
Figure 2: Law of Motion for Capital
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Transitional Dynamics
I Transitional dynamics depend on how much capital lost
during the recession
I More capital lost during the recession, slower the recovery.
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Transitional Dynamics
10 20 30 40 50 60 70 80 90 1000.92
0.94
0.96
0.98
1Output
10 20 30 40 50 60 70 80 90 1000.92
0.94
0.96
0.98
1Labor
10 20 30 40 50 60 70 80 90 1000.92
0.94
0.96
0.98
1
1.02Investment
Small RecessionMedium RecessionLarge Recession
10 20 30 40 50 60 70 80 90 1000.8
0.85
0.9
0.95
1Land Price
33 / 44
Isolating the Collateral Channel
I Consider an alternative economy where land price is
exogenously fixed at the unconstrained steady state level
(call it fixed-p economy)
I This captures scenario where there is a severe recession but
without financial amplification through collateral constraint
I Model no longer displays slow recovery
34 / 44
Transitional Dynamics(Fixed-p Economy)
10 20 30 40 50 60 70 80 90 1000.975
0.98
0.985
0.99
0.995
1Output
10 20 30 40 50 60 70 80 90 1000.98
0.985
0.99
0.995
1Labor
10 20 30 40 50 60 70 80 90 1001
1.005
1.01
1.015
1.02Investment
10 20 30 40 50 60 70 80 90 1000.85
0.9
0.95
1Land Price
Small RecessionMedium RecessionLarge Recession
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Accounting for the Slow Recovery
36 / 44
Narratives of the Great Recession and Aftermath
I Large swings in house demand create boom-bust in house prices
I Collapse of the financial sector lead to large financial shocks
I Productivity slow down after the Great Recession
37 / 44
Quantitative Strategy
Feed into the model:
I A sequence of housing demand shocks
I To match house prices between 2007Q4 to 2016Q1
I Not just the decline but the subsequent house price recovery
I A sequence of credit shocks
I To match output decline between 2007Q4 to 2009Q4
I Examine the model’s ability to explain subsequent stagnation
I A sequence of productivity shocks
I Independently computed as the Solow residual
38 / 44
Accounting for the Slow Recovery
2008 2009 2010 2011 2012 2013 2014 2015 2016-1
-0.5
0
% D
evia
tion
Demand (Taste) Shock
2008 2009 2010 2011 2012 2013 2014 2015 2016
-0.2
-0.1
0
0.1
% D
evia
tion Lehman Bankruptcy Credit Shock
2008 2009 2010 2011 2012 2013 2014 2015 2016
Year
-0.04
-0.02
0
0.02
0.04
% D
evia
tion
Productivity Shock
39 / 44
Accounting for the Slow Recovery
2008 2010 2012 2014 2016-0.2
-0.15
-0.1
-0.05
0
% D
evia
tion
Output
DataModel
2008 2010 2012 2014 2016-0.2
-0.15
-0.1
-0.05
0
% D
evia
tion
Hours
2008 2010 2012 2014 2016
Year
-0.5
-0.4
-0.3
-0.2
-0.1
0
% D
evia
tion
Investment
2008 2010 2012 2014 2016
Year
-0.5
-0.4
-0.3
-0.2
-0.1
0
% D
evia
tion
House Price
40 / 44
Compared to Fixed-p Model without Financial Amplification
2008 2010 2012 2014 2016-0.2
-0.15
-0.1
-0.05
0%
Dev
iatio
n
Output
DataBench ModelFixed-p Model
2008 2010 2012 2014 2016-0.2
-0.15
-0.1
-0.05
0
% D
evia
tion
Hours
2008 2010 2012 2014 2016-0.5
-0.4
-0.3
-0.2
-0.1
0Investment
2008 2010 2012 2014 2016
Year
-0.5
-0.4
-0.3
-0.2
-0.1
0
% D
evia
tion
House Prices
41 / 44
Decomposition of Output
2008 2009 2010 2011 2012 2013 2014 2015 2016-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
% D
evia
tion
Fro
m P
re-c
risis
Lev
el
-16.9
-13.5
-4.3-4.9
-3.3
DataModel (All Three Shocks)Demand Shock OnlyProd. Shock OnlyCredit Shock Only
42 / 44
Interest Rate
2008 2009 2010 2011 2012 2013 2014 2015 2016-8
-6
-4
-2
0
2
4
6
Per
cent
age
Poi
nts
%
Annualized Interest Rate
Data (Federal Funds Rate)ModelConstrained Interest Rate=0.85%
43 / 44
Conclusion
I The paper: A model to explain the slow recovery after the 2008
financial crisis
I Key feature: Multiple steady states and nonlinear dynamics
I Crucial ingredient: Dual role of land as households’ consumption and
firms’ collateral
I Quantitative discipline: Housing-consumption complementarity from
cross-sectional evidences and structural estimates
I Quantitative findings:
I The model can generate persistent recessions comparable to
post-Great Recession data
I Credit Shock, albeit short-lived, contributes non-trivially to the
slow recovery
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Real GDP Back
8.5
99.
510
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
1 / 8
House Price Index Back
11.
52
2.5
1975 1985 1995 2005 2015Real House Price Index
Constant 2% Growth Trend
S&P/Case-Shiller U.S. National Home Price Index, deflated by GDP deflator
2 / 8
Land Price Index Back
12
34
56
1975 1985 1995 2005 2015Real Land Price Index
Constant Growth Trend
Lincoln Institute of Land Policy, Davis and Heathcote(2007)
3 / 8
Motivation Back
-.08
-.06
-.04
-.02
0.0
2%
dev
iatio
n fr
om tr
end
0 5 10 15 20Quarters after recessions start
GDP
-.4
-.3
-.2
-.1
0.1
% d
evia
tion
from
tren
d
0 5 10 15 20Quarters after recessions start
Investment
-.1
-.05
0.0
5%
dev
iatio
n fr
om tr
end
0 5 10 15 20Quarters after recessions start
Labor
-.4
-.3
-.2
-.1
0.1
% d
evia
tion
from
tren
d
0 5 10 15 20Quarters after recessions start
House Price
Detrended with a Structual Break at Year 1989
4 / 8
Cross sectional evidenceQuestion: Is there a systematic relation between the extent ofhousing price drop and pace of recovery at the MSA level?
-.2
-.15
-.1
-.05
0.0
5Lo
g D
evia
tion
Fro
m T
rend
1990 1995 2000 2005 2010 2015Employment
MSA with smallest housing price delineMSA with medium housing price delineMSA with biggest housing price deline
5 / 8
Quantity of land grows smoothly.8
.91
1.1
1.2
1.3
1.4
1.5
1975 1985 1995 2005 2015Quantity Index of Residential Land
Lincoln Institute of Land Policy, Davis and Heathcote(2007)
6 / 8
Quantity of land grows smoothlyBack
11.
21.
41.
61.
8
1950 1960 1970 1980 1990Quantity Index of Commercial Land
Lincoln Institute of Land Policy, Davis and Heathcote(2007)7 / 8
Accounting for the labor wedge Back
2004 2006 2008 2010 2012 2014 2016-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12Data
2004 2006 2008 2010 2012 2014 2016-0.2
0
0.2
0.4
0.6
0.8
1
1.2Model
Labor WedgeFirm Component
8 / 8