22

.5 Real consumption.5 Real residential investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.5 Real house prices.5 Real fixed investment.5.5.5 965 975 985 995 25.5 965 975 985 995 25.3 Inflation rate.3 Short term nominal interest rate.2.2.....2 965 975 985 995 25.2 965 975 985 995 25.3 Hours worked goods sector.3 Hours worked housing sector.2.2.....2 965 975 985 995 25.2 965 975 985 995 25 Figure Data Note: Variables in the top panel (with the exception of real house prices) are divided bycivilian noninstitutional population age 6 and over, log-transformed. The first observation (965:) is normalized to zero. Variables in the bottom panel are de-meaned. Hours worked in the two sectors are defined as total hours divided by population. 23

Real consumption.4 Real fixed investment.8.2.6.8.4.6.2.4.2 965 975 985 995 25 965 975 985 995 25 Real residential investment.8 Real house prices.6.4.2.2.4.6.6.4.2 965 975 985 995 25 965 975 985 995 25 Figure 2 Data and estimated trends Note: Red dashed line corresponds to the median of the posterior distribution of the trend. Red dotted lines corresponds to 5 and 95 percentiles, blue solid line the data. 24

.4 Nominal interest rate.2 Real consumption.2..2.4 Inflation Real residential investment.2.5.2 2 Real house price.2 Real fixed investment.5.5.2 Hours worked goods sector.2 Hours worked housing sector.5.2 5 5 2 5 5 2. Real consumption: lenders.2 Real consumption: borrowers.5.8.6.5.4..2.5.2.5 Housing stock: lenders 8 Housing stock: borrowers 6.5 4.5 2 2 5 5 2 5 5 2 Figure 3 Impulse responses to a positive housing preference shock 25

. Nominal interest rate Real consumption.5. Inflation Real residential investment.5.5. Real house price Real fixed investment.5.5.5 Hours worked goods sector.5 Hours worked housing sector.5 5 5 2.5 5 5 2.8 Real consumption: lenders.8 Real consumption: borrowers.7.6.6.5.4.4.2.3.2..2.4 Housing stock: lenders.5 Housing stock: borrowers.3.2..5. 5 5 2.5 5 5 2 Figure 4 Impulse responses to a positive technology shock in the goods sector 26

.6 Nominal interest rate. Real consumption.4.2.2 Inflation. 6 Real residential investment. 4 2. Real house price.2 Real fixed investment.2.4.2 Hours worked goods sector.2 2 Hours worked housing sector.2 5 5 2 5 5 2.5 Real consumption: lenders.25 Real consumption: borrowers.4.2.3.5.2...5..5.2..5 Housing stock: lenders Housing stock: borrowers.4.5.3.5.2. 5 5 2.5 5 5 2 Figure 5 Impulse responses to a positive technology shock in the housing sector 27

.5 Nominal interest rate.5 Real consumption.5. Inflation.5.5 Real residential investment..5 Real house price.5 Real fixed investment.5.5 Hours worked goods sector 2.5 Hours worked housing sector.5 5 5 2.5 5 5 2.2 Real consumption: lenders.5 Real consumption: borrowers...5.2.3.5.5 Housing stock: lenders 2 Housing stock: borrowers.5 2 4 6.5 5 5 2 8 5 5 2 Figure 6 Impulse responses to a negative monetary policy shock 28

.2 Nominal interest rate Real consumption.5.2.5 Inflation.5 Real residential investment.5.5.5 Real house price Real fixed investment.5 Hours worked goods sector 2.5 Hours worked housing sector.5 2 5 5 2 5 5 2.2 Real consumption: lenders Real consumption: borrowers.5.2.4.5 2.6 2.5.8 3 2.5 Housing stock: lenders 2 Housing stock: borrowers 2.5.5 2 4 6 8.5 5 5 2 2 5 5 2 Figure 7 Impulse responses to a negative cost-push shock 29

.2 Nominal interest rate.4 Real consumption..2.6 Inflation. Real residential investment.4.2.5 Real house price. 3 Real fixed investment 2.5.5 Hours worked goods sector.2 Hours worked housing sector.5 5 5 2.2 5 5 2.4 Real consumption: lenders.5 Real consumption: borrowers.3.4.2.3..2... Housing stock: lenders Housing stock: borrowers.5.8.6.4.5.2..2.5 5 5 2.4 5 5 2 Figure 8 Impulse responses to a positive investment specific technology 3

.2 Nominal interest rate Real consumption..5.2 Inflation.5.5 Real residential investment.5.2 Real house price.5 Real fixed investment.5.5 Hours worked goods sector.5 Hours worked housing sector.5.5.5 5 5 2 5 5 2.8 Real consumption: lenders.5 Real consumption: borrowers.6.4.2.5.2.5.4 Housing stock: lenders 5 Housing stock: borrowers.2 4.2.4.6 3 2.8 5 5 2 5 5 2 Figure 9 Impulse responses to a positive preference shock 3

.2 Nominal interest rate Real consumption.5.2.5 Inflation Real residential investment 2.5 Real house price 3 Real fixed investment.5 Hours worked goods sector 2 Hours worked housing sector 2 2 5 5 2 3 5 5 2 Real consumption: lenders.5 Real consumption: borrowers.2.4.6.5.8.2.5.4 Housing stock: lenders Housing stock: borrowers 6.2 5.4 4.6 3.8 2.2.4 5 5 2 5 5 2 Figure Impulse responses to a negative labor supply shock 32

.4 Real consumption.2 Real house prices.2. Real business investment.2.4 Real residential investment.2. Short term nominal interest rate Inflation rate.5..5.5.6 Hours worked goods sector..25 Hours worked housing sector.4.2.2.5 22 23 24 25. 22 23 24 25 Figure Counterfactual experiment: What if there had been no housing demand shocks from 22: onwards Note: Red dotted lines correspond to the path of the variables in the counterfactual experiment. Blue solid line corresponds to the data. In the simulation the mean of the posterior distribution has been used. 33

. Real consumption.2 Real house prices..5 Real business investment.2.5 Real residential investment.5.5.4 Short term nominal interest rate.4 Inflation rate.2.2.2.2 Hours worked goods sector.2.5 Hours worked housing sector.2 965 975 985 995 25.5 965 975 985 995 25 Figure 2 Counterfactual experiment: What if there had been no housing demand shocks from 965: onwards Note: Red dotted lines correspond to the path of the variables in the counterfactual experiment. In the simulation the mean of the posterior distribution has been used. 34

. Real consumption.2 Real house prices..5 Real business investment.2.5 Real residential investment.5.5.4 Short term nominal interest rate.4 Inflation rate.2.2.2. Hours worked goods sector.2.5 Hours worked housing sector. 965 975 985 995 25.5 965 975 985 995 25 Figure 3 Counterfactual experiment: What if there had been no technology shocks in the housing sector from 965: onwards Note: Red dotted lines correspond to the path of the variables in the counterfactual experiment. In the simulation the mean of the posterior distribution has been used. 35

. Real consumption.2 Real house prices..5 Real business investment.2.5 Real residential investment.5.5.4 Short term nominal interest rate.4 Inflation rate.2.2.2.2 Hours worked goods sector.2.5 Hours worked housing sector.2 965 975 985 995 25.5 965 975 985 995 25 Figure 4 Counterfactual experiment: What if there had been no monetary policy shocks from 965: onwards Note: Red dotted lines correspond to the path of the variables in the counterfactual experiment. In the simulation the mean of the posterior distribution has been used. 36

.6 Real consumption.2 Real house prices.4.2. Real business investment.2.4 Real residential investment.2. Short term nominal interest rate Inflation rate..5..2. Hours worked goods sector.5.25 Hours worked housing sector.2.5. 22 23 24 25. 22 23 24 25 Figure 5 Counterfactual experiment: What if the Federal Reserve had responded to real house prices since 22: Note: Red dotted lines correspond to the path of the variables in the counterfactual experiment. In the simulation the mean of the posterior distribution has been used. 37

.35.3.25.2 elasticity of C to q elasticity of IH to q elasticity of IK to q.5..5.5.5.55.6.65.7.75.8.85.9.95 α Figure 6 Elasticity of aggregate demand components to real house prices following a housing preference shock: the effect of varying the share of constrained agents Note: The elasticities are computed as ratios of the four quarters averages of the responses. Results based on the output of the Metropolis algorithm. 38

Credit constraints and age distribution.35 Wage share constrained people (model) Fraction of population aged 25 39 (data).3.25.2.5 975 98 985 99 995 Figure 7 Credit constraints and age distribution of population Note: Black dotted line corresponds to the share of constrained person in the U.S. Blue solid thick line corresponds to the mean recursive estimates of ( α), while blue solid thin lines denote the 9 percent probabilty intervals. The model has been estimated recursively over a moving window of 2 years. 39

Table. Summary statistics for the posterior distribution of the parameters posterior prior parameter 2.5 5 97.5 mean st. dev. mean st. dev. Type ɛ.423.533.623.53.52.5.75 Beta ɛ.438.732.888.72.32.5.75 Beta η.38.6.876.67.26.25. Gamma η.299.456.672.464.94.25. Gamma ν -2.894-2.296 -.8-2.36.278-2..5 Normal ν -3.3-2.65 -.77-2.7.468-2..5 Normal φ k,c 2.37 23.436 26.88 23.467.74. 2.5 Gamma φ k,h 9.575.832 3.89.84.3. 2.5 Gamma α.679.79.867.784.5.7.5 Beta m.734.79.844.789.28.8.25 Beta r R.643.689.73.688.22.75. Beta r Π.86.38.464.39.72.5. Normal r Y.277.45.532.46.64.. Normal θ.94.922.937.92.9.75.5 Beta γ.75.848.963.784.5.5.2 Beta g a,c.3.32.34.32..5. Normal g a,h -.29 -.23 -.7 -.23.3.5. Normal g a,k.2.28.35.28.3.5. Normal ρ j.949.972.99.972..8. Beta ρ a,c.92.949.977.947.7.8. Beta ρ a,h.839.883.99.882.2.8. Beta ρ a,k.899.937.974.937.9.8. Beta ρ z.539.77.858.7.83.8. Beta ρ τ.83.876.95.875.2.8. Beta σ a,c...3...5. Gamma σ a,h.46.52.58.52.3.5. Gamma σ a,k.2.24.28.24.2.5. Gamma σ j.29.49.76.5.2.5. Gamma σ u.5.6.7.6..5. Gamma σ R.2.3.3.3..5. Gamma σ z.3.8.25.8.3.5. Gamma σ τ.38.5.64.5.7.5. Gamma N ote: Results based on 5, draws from the posterior distribution obtained using the Metropolis algorithm. 4

Table 2. Business cycle properties of the model Data 5 5 95 Standard deviation (perc.) C.23.39.84 2.46 IH.2 5.84 7.5 8.5 IK 4.97 3.57 4.38 5.37 Q.87 2.39 2.92 3.56 NC.43 2.47 3.7 4.2 NH 4.8 3.5 4.33 5.36 π c.4.5.62.74 R.32.33.42.52 Y 4.3 3.6 3.84 4.86 Correlations C, Y.86.6.77.87 IK,Y.75.39.6.75 IH,Y.85.44.62.76 Q, Y.57.49.67.79 Q, C.49.3.55.72 Q, IH.4 -..6.4 Q, IK.59.26.49.67 First order correlation C.87.83.88.9 IH.9.57.68.77 IK.9.65.74.8 Q.78.65.75.82 NC.9.74.82.87 NH.89.63.73.8 π c.47.49.6.7 R.8.65.75.82 Y.92.72.8.86 Lead-lag correlations IH (t ),Y (t).89.24.5.68 IH (t),y (t).85.44.62.76 IH (t +),Y (t).67.29.5.66 N ote: Results based on 5, draws from the posterior distribution obtained using the Metropolis algorithm. 4

Table 3. Decomposition of the asymptotic variance of the forecast error j a c a h ɛ R u a k z τ C t.9 2.58.7.76 5.65 8.68 5.48 3.76 [.,.4] [.8,4.6] [.,.] [.9,3.] [9.8,2.9] [.4,35.2] [3.5,8.] [9.,43.3] π t.28 3.84.6 4.2 52.56.8 7.5 28. [.,.] [2.9,5.3] [.,.2] [2.,8.] [45.2,59.] [.,3.2] [3.,5.] [2.2,36.] IH t 5. 6.47 68.29.8.64..2 7. [2.8,.8] [3.7,.6] [59.6,75.5] [.,.2] [.,.6] [.,.2] [.,.6] [2.2,23.3] Q t 66.4 3.93 4..45 5.5 5.35.57. [55.4,78.2] [2.,6.9] [2.2,7.] [.9,2.] [3.2,7.3] [2.8,.8] [.,2.2] [5.9,5.2] R t.66 5.75.62 2.66 2.77 8.56.78 36.6 [.2,2.] [4.3,7.7] [.,.] [9.8,5.8] [5.2,26.3] [6.,2.2] [5.,25.7] [26.9,45.3] IK t.4 5.9.5.5 8.24 69.7.5.6 [.,.3] [2.8,2.4] [.,.] [.9,2.2] [5.,2.] [57.7,82.] [.,2.] [6.2,8.5] N c,t.42 5.2.7 4.55 32..32 4.9 52.3 [.2,.8] [3.5,7.2] [.,.2] [3.2,6.8] [25.9,39.4] [.,.9] [3.,6.] [4.8,6.7] N h,t 3.5.84 5.26.36 2.37..58 65.4 [8.2,23.4] [.5,.5] [.6,2.7] [.,.9] [.3,5.4] [.,.] [.,2.5] [55.,73.3] N ote: The table reports posterior medians and 9-percent probability intervals (in brackets). Statistics are computed using 5, draws obtained from the Metropolis algorithm. 42