Preliminary: please do not quote wi e ission

Tuesday, September 04, 2007 

Estimates of State Price Levels for Consumption Goods and 

Services: a first brush

∗

Bettina H. Aten 

This paper develops exploratory estimates of the spatial price differences for 

consumption goods and services at the U.S. state level. The estimates are built up from 

two main data sets. The first is the principal source of consumer price information in the 

United States, the Bureau of Labor Statistics Consumer Price Index (CPI) for 38 

metropolitan and urban areas, which is of course a time-to-time index. Aten (2006) 

presented spatial (place-to-place) price index estimates for 2003 and 2004 for these 38 

areas, which cover 87% of the population but only about 15% of U.S. counties. In 

addition, some states are not covered at all by the CPI. The second source of information 

is the county level rent surveys from the U.S. Census Bureau. The estimates presented 

here are generated using a multi-stage approach that bridges the results in the areas 

sampled by the CPI price surveys to the remaining non-sampled areas using the Census 

rent information. 

General description 

The background to this paper is the work detailed in Aten (2005, 2006) on estimating 

place-to-place indexes for 38 metropolitan and urban areas in 2003 and 2004. These 

indexes are termed spatial price indexes (SPI) to distinguish them from the Consumer 

Price Index (CPI) that tracks changes over time in one place. The CPI survey is designed 

to cover a fixed set of geographical areas, so that SPIs can only be directly estimated at 

this 38 metropolitan and urban area level. More disaggregated calculations or more 

extensive geographical coverage would require a redesign of the CPI survey, something 

that is not feasible in the short run. Given that there are significant differences in price 

levels for the metropolitan and urban areas covered by the CPI, there is much interest in 

a) adjusting economic data to reflect these price differences, such as when making 

comparisons of income levels and expenditure levels (Bernstein et al [2000], Johnson et 

al [2001]) and b) assessing the feasibility of estimating SPIs for different geographies, 

such as states and regions (see for example Fuchs et al [1979], Ball and Fenwick [2004], 

Roos [2006]). Any such use involves making inferences for areas not sampled by the 

CPI. 

One problem in making these inferences is the change of scale that arises in aggregations 

that are different from the observed levels, for example, from metro area to counties or 

from metro areas to states. A related problem is that some of the CPI areas cross state 

∗

 These are preliminary results, and should not be quoted without the author’s permission. 

Bettina H. Aten is an economist in the Regional Economics Directorate, Bureau of Economic Analysis. The 

results presented here are the responsibility of the author and not of the Bureau of Economic Analysis. 

Email: Bettina.Aten@bea.gov 

1 
 

 

lines, while others refer to single counties1. For example, the District of Columbia is only 

one of 26 counties in the Greater Washington metropolitan area as defined in the CPI, but 

it is also a quasi state, or at least, for many purposes, a separate entity from the states of 

Virginia or Maryland. Los Angeles is one county and one CPI area by itself, but only 

one of 58 counties in the state of California. The CPI area termed South B (medium and 

small urban areas in the South Region), is made up of 84 smaller units, scattered across 

states such as Georgia, Tennessee, and South Carolina. Combining and using these 

disparate spatial units is problematic for a number of reasons. The approach applied here 

is to break down these areas into somewhat less heterogeneous units, namely counties, 

then build up the county data back into state level estimates. 

The second main issue is the lack of data for a great number of areas. We know from the 

survey design of the CPI that these non-sampled areas are systematically excluded 

because of their smaller, less dense populations and lower volumes of expenditures. This 

means that direct inferences from the sampled areas of the CPI to the non-sampled areas 

would be misleading because the distribution of expenditures and prices are also likely to 

be systematically different. The second stage of this paper aims to bridge the gap 

between the sampled and non-sampled CPI areas indirectly, using data on rental price 

levels from the 2000 Census. 

The consequences of scale, classification inconsistencies and sampling coverage that 

characterize these data have been discussed in the spatial statistical literature (Goodchild, 

Anselin and Deichmann [1993], Gotway and Young [2002], Baneerje and Gelfand 

[2004], Anselin and Gallo [2006]). In the social sciences, issues in spatial aggregation 

are known as the ecological fallacy problem and the modifiable areal unit problem. 

Anselin (2002), among others, extensively reviews the conceptual and practical 

consequences for applied spatial models in the econometric literature. 

The methods adopted here attempt to mitigate, not resolve, some of the major estimating 

problems associated with changes of scale and spatial aggregation, but are by necessity 

data-driven. They are summarized below and then discussed more extensively in 

subsequent sections. 

The estimation of the spatial price indexes (SPIs) at the state level is divided into three 

stages. The first takes the 38 CPI areas and decomposes them into smaller and more 

consistent geographical areas, generally counties. The relationship between the average 

price levels for these areas and the observed county rents are modeled, and price levels 

are predicted for the individual counties within the 38 CPI areas. 

The second stage involves bridging these predictions to the remaining counties in the 

U.S. that are not in the CPI sample, counties which tend to be in primarily nonmetropolitan and rural areas. It is subdivided into two steps, the first one assigns initial 

values to all counties, while the second one again relies heavily on the modeled 

1

 Some areas refer to townships within counties. The term county in this paper refers to counties and 

county equivalents, plus the 78 municipalities of Puerto Rico. More details on the geographical boundaries 

can be found in the next section. 

2 
 

 

 

 

 

 

 

 

relationship between price levels and rents, which are observed for all U.S. counties 

covered by the Census, including those not in the CPI sample. The final stage builds up 

the aggregate state price levels based on these estimated county price levels, and tests the 

sensitivity of these results to alternative specifications. 

Background on the Data 

Interarea Price Levels and Census Rents 

The methodology for estimating SPIs for the 38 metropolitan and urban areas of the CPI 

has been detailed in Aten (2005, 2006) using 2003 and 2004 prices. It includes 

estimating a weighted hedonic regression for each expenditure item that make up 

consumer goods and services in the U.S., a total of about 400 items. These range from 

rents and new automobiles to shoes and haircuts. The hedonic regressions take into 

account item characteristics, such as unit size and packaging, as well as the location and 

type of outlet where it is sold, and uses probability sampling quotes as weights. The 

resulting item price levels are then aggregated into major categories, such as Food and 

Beverages, Transportation, and Housing, and up to an overall SPI for consumption, using 

item expenditure weights at the 38 area level (see Appendix Table A1 for a list of all 

counties comprising these areas). 

The 2000 Census rents consist of monthly rental estimates at seven levels of geographic 

aggregation, three definitions of units, and five bedroom size categories. The non-cash 

rental units were excluded in this study. The recent movers are included, defined as 

having moved within the last two years. These rental observations are averaged 

geometrically across five bedroom size categories: from zero to four bedrooms, weighted 

by the number of units in each category. The Census data include state, county, 

metropolitan area, place and county subdivision code, thus permitting a good 

geographical matching to the BLS Consumer Price Index (CPI) data. The 38 CPI areas 

correspond to 147 metropolitan areas, counties and places, and at the lowest geographical 

level, to 425 counties2

. 

The SPIs refer to 2003 prices, but the Census rents are for the year 2000. In principle, 

one would need to redo the SPIs using 2000 prices, but for experimental purposes, the 

2

 A few counties span more than one CPI area, primarily when the county is comprised of townships. In 

these cases, the FIPS code of the county was assigned to one area only, based on the size of the sample 

and/or the population that it covered. They are the following: 

Litchfield, CT to area A110 (New York Suburbs) 

Middlesex, CT to area X100 (Northeast B region) 

Windham, CT to area X100 (Northeast B region) 

Hampden, MA to area X100 (Northeast B region). 

Eight towns within Litchfield are in the A110 area and five are in the X100 region but the ones in the A110 

area account for two thirds of the population. Seven out of eight towns in Middlesex are in the X100 area, 

with 79% of the population. In Windham, only Thompson town with 11% of the population is in the A103 

Boston with the rest in the X100 area, and similarly in Hampden, only Holland town with less than one 

percent of the population is in A103, with the remainder in the X100 Northeast B area. 

3 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2003 results from Aten (2006) have been moved back to 2000 using the CPI-Urban price 

change for each area3. Table 1 shows these SPIs and also the corresponding average rent 

for each area from the Census data. 

Table 1. Observed Price Levels and Rents by Area 

Region Area Freq Area Name SPI Rent ($) Rent Level 

North East A102 14 Philadelphia 1.01 658 0.99 

 A103 12 Boston 1.12 755 1.14 

 A104 6 Pittsburgh 0.84 492 0.74

 A109 5 NY city 1.28 750 1.13 

 A110 10 NY suburbs 1.29 893 1.35 

 A111 15 NJ suburbs 1.14 779 1.18 

Mid West A207 13 Chicago 1.05 669 1.01 

 A208 10 Detroit 0.94 596 0.90 

 A209 13 St. Louis 0.87 528 0.80 

 A210 8 Cleveland 0.89 552 0.83 

 A211 13 Minneapolis 0.99 655 0.99 

 A212 5 Milwaukee 0.91 578 0.87 

 A213 13 Cincinnati 0.87 521 0.79 

 A214 11 Kansas City 0.86 576 0.87 

South A312 26 DC 1.06 806 1.22 

 A313 7 Baltimore 0.97 629 0.95 

 A316 12 Dallas 0.97 659 0.99 

 A318 8 Houston 0.95 600 0.91 

 A319 20 Atlanta 0.94 749 1.13 

 A320 2 Miami 1.02 701 1.06 

 A321 4 Tampa 0.92 617 0.93 

West A419 1 Los Angeles 1.20 721 1.09 

 A420 4 Greater LA 1.07 804 1.21 

 A422 10 San Francisco 1.34 1017 1.53 max 

 A423 6 Seattle 1.05 735 1.11

 A424 1 San Diego 1.14 783 1.18 

 A425 8 Portland 0.98 665 1.00 mean 

 A426 1 Honolulu 1.38 max 846 1.28 

 A427 1 Anchorage 1.06 752 1.13 

 A429 2 Phoenix 0.93 672 1.01 

 A433 7 Denver 1.00 mean 720 1.09 

Non-metro D200 7 MW Cs 0.80 408 0.62 min 

 D300 9 South Cs 0.80 min 423 0.64 

 D400 2 West Cs 0.88 576 0.87 

 X100 21 NE Bs 0.92 551 0.83 

 X200 25 MW Bs 0.85 547 0.82 

 X300 84 South Bs 0.87 557 0.84 

 X499 9 West Bs 0.88 661 1.00 

3

 Aten (2006) compares an extrapolation of 2003 to 2004 versus a direct estimate for the year 2004 and 

finds that there are minor differences when an aggregate CPI rate is used as the deflator, but negligible 

differences with a detailed item-level CPI deflator. Another way to reconcile the disparate data sets would 

be to move the Census rents to 2003, but that would mean that all population estimates for the counties 

would also need to be adjusted to 2003, as well as any other right-hand variable that is tested. 

4 
 

 

 

 

 

Region Area Freq Area Name SPI Rent ($) Rent Level 

Sum 425 Mean 1.00 663 1.00 

Max 1.38 1017 1.53 

Min 0.80 408 0.62 

Range 0.58 609 0.92 

The column labeled Freq denotes the number of counties that make up the BLS area 

(four areas are made up of only one county: Los Angeles, San Diego, Honolulu and 

Anchorage). The mean of the price levels across the 38 areas is 1.00 by construction, 

while that of the unweighted rents is US$ 663. The range of the rents far exceeds that of 

the SPIs: 0.92 versus 0.58. The San Francisco area had the highest rent, with an average 

of $1,017 and a rent level of 1.53, while the Midwest C urban areas, comprised of Rice 

MN, Allen and Neosho KS, Brookings, Lake, Moody SD and Jefferson IL were the 

lowest, with rents averaging $408 and a rent level of 0.62. 

Figure 1 plots the relationship between these two variables. 

Figure 1.SPIs vs. Rents by Area 

Price Levels 

1.50 

1.40 

1.30 

1.20 

1.10 

1.00 

0.90 

0.80 

0.70 

South C 

MW C 

Honolulu 

NY city 

NY suburbs 

Atlanta 

San Francisco 

400 500 600 700 800 900 1000 1100 

Rents ($) 

Methodology 

First Stage 

5 
 

 

 

The first stage consists of obtaining a relationship between the price levels and the rents 

at the county level for all CPI areas. The 38 areas are mapped to their corresponding 

counties4, a total of 425 observations listed as Freq in Table 1. For these 425 counties, 

the observed rents are averaged geometrically across five bedroom-size categories, 

weighted by the number of housing units that were sampled in each category. 

A simple log-linear relationship was posited, shown in Equations (i) to (iii). Alternatives 

specifications were tested, such as a log-log version, a non-linear function of rents, and 

one that included other sources of data, such as incomes (from the Internal Revenue 

Service), and census demographic variables. Introducing incomes and demographic 

variables raises endogeneity issues, namely whether incomes determine prices or viceversa. It was also unclear whether one wants to use differences in racial and ethnic 

make-up to control for geographic price differences5. Since the objective is not to 

explain price levels, but rather to obtain estimates based on their correlation to price 

indicators that have a more extensive geographical coverage, it was felt that these 

variables should not be included, and only rents and population densities were retained as 

independent variables. 

Equations (i)-(iii): First Stage Base Models 

 

( ) ln Pi = ∑ β j X j + ε i i ; (NonS) 

j 

ε i ≈ N(0, σ

2

) 

( ) ln Pi = ρW ln Pi + ∑ β j X j + ε i ii ; (SLag) 

j 

ε i ≈ N(0, σ

2

) 

(iii) ln Pi = ∑ β j X j + ε i (SErr) 

j 

ε = λW ε + μ ;

i i i 

μ i ≈ N(0, σ

2

) 

The dependent variable, the price level for the area, is repeated across the counties 

belonging to the same area, whereas the independent variables (observed rents and 

population density) are specific to individual counties within the areas. This induces a 

4

 Observations in the Census data follow several designations: county is the lowest aggregation for many 

states, but for others there are Places and MCDs within a county FIPS code. For example, there are five 

townships in Maine that are part of York County, which in turn is one of the ten counties in the A103 

Boston metropolitan area. Connecticut, Massachusetts, Vermont and New Hampshire also have several 

towns or cities within a county code. Unless otherwise noted, the subdivisions are aggregated to the county 

level. In the case of rents, this is the weighted geometric mean of the Places or MCDs within each county. 

5

 Aten (2005) looks at the sensitivity of housing rent price levels to variables in the Census. 

6 
 

 

 

 

 

non-constant variance to the error term. The error terms are also likely to be 

autocorrelated, as both rents and prices tend to be similar in nearby locations. Some 

effort was made to reduce heteroskedasticity in the covariance structure of the error term 

by specifying a spatial stochastic process and by using individually weighted 

observations. 

An alternative to this specification is to use only the average of the independent variables 

for each area, reducing the number of observations to their original 38 areas. Although 

such a framework reduces heteroskedasticity, it exacerbates the change of scale and 

ecological fallacy problem, as one would then have to apply the coefficients estimated for 

38 areas to all counties within those areas. Some adjustments can be made to deal with 

the differences between the aggregation levels (see for example, Holt, Trammer, Stell and 

Wrigley [1996], Huang and Cressie [1997]), but these seem to induce more, and arguably 

less transparent, assumptions about the relationship among the geographical levels, 

especially when trying to take into account spatial autocorrelation among the units of 

observation. 

Equation (i) is a simple non-spatial model (NonS) with the log of the prices as the 

dependent variable and rents and population density as independent variables. Equations 

(ii) and (iii) have an explicit spatial component. The SLag model is a spatial autoregressive model because of the addition of a spatial ‘lag’ in the form of W*( lnPi) on the 

right-hand side while the SErr model is a spatial error model, with residual spatial 

autocorrelation in both dependent and independent variables captured in the error term. 

For a review of spatial econometric models, including their specification and testing, see 

for example, Anselin (1988, 2004), Getis et al (2004), LeSage et al (2004). 

W is an n x n spatial weights matrix that specifies the relationship between the n 

observations. A non-zero element Wik defines k as being a geographical neighbor to i. 

The term neighbor ranges in this context from nearest neighbors, to contiguity, to inverse 

distance matrix definitions of neighbors. For example, a first-order nearest neighbor 

matrix will have ones in the row and columns corresponding to observations that are 

closest to each other geographically, and zero otherwise6. Inverse distance matrices will 

have entries in all the elements (except the main diagonal) indicating the inverse of the 

distance between the observations. The contiguity matrix is defined using a Delaunay 

triangulation7, with observations having from three to twelve neighbors. 

One interpretation of W is that of a spatial multiplier, (I-ρW)-1 in the SLag model and (IλW)-1 in the SErr model, allowing for endogeneity in the dependent variable or in both 

dependent and independent variables, respectively8. The use of spatial weight matrices 

6

 Other metrics, such as trade or commuting flows may be used in the W matrix, but distance is an easy to 

compute variable that is clearly exogenous, and has been shown to be correlated to price levels in other 

studies (Aten [1996, 1997]). 

7

 Delaunay triangles (the dual of a Voronoi diagram, also know as Thiessen polygons) returns a set of 

triangles such that no data points are contained in any triangle's circumcircle. The contiguity matrix is the 

adjacency matrix derived from this triangulation.

8

 In the SLag model, (I-ρW)ln P=∑βX + ε; in the SErr model, the ‘lag’ applies to both dependent and 

independent variables – translating into the error term after some algebraic manipulation: (I-そW)ln P =(I7 
 

may be loosely interpreted as a ‘de-trending’ mechanism, intended to reduce the bias in 

the rent coefficients in the presence of spatial auto-correlation, similar to the use of 

spatial lags in time-series analysis. For a comprehensive discussion on interpreting 

spatial models, see Anselin (2002). 

 The parameters are found using weighted least squares (NonS model) and maximum 

likelihood estimators (in SLag and SErr models), with weights proportional to the 

population9. The weights are intended to reduce the variance of the residuals and 

increase the efficiency of the estimates. In addition to the rent and density variables, 

regional and size dummies were tested to help determine the stability of the rent and 

density parameters in each model. 

The results of the ‘best’ model in each of the three specifications are presented in the 

Results section, but numerous variations were tested, and a summary of the sensitivity of 

the estimates to different combinations of spatial weights matrices W is shown at the end 

of the paper. The predicted individual county price levels are normalized so that their 

weighted average equals the average price level for the area. That is, the weighted 

averages of the within-area county price levels equal the original observed input price 

levels. 

Second Stage 

The second stage involves bridging the predicted price levels in the 425 counties from the 

previous stage to all U.S. counties that are covered by the Census, including areas not 

sampled by the CPI. This is done in several steps. For ease of exposition, the 425 

counties that constitute the 38 areas sampled by the CPI are denoted ‘overlap’ counties 

because they are in both the BLS CPI sample data and the Census rental data. The areas 

not sampled in the CPI are denoted ‘census only’ counties. Together, the overlap and 

census-only counties cover the 3219 counties. 

First, the ratio of the weighted geometric mean of rents in census-only areas to overlap 

areas is calculated. This ratio is then multiplied by the weighted geometric average of the 

price levels in the counties predicted in Stage One. In Equations (iv), ‘over’ refers to 

overlap counties, while ‘census’ refers to counties only in the Census rent sample. The 

weights refer to population weights. 

For example, in Missouri, the rent ratio is 0.87, with fifteen counties that overlap 

averaging $540 in rents and 172 counties only in the census averaging $468. This ratio is 

then multiplied by the weighted geometric average of the price levels in the fifteen 

counties predicted in the first stage (0.86). For Missouri, this includes eight counties in 

そW) ∑βX+ た, which implies ln P = ∑βX+ (I-そW)-1 た, with ε= そW ε + た. Another interpretation is that (IρW) and (I-そW) are spatial filters, as in a first differencing approach for time series. 

9

 These weights are assumed to be inversely proportional to the variances, as larger areas will generally 

sample more prices (and rents). 

8 
 

 

St. Louis (A209) and seven in Kansas City (A214). The result, 0.75, is an average 

estimated price level for the remaining non-sampled 172 counties in Missouri. 

Equations (iv): Bridge Ratios 

Ratio = (Rent census Rent overlap ) 

where Rent census = exp( ∑ wj ln Rent j ∑ wj ) 

j∈census j∈census 

Rent overlap = exp( ∑ wi ln Renti ∑ wi ), 

i overlap ∈ i overlap ∈

PLcensus = PLoverlap * Ratio 

where PLoverlap = exp( ∑ wi ln PL i ∑ wi ) 

i overlap ∈ i overlap ∈

The process is repeated for all states, with the exception of states that have no overlap at 

all. These are Iowa, Montana, New Mexico, North Dakota, Rhode Island, Wyoming and 

Puerto Rico10, where a higher geographical aggregation, the division, is used instead of 

the state. There are nine divisions, their average rents and ratios are listed in Table 3 in 

the Results section. 

The bridged price level estimates from Equation (iv) become the dependent variables in 

the second stage regression model. It mirrors the first stage regressions in that the 

estimated price levels for each county enter as dependent variables, and are repeated 

across areas bridged by the same ratio. The actual individual rents as well as observed 

population densities for each county are the independent variables. The observations are 

weighted in proportion to the population. A weighted least squares formulation is tested 

(NonS) as well as two spatial models– the spatial lag (SLag) and the spatial error (SErr) 

models, identical in form to Equations (i) to (iii) depicted earlier. As in the first stage, 

different spatial weight matrices are used but instead of 425 observations, n increases to 

3219, corresponding to all uniquely identified FIPS county codes in the Census rent data. 

Final Stage 

The final stage estimates the State Price Indexes or SPIs using the weighted geometric 

average of the predicted county values from the previous step. Ideally one would use 

expenditure weights but these are not available below the 38 area level, so population 

weights are used. The results are described in more detail below, followed by a 

discussion of their sensitivity to various specifications. 

10 Puerto Rico is included in this study even though it is a territory and not a state as it has a full set of 

sampled rents for its 78 municipalities. 

9 
 

 

 

Results 

First Stage Results 

The first stage estimation results consist of the three basic equations: a non-spatial 

(NonS) formulation and two spatial (SLag and SErr) models. The independent variables 

are the rents and the population density. The base models shown in Table 2 have 

separate regional intercept dummies. Alternative constraints and combinations were 

tested, including twelve different weight matrices (Ws) for each formulation. These are 

discussed in more detail in the Sensitivity section. 

Table 2. First Stage Regressions Base Models 

Dependent: Ln P NonS SLag SErr 

 

West -0.26** -0.16** -0.05* 

Northeast 0.01 -0.01 -0.03 

Midwest -0.09** -0.07** -0.15** 

South -0.11** -0.08** -0.15**

 - - -

Rents (x10-3) 0.47** 0.29** 0.22** 

Density(x10-4) 0.10** 0.08** 0.07** 

Rho (ρ) - 0.47** -

Lambda (λ) - - 0.69** 

Spatial Matrix W - C C 

Rbar2 0.69 0.72 0.76 

MSE 410 309 304 

LLikelihood - -1684 -1695 

Nobs, Nvar 425,6 425,6 425,6 

** significant at 1% level, * significant at 5% level 

The base models shown are the ones with a combination of low unexplained variance 

(Mean Square Error [MSE]), high log likelihood ratio (LLikelihood), and significant 

coefficients. The Rbar2 is a ‘pseudo’ R2 measure in the spatial models and equals the 

squared correlation between the predicted and observed price levels. These bases models 

are not significantly different vis-à-vis the unconstrained model11. Also, residuals were 

visually inspected for patterns, including heteroskedasticity and autocorrelation. 

Differences between SLag and SErr models were greater than differences between spatial 

weight matrices (except in the case of inverse distances), with SErr residuals behaving 

more ‘normally’ as might be expected. This is because the SLag models are correcting 

11 The F-test with (3, 425) degrees of freedom for the semi-constrained versus the unconstrained model in 

all cases averaged 2.0. 

10 
2

2

1

1

2

03

04

10

11

07

08

09

10

13

14

12

12

12

13

16

18

19

19

20

22

25

29

00

00

X100

100

X200

X200

200

300

300

300

X300

300

X300

300

300

X499 

10

10

11

21

21

A

A

A1

A1

A1

A1

A

A2

A2

A2

A2

A

A

A2

A2

A3

A3

A3

A3

A3

A3

A3

A3

A4

A4

A4

A4

D2

D3

X

X

X

X

X

X

X

X

for the autocorrelation of the dependent variable, but not adjusting for the autocorrelation 

in the rents or in the densities as well, which the SErr model does. 

Figure 2. Predicted Price Levels First Stage Regression 

0.70 

0.80 

0.90 

1.00 

1.10 

1.20 

1.30 

1.40 

1.50 

Price Level

Predicted 

Input 

__North East__ __Mid West__ ___South___ _West_ ________Non-metro/Urban______ 

38 areas, 425 counties 

The inverse distance spatial weight matrix resulted in some implausibly high (or low) 

predicted values for some observations. This occurs when the distance between two 

spatial units are very small, causing the inverse of the distance to be extremely large. For 

example in Virginia, Fairfax city and Fairfax county are separate observations in the 

Census, but they are technically within a few hundred feet of each other. The predicted 

price level for each observation is subtracted by its lagged value, the lag equaling ρW. If 

the relevant elements of W are disproportionately high as in this example, then the result 

can be a disproportionately low predicted value. A full listing of the 425 predicted price 

levels from this stage can be found in Table A1 the Appendix. 

Figure 2 highlights the results, showing the observed input price levels and the predicted 

levels using only the SErr base model in Table 2. The leftmost set of points on the 

horizontal axes of Figure 2, represent Philadelphia (A102) in the North East region. 

Philadelphia has an observed input price level of 1.005 with an average weighted rent of 

$658 (Table A1 in the Appendix). There are fourteen counties that make up the 

Philadelphia area. The lowest predicted price level is 0.992 for both Cumberland county 

NJ, and Cecil county MD, while the highest is 1.025 for Burlington county NJ, closely 

followed by Chester county, PA. The corresponding rent variation is $622 for 

Cumberland and $778 for Burlington, but the lowest rents are for Philadelphia county 

PA, at $576. Philadelphia’s predicted price level is 0.996, higher than Cumberland or 

11 
 

 

Cecil counties’ level, partly due to its higher population density and the spillover effect of 

having neighbors with higher price levels. 

Second Stage Results: Rent Ratios 

The predicted price levels from the previous stage are for the 425 counties within the 38 

areas of the CPI. These 425 counties were denoted overlap counties because they are 

both in the CPI and in the Census, which includes all U.S. counties. Although these 

overlap counties account for roughly 87% of the population, the remaining counties are 

predominantly non-metropolitan and non-urban areas, and include entire states. This 

stage attempts to find a reasonable bridge between the overlap counties and the censusonly counties. 

The first step in bridging the two areas is to multiply the weighted geometric average of 

the price levels in the overlapping areas by the ratio of the rents (Equation (iv)). A 

summary of these results is shown in Table 3. Rents for overlap counties in each Division 

and Region12 are shown in column (2), while rents for census-only counties are in column 

(1). These are labeled ‘overlap’ and ‘census’ respectively. The ratio of the two is in 

column (3). The price level from the first stage for the overlap counties is in column (4), 

and the bridged price levels in column (5). 

Overall, the ratio of rents in census-only counties to rents in overlap counties is 0.86, 

shown on the last line of Table 3, while the bridged price level for census-only counties is 

0.89 compared to the price level of 1.04 for overlap counties. 

Table 3. Rent Ratios and Bridged Price Levels 

Region Division Rent* Rent* Ratio Price Bridged 

census overlap census/overlap Level* Level 

($) ($) overlap census 

(1) (2) (3)=(2)/(1) (4) (5)=(3)*(4) 

1. 638 718 0.89 1.14 1.01 

Northeast 

 1. New 639 738 0.87 1.09 0.94 

England 

 2. Middle 637 713 0.89 1.15 1.03 

Atlantic 

2. 521 595 0.88 0.93 0.82 

Midwest 

3. East North 539 597 0.90 0.94 0.85 

Central 

4. West North 487 587 0.83 0.91 0.75 

Central 

3. South 544 641 0.85 0.94 0.80 

12 Since the rents are taken from the Census Bureau, their Regions and Divisions are used rather than BLS 

or BEA Regions. 

12 
 

Region Division Rent* Rent* Ratio Price Bridged 

census overlap census/overlap Level* Level 

($) ($) overlap census 

(1) (2) (3)=(2)/(1) (4) (5)=(3)*(4) 

 5. South 578 686 0.84 0.96 0.81 

Atlantic 

6. East South 482 506 0.95 0.86 0.81 

Central 

7. West South 532 592 0.90 0.93 0.84 

Central 

4. West 686 771 0.89 1.12 0.99 

 8. Mountain 599 688 0.87 0.94 0.81 

 9. Pacific 726 790 0.92 1.16 1.07 

Metro 619 687 0.90 1.04 0.94 

Non- 449 460 0.98 0.82 0.80 

Metro 

Overall 587 686 0.86 1.04 0.89 

*Weighted geometric means across counties. ‘Overlap’ denotes counties in the CPI and in the 

Census, ‘Census’ denotes census-only counties. 

Rents in overlap areas are generally higher than in census-only areas. The highest rents 

are in the Northeast and West, especially in the Pacific division that includes California, 

Hawaii, Alaska, Oregon and Washington. The lowest rents are in the East South Central 

division comprised of Alabama, Kentucky, Mississippi and Tennessee. The complete list 

of state rents and ratios is shown in Table A2 in the Appendix. 

Only Arkansas, Mississippi, South Carolina, South Dakota and Tennessee have ratios 

above one, meaning that the census-only counties have rents that are on average higher 

than the rents in overlap counties. In all these states, the overlap counties belong to ‘B’ 

or ‘C’ size BLS areas, namely they are part of medium and small cities or urban but nonmetropolitan areas. For example, in Arkansas, the overlap county is Jefferson whose 

largest town is Pine Bluff, rather than Pulaski, the larger county where Little Rock is 

located. Similarly, for Mississippi, the overlap county is Pearl River, where Picayune is 

the largest town. The composition of counties within areas and states is in the Appendix, 

Table A1. 

Maine and Georgia have the lowest ratios: 0.74 and 0.76 respectively. Maine’s overlap 

county is York, home of Kennebunkport, and part of the Boston metropolitan area 

(A103), with high rents compared to the rest of Maine. Although some of Georgia’s 

counties are in ‘B’ and ‘C’ size areas, the bulk of the overlap counties are part of the 

Atlanta metropolitan area (A319), also with relatively high observed rents. Iowa, 

Montana, New Mexico, North Dakota, Rhode Island, Wyoming and Puerto Rico are 

states with no overlap counties, and therefore no rent ratios. In these cases, the division 

level ratio (Table 2) is used as a bridge instead of the state level ratio. 

Second Stage Results: Regressions 

13 
 

 

 

 

 

The majority of the values for the dependent variable in this stage are derived from the 

rent ratios described above, as we have no direct information on their price levels. That 

is, for census-only counties, the ‘bridge’ price levels are the same across a state or a 

division, because they are based on the ratio of rents between the census-only and the 

overlap counties in that state or region. For the overlap counties, the price levels are the 

ones from the first stage. Both overlap and census-only bridge price levels are regressed 

against rents and densities, using the model structures introduced earlier: a non-spatial, a 

spatial lag and a spatial error model. 

Table 4 is a summary of the input data for the second stage regressions. 

Table 4. Input Data Summary 

(n=3219) Mean CV Range Minimum Maximum 

Input Price levels 0.849 12% 0.71 0.69 1.40 

(non-urban areas, KS) (New York, NY) 

Rent ($) $442 30% $1,119 $100 $1,219 

(Kalawao13, HI) (Santa Clara, CA) 

Density* 51 909% 19,720 0.002 19,720 

(Yukon-Koyukuk, AK) (New York, NY) 

* in square nautical miles (1 nautical mile is equal to 1.151 miles) 

Table 5 shows the results of the three regressions, using the contiguity spatial matrix for 

3219 counties. As in the first stage, both the spatial lag (SLag) and spatial error (SErr) 

models have a much lower mean square error (MSE) than the non-spatial model. Unlike 

the first stage the table does not include regional dummies. They are discussed in more 

detail in the Sensitivity section. 

Table 5. Second Stage Regressions 

Dependent: Ln P NonS SLag SErr 

 

Intercept -0.48** -0.32** -0.38* 

Rents (x10-3) 0.68** 0.45** 0.51** 

Density(x10-4) 0.16** 0.12** 0.13** 

Rho (ρ) - 0.46** -

Lambda (λ) - - 0.66** 

Matrix W - C C 

Rbar2 0.55 0.57 0.68 

MSE 135 100 95 

13 The county is on a small peninsula called Kalaupapa on the north coast of the island of Moloka’i. It is 

isolated from the rest of Moloka'i by sea cliffs over a quarter-mile high — the only land access is a mule 

trail. The state once exiled people with Hansen’s disease in Kalaupapa, and it is the second smallest county 

in the U.S, behind Loving County, TX. (Wikipedia). 

14 
 

 

Dependent: Ln P NonS SLag SErr 

LLikelihood - -10927 -10939 

Nobs, Nvar 3219,3 3219,3 3219,3 

Table 6 shows the predicted price levels from the coefficients in the three second stage 

regressions. The non-spatial (NonS) and the spatial error (SErr) models result in more 

similar predicted price levels than the spatial lag (SLag) model. This is partly because 

the spatial error adjusts for autocorrelation in the independent variables (rents and 

densities), as well as in the dependent variable. The SLag model does not take into 

account neighboring rents and densities, and as a result, the size of the errors in 

observations that are extreme will be exaggerated, especially when their weights are also 

very small. 

Table 6. Summary of Predicted Price Levels 

(n=3219) Mean CV Range Lowest values Highest values 

NonS 

SLag 

SErr 

0.84 

0.79 

0.86 

9.9% 

14.7% 

7.3% 

0.87 

1.74 

0.67 

0.66 (Kalawao, HI) 

0.69 (King, TX) 

0.04 (Kenedy, TX) 

0.06 (Loving, TX) 

0.72 (Kalawao, HI) 

0.74 (King, TX) 

1.53 (New York, NY) 

1.43 (Santa Clara, CA) 

1.78 (Falls Church city, VA) 

1.66 (Manassas Park city, VA) 

1.39 (New York, NY) 

1.28 (Santa Clara, CA) 

Two observations have implausibly low predicted price levels (0.04 and 0.06) using the 

SLag model: Kenedy and Loving, TX respectively. They have extremely small 

populations (400 and 67 people), and very low population densities. Even the most 

extreme low density area, Yukon-Koyokuk in Alaska, has over 6000 people, one hundred 

times the reported population of Loving. 

Similarly, Falls Church city has an extremely high density because of its small area (with 

a relatively low population count as well as high rents), and its predicted price level is 

overstated. The disparities between the detailed predictions for the SLag model could be 

smoothed over if the observations were grouped or adjusted individually – by combining 

independent cities for example, in the case of the Virginia observations14, but this was not 

done here. 

The county price level predictions from the SErr model are used in estimating the state 

price levels, shown graphically in Figure 3. The horizontal bars show the bridged input 

price levels while the individual points are the predicted levels using the SErr model 

coefficients. These have also been averaged within states, or there would be too many 

points (3219) to show on the graph. 

14 BEA does combine cities and counties in VA but these observations follow the BLS and Census 

definitions. 

15 
 

AL

AZ

CA

CT

DC

GA 

ID 

IN

KS

LA

MD 

MI

MS

MT

NV

NJ

NY

ND

OK

PA

SC

TN

UT

VA

WV

WY 

Figure 3. Stage 2 Regression Inputs and Price Levels

0.70 

0.80 

0.90 

1.00 

1.10 

1.20 

1.30 

1.40 

1.50 

1.60 

Price Level (US=1) 

PREDICTED LEVELS: SERR C 

INPUT LEVELS 

Final Stage Results: Spatial Price Indexes (SPIs) for States 

The SPIs for each state are the population weighted geometric averages of county price 

levels calculated in the following way. If the county was in the original sample of metro 

and urban areas, then the original input price level is used. If not, that is, if the county is 

a bridged county, then the predicted price level from the SErr (contiguity) model is used. 

Table 7 shows the estimated state price levels by SPI rank, normalized so that the average 

of the states equals one. The last two columns show the actual rents observed from the 

Census, and the corresponding rent levels when these are also normalized across the 

states to equal one. They are depicted in Figure 4 with rents on the horizontal axis and 

SPIs on the vertical axis. These mimic Table 1 and Figure 1 at the beginning of the paper 

with the input SPIs and rent levels for the 38 areas. Hawaii has the highest rent level 

(1.44) and the highest SPI (1.36). New York has the second highest predicted SPI (1.26) 

but only the 7th highest rent level (1.24), a result that would be consistent with rent 

controls in effect. 

Table 7. Predicted Price Levels and Rents by State 

Rank By SPI SPI Rank By Rent Rent ($) Rent 

(predicted) (actual) Level 

1 Hawaii 1.355 1 Hawaii 815 1.440 

2 New York 1.253 2 California 772 1.364 

16 
5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

5

10 

15 

20 

25 

30 

35 

40 

45 

50 

Rank By SPI SPI Rank By Rent Rent ($) Rent 

(predicted) (actual) Level 

3 California 1.222 3 New Jersey 762 1.347 

4 New Jersey 1.196 4 Alaska 746 1.319 

Massachusetts 1.151 Massachusetts 715 1.263 

6 New Hampshire 1.113 6 Nevada 711 1.257 

7 Alaska 1.104 7 New York 701 1.240 

8 District of Columbia 1.104 8 Connecticut 701 1.238 

9 Washington 1.073 9 Maryland 686 1.212 

Maryland 1.066 Colorado 680 1.202 

11 Illinois 1.061 11 Washington 667 1.178 

12 Colorado 1.050 12 Virginia 655 1.158 

13 Delaware 1.048 13 New Hampshire 647 1.144 

14 Connecticut 1.042 14 District of Columbia 646 1.142 

Florida 1.025 Florida 646 1.142 

16 Oregon 1.016 16 Delaware 646 1.142 

17 Minnesota 1.008 17 Arizona 626 1.106 

18 Virginia 1.007 18 Oregon 617 1.090 

19 Texas 0.994 19 Georgia 609 1.076 

Utah 0.988 Illinois 606 1.072 

21 Arizona 0.984 21 Utah 602 1.064 

22 Rhode Island 0.984 22 Texas 579 1.023 

23 Pennsylvania 0.980 23 Vermont 568 1.005 

24 Vermont 0.978 24 Minnesota 564 0.997 

Michigan 0.977 Rhode Island 560 0.989 

26 Georgia 0.976 26 North Carolina 559 0.988 

27 Nevada 0.972 27 Michigan 553 0.977 

28 Indiana 0.970 28 Wisconsin 539 0.952 

29 North Carolina 0.966 29 Pennsylvania 537 0.949 

New Mexico 0.959 Indiana 525 0.928 

31 Tennessee 0.955 31 South Carolina 521 0.920 

32 Wisconsin 0.955 32 Ohio 520 0.919 

33 Maine 0.954 33 New Mexico 513 0.907 

34 South Carolina 0.951 34 Tennessee 513 0.906 

Iowa 0.935 Idaho 511 0.904 

36 Nebraska 0.935 36 Maine 506 0.894 

37 Idaho 0.931 37 Kansas 496 0.876 

38 Ohio 0.931 38 Nebraska 487 0.861 

39 Louisiana 0.930 39 Missouri 482 0.851 

Kansas 0.929 Louisiana 470 0.831 

41 Arkansas 0.926 41 Iowa 468 0.828 

42 Montana 0.926 42 Oklahoma 459 0.812 

43 Mississippi 0.925 43 Alabama 456 0.806 

44 Kentucky 0.924 44 Arkansas 452 0.798 

Wyoming 0.924 Montana 450 0.795 

46 Alabama 0.920 46 Kentucky 448 0.792 

47 Oklahoma 0.919 47 Mississippi 446 0.789 

48 Missouri 0.917 48 Wyoming 446 0.787 

49 West Virginia 0.911 49 South Dakota 418 0.739 

South Dakota 0.908 West Virginia 406 0.718 

17 
 

 

 

 

Rank By SPI SPI Rank By Rent Rent ($) Rent 

(predicted) (actual) Level 

51 North Dakota 0.904 51 North Dakota 403 0.712 

52 Puerto Rico 0.868 52 Puerto Rico 312 0.551 

Average 1.00 566 1.00 

 Maximum 1.35 815 1.44 

 Minimum 0.87 312 0.55 

Range 0.49 503 0.89 

CV 10% 20% 

The predicted state SPIs have a much smaller range than the rents (0.49 vs 0.89), and it is 

interesting to note the change in rank order among the states. In addition to Hawaii, 

California, New Jersey, Alaska and Massachusetts, Nevada is reported to have one of the 

highest rents, with an observed average of $711, higher than New York state as a whole. 

The main counties responsible for this relatively high rent are Clark and Douglas 

counties, which include Las Vegas and Tahoe, respectively. Also noteworthy is the 

relatively high SPI for New Hampshire. Four out of ten counties in New Hampshire are 

considered part of the Boston metro area, with high input price levels. 

Figure 4. SPIs vs. Rents by State 

Price Levels by State 

1.40 

1.30 

1.20 

1.10 

1.00 

0.90 

0.80 

300 400 500 600 700 800 900 

Rents ($) 

Puerto Rico 

New York 

Nevada 

Hawaii 

18 
 

Sensitivity of SPIs 

Since there are various stages where key assumptions are made in the estimation process, 

the sensitivity of the results to alternative formulations and models were analyzed at each 

stage. The following differences are highlighted: 

a. sensitivity to geographic outliers in the first stage (Alaska and Hawaii) 

b. sensitivity to the choice of weight matrix in the first stage 

c. sensitivity to the choice of model and weight matrix in the second stage 

a. Sensitivity to Outliers: Alaska and Hawaii 

In the first stage, four out of the 38 areas consist of a single county: Los Angeles, (not 

including Greater LA, which is a separate area), San Diego, Honolulu and Anchorage. 

Since Hawaii and Alaska are geographic outliers, and two of the base models (the SLag 

and SErr models) explicitly use the geographic relationship among the areas, Honolulu 

and Anchorage were excluded as a test of out-of-sample sensitivity. The predicted price 

levels for the two areas were compared to the predictions from the full (within-sample) 

model15

. 

Within-sample and out-of-sample predictions were very close to each other when the 

SErr model was used, but all models under-predicted the price level for these two areas. 

The differences were minor for Anchorage (averaging -2.2% across all models and 

weight matrices for the out-of-sample prediction and -1.6% for the in-sample 

predictions). For Honolulu, the differences were significant (averaging -21.6% and -19% 

respectively), but the magnitude of the differences was similar regardless of model and/or 

weight matrix. 

Figure 5 show the differences between predicted and observed price levels for Hawaii 

and Anchorage respectively. 

The horizontal axis describes each model: OLS, SLag and SErr, with different weight 

matrices. These include the contiguity matrix plus eleven other weight matrices (ranging 

from one nearest-neighbor to twenty-one nearest neighbors, plus the inverse distance 

matrix) for each of the SLag and SErr models. The vertical axis is the difference between 

the predicted price level and the input price level, in percentage terms. The input price 

level for Anchorage was 1.06 and for Honolulu, 1.38 (Table 1). 

15 The predicted out-of-sample price levels assume that the weight matrix entries for Honolulu and 

Anchorage are zero, that is, they are geographically isolated from other areas. 

19 
Figure 5. Outlier Predictions (AK and HI) 

-25% 

-20% 

-15% 

-10% 

-5% 

0% 

5% 

OLS 

C

N1

N2

n3

n4

n5

n6

n7

n9

n11

n21

Nidist 

C

N1

N2

n3

n4

n5

n6

n7

n9

n11

n21

Nidist 

Difference (%) 

Anchorage 

Honolulu 

Out-of-sample 

Within-sample 

SLag SErr 

One reason for the large difference between predicted and input price levels for Honolulu 

is that the only independent price information that is being used in this study are rents. 

Although rents are high in Honolulu (1.28 in Table 1), they were only 84% of the rent 

levels in San Francisco, according to the Census data, while the SPI for Honolulu was 3% 

higher than for San Francisco (Table 1). It could be argued that other consumption 

characteristics of Hawaii that are likely to raise price levels are not being captured. For 

example, the higher cost of shipping is important in raising gas prices, and it was shown 

in Aten (2005) that price levels for most other consumption goods in Honolulu were also 

relatively high compared to the rest of the U.S. 

Note that although the model severely under-predicts the price level for Honolulu, the 

observed price level is the one used for subsequent stages, as there is only one county in 

Honolulu. This is true for Anchorage and the other two single county areas (Los Angeles 

and San Diego) as well. For areas with more than one county, the mean of the predicted 

price level is normalized to the observed price level, so that in effect, we are using only 

the variation about the mean for the prediction of the within-area counties, not the actual 

levels. 

b. Sensitivity to the choice of weight matrix in the first stage 

The first stage regression results shown in Table 2 used the Contiguity matrix as the 

spatial weight. Eleven other matrices were created to test the sensitivity of the model to 

the choice of weights in the SLag and SErr models. These consist of nearest neighbor 

matrices ranging from first-order nearest neighbor to twenty-first order (one to seven, 

nine, eleven and twenty-one neighbors), and an inverse distance matrix. The latter 

resulted in some disproportionately high and low values in the SLag model, partly due to 

some spatial units that are very close together, as discussed earlier in the text. 

20 
 

 

T 

S

 C

 N1

 N2

 N3

 N4

 N5

 N6

 N7

 N9

11

 N21

T

 C

 N1

 N2

 N3

 N4

 N5

 N6

 N7

 N9

 N11

 N21

T 

U

OL

IS

IS

P

 N

IN

 ID

 ID

In the first-order nearest neighbor matrix W, each row has only one entry (equal to 1), 

corresponding to the nearest observation. For example, W19 = 1 (the 9th observation is the 

nearest neighbor to the first observation). However, W is not necessarily symmetric, as 

the nearest neighbor to the 9th observation is observation 8, so W91=0 and W98=1. The 

second-order nearest neighbor matrix will have two entries per row, each equal to 0.5, 

while the twenty-first order matrix has 21 entries, each equal to 0.0476. 

In Figure 6 the different methods are listed on the horizontal axis while the range of the 

resulting SPIs are on the vertical axis. The range is the maximum predicted county price 

level minus the minimum predicted county price level for the 425 counties comprising 

the 38 input areas. 

Figure 6. Sensitivity of Predicted SPIs (n=425) in First Stage 

0.60 

1.10 

1.60 

2.10 

2.60 

3.10 

3.60 

4.10 

High-Low Mean SPI

Max 

Min 

Mean 

SErr 

SLag 

OLS 

Models and Weight Matrices 

The SErr models have the least spread overall, and differences across matrices are slight 

compared to differences between the methods. The mean SErr range is 0.65 (from a 

minimum of 0.62 for the contiguity matrix to a maximum of 0.69 for the first nearest 

neighbor and the inverse distance matrix). The mean SLag range is higher at 0.97 

(minimum is 0.75 for the second-order nearest neighbor to 2.75 for inverse distance), 

while the OLS model predicts a SPI range of 0.72. 

Looking at actual levels, the lowest input price level was 0.80 for the South C areas 

(Table 1) and the highest one for Honolulu at 1.38. The SErr C model predicts the 

within-area low-high price levels to be 0.779 and 1.396, for Screven GA, and New York 

21 
NY, respectively (Table A1 Appendix). The input price level for the New York area was 

1.28 (Table 1), but the predicted levels for its counties ranged from a low of 1.202 for 

Richmond, to 1.396 for NY city. Honolulu, HI is only fifth-highest, being a single 

county and normalized to its input level of 1.38 (Table A1 Appendix). The SErr model 

with a contiguity matrix is the most conservative, as it results in the lowest spread across 

the 425 counties within the 38 areas. 

c. Sensitivity to the choice of model and weight matrix in the second stage 

This section looks at the differences in state SPIs when different weight matrices and 

model specifications are used in the second stage regression. The three base models 

(non-spatial, spatial lag and spatial error with a contiguity matrix) were described earlier. 

The spatial lag model gives rise to implausible predicted levels when the values of the 

independent variables are extreme, combined with very low weights. These differences 

can be mitigated by joining observations to form different spatial units, but this exercise

was not done here. Instead, various weight matrices were created for the full set of 3219 

observations, and the resulting state SPIs were compared. 

Table A3 in the Appendix lists the states in alphabetical order. The Freq column indicates 

the number of counties within each state. The other columns are the price levels of 

observed rents (column 1), the input price levels for the first stage regression (column 2), 

the input price levels for the second stage regression (column 3) and then the various 

estimated final state SPIs using different methods and matrices. These are the preferred 

method with the SErr model and contiguity matrix (column 4), the SLag with contiguity 

(column 5), the NonS model (column 6), followed by columns 7-12 containing the SErr 

model with a first-order nearest neighbor matrix (n1), a third-order matrix (n3), fifthorder (n5), seventh-order (n7), ninth-order (n9), and eleventh-order (n11) nearest 

neighbor matrix. Lastly, two more SErr models are shown, one with only regional 

dummies (column 13), and one with both regional dummies and separate slopes for rents 

and densities (column 14). Both use the contiguity spatial weight matrix. All levels are 

normalized to the average of the states for comparison purposes. 

Hawaii is consistently the highest priced state, followed by New York, California and 

New Jersey. Puerto Rico is always the lowest, with West Virginia or North Dakota vying 

for second lowest place. The results are fairly consistent across methods, with the largest 

differences to be found between the SErr models, regardless of matrix, and the SLag and 

NonS models (columns 5 & 6). The latter two predict state SPIs that are more similar to 

those of the SErr models with dummy variables (columns 13 &14). 

The greatest range was in the SLag model and the NonS model (0.57), while the smallest 

range (0.49) was in the SErr models, for the contiguity matrix (column 4) and the fifth to 

eleventh nearest neighbor matrices (columns 9-12). 

One disadvantage of the unconstrained SErr model with separate slopes and intercepts by 

region (column 14), is that there are outliers within each region, resulting in predicted SPI 

22 
 

for these outliers that are arguably under or over-predictions. For example, states in the 

Northeast region versus the South. The Northeast region has a higher average and thus 

Maine’s predicted SPI is 1.01 in column 14, but only 0.95 in all other columns. 

Conversely, Alabama and Arkansas drop from about 0.92 in the SErr models to 0.89 with 

a regional dummy for the South, as in column 14. In the first stage, the use of regional 

dummies was justified because it was a subset of counties that represented only 

metropolitan and urban areas, and these were scattered across the country. In this second 

stage, all counties are included and the geographic coverage is over a more continuous 

surface. 

Conclusions 

The state SPIs are constructed from a starting set of 38 metropolitan and urban area price 

levels for consumption goods and services, plus detailed rent data for all U.S. counties 

from the 2000 Census. Although the 38 areas in the CPI cover approximately 87% of the 

U.S. population, geographically they account for only 15% of the counties. The first 

stage of this exercise breaks down the original 38 areas into 425 counties and estimates 

price levels that are based on the relationship between rents, population densities and 

geographic proximity among the observations, and then normalizes them to the original 

observed BLS means in each area. 

The second stage involves bridging the estimates for these 425 counties to all other 

counties, 3219 in total (including the 78 municipalities in Puerto Rico). There is no 

direct price level information from the BLS for these other counties, as they are not 

included in the BLS sampling framework of the CPI. However, the Census does have 

detailed rent data and complete coverage of all counties, and as rents16, on average, 

account for nearly thirty percent of overall consumer expenditures, they are used as the 

main auxiliary data in this stage. As first step, we take the rent ratios between sampled 

and non-sampled areas and apply that ratio to the existing price levels. The assumption is 

that as a first approximation, the ratio of price levels between the overlap counties 

(belonging to both BLS and Census samples) and the counties only sampled by the 

Census is the same as the ratio of their rents. 

These initial price levels, called bridged price levels, are then regressed against the 

individual rents and population densities for all 3219 counties. The regression model 

mirrors the first stage model, and includes a spatial matrix that makes explicit the 

geographic proximity of the counties, this time with fuller and continuous coverage. The 

resulting predicted price levels for each non-sampled county are then aggregated to the 

state level, resulting in a second-round approximation of the state-level spatial price 

indexes or SPIs. 

Hawaii had the highest SPI: 35.5% higher than the average of the states, followed by 

New York and California. Other states that were at least ten percent higher than the 

16 Rents in the BLS include both Rents and Owner Equivalent Rents (for a more detailed description, see 

Aten [2006]) 

23 
 

average were New Jersey, Massachusetts, New Hampshire, Alaska, and the District of 

Columbia. States with the lowest price level index were Puerto Rico17 at 86.8% of the 

average, North and South Dakota and West Virginia, all around the 91% level. Nevada is 

a state with relatively high rent levels (1.26) but a low SPI (0.97). while New York is the 

opposite: lower rent level (1.24) but a higher relative SPI (1.25). The range of the SPIs is 

about 50%, from 15% below average to 35% above average, a much lower range than the 

rents that vary from a minimum of $312 to a maximum of $815, equivalent to a range of 

90%. 

The results demonstrate the feasibility of estimating state price levels from the best 

information available on prices and rents from the Bureau of Labor Statistics and the 

Census Bureau18. Future applications of the results should feed back into checks on the 

robustness of the methods developed in this paper. For example, one planned application 

is to adjust nominal personal income at the metropolitan or the state level to reflect 

differences in consumption prices. These adjusted incomes can then be compared to 

results obtained using unadjusted personal incomes. 

Another important extension of this work is to explore the use of state SPIs in developing 

GDP (Gross Domestic Product) by State estimates adjusted for price differences. In 

international comparisons, the price level of consumption is often a good approximation 

of that for all of GDP from the expenditure side. This is because the relative prices of 

investment and government change systematically in opposite directions when measured 

across per capita incomes. It is not clear whether this pattern would be found across 

states within one country, but it seems worth examination. One approach to this would 

be to see if there is a pattern across states in salaries and prices of inputs and outputs 

related to construction, producers’ durable equipment and government compensation. 

A third outgrowth of this work is to look at differences in price levels within expenditure 

categories, such as Food and Beverages, and within income groups, in order to make 

adjustments to federal and state aid programs that aim to target particular populations. 

Most of the non-urban counties in the United States had lower rents than their urban 

counterparts within a state, but the price levels of goods, such as fresh vegetables, and of 

medical and educational services were sometimes higher. Using both the time-to-time 

CPI index and the spatial price index (SPI) may broaden the analysis of patterns of 

consumption price levels while enabling a more focused approach to targeting areas of 

concern. 

17 As noted earlier, Puerto Rico is not a state but has a full set of sampled rents in the Census, so was 

included in this study.

18 Since the Census is decennial, other auxiliary sources of price data should be considered, such as the 

more timely American Community Survey. 

24 
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Basic Family Budgets for Working Families’, Economic Policy Institute, Washington, D.C.. 

Fuchs, Victor, Michael Roberts and Sharon Scott (1979), ‘A State Price Index’, National Bureau 

of Economic Research, Working Paper Series, February. 

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Palgrave Macmillan. 

Goodchild, Michael, Luc Anselin and U. Deichmann (1993), ‘A Framework for the areal 

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Gotway, Carol and Linda Young (2002), ‘ Combining Incompatible Spatial Data’, Journal of the 

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Huang, H.-C. and Cressie, N. (1997), ‘Multiscale spatial modeling’, in 1997 Proceedings of the 

Section on Statistics and the Environment, 49-54. American Statistical Association, Alexandria, VA. 

25 
Johnson, David S., John M. Rogers, and Lucilla Tan. 2001. "A Century of Family Budgets in the 

United States." Monthly Labor Review, Vol. 124, No. 5. Bureau of Labor Statistics, Washington, 

DC. 

LeSage, J.P. & Pace, R.K. (2004), ‘Advances in Econometrics: Spatial and Spatiotemporal 

Econometrics’, Elsevier Science, Oxford. 

Roos, Michael (2006), ‘Regional Price Levels in Germany’, Applied Economics, Vol.38, Issue 

13. July. 

26 
5

10

15

20

25

30

35

40

45

50

55

Appendix Table A1. Predicted Price Levels First Stage 

Obs Area 

Name 

1 Philadelphia 

2 

3 

4 

6 

7 

8 

9 

11 

12 

13 

14 

Area 

Code 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

A102 

County 

Name 

New Castle 

Cecil 

Atlantic 

Burlington 

Camden 

Cape May 

Cumberland 

Gloucester 

Salem 

Bucks 

Chester 

Delaware 

Montgomery 

Philadelphia 

State 

DE 

MD 

NJ 

NJ 

NJ 

NJ 

NJ 

NJ 

NJ 

PA 

PA 

PA 

PA 

PA 

County 

Fips 

10003 

24015 

34001 

34005 

34007 

34009 

34011 

34015 

34033 

42017 

42029 

42045 

42091 

42101 

Input 

Plevel 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

1.005 

Predicted 

Plevel 

1.006 

0.992 

1.007 

1.025 

1.000 

0.997 

0.992 

1.003 

0.989 

1.019 

1.024 

1.003 

1.022 

0.996 

Actual 

Rent ($) 

686 

623 

695 

778 

651 

649 

622 

674 

610 

745 

770 

666 

758 

576 

Wtd Mean 

Rent* ($) 

658 

658 

658 

658 

658 

658 

658 

658 

658 

658 

658 

658 

658 

658 

Boston 

16 

17 

18 

19 

21 

22 

23 

24 

26 

A103 

A103 

A103 

A103 

A103 

A103 

A103 

A103 

A103 

A103 

A103 

A103 

York 

Bristol 

Essex 

Middlesex 

Norfolk 

Plymouth 

Suffolk 

Worcester 

Hillsborough 

Merrimack 

Rockingham 

Strafford 

ME 

MD 

MD 

MD 

MD 

MD 

MD 

MD 

NH 

NH 

NH 

NH 

23031 

25005 

25009 

25017 

25021 

25023 

25025 

25027 

33011 

33013 

33015 

33017 

1.116 

1.116 

1.116 

1.116 

1.116 

1.116 

1.116 

1.116 

1.116 

1.116 

1.116 

1.116 

1.088 

1.054 

1.089 

1.139 

1.141 

1.086 

1.151 

1.068 

1.096 

1.072 

1.101 

1.079 

677 

525 

672 

880 

890 

666 

832 

587 

706 

606 

731 

633 

755 

755 

755 

755 

755 

755 

755 

755 

755 

755 

755 

755 

27 Pittsburth 

28 

29 

31 

32 

A104 

A104 

A104 

A104 

A104 

A104 

Allegheny 

Beaver 

Butler 

Fayette 

Washington 

Westmoreland 

PA 

PA 

PA 

PA 

PA 

PA 

42003 

42007 

42019 

42051 

42125 

42129 

0.843 

0.843 

0.843 

0.843 

0.843 

0.843 

0.849 

0.835 

0.842 

0.821 

0.831 

0.831 

525 

453 

491 

376 

431 

435 

492 

492 

492 

492 

492 

492 

33 NY City 

34 

36 

37 

A109 

A109 

A109 

A109 

A109 

Bronx 

Kings 

New York 

Queens 

Richmond 

NY 

NY 

NY 

NY 

NY 

36005 

36047 

36061 

36081 

36085 

1.278 

1.278 

1.278 

1.278 

1.278 

1.227 

1.244 

1.396 

1.232 

1.202 

636 

691 

868 

794 

773 

750 

750 

750 

750 

750 

38 NY suburbs 

39 

41 

42 

43 

44 

46 

47 

A110 

A110 

A110 

A110 

A110 

A110 

A110 

A110 

A110 

A110 

Fairfield 

Litchfield 

New Haven 

Dutchess 

Nassau 

Orange 

Putnam 

Rockland 

Suffolk 

Westchester 

CT 

CT 

CT 

NY 

NY 

NY 

NY 

NY 

NY 

NY 

9001 

9005 

9009 

36027 

36059 

36071 

36079 

36087 

36103 

36119 

1.286 

1.286 

1.286 

1.286 

1.286 

1.286 

1.286 

1.286 

1.286 

1.286 

1.357 

1.241 

1.252 

1.235 

1.312 

1.237 

1.293 

1.289 

1.305 

1.278 

1157 

742 

779 

717 

991 

725 

932 

912 

971 

869 

893 

893 

893 

893 

893 

893 

893 

893 

893 

893 

48 NJ suburbs 

49 

51 

52 

53 

54 

56 

A111 

A111 

A111 

A111 

A111 

A111 

A111 

A111 

A111 

Bergen 

Essex 

Hudson 

Hunterdon 

Mercer 

Middlesex 

Monmouth 

Morris 

Ocean 

NJ 

NJ 

NJ 

NJ 

NJ 

NJ 

NJ 

NJ 

NJ 

34003 

34013 

34017 

34019 

34021 

34023 

34025 

34027 

34029 

1.140 

1.140 

1.140 

1.140 

1.140 

1.140 

1.140 

1.140 

1.140 

1.165 

1.118 

1.141 

1.160 

1.125 

1.157 

1.133 

1.166 

1.142 

901 

681 

712 

897 

748 

875 

784 

920 

824 

779 

779 

779 

779 

779 

779 

779 

779 

779 

Table A1. Page 1 of 8 
Appendix Table A1. Predicted Price Levels First Stage 

Obs Area 

Name 

57 

58 

59 

60 

61 

62 

Area 

Code 

A111 

A111 

A111 

A111 

A111 

A111 

County 

Name 

Passaic 

Somerset 

Sussex 

Union 

Warren 

Pike 

State 

NJ 

NJ 

NJ 

NJ 

NJ 

PA 

County 

Fips 

34031 

34035 

34037 

34039 

34041 

42103 

Input 

Plevel 

1.140 

1.140 

1.140 

1.140 

1.140 

1.140 

Predicted 

Plevel 

1.127 

1.169 

1.138 

1.134 

1.115 

1.117 

Actual 

Rent ($) 

752 

934 

809 

766 

714 

722 

Wtd Mean 

Rent* ($) 

779 

779 

779 

779 

779 

779 

63 Chicago 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

A207 

A207 

A207 

A207 

A207 

A207 

A207 

A207 

A207 

A207 

A207 

A207 

A207 

Cook 

DeKalb 

DuPage 

Grundy 

Kane 

Kankakee 

Kendall 

Lake 

McHenry 

Will 

Lake 

Porter 

Kenosha 

IL 

IL 

IL 

IL 

IL 

IL 

IL 

IL 

IL 

IL 

IN 

IN 

WI 

17031 

17037 

17043 

17063 

17089 

17091 

17093 

17097 

17111 

17197 

18089 

18127 

55059 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.045 

1.019 

1.082 

1.026 

1.045 

1.010 

1.048 

1.060 

1.062 

1.034 

1.014 

1.029 

1.022 

662 

578 

850 

609 

693 

536 

711 

759 

770 

646 

551 

623 

591 

669 

669 

669 

669 

669 

669 

669 

669 

669 

669 

669 

669 

669 

76 Detroit 

77 

78 

79 

80 

81 

82 

83 

84 

85 

A208 

A208 

A208 

A208 

A208 

A208 

A208 

A208 

A208 

A208 

Genesee 

Lapeer 

Lenawee 

Livingston 

Macomb 

Monroe 

Oakland 

St. Clair 

Washtenaw 

Wayne 

MI 

MI 

MI 

MI 

MI 

MI 

MI 

MI 

MI 

MI 

26049 

26087 

26091 

26093 

26099 

26115 

26125 

26147 

26161 

26163 

0.935 

0.935 

0.935 

0.935 

0.935 

0.935 

0.935 

0.935 

0.935 

0.935 

0.915 

0.924 

0.916 

0.953 

0.939 

0.925 

0.959 

0.921 

0.957 

0.923 

507 

556 

517 

698 

623 

561 

721 

538 

715 

534 

596 

596 

596 

596 

596 

596 

596 

596 

596 

596 

86 St. Louis 

87 

88 

89 

90 

91 

92 

93 

94 

95 

96 

97 

98 

A209 

A209 

A209 

A209 

A209 

A209 

A209 

A209 

A209 

A209 

A209 

A209 

A209 

Clinton 

Jersey 

Madison 

Monroe 

St. Clair 

Crawford 

Franklin 

Jefferson 

Lincoln 

St. Charles 

St. Louis 

Warren 

St. Louis City 

IL 

IL 

IL 

IL 

IL 

MO 

MO 

MO 

MO 

MO 

MO 

MO 

MO 

17027 

17083 

17119 

17133 

17163 

29055 

29071 

29099 

29113 

29183 

29189 

29219 

29510 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.866 

0.844 

0.843 

0.855 

0.867 

0.860 

0.836 

0.851 

0.858 

0.851 

0.883 

0.877 

0.847 

0.857 

433 

428 

490 

559 

516 

389 

472 

510 

471 

639 

603 

448 

451 

528 

528 

528 

528 

528 

528 

528 

528 

528 

528 

528 

528 

528 

99 Cleveland 

100 

101 

102 

103 

104 

105 

106 

A210 

A210 

A210 

A210 

A210 

A210 

A210 

A210 

Ashtabula 

Cuyahoga 

Geauga 

Lake 

Lorain 

Medina 

Portage 

Summit 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

39007 

39035 

39055 

39085 

39093 

39103 

39133 

39153 

0.887 

0.887 

0.887 

0.887 

0.887 

0.887 

0.887 

0.887 

0.871 

0.888 

0.896 

0.900 

0.881 

0.898 

0.886 

0.886 

477 

548 

608 

629 

528 

622 

555 

550 

552 

552 

552 

552 

552 

552 

552 

552 

107 Minneapolis 

108 

109 

110 

111 

112 

A211 

A211 

A211 

A211 

A211 

A211 

Anoka 

Carver 

Chisago 

Dakota 

Hennepin 

Isanti 

MN 

MN 

MN 

MN 

MN 

MN 

27003 

27019 

27025 

27037 

27053 

27059 

0.993 

0.993 

0.993 

0.993 

0.993 

0.993 

0.992 

0.991 

0.962 

1.013 

0.996 

0.960 

657 

656 

515 

754 

668 

509 

655 

655 

655 

655 

655 

655 

Table A1. Page 2 of 8 
Appendix Table A1. Predicted Price Levels First Stage 

Obs Area 

Name 

113 

114 

115 

116 

117 

118 

119 

Area 

Code 

A211 

A211 

A211 

A211 

A211 

A211 

A211 

County 

Name 

Ramsey 

Scott 

Sherburne 

Washington 

Wright 

Pierce 

St. Croix 

State 

MN 

MN 

MN 

MN 

MN 

WI 

WI 

County 

Fips 

27123 

27139 

27141 

27163 

27171 

55093 

55109 

Input 

Plevel 

0.993 

0.993 

0.993 

0.993 

0.993 

0.993 

0.993 

Predicted 

Plevel 

0.986 

0.994 

0.973 

1.001 

0.963 

0.966 

0.973 

Actual 

Rent ($) 

615 

667 

568 

701 

521 

538 

571 

Wtd Mean 

Rent* ($) 

655 

655 

655 

655 

655 

655 

655 

120 Milwaukee 

121 

122 

123 

124 

A212 

A212 

A212 

A212 

A212 

Milwaukee 

Ozaukee 

Racine 

Washington 

Waukesha 

WI 

WI 

WI 

WI 

WI 

55079 

55089 

55101 

55131 

55133 

0.908 

0.908 

0.908 

0.908 

0.908 

0.904 

0.918 

0.898 

0.913 

0.931 

555 

651 

548 

627 

718 

578 

578 

578 

578 

578 

125 Cincinnati 

126 

127 

128 

129 

130 

131 

132 

133 

134 

135 

136 

137 

A213 

A213 

A213 

A213 

A213 

A213 

A213 

A213 

A213 

A213 

A213 

A213 

A213 

Dearborn 

Ohio 

Boone 

Campbell 

Gallatin 

Grant 

Kenton 

Pendleton 

Brown 

Butler 

Clermont 

Hamilton 

Warren 

IN 

IN 

KY 

KY 

KY 

KY 

KY 

KY 

OH 

OH 

OH 

OH 

OH 

18029 

18115 

21015 

21037 

21077 

21081 

21117 

21191 

39015 

39017 

39025 

39061 

39165 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.874 

0.870 

0.863 

0.889 

0.872 

0.853 

0.871 

0.873 

0.853 

0.858 

0.882 

0.880 

0.871 

0.888 

509 

469 

607 

515 

416 

516 

520 

416 

442 

567 

558 

498 

605 

521 

521 

521 

521 

521 

521 

521 

521 

521 

521 

521 

521 

521 

138 Kansas City 

139 

140 

141 

142 

143 

144 

145 

146 

147 

148 

A214 

A214 

A214 

A214 

A214 

A214 

A214 

A214 

A214 

A214 

A214 

Johnson 

Leavenworth 

Miami 

Wyandotte 

Cass 

Clay 

Clinton 

Jackson 

Lafayette 

Platte 

Ray 

KS 

KS 

KS 

KS 

MO 

MO 

MO 

MO 

MO 

MO 

MO 

20091 

20103 

20121 

20209 

29037 

29047 

29049 

29095 

29107 

29165 

29177 

0.860 

0.860 

0.860 

0.860 

0.860 

0.860 

0.860 

0.860 

0.860 

0.860 

0.860 

0.885 

0.857 

0.842 

0.845 

0.847 

0.861 

0.833 

0.853 

0.829 

0.873 

0.834 

716 

567 

484 

496 

515 

589 

434 

538 

416 

652 

443 

576 

576 

576 

576 

576 

576 

576 

576 

576 

576 

576 

149 DC 

150 

151 

152 

153 

154 

155 

156 

157 

158 

159 

160 

161 

162 

163 

164 

165 

166 

167 

168 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

A312 

District of Columbia 

Calvert 

Charles 

Frederick 

Montgomery 

Prince George's 

Washington 

Arlington 

Clarke 

Culpeper 

Fairfax 

Fauquier 

King George 

Loudoun 

Prince William 

Spotsylvania 

Stafford 

Warren 

Alexandria City 

Fairfax City 

DC 

MD 

MD 

MD 

MD 

MD 

MD 

VA 

VA 

VA 

VA 

VA 

VA 

VA 

VA 

VA 

VA 

VA 

VA 

VA 

11001 

24009 

24017 

24021 

24031 

24033 

24043 

51013 

51043 

51047 

51059 

51061 

51099 

51107 

51153 

51177 

51179 

51187 

51510 

51600 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

1.031 

1.046 

1.054 

1.032 

1.078 

1.037 

0.978 

1.098 

1.006 

0.998 

1.100 

1.034 

1.008 

1.088 

1.060 

1.049 

1.059 

0.988 

1.089 

1.090 

646 

804 

838 

740 

934 

756 

489 

946 

620 

586 

1027 

748 

631 

988 

863 

815 

861 

539 

880 

976 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

806 

Table A1. Page 3 of 8 
Appendix Table A1. Predicted Price Levels First Stage 

Obs Area 

Name 

169 

170 

171 

172 

173 

174 

Area 

Code 

A312 

A312 

A312 

A312 

A312 

A312 

County 

Name 

Falls Church City 

Fredericksburg City 

Manassas City 

Manassas Park City 

Berkeley 

Jefferson 

State 

VA 

VA 

VA 

VA 

WV 

WV 

County 

Fips 

51610 

51630 

51683 

51685 

54003 

54037 

Input 

Plevel 

1.058 

1.058 

1.058 

1.058 

1.058 

1.058 

Predicted 

Plevel 

1.098 

1.020 

1.055 

1.078 

0.982 

0.984 

Actual 

Rent ($) 

991 

663 

826 

931 

507 

517 

Wtd Mean 

Rent* ($) 

806 

806 

806 

806 

806 

806 

175 Baltimore 

176 

177 

178 

179 

180 

181 

A313 

A313 

A313 

A313 

A313 

A313 

A313 

Anne Arundel 

Baltimore 

Carroll 

Harford 

Howard 

Queen Anne's 

Baltimore City 

MD 

MD 

MD 

MD 

MD 

MD 

MD 

24003 

24005 

24013 

24025 

24027 

24035 

24510 

0.966 

0.966 

0.966 

0.966 

0.966 

0.966 

0.966 

0.999 

0.969 

0.961 

0.965 

1.016 

0.963 

0.945 

817 

672 

642 

658 

895 

649 

506 

629 

629 

629 

629 

629 

629 

629 

182 Dallas 

183 

184 

185 

186 

187 

188 

189 

190 

191 

192 

193 

A316 

A316 

A316 

A316 

A316 

A316 

A316 

A316 

A316 

A316 

A316 

A316 

Collin 

Dallas 

Denton 

Ellis 

Henderson 

Hood 

Hunt 

Johnson 

Kaufman 

Parker 

Rockwall 

Tarrant 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

48085 

48113 

48121 

48139 

48213 

48221 

48231 

48251 

48257 

48367 

48397 

48439 

0.971 

0.971 

0.971 

0.971 

0.971 

0.971 

0.971 

0.971 

0.971 

0.971 

0.971 

0.971 

1.003 

0.971 

0.985 

0.956 

0.927 

0.945 

0.931 

0.945 

0.943 

0.946 

0.986 

0.963 

823 

656 

739 

603 

463 

552 

480 

550 

541 

554 

747 

629 

659 

659 

659 

659 

659 

659 

659 

659 

659 

659 

659 

659 

194 Houston 

195 

196 

197 

198 

199 

200 

201 

A318 

A318 

A318 

A318 

A318 

A318 

A318 

A318 

Brazoria 

Chambers 

Fort Bend 

Galveston 

Harris 

Liberty 

Montgomery 

Waller 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

TX 

48039 

48071 

48157 

48167 

48201 

48291 

48339 

48473 

0.951 

0.951 

0.951 

0.951 

0.951 

0.951 

0.951 

0.951 

0.938 

0.928 

0.979 

0.947 

0.951 

0.918 

0.953 

0.926 

546 

498 

748 

589 

600 

449 

623 

488 

600 

600 

600 

600 

600 

600 

600 

600 

202 Atlanta 

203 

204 

205 

206 

207 

208 

209 

210 

211 

212 

213 

214 

215 

216 

217 

218 

219 

220 

221 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

A319 

Barrow 

Bartow 

Carroll 

Cherokee 

Clayton 

Cobb 

Coweta 

DeKalb 

Douglas 

Fayette 

Forsyth 

Fulton 

Gwinnett 

Henry 

Newton 

Paulding 

Pickens 

Rockdale 

Spalding 

Walton 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

GA 

13013 

13015 

13045 

13057 

13063 

13067 

13077 

13089 

13097 

13113 

13117 

13121 

13135 

13151 

13217 

13223 

13227 

13247 

13255 

13297 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.944 

0.909 

0.909 

0.891 

0.943 

0.933 

0.957 

0.918 

0.949 

0.941 

0.974 

0.931 

0.941 

0.959 

0.941 

0.910 

0.923 

0.888 

0.947 

0.897 

0.904 

590 

588 

498 

758 

700 

820 

636 

774 

748 

911 

700 

736 

834 

751 

594 

660 

480 

777 

528 

564 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

749 

222 Miami 

223 

A320 

A320 

Broward 

Miami-Dade 

FL 

FL 

12011 

12086 

1.017 

1.017 

1.031 

1.009 

765 

664 

701 

701 

224 Tampa A321 Hernando FL 12053 0.920 0.906 561 617 

Table A1. Page 4 of 8 
Appendix Table A1. Predicted Price Levels First Stage 

Obs Area Area 

Name Code 

225 A321 

226 A321 

227 A321 

County State 

Name 

Hillsborough FL 

Pasco FL 

Pinellas FL 

County 

Fips 

12057 

12101 

12103 

Input 

Plevel 

0.920 

0.920 

0.920 

Predicted 

Plevel 

0.922 

0.899 

0.921 

Actual 

Rent ($) 

636 

522 

620 

Wtd Mean 

Rent* ($) 

617 

617 

617 

228 Los Angeles A419 Los Angeles CA 6037 1.197 1.197 721 721 

229 Greater LA A420 

230 A420 

231 A420 

232 A420 

Orange CA 

Riverside CA 

San Bernardino CA 

Ventura CA 

6059 

6065 

6071 

6111 

1.068 

1.068 

1.068 

1.068 

1.101 

1.033 

1.030 

1.090 

947 

669 

654 

919 

804 

804 

804 

804 

233 San Francisco A422 

234 A422 

235 A422 

236 A422 

237 A422 

238 A422 

239 A422 

240 A422 

241 A422 

242 A422 

Alameda CA 

Contra Costa CA 

Marin CA 

Napa CA 

San Francisco CA 

San Mateo CA 

Santa Clara CA 

Santa Cruz CA 

Solano CA 

Sonoma CA 

6001 

6013 

6041 

6055 

6075 

6081 

6085 

6087 

6095 

6097 

1.343 

1.343 

1.343 

1.343 

1.343 

1.343 

1.343 

1.343 

1.343 

1.343 

1.295 

1.307 

1.386 

1.277 

1.378 

1.383 

1.390 

1.320 

1.272 

1.291 

884 

935 

1208 

830 

1021 

1194 

1219 

982 

811 

881 

1017 

1017 

1017 

1017 

1017 

1017 

1017 

1017 

1017 

1017 

243 Seattle A423 

244 A423 

245 A423 

246 A423 

247 A423 

248 A423 

Island WA 

King WA 

Kitsap WA 

Pierce WA 

Snohomish WA 

Thurston WA 

53029 

53033 

53035 

53053 

53061 

53067 

1.054 

1.054 

1.054 

1.054 

1.054 

1.054 

1.044 

1.064 

1.037 

1.028 

1.062 

1.035 

697 

781 

665 

626 

778 

658 

735 

735 

735 

735 

735 

735 

249 San Diego A424 San Diego CA 6073 1.144 1.144 783 783 

250 Portland A425 

251 A425 

252 A425 

253 A425 

254 A425 

255 A425 

256 A425 

257 A425 

Clackamas OR 

Columbia OR 

Marion OR 

Multnomah OR 

Polk OR 

Washington OR 

Yamhill OR 

Clark WA 

41005 

41009 

41047 

41051 

41053 

41067 

41071 

53011 

0.977 

0.977 

0.977 

0.977 

0.977 

0.977 

0.977 

0.977 

0.987 

0.964 

0.958 

0.973 

0.953 

0.991 

0.969 

0.983 

716 

608 

578 

642 

557 

732 

631 

695 

665 

665 

665 

665 

665 

665 

665 

665 

258 Honolulu A426 Honolulu HI 15003 1.379 1.379 846 846 

259 Anchorage A427 Anchorage Municipality AK 2020 1.059 1.059 752 752 

260 Phoenix A429 

261 A429 

Maricopa AZ 

Pinal AZ 

4013 

4021 

0.929 

0.929 

0.930 

0.898 

677 

514 

672 

672 

262 Denver A433 

263 A433 

264 A433 

265 A433 

266 A433 

267 A433 

268 A433 

Adams CO 

Arapahoe CO 

Boulder CO 

Denver CO 

Douglas CO 

Jefferson CO 

Weld CO 

8001 

8005 

8013 

8031 

8035 

8059 

8123 

1.001 

1.001 

1.001 

1.001 

1.001 

1.001 

1.001 

0.994 

1.003 

1.028 

0.989 

1.075 

1.009 

0.966 

706 

747 

861 

652 

1072 

772 

572 

720 

720 

720 

720 

720 

720 

720 

269 MW Cs D200 

270 D200 

271 D200 

272 D200 

273 D200 

274 D200 

275 D200 

Jefferson IL 

Allen KS 

Neosho KS 

Rice MN 

Brookings SD 

Lake SD 

Moody SD 

17081 

20001 

20133 

27131 

46011 

46079 

46101 

0.797 

0.797 

0.797 

0.797 

0.797 

0.797 

0.797 

0.795 

0.787 

0.787 

0.815 

0.793 

0.790 

0.792 

400 

353 

351 

515 

389 

372 

379 

408 

408 

408 

408 

408 

408 

408 

276 South Cs D300 

277 D300 

278 D300 

279 D300 

280 D300 

DeSoto FL 

Hardee FL 

Bulloch GA 

Burke GA 

Jenkins GA 

12027 

12049 

13031 

13033 

13165 

0.796 

0.796 

0.796 

0.796 

0.796 

0.801 

0.799 

0.801 

0.779 

0.781 

457 

444 

452 

324 

335 

423 

423 

423 

423 

423 

Table A1. Page 5 of 8 
Appendix Table A1. Predicted Price Levels First Stage 

Obs Area 

Name 

281 

282 

283 

284 

Area 

Code 

D300 

D300 

D300 

D300 

County 

Name 

Screven 

Pearl River 

Hamblen 

Jefferson 

State 

GA 

MS 

TN 

TN 

County 

Fips 

13251 

28109 

47063 

47089 

Input 

Plevel 

0.796 

0.796 

0.796 

0.796 

Predicted 

Plevel 

0.779 

0.794 

0.795 

0.797 

Actual 

Rent ($) 

323 

412 

418 

429 

Wtd Mean 

Rent* ($) 

423 

423 

423 

423 

285 West Cs 

286 

D400 

D400 

Deschutes 

Whitman 

OR 

WA 

41017 

53075 

0.879 

0.879 

0.890 

0.862 

641 

492 

576 

576 

287 NE Bs 

288 

289 

290 

291 

292 

293 

294 

295 

296 

297 

298 

299 

300 

301 

302 

303 

304 

305 

306 

307 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

X100 

Hartford 

Middlesex 

New London 

Tolland 

Windham 

Franklin 

Hampden 

Hampshire 

Cayuga 

Erie 

Madison 

Niagara 

Onondaga 

Oswego 

Berks 

Cambria 

Mercer 

Somerset 

Chittenden 

Franklin 

Grand Isle 

CT 

CT 

CT 

CT 

CT 

MA 

MA 

MA 

NY 

NY 

NY 

NY 

NY 

NY 

PA 

PA 

PA 

PA 

VT 

VT 

VT 

9003 

9007 

9011 

9013 

9015 

25011 

25013 

25015 

36011 

36029 

36053 

36063 

36067 

36075 

42011 

42021 

42085 

42111 

50007 

50011 

50013 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.920 

0.955 

0.947 

0.943 

0.943 

0.922 

0.952 

0.915 

0.939 

0.907 

0.913 

0.910 

0.905 

0.919 

0.910 

0.916 

0.881 

0.899 

0.884 

0.943 

0.920 

0.920 

728 

691 

674 

670 

566 

718 

531 

653 

489 

520 

505 

481 

551 

507 

538 

357 

448 

371 

674 

556 

557 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

551 

308 MW Bs 

309 

310 

311 

312 

313 

314 

315 

316 

317 

318 

319 

320 

321 

322 

323 

324 

325 

326 

327 

328 

329 

330 

331 

332 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

X200 

Macon 

Elkhart 

Posey 

Vanderburgh 

Warrick 

Henderson 

Bay 

Midland 

Saginaw 

Lancaster 

Clark 

Columbiana 

Delaware 

Fairfield 

Franklin 

Greene 

Licking 

Madison 

Mahoning 

Miami 

Montgomery 

Pickaway 

Trumbull 

Dane 

Marathon 

IL 

IN 

IN 

IN 

IN 

KY 

MI 

MI 

MI 

NE 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

OH 

WI 

WI 

17115 

18039 

18129 

18163 

18173 

21101 

26017 

26111 

26145 

31109 

39023 

39029 

39041 

39045 

39049 

39057 

39089 

39097 

39099 

39109 

39113 

39129 

39155 

55025 

55073 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.851 

0.831 

0.848 

0.827 

0.834 

0.837 

0.825 

0.829 

0.841 

0.838 

0.844 

0.839 

0.828 

0.867 

0.850 

0.861 

0.859 

0.842 

0.844 

0.833 

0.846 

0.847 

0.839 

0.835 

0.869 

0.839 

449 

542 

426 

459 

482 

416 

436 

505 

485 

515 

491 

431 

646 

552 

595 

600 

510 

520 

458 

529 

532 

494 

470 

656 

495 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

547 

333 South Bs 

334 

335 

336 

X300 

X300 

X300 

X300 

Blount 

Colbert 

Jefferson 

Lauderdale 

AL 

AL 

AL 

AL 

1009 

1033 

1073 

1077 

0.866 

0.866 

0.866 

0.866 

0.834 

0.837 

0.857 

0.840 

390 

412 

515 

428 

557 

557 

557 

557 

Table A1. Page 6 of 8 
Appendix Table A1. Predicted Price Levels First Stage 

Obs Area Area County State County Input Predicted Actual Wtd Mean 

Name Code Name Fips Plevel Plevel Rent ($) Rent* ($) 

337 X300 St. Clair AL 1115 0.866 0.852 493 557 

338 X300 Shelby AL 1117 0.866 0.883 659 557 

339 X300 Jefferson AR 5069 0.866 0.847 464 557 

340 X300 Alachua FL 12001 0.866 0.867 569 557 

341 X300 Brevard FL 12009 0.866 0.874 608 557 

342 X300 Lee FL 12071 0.866 0.883 655 557 

343 X300 Marion FL 12083 0.866 0.857 518 557 

344 X300 Catoosa GA 13047 0.866 0.852 489 557 

345 X300 Dade GA 13083 0.866 0.837 410 557 

346 X300 Dougherty GA 13095 0.866 0.850 480 557 

347 X300 Lee GA 13177 0.866 0.868 581 557 

348 X300 Walker GA 13295 0.866 0.843 442 557 

349 X300 Acadia LA 22001 0.866 0.823 333 557 

350 X300 Ascension LA 22005 0.866 0.846 459 557 

351 X300 East Baton Rouge LA 22033 0.866 0.859 524 557 

352 X300 Lafayette LA 22055 0.866 0.852 489 557 

353 X300 Livingston LA 22063 0.866 0.852 490 557 

354 X300 St. Landry LA 22097 0.866 0.821 317 557 

355 X300 St. Martin LA 22099 0.866 0.827 352 557 

356 X300 West Baton Rouge LA 22121 0.866 0.843 445 557 

357 X300 Chatham NC 37037 0.866 0.865 561 557 

358 X300 Currituck NC 37053 0.866 0.870 587 557 

359 X300 Durham NC 37063 0.866 0.885 665 557 

360 X300 Franklin NC 37069 0.866 0.853 496 557 

361 X300 Johnston NC 37101 0.866 0.852 492 557 

362 X300 Orange NC 37135 0.866 0.889 690 557 

363 X300 Wake NC 37183 0.866 0.901 750 557 

364 X300 Canadian OK 40017 0.866 0.858 523 557 

365 X300 Cleveland OK 40027 0.866 0.861 538 557 

366 X300 Logan OK 40083 0.866 0.837 408 557 

367 X300 McClain OK 40087 0.866 0.842 439 557 

368 X300 Oklahoma OK 40109 0.866 0.852 488 557 

369 X300 Pottawatomie OK 40125 0.866 0.842 438 557 

370 X300 Anderson SC 45007 0.866 0.847 465 557 

371 X300 Cherokee SC 45021 0.866 0.836 405 557 

372 X300 Florence SC 45041 0.866 0.845 453 557 

373 X300 Greenville SC 45045 0.866 0.866 566 557 

374 X300 Pickens SC 45077 0.866 0.854 500 557 

375 X300 Spartanburg SC 45083 0.866 0.852 492 557 

376 X300 Hamilton TN 47065 0.866 0.858 520 557 

377 X300 Marion TN 47115 0.866 0.840 426 557 

378 X300 Bexar TX 48029 0.866 0.869 576 557 

379 X300 Cameron TX 48061 0.866 0.839 420 557 

380 X300 Comal TX 48091 0.866 0.878 633 557 

381 X300 Ector TX 48135 0.866 0.838 417 557 

382 X300 Guadalupe TX 48187 0.866 0.857 519 557 

383 X300 Hardin TX 48199 0.866 0.851 488 557 

384 X300 Jefferson TX 48245 0.866 0.851 486 557 

385 X300 Midland TX 48329 0.866 0.848 470 557 

386 X300 Orange TX 48361 0.866 0.851 487 557 

387 X300 Potter TX 48375 0.866 0.845 454 557 

388 X300 Randall TX 48381 0.866 0.857 519 557 

389 X300 Wilson TX 48493 0.866 0.842 436 557 

390 X300 Charles City VA 51036 0.866 0.839 422 557 

391 X300 Chesterfield VA 51041 0.866 0.894 713 557 

392 X300 Dinwiddie VA 51053 0.866 0.866 569 557 

Table A1. Page 7 of 8 
Appendix Table A1. Predicted Price Levels First Stage 

Obs Area Area County State County Input Predicted Actual Wtd Mean 

Name Code Name Fips Plevel Plevel Rent ($) Rent* ($) 

393 X300 Gloucester VA 51073 0.866 0.862 547 557 

394 X300 Goochland VA 51075 0.866 0.876 622 557 

395 X300 Hanover VA 51085 0.866 0.892 705 557 

396 X300 Henrico VA 51087 0.866 0.889 685 557 

397 X300 Isle of Wight VA 51093 0.866 0.855 507 557 

398 X300 James City VA 51095 0.866 0.887 676 557 

399 X300 Mathews VA 51115 0.866 0.853 498 557 

400 X300 New Kent VA 51127 0.866 0.870 587 557 

401 X300 Powhatan VA 51145 0.866 0.881 650 557 

402 X300 Prince George VA 51149 0.866 0.877 627 557 

403 X300 York VA 51199 0.866 0.900 745 557 

404 X300 Chesapeake City VA 51550 0.866 0.883 657 557 

405 X300 Colonial Heights City VA 51570 0.866 0.882 640 557 

406 X300 Hampton City VA 51650 0.866 0.878 616 557 

407 X300 Hopewell City VA 51670 0.866 0.859 516 557 

408 X300 Newport News City VA 51700 0.866 0.871 576 557 

409 X300 Norfolk City VA 51710 0.866 0.870 554 557 

410 X300 Petersburg City VA 51730 0.866 0.855 499 557 

411 X300 Poquoson City VA 51735 0.866 0.907 785 557 

412 X300 Portsmouth City VA 51740 0.866 0.867 556 557 

413 X300 Richmond City VA 51760 0.866 0.870 559 557 

414 X300 Suffolk City VA 51800 0.866 0.855 509 557 

415 X300 Virginia Beach City VA 51810 0.866 0.901 747 557 

416 X300 Williamsburg City VA 51830 0.866 0.881 637 557 

417 West Bs X499 Mohave AZ 4015 0.876 0.857 563 661 

418 X499 Yuma AZ 4027 0.876 0.852 536 661 

419 X499 Butte CA 6007 0.876 0.858 566 661 

420 X499 Stanislaus CA 6099 0.876 0.868 620 661 

421 X499 Ada ID 16001 0.876 0.868 622 661 

422 X499 Canyon ID 16027 0.876 0.849 516 661 

423 X499 Clark NV 32003 0.876 0.889 732 661 

424 X499 Nye NV 32023 0.876 0.853 542 661 

425 X499 Utah VT 49049 0.876 0.865 604 661 

* Weighted mean rent by Area 

Table A1. Page 8 of 8 
Appendix Table A2. Rent Ratios and Bridged Price Levels 

State Rent* Rent* Ratio Price Bridged 

Census Overlap Census/Overlap Level* Level 

($) ($) Overlap Census 

(1) (2) (3)=(1)/(2) (4) (5) = (3)*(4) 

1 Alabama 455 510 0.89 0.86 0.76 

2 Alaska 746 752 0.99 1.06 1.05 

3 Arizona 615 662 0.93 0.92 0.86 

4 Arkansas 465 464 1.00 0.85 0.85 

5 California 753 811 0.93 1.19 1.11 

6 Colorado 665 720 0.92 1.00 0.92 

7 Connecticut 687 776 0.89 1.08 0.95 

8 Delaware 610 686 0.89 1.01 0.90 

9 District of Columb 646 646 1.00 1.03 1.03 

10 Florida 646 656 0.99 0.96 0.95 

11 Georgia 548 723 0.76 0.94 0.71 

12 Hawaii 787 846 0.93 1.38 1.28 

13 Idaho 497 594 0.84 0.86 0.72 

14 Illinois 585 662 0.88 1.03 0.91 

15 Indiana 530 531 1.00 0.94 0.93 

16 Iowa 484 

17 Kansas 490 617 0.80 0.87 0.69 

18 Kentucky 454 515 0.88 0.87 0.77 

19 Louisiana 477 479 1.00 0.85 0.85 

20 Maine 504 677 0.74 1.09 0.81 

21 Maryland 668 700 0.95 1.00 0.96 

22 Massachusetts 696 738 0.94 1.10 1.03 

23 Michigan 540 588 0.92 0.93 0.85 

24 Minnesota 543 655 0.83 0.99 0.82 

25 Mississippi 460 412 1.11 0.79 0.88 

26 Missouri 468 540 0.87 0.86 0.75 

27 Montana 458 

28 Nebraska 499 515 0.97 0.84 0.82 

29 Nevada 704 729 0.97 0.89 0.86 

30 New Hampshire 625 698 0.90 1.09 0.98 

31 New Jersey 747 762 0.98 1.12 1.09 

32 New Mexico 521 

33 New York 666 743 0.90 1.24 1.11 

34 North Carolina 563 690 0.82 0.89 0.73 

35 North Dakota 417 

36 Ohio 505 545 0.93 0.87 0.81 

37 Oklahoma 465 494 0.94 0.85 0.80 

38 Oregon 601 659 0.91 0.97 0.89 

39 Pennsylvania 514 573 0.90 0.94 0.84 

40 Rhode Island 560 

41 South Carolina 540 510 1.06 0.86 0.91 

42 South Dakota 433 385 1.12 0.79 0.89 

43 Tennessee 527 497 1.06 0.85 0.90 

44 Texas 571 611 0.93 0.94 0.88 

45 Utah 603 604 1.00 0.86 0.86 

46 Vermont 553 657 0.84 0.94 0.79 

47 Virginia 619 741 0.84 0.96 0.81 

48 Washington 640 727 0.88 1.04 0.92 

49 West Virginia 407 510 0.80 0.98 0.78 

50 Wisconsin 523 591 0.88 0.90 0.80 

51 Wyoming 446 

52 Puerto Rico 318 

* Weighted geometric mean.

 Overlap denotes counties in CPI and Census, Census denotes counties only in Census. 

Table A2. Page 1 of 1 
Appendix Table A3. SPIs using different models and weight matrices 

State Freq Rent PL 38 Plevel SERR SLAG OLS SERR 

Input N1 N3 N5 N7 N9 N11 DUMS UNCON 

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 

1 Alabama 67 0.81 0.90 0.87 0.92 0.90 0.90 0.91 0.92 0.92 0.92 0.92 0.92 0.89 0.89 

2 Alaska 27 1.32 1.09 1.16 1.10 1.13 1.13 1.12 1.11 1.10 1.10 1.10 1.11 1.14 1.14 

3 Arizona 15 1.11 0.96 0.99 0.98 1.00 1.00 0.99 0.99 0.98 0.98 0.98 0.99 1.00 1.01 

4 Arkansas 75 0.80 0.90 0.93 0.93 0.90 0.90 0.92 0.92 0.93 0.93 0.93 0.92 0.89 0.89 

5 California 58 1.36 1.23 1.29 1.22 1.25 1.25 1.23 1.22 1.22 1.22 1.22 1.22 1.23 1.24 

6 Colorado 63 1.20 1.03 1.07 1.05 1.07 1.07 1.06 1.05 1.05 1.05 1.05 1.05 1.07 1.08 

7 Connecticut 8 1.24 1.14 1.07 1.04 1.06 1.06 1.05 1.04 1.04 1.04 1.04 1.04 1.04 1.04 

8 Delaware 3 1.14 1.04 1.07 1.05 1.06 1.06 1.05 1.05 1.05 1.05 1.05 1.05 1.03 1.03 

9 District of Columbia 1 1.14 1.09 1.13 1.10 1.12 1.12 1.11 1.10 1.10 1.10 1.11 1.11 1.10 1.11 

10 Florida 67 1.14 0.99 1.05 1.03 1.04 1.04 1.03 1.03 1.02 1.03 1.03 1.03 1.00 1.00 

11 Georgia 159 1.08 0.97 0.92 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.96 0.96 

12 Hawaii 5 1.44 1.43 1.49 1.35 1.39 1.39 1.37 1.36 1.35 1.36 1.36 1.36 1.37 1.38 

13 Idaho 44 0.90 0.91 0.85 0.93 0.92 0.92 0.93 0.93 0.93 0.93 0.93 0.93 0.98 0.98 

14 Illinois 102 1.07 1.07 1.10 1.06 1.07 1.07 1.06 1.06 1.06 1.06 1.06 1.06 1.05 1.05 

15 Indiana 92 0.93 0.99 1.03 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.95 0.93 

16 Iowa 99 0.83 0.83 0.94 0.91 0.91 0.93 0.93 0.94 0.93 0.93 0.93 0.91 0.88 

17 Kansas 105 0.88 0.89 0.81 0.93 0.92 0.92 0.92 0.93 0.93 0.93 0.93 0.93 0.91 0.89 

18 Kentucky 120 0.79 0.90 0.85 0.92 0.91 0.91 0.92 0.92 0.92 0.92 0.92 0.92 0.89 0.90 

19 Louisiana 64 0.83 0.90 0.93 0.93 0.92 0.92 0.93 0.93 0.93 0.93 0.93 0.93 0.90 0.90 

20 Maine 16 0.89 1.15 0.91 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.95 1.00 1.01 

21 Maryland 24 1.21 1.04 1.10 1.07 1.08 1.08 1.07 1.07 1.07 1.07 1.07 1.07 1.06 1.06 

22 Massachusetts 14 1.26 1.13 1.19 1.15 1.17 1.17 1.16 1.15 1.15 1.15 1.15 1.15 1.15 1.16 

23 Michigan 83 0.98 0.96 0.99 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.96 0.95 

24 Minnesota 87 1.00 1.02 1.02 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.00 0.99 

25 Mississippi 82 0.79 0.82 0.97 0.93 0.89 0.89 0.92 0.92 0.93 0.92 0.92 0.92 0.89 0.89 

26 Missouri 115 0.85 0.89 0.89 0.92 0.91 0.91 0.91 0.92 0.92 0.92 0.92 0.92 0.91 0.89 

27 Montana 56 0.80 0.90 0.93 0.91 0.91 0.92 0.92 0.93 0.93 0.92 0.92 1.01 1.01 

28 Nebraska 93 0.86 0.88 0.90 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.91 0.89 

29 Nevada 17 1.26 0.91 0.97 0.97 0.99 0.99 0.98 0.97 0.97 0.97 0.97 0.97 0.99 0.99 

30 New Hampshire 10 1.14 1.15 1.16 1.11 1.12 1.12 1.12 1.11 1.11 1.11 1.11 1.11 1.12 1.13 

31 New Jersey 21 1.35 1.15 1.23 1.20 1.22 1.22 1.20 1.20 1.20 1.20 1.20 1.20 1.19 1.20 

32 New Mexico 33 0.91 0.90 0.96 0.95 0.95 0.96 0.96 0.96 0.96 0.96 0.96 1.04 1.04 

33 New York 62 1.24 1.28 1.33 1.25 1.27 1.27 1.26 1.25 1.25 1.25 1.25 1.25 1.26 1.27 

34 North Carolina 100 0.99 0.90 0.83 0.97 0.96 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.93 0.93 

35 North Dakota 53 0.71 0.83 0.90 0.89 0.89 0.89 0.90 0.90 0.90 0.90 0.90 0.89 0.85 

36 Ohio 88 0.92 0.90 0.94 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.92 0.92 

37 Oklahoma 77 0.81 0.90 0.90 0.92 0.91 0.91 0.91 0.92 0.92 0.92 0.92 0.92 0.89 0.90 

38 Oregon 36 1.09 1.01 1.03 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.02 1.04 1.05 

Table A3. Page 1 of 2 
Appendix Table A3. SPIs using different models and weight matrices 

State Freq Rent PL 38 Plevel SERR SLAG OLS SERR 

Input N1 N3 N5 N7 N9 N11 DUMS UNCON 

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) 

39 Pennsylvania 67 0.95 0.97 0.99 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98 0.98 1.00 1.01 

40 Rhode Island 5 0.99 1.04 0.98 1.02 1.02 0.99 0.99 0.98 0.98 0.98 0.98 1.03 1.05 

41 South Carolina 46 0.92 0.90 0.98 0.95 0.94 0.94 0.95 0.95 0.95 0.95 0.95 0.95 0.92 0.92 

42 South Dakota 66 0.74 0.82 0.97 0.91 0.89 0.89 0.90 0.91 0.91 0.91 0.91 0.91 0.89 0.85 

43 Tennessee 95 0.91 0.88 0.98 0.96 0.95 0.95 0.95 0.96 0.96 0.95 0.95 0.95 0.92 0.92 

44 Texas 254 1.02 0.98 1.01 0.99 1.00 1.00 1.00 0.99 0.99 0.99 0.99 0.99 0.97 0.98 

45 Utah 29 1.06 0.91 0.95 0.99 1.00 1.00 1.00 0.99 0.99 0.99 0.99 0.99 1.05 1.05 

46 Vermont 14 1.00 0.95 0.92 0.98 0.97 0.97 0.98 0.98 0.98 0.98 0.98 0.98 1.01 1.02 

47 Virginia 135 1.16 0.98 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 1.01 0.99 1.00 

48 Washington 39 1.18 1.08 1.11 1.07 1.09 1.09 1.08 1.07 1.07 1.07 1.07 1.07 1.09 1.10 

49 West Virginia 55 0.72 1.09 0.88 0.91 0.87 0.87 0.90 0.91 0.91 0.91 0.91 0.91 0.88 0.88 

50 Wisconsin 72 0.95 0.93 0.94 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.96 0.96 0.94 0.93 

51 Wyoming 23 0.79 0.90 0.92 0.90 0.90 0.91 0.92 0.92 0.92 0.92 0.92 1.01 1.01 

52 Puerto Rico 78 0.55 0.89 0.87 0.82 0.82 0.85 0.86 0.87 0.87 0.87 0.87 0.84 0.86 

sum 3219 mean 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 

max 254 1.44 1.43 1.49 1.35 1.39 1.39 1.37 1.36 1.35 1.36 1.36 1.36 1.37 1.38 

min 1 0.55 0.82 0.81 0.87 0.82 0.82 0.85 0.86 0.87 0.87 0.87 0.87 0.84 0.85 

range 253 0.89 0.60 0.68 0.49 0.57 0.57 0.52 0.50 0.49 0.49 0.49 0.49 0.53 0.53 

stdev 46.4 0.20 0.13 0.14 0.10 0.11 0.11 0.10 0.10 0.10 0.10 0.10 0.10 0.11 0.11 

cv 1.4% 20% 13% 14% 10% 11% 11% 10% 10% 10% 10% 10% 10% 11% 11% 

Table A3. Page 2 of 2