A Factor Analysis of Housing Market Dynamics in the U.S. and the Regions

Transcription

1 A Factor Analysis of Housing Market Dynamics in the U.S. and the Regions Serena Ng Emanuel Moench 2 Columbia University 2 Federal Reserve Bank of New York April 29 The views expressed here are those of the authors and do not necessarily reflect those of the Federal Reserve Bank of New York or the Federal Reserve System

2 Overview 2 Data 3 Factor Model 4 Estimation 5 Factor Estimates 6 FVAR

3 This paper performs a FAVAR analysis of The dynamic effects of housing market shocks to (regional and national) retail sales The policies and economic conditions that affect the housing market. Sample: 973:-28:5

4 Motivation The U.S. experienced a big housing boom and a even bigger housing market collapse. Question: To what extent have the boom and bust of the housing market fed through to consumption? Previous literature: Most studies use a single house price indicator. Point estimates using micro data for selected samples. Little evidence at the regional level.

5 Three novel features: i) distinguish regional from national variations 4 Census regions: North-East, West, Mid-West, South. ii) Distinguish house price from housing market variations, i.e. use data on prices and volume. iii) Combine data that are sampled at monthly and quarterly frequencies and available over different time spans.

6 Regional Data Series Source Frequency First Obs Price data Median Sales Price of Single Family Existing Homes NAR mly Jan968 Single Family Median Home Sales Price CENSUS qly Q-968 Average Existing Home Prices NAR qly Q-97 Average New Home Prices NAR qly Q-97 Conventional Mortgage Home Price Index FHLMC qly Q-97 OFHEO Purchase-only Index OFHEO mly Jan986 OFHEO Home Prices OFHEO qly Q-97 *Rent of Primary Residence BLS mly Dec972 *Owners Equiv Rent BLS mly Dec977 *Mobile Home Average Sales Price CENSUS mly Jan975 Volume data New -Family Houses Sold CENSUS mly Jan968 New -Family Houses For Sale CENSUS mly Jan968 Single-Family Housing Units Under Construction CENSUS mly Jan98 Multifamily Units Under Construction CENSUS mly Jan98 Homeownership Rate CENSUS qly Q-968 Homeowner Vacancy Rate CENSUS qly Q-968 Rental Vacancy Rate CENSUS qly Q-968 *Mobile Home Placements CENSUS mly Jan975 *Multifamily Completions CENSUS mly Jan98 *Employment: Construction BLS mly Jan985 Other Housing Affordability Composite Index NAR mly Jan984 Monthly Mortgage Rate NAR mly Jan984 Median as % of Income NAR mly Jan984 Family Income NAR mly Jan984 Princp.& Interest Payment NAR mly Jan984 Qualifying Income NAR mly Jan984 Unemployment Rate BLS mly Jan97 Retail Sales BTM mly Jan968

7 National Data Series Source Frequency First Obs Price data Median Sales Price of Single Family Existing Homes NAR mly Jan968 Median Sales Price of Single Family New Homes Census mly Jan968 Single Family Median Home Sales Price CENSUS qly Q-968 Average Existing Home Prices NAR mly Jan994 Average New Home Prices CENSUS mly Jan97 S&P/Case-Shiller Home Price Index S&P qly Q-982 Conventional Mortgage Home Price Index FHLMC qly Q-968 OFHEO Purchase-only Index OFHEO mly Jan986 OFHEO Home Prices OFHEO qly Q-97 *Rent of Primary Residence BLS mly Jan976 *Mobile Home Average Sales Price CENSUS mly Jan975 Volume data New -Family Houses For Sale CENSUS mly Jan968 Housing Units Authorized by Permit: -Unit CENSUS mly Jan968 Multifamily Units Under Construction CENSUS mly Jan968 Multifamily Permits US CENSUS mly Jan968 Multifamily Starts US CENSUS mly Jan968 Multifamily Completions CENSUS mly Jan968 Homeowner Vacancy Rate CENSUS qly Q-968 Homeownership Rate CENSUS qly Q-968 Rental Vacancy Rate CENSUS qly Q-968 *New -Family Houses Sold CENSUS mly Jan968 *Single-Family Housing Units Under Construction CENSUS mly Jan968 *Mobile Home Placements CENSUS mly Jan975 *Employment: Construction BLS mly Jan968 Other Housing Affordability Composite Index NAR mly Jan968 Unemployment Rate BLS mly Jan968 Retail Sales BTM mly Jan968

8 House Price Data simple approach: report means and medians NRA, Bureau of Census subject to changing composition of high and low priced units. 2 repeat sales method OFHEO (exclude jumbo loans) Case-Shiller (include foreclosures, gives more weight to higher price homes) price indices, not actual measures of prices 3 hedonic approach.

9 Many house price series: price measures subject to compositional effects are better measures of the amount required to purchase a house than the house price change. price indices based on repeat transactions are better at measuring house price appreciation. different geographical coverage available over different samples and at different frequencies.

10 Volume data: single and multi-family units sold, units available for sale, data on construction employment, homeowner vacancy rate. Leamer (27): volume cycle Stein (995) more intense trading activity in rising markets. Loss on existing homes as house prices come down make it harder for would-be movers to make downpayments on new homes. Case and Shiller (989): in a falling market, homeowners tend to hold on to their investment in the hope of higher future returns.

11 In this study: Regional level 7 price series 4 price and volume series. National level 9 price series 7 price and volume series.

12 Three Level Dynamic Factor model For each series i in region b: X ibt = Λ Gb.i (L)G bt + e ixbt. Let G t = (G t G 2t... G Bt ) the set of regional factors Let Y t be observed aggregate indices: ( ) Gt = Λ F (L)F t + Y t ( egt e Yt ) Identification: Λ Gb () is lower triangular with s on the diagonal Λ F () is lower triangular with s on the diagonal.

13 Dynamics: F t = Ψ F. F t Ψ F.qF F t qf + ɛ Ft e Gbt = Ψ G.b e Gb,t Ψ G.bqGb e Gb,t qgb + ɛ Gbt e Xbit = Ψ X.bi e Xbi,t Ψ X.biqXb e Xbi,t qxb + ɛ Xbit A 3 level factor model: level variations: e Xibt, series specific level 2 variations: e Gbt, region specific level 3 variations: ɛ Ft, common across regions and aggregate indices.

14 A three level model implies X bit = Λ Gbi (L)Λ Fb (L)F t + Λ Gbi (L)e Gbit + e Xbit Contrast with two level factor model: X it = Λ i F t + e it omits independent variations at the block level lumps Λ Gbi (L)e Gbit with e Xbit.

15 A different model with regional effects: X bit = b i F t + c bi G bt + e bit Del Negro and Otrok (27), Fu (27), Stock and Watson (28). Their model directly estimates F t and G bt, which are unconditionally uncorrelated. In our model, F t and G bt are correlated. Our model has more structure and is thus more parsimonious. Restricts how series within a block respond to F

16 Estimation Number of series too small for principal components Estimation by MCMC: 2 nested state space models X bit is linear in G bt G t and Y t are linear in F t. Can easily handle missing data and mixed sampling frequencies. We can easily combine Y with G to estimate F. Probability bands for FAVAR easy to compute.

17 Three econometric issues: A mix of monthly and quarterly series. data augmentation: where X bt.k t = Λ Gb.k (L)G bt + e Xbt.k t e Xbt.k t = ψ Xb.k, e Xbt.k +... ψ Xb.k,qXbk e Xbt qxbk.k. Similarly, Y t.m t = Λ Fm(L)F t + e Yt.m t. over the sample that the quarterly data are available.

18 2 Some series are available much later in the sample. no data, no (Kalman) gain! let W t be a selection matrix that picks out variables that are not missing before t. WX bt = WΛ Gb (L)G bt + We Xbt.

19 3 G bt depends on F t. the transition equation in the state space model has a time varying intercept. G bt = α F.bt + Ψ G.b G bt +... Ψ G.bqGb G bt qgb + ɛ Gbt where α F.bt = Ψ G.b (L)Λ F (L)F t depends on t. the conditional mean of G t is unaffected by α G.bt since it is conditionally zero in value. the conditional variance of G t will be inflated by the variability in α G.bt. updating and smoothing equations modified to take this into account.

20 MCMC Algorithm Conditional on Λ, Ψ, Σ, {G t } and {Y t }, draw {F t }. 2 Conditional on {F t }, draw Ψ F, Σ F and Λ Fb. 3 Conditional on Λ, Ψ, Σ and {F t }, draw G bt taking into account time varying intercepts. 4 Conditional on G bt and Y t, draw Ψ Gb and Σ Gb. 5 Conditional on G bt, draw Λ Gbi. Draw Ψ Xbi and σ 2 Xbi. 6 Data augmentation: i) For each b and conditional on G bt and the parameters of the model, draw monthly values for elements of X bt that are observed at lower frequencies. ii) Conditional on F t and the parameters of the model, draw monthly values for those Y t that are observed at lower frequencies. iii) Draw Ψ Y using the augmented data vector for Y.

21 Model Specification Number of factors at regional level: k Gb = Number of factors at national level: K F = Number of lags in regional factor loadings: s Gb = 2 Number of lags in national factor loadings: s F = 2 Number of lags in AR processes: ψ F = ψ Xb.i = ψ Gb = Burn in draws: 2, Keep every 5 or the additional 5, draws.

22 Table : Estimates of Ψ and σ F : House Price Model F Ψ F s.e. σf 2 s.e G b Ψ G s.e. σgb 2 s.e. NE W MW South Decomposition of variance: F s.e. G b s.e. e Xb s.e. NE W MW South

23 National and regional house price factor estimates Figure 3 Northeast 6 West 2 F p 4 F p G p 2 G p Mid West.5 South F p.5 F p 2 G p 2 G p

24 House price factor and price series Figure 2 4 BLS 2 CMHPI F p.5 F p 4 BLS 2 CMHPI OFHEO.5 Case Shiller F p OFHEO F p Case Shiller

25 Table 2: Estimates of Ψ and σ F : Housing Market Model F Ψ F s.e. σf 2 s.e G b Ψ G s.e. σgb 2 s.e. NE W MW South Decomposition of variance: F s.e. G b s.e. e Xb s.e. NE W MW South

26 Regional House Price Factor vs Regional Housing Factor Figure 3 3 Northeast 3 West 2 G p 2 G p G pq G pq MidWest 2 South.5 G p.5 G p G pq G pq

27 National House Price Factor vs National Housing Factor.5 Figure 4: House Price vs. Housing Factor F p F pq

28 How do house price movements affect consumption? trade-down effect (positive) collateral effect (positive) common external stimulus (positive) trade-up effect (negative) higher rents (negative) market imperfections: homeowners not fully hedged against fluctuations in house price. CBO survey: housing effect: 2 to 7 cents per dollar spent.

29 Sample 978::28:5. FAVAR: F pq, G pq.b, U, U b, C b. for each of the draws of the factors: estimate a FAVAR with 2 lags posterior mean and 9% probability bands

30 How Do Regional Retail Sales Respond to National Housing Shocks? Figure 5: Response of Retail Sales to Fp 4 x 3 Northeast max: x 3 4 West max: sum: sum: x MidWest max: x South max: sum: sum:

31 How Do Regional Retail Sales Respond to Regional Housing Shocks? Figure 6: Response of Retail Sales to Gp.5 x 3 Northeast 3.5 x 3 3 West 2.5 max: max: sum: sum: x 3 MidWest 2.5 x 3 South max: max:.46.5 sum: sum:

32 How Do National Retail Sales Respond to National Housing Shocks? Figure 9: Response to Fpq 5 x 3 4 max: sum: RS U max: F sum:

33 response of regional consumption: much larger response to F pq than to G pq.b responses peak about periods after the shock. 3 period cumulative response:.76,.88,.77,.79. response of aggregate consumption: response peaks after 2 months 3 month cumulative response of.99. F pq in 28:5 is one standard deviation below mean, corresponding to a two standard deviation shock. a 3 month cumulative drop in consumption of 2%.

34 What does Housing Respond to? 6 variable FAVAR: unemployment rate (U) the fed funds rate (FF) 3 year effective mortgage rate (MR) housing factor, F pq. Michigan s survey of consumer sentiment (MICH) the annual difference of log S&P 5 index (SP)

35 Benchmark: shock std max + cum(3) U FF MR Mich SP standard deviation of shocks to F pq in FAVAR=.245. F pq in 28: 5 = -.57 ; F p in 28: 5 = -2.6 cut in mortgage rate is effective. low stock returns and consumer confidence can slow recovery.

36 Impulse Responses of National Housing Factor to Different Shocks Figure : Response of Fpq max:.4984 U.6.4 max:.4936 FF sum:.2 sum: max: Mortgage.3 max: Fpq.2.2. sum: sum: max:.3886 Michigan.4 max: SP.2.2 sum: sum:

37 Conclusion Housing market factor much stronger than house price factor since 26 House price factor is smoother than any observed price series Regional shocks are relatively more important in the West, but regional shocks have small consumption effects. Negative housing shocks depress consumption. One standard deviation shock has a consumption effect of.848 in 3 periods. interest rate cuts can be effective, but recovery can be slow if confidence and stock returns remain low.