Regional Housing Trends A Look at Price Aggregates Department of Economics University of Missouri at Saint Louis Email: rogerswil@umsl.edu January 27, 2011
Why are Housing Price Aggregates Important? Shelter is important Housing affordability is a major policy concern in most areas Homeownership (also a major policy concern) may be affected by housing prices Real estate (mainly in the form of housing) is a major source of wealth Real estate markets may have a major influence on business cycles The wealth effect: although most estimates suggest a weak connection Housing construction has been a good predictor of business cycles (post hoc ergo propter hoc?)
Why are Housing Price Aggregates Difficult to Measure? Housing data is widely collected, but most of it is proprietary Real estate data sources National Association of Realtors (Multiple Listing Services) Large sample; timely (quarterly); includes a seasonal adjustment; but much of the information is proprietary The Census Bureau (new home construction) Same advantages plus free historical data; new construction only (in what ways might this be a problem?)
Price Index Type I: Median Price Index The simplest measure is the median Advantage: mean, median, and mode are easy to calculate Median is most popular because it tempers extreme values So let s look at some data Saint Louis County single-family housing from 2000 through 2010 2 nd Qtr. Saint Louis County Assessor s Office: actual transactions, not assessments
Saint Louis Co. Housing Sales: 2000 2010 Single Family Housing Sales by Quarter 4,000 3,000 2,000 1,000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Saint Louis Co. Housing Sales: 2000 2010 2002 2004 2006 2008 Sales Count 20 40 60 80 100 120 140
Saint Louis Co. Median Housing Price: 2000 2010 $220,000 $200,000 Median Sales Price by Quarter $180,000 $160,000 $140,000 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Price Index Type I: Median Price Index Notice the following: General upward trend (Did you see a bubble?) Noisy data; strong seasonal component We could apply a seasonal adjustment to the series How should we present the data? Indexes are a nice way to present results because they re unit free 100; units cancel P t P 0 Fine, but we re assuming constant housing quality across months Let s look at housing quality data
Saint Louis Co. Median Housing Quality: 2000-2009 1,600 1,550 1,500 1,450 1,400 1,350 0.220 0.215 0.210 0.205 0.200 46 44 42 40 38 Unit Size (Sq.Ft.) Lot Size (Acres) Unit Age (Years) 36 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Price Index Type I: Median Price Index Notice the following General upward and downward trends; thus quality changes Noisy data; strong seasonal component A median price index does not hold quality constant Tells us about the typical housing expenditure Does not tell us about house price appreciation
What is a Price Index? An ideal price index tells us about constant-quality price changes Laspeyres index: I t = P t Q 0 P 0 Q 0 100 Paasche index: I t = P t Q t P 0 Q t 100 The above indexes generally overstate price changes due to the substitution bias Fisher Index: It = Pt Q 0 P 0 Q 0 Pt Q t P 0 Q t 100 Chain-weighting has become popular... more on that later
Price Index Type II: Hedonic Index Rationale: housing is like a bundle of homogeneous services The hedonic model estimates the shadow price of each service in order to measure the overall change in housing series prices Hedonic traditions: (1) explicit time and (2) imputation Let s focus on the explicit time approach first For simplicity, consider a semi-log hedonic model lnp th = C β c z cth + c=1 T δ t d th + ε th (1) t=1
Hedonic Index: Explicit Time Model There are three variants on the explicit time approach (1) single equation, (2) overlapping equation, and (3) repeat sales The single equation model includes a time variable (or set of dummy variables) The overlapping equation model uses a chain of overlapping time periods The repeat sales model is a ratio of two explicit-time models
Hedonic Index: Repeat Sales Model The repeat sales model is not normally thought of as a hedonic model Consider a house that sells in 2000 and again in 2008 lnp 2000 = lnp 2008 = C β c z c,2000 + δ 2000 d 2000 (2) c=1 C β c z c,2008 + δ 2008 d 2008 (3) c=1 Assuming the house s bundle has not changed, consider the following equation lnp 2008 lnp 2000 = δ 2008 d 2008 δ 2000 d 2000 (4)
Hedonic Index: Repeat Sales Model Federal Housing Finance Agency (FHFA) Fannie & Freddie loans: large but biased sample Estimates by the 9 Census divisions and weighted by housing units Case-Shiller (published by Standard & Poor s) Uses deed records, where suspected non-arms-length transactions are excluded Estimates by the 9 Census divisions and weighted by estimated housing values: PE Ratio
Hedonic Index: Repeat Sales Model Advantages of a repeat sales model Some control of quality: depend on reinvestment Data requirements are only slightly larger than the median measure Disadvantages of the repeat sales model Housing reinvestment and embedded depreciation Repeat sales sample bias Disaggregation is difficult Past measures change when new sales are added
Hedonic Index: Imputation Method Single equation and repeat sales models assume a constant set of shadow prices (substitution bias), and change when new sales are added The imputation method allows shadow prices to change over time and space, and does not change when new sales are added Shadow prices are then used to estimate the price ratio p kt = p kt(z kt ) p js p js (z kt ) p js(z kt ) p js (z js ) (5) The first term represents a constant quality price index, and the second is a quantity index
Saint Louis Co. Housing Price Paths: 2000 2010 170 160 150 Price Index 140 130 Measurement Type Chain Median Repeat 120 110 100 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Hedonic Index: Imputation Method Notice the following You can see the downturn happen sooner Seasonal component still exists, but is weaker We still need to apply a seasonal adjustment to the series What are we assuming about the housing market? (I.e. what are we holding constant? Assuming accurate data and OLS assumptions what s new? Assuming coefficients constant over time and space
Saint Louis Co. Housing Values: 2000 & 2010 Relative Price 60 80 100 120 140 160 Relative Price 50 100 150 200 180 200
Saint Louis Co. Mean Annual Appreciation: 2000 2010 Mean Annual Appreciation 0 2 4 6 8
Median and Chain Comparison: 2000 2010 63146 63144 63143 63141 63138 63137 63136 63135 63134 63132 63131 63130 63129 63128 63127 63126 63125 63124 63123 63122 63121 63119 63117 63114 63105 63088 63074 63044 63043 63042 63040 63038 63034 63033 63031 63026 63025 63021 63017 63011 63005 Relative Price Measurement Type Chain Median 50 100 150
Median and Chain Comparison: 2000 2010 63105 63124 63131 63005 63141 63144 63122 63132 63117 63017 63130 63127 63038 63119 63040 63143 63011 63021 63126 63026 63128 63123 63146 63129 63043 63025 63088 63044 63125 63034 63074 63031 63042 63033 63114 63134 63138 63135 63137 63121 63136 Relative Price Measurement Type Chain Median 50 100 150
Median and Chain Comparison: 2000 2010 63143 63132 63144 63130 63134 63122 63117 63114 63074 63131 63011 63125 63119 63123 63021 63026 63126 63044 63088 63040 63042 63043 63031 63005 63017 63129 63146 63135 63033 63124 63141 63128 63105 63127 63038 63034 63138 63025 63121 63137 63136 Mean Annual Appreciation Measurement Type Chain Median 0 2 4 6 8
Parting Comments Price indexes provide a better handle on appreciation Many other estimation techniques Hedonic can be employed on identification problems