Secular Stagnation, Land Prices, and Collateral Constraints Zhifeng - PowerPoint PPT Presentation

Secular Stagnation, Land Prices, and Collateral Constraints Zhifeng Cai UMN November 29, 2016 1 / 33

Motivation ◮ The 2007-2008 Financial Crisis differs considerably from other postwar recessions ◮ Larger declines of macro variables ◮ Slower recovery 2 / 33

Motivation Housing Price GDP GDP Investment .1 0 % deviation from trend % deviation from trend 0 -.05 -.1 -.2 -.1 -.3 The Great Recession Previous Recessions -.15 -.4 0 5 10 15 20 0 5 10 15 20 Quarters after recessions start Quarters after recessions start Labor Housing Price .1 0 % deviation from trend % deviation from trend 0 -.05 -.1 -.2 -.1 -.3 -.15 -.4 0 5 10 15 20 0 5 10 15 20 Quarters after recessions start Quarters after recessions start 3 / 33

Overview ◮ Question: 1. Why slow recovery following the Great Recession? 2. What role did the real-estate(land) sector play? ◮ Proposes a standard neoclassical model with a land sector where land serves dual roles: 1. As consumption for the households 2. As collateral for the firms to finance borrowing and working capital ◮ Results: 1. Theory: existence of multiple steady states. 2. Quantitative: substantial persistence upon large recessions ◮ Large recessions trigger transitions across steady states 4 / 33

Mechanism 𝐻ood Steady State 𝐶𝑏𝑒 Steady State 𝐼𝑗𝑕ℎ 𝐷𝑏𝑞𝑗𝑢𝑏𝑚 𝐵𝑑𝑑𝑣𝑛𝑣𝑚𝑏𝑢𝑗𝑝𝑜 𝑀𝑝𝑥 𝐷𝑏𝑞𝑗𝑢𝑏𝑚 𝐵𝑑𝑑𝑣𝑛𝑣𝑚𝑏𝑢𝑗𝑝𝑜 𝐼𝑗𝑕ℎ 𝐼𝑝𝑣𝑡𝑓ℎ𝑝𝑚𝑒𝑡 𝑋𝑓𝑏𝑚𝑢ℎ 𝑀𝑝𝑥 𝐼𝑝𝑣𝑡𝑓ℎ𝑝𝑚𝑒𝑡 𝑥𝑓𝑏𝑚𝑢ℎ 𝐼𝑗𝑕ℎ 𝑀𝑏𝑜𝑒 𝑄𝑠𝑗𝑑𝑓 𝑀𝑝𝑥 𝑀𝑏𝑜𝑒 𝑄𝑠𝑗𝑑𝑓 𝑆𝑓𝑚𝑏𝑦𝑓𝑒 𝐺𝑗𝑠𝑛 𝑋𝑝𝑠𝑙𝑗𝑜𝑕 𝐷𝑏𝑞𝑗𝑢𝑏𝑚 𝐷𝑝𝑜𝑡𝑢𝑠𝑏𝑗𝑜𝑢 𝑈𝑗𝑕ℎ𝑢𝑓𝑜𝑓𝑒 𝐺𝑗𝑠𝑛 𝑋𝑝𝑠𝑙𝑗𝑜𝑕 𝐷𝑏𝑞𝑗𝑢𝑏𝑚 𝐷𝑝𝑜𝑡𝑢𝑠𝑏𝑗𝑜𝑢 𝐼𝑗𝑕ℎ 𝐹𝑛𝑞𝑚𝑝𝑧𝑛𝑓𝑜𝑢 𝑀𝑝𝑥 𝐹𝑛𝑞𝑚𝑝𝑧𝑛𝑓𝑜𝑢 5 / 33

Related Literature ◮ The paper relates to macro models with collateral constraints (Kiyotaki and Moore, 1997) ◮ Typical model features a unique steady state ◮ Recent extensions still feature a unique steady state: 1. Consumption role of land: Liu, Wang, and Zha (2013), Iacoviello (2005) 2. Working capital: Jermann and Quadrini (2012), Mendoza (2010) ◮ The paper incorporates both the consumption role of land and working capital → Multiple steady states 6 / 33

Road Map ◮ Start with a stylized model ◮ Isolate the key complementary forces ◮ Characterize conditions steady state multiplicity arises ◮ Extended model ◮ Sensitivity check ◮ The mechanism generates substantial persistence 7 / 33

Model 8 / 33

A Stylized Model ◮ Discrete time. Infinite horizon ◮ A continuum identical households: ◮ Consume consumption goods and land, supply labor, and accumulate capital ◮ Owns a single private firm ◮ Constant-returns-to-scale production technology ◮ Working capital subject to collateral constraint ◮ Land supply is fixed 9 / 33

Households problem ∞ � β t U ( c t , n t , l t − 1 ) max c,l,n,n d ,k t =1 Subject to: c t + p t l t + k t ≤ w t n t + π t + p t l t − 1 + (1 − δ ) k t − 1 A ( n d t ) 1 − α k α t − 1 − w t n d π t = t w t n d ≤ ξp t l t + κk t Timeline t 0 ≤ n t ≤ n 0 , c t , l t , k t ≥ 0 , l 0 , k 0 given 10 / 33

Preference � 1 − 1 /σ c − χ n 1+1 /ν � + ω l 1 − 1 /σ 1 + 1 /ν U ( c, l, h ) = 1 − 1 /σ 1 − 1 /σ ◮ No wealth effect on labor supply (GHH preference) ◮ σ is both: ◮ Intratemporal elasticity of substitution (Matters) ◮ (Inverse of) intertemporal elasticity of substitution (Not matter) 11 / 33

Competitive Equilibrium Definition A competitive equilibrium is { c t , k t +1 , l t +1 , n t , n d t } ∞ t =1 and { p t , w t , q t } ∞ t =1 such that: 1. Given prices, allocations solve the households problem. 2. Land and labor market clears every period: l = l 0 , n = n d ◮ A steady state is a competitive equilibrium where capital stock k t is time invariant. 12 / 33

Theorem Suppose that 1. Consumption and land are complementary (Low σ ) 2. Labor supply is elastic (High ν ) Then there exists an open set U ∈ R 2 such that for any combinations of loan to value ratios ( κ, ξ ) ∈ U , there exists more than one locally-stable steady states. 13 / 33

Warm-Up: the Frictionless Case ◮ Suppose there is no credit constraint ◮ The steady state ( c, k, n, w, p ) is fully characterized by: c + δk = Ak α n 1 − α (Resources Constraint) 1 n ν = w (Labor supply) � (1 − α ) A � 1 α k = n (Labor demand) w Aα ( k/n ) α − 1 + (1 − δ ) � � β = 1 (Capital FOC) � 1 /σ c − χ n 1+ 1 � ν ωl − σ + βp − p = 0 (Land FOC) 0 1 + 1 ν ◮ The four equations in the box solve real allocations independent of land price p . 14 / 33

Frictional Case ◮ The steady state ( c, k, n, w, p ) is fully characterized by: c + δk − Ak α n 1 − α = 0 1 ν = w n � (1 − α ) A � 1 � � ξpl 0 + κk α min , k = n w w � (1 − α ) A ( k/n ) α � � � Aαk α − 1 ( n ) 1 − α + (1 − δ ) + β − 1 κ = 1 w � (1 − α ) A ( k/n ) α � 1 /σ c − χ n 1+ 1 � � ν F ( p, c, k, w, n ) := ωl − σ − (1 − β ) p + − 1 ξp = 0 0 1 + 1 w ν ( Land FOC ) ◮ Real allocations cannot be solved independent of land price p 15 / 33

Strategy ◮ Resources Constraint, labor demand, labor supply, capital FOC jointly define a mapping from land price p to ( c, k, w, n ) ◮ This mapping is constant in the frictionless case. ◮ Write the land FOC as F ( p, c, k, w, n ) = 0 ◮ Plug the mapping into the land FOC ⇒ 1 equation 1 unknown: f ( p ) := F ( p, c ( p ) , k ( p ) , w ( p ) , n ( p )) = 0 16 / 33

Frictional Case Willingness to buy function ◮ ’Willingness to buy’ function: � � 1 /σ c ( p ) − χl ( p ) 1+ 1 � (1 − α ) Ak ( p ) α l ( p ) − α � ν ωl − σ f ( p ) = + − 1 ξp − (1 − β ) p 0 1 + 1 w ( p ) � �� � ν Net cost � �� � Benefit ◮ Land price p is part of steady state iff f ( p ) = 0. ◮ Crucial: f is nonmonotonic 17 / 33

f ( p ) is Nonmonotonic Proof 0.02 0.015 0.01 0.005 f(p) 0 -0.005 -0.01 -0.015 -0.02 0 2 4 6 8 10 12 p 18 / 33

Why Nonmonotonic? Land First Order Condition � �� � f ( p ) := F ( p, c ( p ) , k ( p ) , w ( p ) , n ( p ) ) = 0 � �� � Other conditions ∂f ( p ) ∂F ∂F ∂c = + + other terms (1) ∂p ∂p ∂c ∂p ���� � �� � Direct Price Effect − Indirect Collateral Effect+ Two opposing forces: ◮ Direct Price Effect: Land gets expensive, less willing to buy. ◮ Indirect Collateral Effect: Land Price ⇑ = ⇒ Consumption ⇑ = ⇒ More willing to buy land 19 / 33

Collateral Effect in Detail 1. Land Price ⇑ 2. Firm working capital constraint relaxed 3. Employment ⇑ , Capital ⇑ 4. Households wealth ⇑ , consumption ⇑ 5. Willingness to buy land ⇑ (Land-consumption complementarity) 20 / 33

Discussion of Assumptions 𝑀𝑏𝑜𝑒 𝑄𝑠𝑗𝑑𝑓 ⇑ 𝐷𝑝𝑜𝑡𝑣𝑛𝑞𝑢𝑗𝑝𝑜 ⇑ 𝑋𝑗𝑚𝑚𝑗𝑜𝑕𝑜𝑓𝑡𝑡 𝑢𝑝 𝑐𝑣𝑧 𝑚𝑏𝑜𝑒 ⇑ C and Land Complementary Labor Supply Elastic (Need High 𝜉) (Need Low 𝜏 ) Otherwise ◮ If labor inelastically supplied ( ν → 0) ⇒ Equilibrium labor not affected by working capital constraint ⇒ Output and consumption not affected by land price ◮ If consumption and land perfect substitutes ( σ → ∞ ) ⇒ Linearity structure implies level of consumption irrelevant 21 / 33

Discussion of Assumptions 𝑀𝑏𝑜𝑒 𝑄𝑠𝑗𝑑𝑓 ⇑ 𝐷𝑝𝑜𝑡𝑣𝑛𝑞𝑢𝑗𝑝𝑜 ⇑ 𝑋𝑗𝑚𝑚𝑗𝑜𝑕𝑜𝑓𝑡𝑡 𝑢𝑝 𝑐𝑣𝑧 𝑚𝑏𝑜𝑒 ⇑ Labor Supply Elastic C and Land Complementary (Need High 𝜉) (Need Low 𝜏 ) ◮ When labor supply is perfectly elastic ( ν → ∞ ), multiple steady states exist if and only if σ < 1. 22 / 33

Quantitative Analysis 23 / 33

The Extended Model: Summary Details ◮ Two types of agents: households and firms. Households(HHs) are owners of the firms. ◮ There is a rental market for land ◮ HHs choose to own land (residential land) or rent it ◮ Firms accumulate land (commercial land) and can allocate it to rental or production use ◮ Land and capital can be used as collateral 24 / 33

The households problem ∞ � β t U ( c t , n t , l t − 1 ) max c,l h ,n t =1 c t + p t l ht + r t l r ≤ p t l ht − 1 + d t + w t n t ht − 1 l t − 1 = l 1 t − 1 + l 2 t − 1 h 10 given , l t ≤ ¯ l, l 1 t − 1 + l 2 t − 1 ≥ 0 ◮ l ht : residential land; l r ht : land rent by households; ◮ p t : land purchase price; r t : land rental rate; 1 − η  � 1 / (1 − 1 /σ )  � ω ( c − χ n 1+ 1 ν ) 1 − 1 /σ +(1 − ω ) l 1 − 1 /σ  1+ 1  ν ◮ U ( c, h, l ) = 1 − η 25 / 33