Housing Prices and Growth

Transcription

1 Housing Prices and Growth James A. Kahn June 2007

2 Motivation Housing market boom-bust has prompted talk of bubbles. But what are fundamentals? What is the right benchmark?

3 Motivation Housing market boom-bust has prompted talk of bubbles. But what are fundamentals? What is the right benchmark? Previous work on productivity growth indicates regimes with di erent long-term trends.

4 Motivation Housing market boom-bust has prompted talk of bubbles. But what are fundamentals? What is the right benchmark? Previous work on productivity growth indicates regimes with di erent long-term trends. What does growth theory say quantitatively about the potential linkage?

5 Motivation Housing market boom-bust has prompted talk of bubbles. But what are fundamentals? What is the right benchmark? Previous work on productivity growth indicates regimes with di erent long-term trends. What does growth theory say quantitatively about the potential linkage? Strategy: Compare changes in trend productivity vs. trend housing prices in model vs. reality

6 Motivation Housing market boom-bust has prompted talk of bubbles. But what are fundamentals? What is the right benchmark? Previous work on productivity growth indicates regimes with di erent long-term trends. What does growth theory say quantitatively about the potential linkage? Strategy: Compare changes in trend productivity vs. trend housing prices in model vs. reality Neoclassical approach:

7 Motivation Housing market boom-bust has prompted talk of bubbles. But what are fundamentals? What is the right benchmark? Previous work on productivity growth indicates regimes with di erent long-term trends. What does growth theory say quantitatively about the potential linkage? Strategy: Compare changes in trend productivity vs. trend housing prices in model vs. reality Neoclassical approach: Ignore credit market frictions especially at low frequency have more to do with rent vs. own decision than with primary variables of interest here

8 Motivation Housing market boom-bust has prompted talk of bubbles. But what are fundamentals? What is the right benchmark? Previous work on productivity growth indicates regimes with di erent long-term trends. What does growth theory say quantitatively about the potential linkage? Strategy: Compare changes in trend productivity vs. trend housing prices in model vs. reality Neoclassical approach: Ignore credit market frictions especially at low frequency have more to do with rent vs. own decision than with primary variables of interest here Flexible prices, rational expectations

9 Background Since 1995, the real quality-adjusted price of new houses has appreciated at an average rate of 2.2 percent annually.

10 Background Since 1995, the real quality-adjusted price of new houses has appreciated at an average rate of 2.2 percent annually. Similarly strong real appreciation took place in the 1960s and 1970s, followed by nearly 20 years of real depreciation.

11 Background Since 1995, the real quality-adjusted price of new houses has appreciated at an average rate of 2.2 percent annually. Similarly strong real appreciation took place in the 1960s and 1970s, followed by nearly 20 years of real depreciation.

12 Background Since 1995, the real quality-adjusted price of new houses has appreciated at an average rate of 2.2 percent annually. Similarly strong real appreciation took place in the 1960s and 1970s, followed by nearly 20 years of real depreciation. 1.4 Figure 1: Real Price of New Homes (Quality Adjusted) Note: logarithmic scale

13 Background (cont.) Housing wealth has averaged 4.6 percent growth since 1952.

14 Background (cont.) Housing wealth has averaged 4.6 percent growth since This compares with

15 Background (cont.) Housing wealth has averaged 4.6 percent growth since This compares with 3.4 percent growth of private net worth excluding real estate

16 Background (cont.) Housing wealth has averaged 4.6 percent growth since This compares with 3.4 percent growth of private net worth excluding real estate 3.5 percent growth of PCE

17 Background (cont.) Housing wealth has averaged 4.6 percent growth since This compares with 3.4 percent growth of private net worth excluding real estate 3.5 percent growth of PCE Real estate was 27 percent of net worth in 1952, 42 percent in 2005.

18 Background (cont.) Housing wealth has averaged 4.6 percent growth since This compares with 3.4 percent growth of private net worth excluding real estate 3.5 percent growth of PCE Real estate was 27 percent of net worth in 1952, 42 percent in 2005.

19 Background (cont.) Housing wealth has averaged 4.6 percent growth since This compares with 3.4 percent growth of private net worth excluding real estate 3.5 percent growth of PCE Real estate was 27 percent of net worth in 1952, 42 percent in Figure 2a: Ratio of Housing Wealth to Consumption Figure 2b: Ratio of Housing Wealth to Total Net Worth

20 What drives housing prices? Population demographics (Mankiw and Weil, 1989).

21 What drives housing prices? Population demographics (Mankiw and Weil, 1989).

22 What drives housing prices? Population demographics (Mankiw and Weil, 1989). Supply restrictions (Glaeser et al, 2005)

23 What drives housing prices? Population demographics (Mankiw and Weil, 1989). Supply restrictions (Glaeser et al, 2005) Productivity growth (this paper) coupled with

24 What drives housing prices? Population demographics (Mankiw and Weil, 1989). Supply restrictions (Glaeser et al, 2005) Productivity growth (this paper) coupled with Fixed factor (land)

25 What drives housing prices? Population demographics (Mankiw and Weil, 1989). Supply restrictions (Glaeser et al, 2005) Productivity growth (this paper) coupled with Fixed factor (land) Sectoral di erences in land intensity

26 What drives housing prices? Population demographics (Mankiw and Weil, 1989). Supply restrictions (Glaeser et al, 2005) Productivity growth (this paper) coupled with Fixed factor (land) Sectoral di erences in land intensity

27 What drives housing prices? Population demographics (Mankiw and Weil, 1989). Supply restrictions (Glaeser et al, 2005) Productivity growth (this paper) coupled with Fixed factor (land) Sectoral di erences in land intensity Figure 5: Real Price of Land Source: BLS Note: Logarithmic scale. The two series are from different vintages of BLS data.

28 What drives housing prices (cont.) HP-trend productivity growth (relative to a linear trend) over the postwar period has followed a similar pattern.

29 What drives housing prices (cont.) HP-trend productivity growth (relative to a linear trend) over the postwar period has followed a similar pattern.

30 What drives housing prices (cont.) HP-trend productivity growth (relative to a linear trend) over the postwar period has followed a similar pattern..08 Figure 6: Detrended HP Filtered Output per Hour

31 A Growth Model with Housing Two sectors Manufacturing (m) produces

32 A Growth Model with Housing Two sectors Manufacturing (m) produces non-housing related goods and services

33 A Growth Model with Housing Two sectors Manufacturing (m) produces non-housing related goods and services capital (structures and durable goods).

34 A Growth Model with Housing Two sectors Manufacturing (m) produces non-housing related goods and services capital (structures and durable goods). Housing (h) uses capital, labor, and land to produce a ow of housing services.

35 A Growth Model with Housing Two sectors Manufacturing (m) produces non-housing related goods and services capital (structures and durable goods). Housing (h) uses capital, labor, and land to produce a ow of housing services.

36 A Growth Model with Housing Two sectors Manufacturing (m) produces non-housing related goods and services capital (structures and durable goods). Housing (h) uses capital, labor, and land to produce a ow of housing services. Other features Balanced aggregate growth, but unbalanced across sectors.

37 A Growth Model with Housing Two sectors Manufacturing (m) produces non-housing related goods and services capital (structures and durable goods). Housing (h) uses capital, labor, and land to produce a ow of housing services. Other features Balanced aggregate growth, but unbalanced across sectors. Regime-switching speci cation for productivity growth in the m sector.

38 A Growth Model with Housing Two sectors Manufacturing (m) produces non-housing related goods and services capital (structures and durable goods). Housing (h) uses capital, labor, and land to produce a ow of housing services. Other features Balanced aggregate growth, but unbalanced across sectors. Regime-switching speci cation for productivity growth in the m sector. Aggregate looks like standard stochastic growth model, but within have sectoral reallocation, relative price changes

39 Details and Notation Population N t growing exponentially at rate ν, allocated to m or h sectors.

40 Details and Notation Population N t growing exponentially at rate ν, allocated to m or h sectors. Fixed total land L, allocated to m or h sectors

41 Details and Notation Population N t growing exponentially at rate ν, allocated to m or h sectors. Fixed total land L, allocated to m or h sectors Aggregate housing services H t (per capita h t )

42 Details and Notation Population N t growing exponentially at rate ν, allocated to m or h sectors. Fixed total land L, allocated to m or h sectors Aggregate housing services H t (per capita h t ) Aggregate non-housing consumption C t (per capita c t )

43 Details and Notation Population N t growing exponentially at rate ν, allocated to m or h sectors. Fixed total land L, allocated to m or h sectors Aggregate housing services H t (per capita h t ) Aggregate non-housing consumption C t (per capita c t ) Per capita work e ort e t

44 Details and Notation Population N t growing exponentially at rate ν, allocated to m or h sectors. Fixed total land L, allocated to m or h sectors Aggregate housing services H t (per capita h t ) Aggregate non-housing consumption C t (per capita c t ) Per capita work e ort e t k i K i /N i, `i = L i /N i, n i N i /N, (i = m, h), k K /N

45 Planner s problem max E 0 ( t=0 (1 + ρ) t ln φ (c t, h t ) ψ (e t ) ) where h φ (c t, h t ) = ω c c (ɛ 1)/ɛ t + ω h h i (ɛ 1)/ɛ ɛ/(ɛ 1) t

46 Planner s problem max E 0 ( t=0 (1 + ρ) t ln φ (c t, h t ) ψ (e t ) ) where h φ (c t, h t ) = ω c c (ɛ 1)/ɛ t + ω h h i (ɛ 1)/ɛ ɛ/(ɛ 1) t subject to resource constraints c t + (1 + ν) k t k t 1 (1 δ) = A mt k α mt`βm mt n mt h t = A ht k α ht`βh ht n ht k mt n mt + k ht n ht = k t 1 `mt n mt + `ht n ht = `t n mt + n ht = 1.

47 Planner s problem (cont.) Assume β h β m

48 Planner s problem (cont.) Assume β h β m k is chosen one period ahead of time, but allocated within the period

49 Planner s problem (cont.) Assume β h β m k is chosen one period ahead of time, but allocated within the period First-order conditions imply

50 Planner s problem (cont.) Assume β h β m k is chosen one period ahead of time, but allocated within the period First-order conditions imply

51 Planner s problem (cont.) Assume β h β m k is chosen one period ahead of time, but allocated within the period First-order conditions imply k m k h = 1 α β h 1 α β m `m `h = β m β h 1 α β h 1 α β m, If p t is price of h in terms of c, then

52 Planner s problem (cont.) Assume β h β m k is chosen one period ahead of time, but allocated within the period First-order conditions imply k m k h = 1 α β h 1 α β m `m `h = β m β h 1 α β h 1 α β m, If p t is price of h in terms of c, then

53 Planner s problem (cont.) Assume β h β m k is chosen one period ahead of time, but allocated within the period First-order conditions imply k m k h = 1 α β h 1 α β m `m `h = β m β h 1 α β h 1 α β m, If p t is price of h in terms of c, then p t = A mkmt α 1 `βm mt A h kht α 1 `βh ht _ (A mt /A ht ) ` (β h β m ) ht

54 Balanced Aggregate Growth under Certainty Dynamic Euler equation is λ mt (1 + ν) (1 + ρ) = E t n λ mt+1 h A mt+1 αk α 1 mt+1`βm mt io δ

55 Balanced Aggregate Growth under Certainty Dynamic Euler equation is λ mt (1 + ν) (1 + ρ) = E t n λ mt+1 h A mt+1 αk α 1 mt+1`βm mt io δ Let x c + ph. Can show that λ m = x 1, so λ mt /λ mt 1 = x t 1 /x t.

56 Balanced Aggregate Growth under Certainty Dynamic Euler equation is λ mt (1 + ν) (1 + ρ) = E t n λ mt+1 h A mt+1 αk α 1 mt+1`βm mt io δ Let x c + ph. Can show that λ m = x 1, so λ mt /λ mt 1 = x t 1 /x t. Balanced Growth: Equilibrium path under certainty in which if A m and A h grow at constant rates

57 Balanced Aggregate Growth under Certainty Dynamic Euler equation is λ mt (1 + ν) (1 + ρ) = E t n λ mt+1 h A mt+1 αk α 1 mt+1`βm mt io δ Let x c + ph. Can show that λ m = x 1, so λ mt /λ mt 1 = x t 1 /x t. Balanced Growth: Equilibrium path under certainty in which if A m and A h grow at constant rates 1 x and k also grow at a constant rate

58 Balanced Aggregate Growth under Certainty Dynamic Euler equation is λ mt (1 + ν) (1 + ρ) = E t n λ mt+1 h A mt+1 αk α 1 mt+1`βm mt io δ Let x c + ph. Can show that λ m = x 1, so λ mt /λ mt 1 = x t 1 /x t. Balanced Growth: Equilibrium path under certainty in which if A m and A h grow at constant rates 1 x and k also grow at a constant rate 2 the interest rate is constant

59 Aggregate balanced growth (cont.) Aggregate growth rate (in terms of m sector output) h i 1/(1 α) g = (1 + γ m ) (1 + ν) β m 1

60 Aggregate balanced growth (cont.) Aggregate growth rate (in terms of m sector output) h i 1/(1 α) g = (1 + γ m ) (1 + ν) β m 1

61 Aggregate balanced growth (cont.) Aggregate growth rate (in terms of m sector output) h i 1/(1 α) g = (1 + γ m ) (1 + ν) β m 1 (1 + ν) (1 + g) ˆk t / ˆk t 1 = ˆk t 1 / (1 + g) α 1 (ˆx t+1 /ˆx t ) (1 + ν) (1 + ρ) (1 + g) = α ˆk t 1 / (1 + g) α 1 This is just the neoclassical growth model. (1 + g) ˆx t / ˆk t δ + 1 δ

62 Unbalanced Sectoral Growth The sectoral variables p, n m, n h, `m, `h, k m, k h, c, and h are nonlinear functions of the aggregate state variables

63 Unbalanced Sectoral Growth The sectoral variables p, n m, n h, `m, `h, k m, k h, c, and h are nonlinear functions of the aggregate state variables Sectoral growth is unbalanced: sectoral variables do not grow at constant rates (except in knife-edge cases ɛ = 1 or γ m = γ h (β h β m ) ν)

64 Unbalanced Sectoral Growth The sectoral variables p, n m, n h, `m, `h, k m, k h, c, and h are nonlinear functions of the aggregate state variables Sectoral growth is unbalanced: sectoral variables do not grow at constant rates (except in knife-edge cases ɛ = 1 or γ m = γ h (β h β m ) ν) Benchmark assumptions: ɛ < 1, γ m > γ h (β h β m ) ν. Get n h growing, n m shrinking ( Baumol s disease ) in practice extremely slowly.

65 Price of Land Rental price of land q t in terms of c

66 Price of Land Rental price of land q t in terms of c Asset price of land: V t = q t + E t fφ t+1 V t+1 g = E t s=t Φ s s t q s

67 Price of Land Rental price of land q t in terms of c Asset price of land: V t = q t + E t fφ t+1 V t+1 g = E t s=t Φ s s t q s

68 Price of Land Rental price of land q t in terms of c Asset price of land: V t = q t + E t fφ t+1 V t+1 g = E t s=t Φ s s t q s where Φ t+1 = x t x t+1 (1 + ν) (1 + ρ) On the balanced growth path we have Φ 1 = (1 + g) (1 + ρ) (1 + ν)

69 Price of Land Rental price of land q t in terms of c Asset price of land: V t = q t + E t fφ t+1 V t+1 g = E t s=t Φ s s t q s where Φ t+1 = x t x t+1 (1 + ν) (1 + ρ) On the balanced growth path we have Φ 1 = (1 + g) (1 + ρ) (1 + ν) Benchmark assumptions imply growth rate of V t exceeds growth rate of income, though asymptotically approaches it.

70 Price of Land Rental price of land q t in terms of c Asset price of land: V t = q t + E t fφ t+1 V t+1 g = E t s=t Φ s s t q s where Φ t+1 = x t x t+1 (1 + ν) (1 + ρ) On the balanced growth path we have Φ 1 = (1 + g) (1 + ρ) (1 + ν) Benchmark assumptions imply growth rate of V t exceeds growth rate of income, though asymptotically approaches it. Price of house is xed-weight value of K h + V t L h

71 Stochastic Growth Kahn-Rich (2007) showed that trend productivity growth is well described by a Markov regime-switching process

72 Stochastic Growth Kahn-Rich (2007) showed that trend productivity growth is well described by a Markov regime-switching process

73 Stochastic Growth Kahn-Rich (2007) showed that trend productivity growth is well described by a Markov regime-switching process 1.0 High Growth Regime Probabilities with hindsight without

74 Stochastic Growth (cont.) Suppose that the growth rate of A h is xed at γ h, but: A mt /A mt 1 = (1 + γ mt ) η t /η t 1

75 Stochastic Growth (cont.) Suppose that the growth rate of A h is xed at γ h, but: A mt /A mt 1 = (1 + γ mt ) η t /η t 1

76 Stochastic Growth (cont.) Suppose that the growth rate of A h is xed at γ h, but: A mt /A mt 1 = (1 + γ mt ) η t /η t 1 where γ mt = γ 1 m if ξ t = 1 γ 0 m ξ t = 0 η t is a transitory disturbance ξ t is a state variable with Markov transition matrix θ Θ = 1 1 θ 0. 1 θ 1 θ 0

77 Calibration Aggregate parameters take on standard values for quarterly data: α = 0.33, ν = 0.025, δ = 0.02, ρ = 0.01

78 Calibration Aggregate parameters take on standard values for quarterly data: α = 0.33, ν = 0.025, δ = 0.02, ρ = 0.01 We set β h = 0.5 and β m = 0.05.

79 Calibration Aggregate parameters take on standard values for quarterly data: α = 0.33, ν = 0.025, δ = 0.02, ρ = 0.01 We set β h = 0.5 and β m = Since housing services represent about 20 percent of overall consumer expenditures, we set ω h = 0.2, ω c = 0.8.

80 Calibration(cont.) From Kahn-Rich: 4 γ 1 m β m ν / (1 α) = 0.029, 4 γ 0 m β m ν / (1 α) = θ 1 = θ 0 =

81 Calibration(cont.) From Kahn-Rich: 4 γ 1 m β m ν / (1 α) = 0.029, 4 γ 0 m β m ν / (1 α) = θ 1 = θ 0 = Implies expected durations of 20 to 25 years

82 Macro Evidence on ɛ Aggregate behavior of housing services expenditures and prices suggests ɛ < 1

83 Macro Evidence on ɛ Aggregate behavior of housing services expenditures and prices suggests ɛ < 1

84 Macro Evidence on ɛ Aggregate behavior of housing services expenditures and prices suggests ɛ < 1 Figure 4: Housing Services: Expenditures and Prices housing services share relative price of housing services

85 Micro Evidence on ɛ Match CEX micro (household) data with regional price indexes for consumption and housing services

86 Micro Evidence on ɛ Match CEX micro (household) data with regional price indexes for consumption and housing services For household i at date t in region j: ln [p jt h it / (x it p jt h it )] = a j + b ln x it + (1 ɛ) ln p jt + z 0 it θ + u itj.

87 Micro Evidence on ɛ Match CEX micro (household) data with regional price indexes for consumption and housing services For household i at date t in region j: ln [p jt h it / (x it p jt h it )] = a j + b ln x it + (1 ɛ) ln p jt + z 0 it θ + u itj. a j is a constant region-speci c factor, z it are demographic controls (age, household size, etc.)

88 Micro Evidence on ɛ Match CEX micro (household) data with regional price indexes for consumption and housing services For household i at date t in region j: ln [p jt h it / (x it p jt h it )] = a j + b ln x it + (1 ɛ) ln p jt + z 0 it θ + u itj. a j is a constant region-speci c factor, z it are demographic controls (age, household size, etc.) x it is likely to be measured with error, instrument with race, education

89 Micro Evidence on ɛ Match CEX micro (household) data with regional price indexes for consumption and housing services For household i at date t in region j: ln [p jt h it / (x it p jt h it )] = a j + b ln x it + (1 ɛ) ln p jt + z 0 it θ + u itj. a j is a constant region-speci c factor, z it are demographic controls (age, household size, etc.) x it is likely to be measured with error, instrument with race, education Get estimates of ɛ in the range. consider ɛ = 0.9. Set ɛ = 0.3, also

90 Simulations Start out in low-growth regime, at t = 12 switch to high-growth; no transitory shocks

91 Simulations Start out in low-growth regime, at t = 12 switch to high-growth; no transitory shocks

92 Simulations Start out in low-growth regime, at t = 12 switch to high-growth; no transitory shocks Figure 7: Home Price Appreciation in Reponse to a Regime Switch % change (y/y) ε = 0.3 % change (y/y) ε = home price per capita income For ɛ = 0.3 case, get 3-year average up by 2.25%; compare to acceleration vs of 2.84%

93 Simulations Start out in low-growth regime, at t = 12 switch to high-growth Figure 8: Housing Wealth and Productivity Regime Change % change (y/y) ε = % change (y/y) ε = per capita housing wealth per capita consumption

94 Simulations Start out in low-growth regime, at t = 12 switch to high-growth Figure 9: Housing Investment and Sectoral Labor % change (y/y) ε = % change (y/y) ε = housing I/K housing services labor

95 Is it really all about land? Model assumes that construction cost of housing (in terms of m sector output) is stationary

96 Is it really all about land? Model assumes that construction cost of housing (in terms of m sector output) is stationary In fact, construction costs trend along with housing prices

97 Is it really all about land? Model assumes that construction cost of housing (in terms of m sector output) is stationary In fact, construction costs trend along with housing prices

98 Is it really all about land? Model assumes that construction cost of housing (in terms of m sector output) is stationary In fact, construction costs trend along with housing prices Figure 10: New Home Prices and Construction Costs real price of new homes real construction cost new home price/construction cost real construction cost

99 Is it really all about land? (cont.) Repeat-sales based index (Conventional Mortage Home Price Index) suggests more action in land prices (Davis-Heathcote)

100 Is it really all about land? (cont.) Repeat-sales based index (Conventional Mortage Home Price Index) suggests more action in land prices (Davis-Heathcote) Still, construction costs clearly trend with productivity; suggests need to distinguish K m and K h technologies so that changes in m sector productivity do not apply to construction:

101 Is it really all about land? (cont.) Repeat-sales based index (Conventional Mortage Home Price Index) suggests more action in land prices (Davis-Heathcote) Still, construction costs clearly trend with productivity; suggests need to distinguish K m and K h technologies so that changes in m sector productivity do not apply to construction: Structures vs. equipment (embodied technological progress as in Greenwood-Hercowitz-Krusell)

102 Is it really all about land? (cont.) Repeat-sales based index (Conventional Mortage Home Price Index) suggests more action in land prices (Davis-Heathcote) Still, construction costs clearly trend with productivity; suggests need to distinguish K m and K h technologies so that changes in m sector productivity do not apply to construction: Structures vs. equipment (embodied technological progress as in Greenwood-Hercowitz-Krusell) Human capital, skilled vs. unskilled labor

103 Conclusions The model seems capable of explaining large swings in prices and real activity in the housing sector

104 Conclusions The model seems capable of explaining large swings in prices and real activity in the housing sector Driving force of productivity trend shifts appears qualitatively and quantitatively reasonable

105 Conclusions The model seems capable of explaining large swings in prices and real activity in the housing sector Driving force of productivity trend shifts appears qualitatively and quantitatively reasonable More work to be done on

106 Conclusions The model seems capable of explaining large swings in prices and real activity in the housing sector Driving force of productivity trend shifts appears qualitatively and quantitatively reasonable More work to be done on additional kinds of shocks (generating reasonable interest rate movements), imperfect information about regimes

107 Conclusions The model seems capable of explaining large swings in prices and real activity in the housing sector Driving force of productivity trend shifts appears qualitatively and quantitatively reasonable More work to be done on additional kinds of shocks (generating reasonable interest rate movements), imperfect information about regimes labor supply shifts, demographics, as additional low frequency factor

108 Conclusions The model seems capable of explaining large swings in prices and real activity in the housing sector Driving force of productivity trend shifts appears qualitatively and quantitatively reasonable More work to be done on additional kinds of shocks (generating reasonable interest rate movements), imperfect information about regimes labor supply shifts, demographics, as additional low frequency factor more realistic (putty-clay) treatment of land in h technology

109 Conclusions The model seems capable of explaining large swings in prices and real activity in the housing sector Driving force of productivity trend shifts appears qualitatively and quantitatively reasonable More work to be done on additional kinds of shocks (generating reasonable interest rate movements), imperfect information about regimes labor supply shifts, demographics, as additional low frequency factor more realistic (putty-clay) treatment of land in h technology breaking link between price of K h and K m