Title Page
 Table of Contents
 List of Figures
 List of Tables
 Supply and demand
 Review of the literature
 The model
 Factors affecting prices
 Results of adjusting for infla...
 Building the model
 Validity of the model
 Testing in the local market
 Working with the model
 Appendix: Business cycle index
 Biographical sketch

Title: Seasonal fluctuations in the price of existing single family houses
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00097441/00001
 Material Information
Title: Seasonal fluctuations in the price of existing single family houses
Physical Description: xi, 94 leaves : ; 28 cm.
Language: English
Creator: McGurn, Kenneth R ( Kenneth Randol )
Publication Date: 1981
Copyright Date: 1981
Subject: Housing -- Prices   ( lcsh )
Finance, Insurance, and Real Estate thesis Ph. D
Dissertations, Academic -- Finance, Insurance, and Real Estate -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis (Ph. D.)--University of Florida, 1981.
Bibliography: Bibliography: leaf 93.
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Kenneth R. McGurn.
 Record Information
Bibliographic ID: UF00097441
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000297456
oclc - 08401626
notis - ABS3830


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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
    List of Figures
        Page vi
    List of Tables
        Page vii
        Page viii
        Page ix
        Page x
        Page xi
        Page 1
        Page 2
        Page 3
        Page 4
    Supply and demand
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    Review of the literature
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
    The model
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
    Factors affecting prices
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
    Results of adjusting for inflation
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
    Building the model
        Page 42
        Page 43
        Page 44
        Page 45
    Validity of the model
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
    Testing in the local market
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
    Working with the model
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
    Appendix: Business cycle index
        Page 91
        Page 92
        Page 93
    Biographical sketch
        Page 94
        Page 95
        Page 96
        Page 97
Full Text






Copyright 1981


Kenneth R. McGurn


I would like to express my thanks to the many people

who have given their time and experience in assisting me

with this study. Special thanks must go to my wife, Linda,

who helped push the completion of this work.









(,mT cmi

SUPPLY AND DEMAND .........................

Reasoning for Seasonal Demand ...........
Shifts in Demand ........................
Shifts in Supply ........................
Notes ...................................

REVIEW OF THE LITERATURE ..................

THE MODEL .................................

The Data ................................
Notes ...................................



Upward Trend in Prices ..................
The Business Cycle ......................
The Seasonal Year .......................
Notes ...................................

BUILDING THE MODEL ........................

The Model is an Index ...................
Methodology .............................
Summary and Results .....................

VALIDITY OF THE MODEL .....................

Graphed Index Results ...................
Variance of the Index ...................
Student's t .............................
Sample Size .............................

Conclusion ....

Note .................................













. .... .... ....... . 57







Using MLS data ....................... 59
Sales in Charlotte, North Carolina ...... 60
Sales in Gainesville, Florida ........... 69
Some Observations on Volume ............ 77
Test Conclusions ........................ 79
Notes .................................. 81

X WORKING WITH THE MODEL ..................... 82

The Formula ............................ 82
Impact on the Appraisal Process ......... 83
A Counseling Tool ....................... 87
Future Regional Indexes ................ 88
Abnormal Profits ........................ 89

APPENDIX BUSINESS CYCLE INDEX ...................... 91

BIBLIOGRAPHY ....................................... 93

BIOGRAPHICAL SKETCH ................................ 94


1. Existing Single-Family Home Sales for the United
States, Monthly, 1968-1978 ....................... 9

2. Total Number of Sales, All Properties, Reported
in Seven Multiple Listing Services, Los Angeles
County, 1953-1960 ................................ 14

3. Average Existing Single-Family House Sales Price
United States Data, Adjusted for Inflation,
1968-1978 ........................................ 29

4. Average Sales Price of Existing Single-Family Homes
United States Data, Seasonally Adjusted and
Adjusted for Inflation

4a. 1968-1972 ............................... 47
4b. 1971-1975 ............................... 48
4c. 1974-1978 ............................... 49

5. Average House Sale Prices Reported to Charlotte,
North Carolina MLS, Adjusted for Inflation
1966-1975 ........................................ 65

6. Average Sales Price of Properties Reported to
Gainesville, Florida MLS, Adjusted for Inflation
1967-1978 ........................................ 74



1. Existing Single-Family Homes Sales Volume Index
Monthly for the United States, 1966-1974 ........ 7

2. Total Number of Sales and Volume Index, All
Properties, Reported in Seven Multiple Listing
Systems, Los Angeles County, 1968-1978 .......... 13

3. Average Sales Price of Existing Single-Family
Homes in the United States, 1968-1978 ........... 20

4. Median Sales Price of Existing Single-Family
Homes in the United States, 1966-1978 ........... 21

5. Housing Price Index (HPI), 1964-1978 .............. 26

6. Average Existing House Sales Adjusted for
Inflation, United States Data ................... 28

7. Median Existing House Sales Adjusted for
Inflation, United States Data ................... 39

8. Average Existing House Sales Price Adjusted for
Inflation and Seasonality, United States Data ... 51

9. Monthly Index and Confidence Ranges for Average
Sales Prices of Existing Single-Family Houses
in the United States ............................ 55

10. Monthly Index and Confidence Ranges for Median
Sales Prices of Existing Single-Family Houses-
in the United States ............................ 56

11. Total Number of House Sales Reported to Multiple
Listing Service, Charlotte, North Carolina ...... 61

12. Average Sales Price of All Sales Reported to
Multiple Listing Service, Charlotte, North
Carolina, 1966-1975 ............................ 62

13. Average Sales Price of All House Sales Reported
to MLS, Adjusted for Inflation, Charlotte,
North Carolina .................................. 64

14. Average Sales Price of All House Sales Reported
to MLS, Adjusted for Inflation and Seasonality,
Charlotte, North Carolina ..... : ................. 67



15. Total Number of Sales, All Properties, Reported
to MLS, Gainesville, Florida, 1967-1978 ........ 71

16. Average Sales Price of All Sales Reported to
MLS, Gainesville, Florida, 1967-1978 ........... 72

17. Average Sales Price of All Sales Reported to
MLS, Gainesville, Florida, Adjusted for
Inflation ...................................... 73

18. Average Sales Price of All Sales Reported to
MLS, Gainesville, Florida, Adjusted for
Inflation and Seasonality ...................... 76

19. Monthly Sales Volume Ranking ..................... 78

20. Examples of Appraisal Errors ..................... 85


Abstract of Dissertation
Presented to the Graduate Council
of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



Kenneth R. McGurn

December 1981

Chairman: Clayton C. Curtis
Major Department: Finance, Insurance, and Real Estate

The major objective of this study was to identify price

changes in the existing single-family house market which

occur in predictable seasonal patterns. National monthly

sale prices from the NATIONAL ASSOCIATION OF REALTORS@ were

used to construct a monthly index which can be used to

seasonally adjust existing single-family home prices.

Changes in the total number of sales were observed from

1968 through 1978. The pattern of volume changes indicated

a strong market demand in the summer with sales falling 30

to 50 percent during the winter, suggesting a sharp seasonal

drop in demand.

The "average" monthly sale price was adjusted for

inflation using the Housing Price Index. This adjustment

left three patterns: a business cycle, a general upward

trend in prices, and a strong seasonal pattern.

The seasonal price pattern appeared to begin at a low

point in the winter months, increasing through the spring to

reach a peak during the summer. The prices then dropped

through September back to the low winter level. The pattern

was reasonably consistent from month to month making a

monthly seasonal index practical. The first step was to use

a seasonal year of September through August to reduce the

effects of the business cycle. Next, the average monthly

price for each year was divided by the observed monthly

prices for that year. This produced 12 indexes for each of

the 12 months in each year. Each index for a specific month

was averaged with the same month's index in the other

years, to arrive at the monthly index which best fitted the

total test period.

Observations of the application of the index to the

national data, and Multiple Listing Service (MLS) data from

Gainesville, Florida, and Charlotte, North Carolina, were

made with a high percentage of reductions in the monthly

variance from the average. Confidence intervals were calculated

to determine the goodness of the estimated monthly index.

The interval appeared to be of a small enough size to accept

the index as representative of the true seasonal index.

Several examples of the application of the index to the

appraisal process are provided, with resulting improvements

in standard comparable sales appraisals of approximately 400

percent. Several other applications of the index are

discussed as well as obvious improvements which are expected

for the index as a next step in the research.


Basic economics teaches us that a change in the supply

or demand of a product will affect the price of that product,

other factors remaining constant. Real estate should be no

different than any other product. Seasonal changes in the

volume of sales of existing single-family houses (shifts in

demand) have been observed for many years, yet corresponding

price fluctuations have not been reported. This study has

identified the seasonal price fluctuation and converted it

into a seasonal index which can be used to seasonally adjust

comparable single-family home selling prices.

National sales volume data from the NATIONAL ASSOCIATION

OF REALTORS (NAR) indicated that the sales of single-family

houses declined sharply in the winter and peaked during the

summer. The national prices fluctuated, but appeared to

have little to do with the fluctuations in volume.

In an effort to adjust out unwanted price influencing

factors, the NAR data were adjusted for inflation using the

United States Housing Price Index. The graphed adjusted

prices showed three distinct patterns:

1. An upward trend in prices which appeared to be
caused by a general increase in the amenities
associated with the average house, "frontloading"
of costs, and possible long term shifts in the
demand curve for housing.

2. The business cycle with a sharp increase in prices
during expansion periods, a decrease in prices
during recessions, and a generally level period
during the initial part of the study period.

3. The seasonal cycle which appeared to repeat itself
each year, when the cycle was begun in September
and ended in August.

No adjustment was made to the data for the general

upward trend in prices because of the relatively minor

effect it had on prices in the short run. However, the

business cycle had a noticeable effect on prices. But,

because of a lack of sufficient data, no statistically valid

conclusion could be made when the data were grouped into the

various business phases. By beginning each year in September

and ending it the following August, the effects of the

business cycle were minimized. However, the observations

made it clear that a seasonal index for each of the three

business phases would produce a more accurate market adjust-

ment than the index in this study, which was derived without

consideration for the business cycle.

To derive the seasonal index, the inflation adjusted

prices, grouped from September to August for each year, were

compared to the mean price for each year. The individual

monthly differences from the mean were added to the differ-

ences for the same month in the other years and divided by

the number of observations for each month to arrive at the

average differences for the test period. These average

monthly differences became the seasonal index.

To test the index, the NAR national data were adjusted

using the index. A comparison was made between the pre-

adjusted and adjusted prices to determine if the overall

variances were reduced. In all but two years, the variance

was decreased by using the index. The calculated confidence

interval for the index produced a narrow interval indicating

the index was a reasonable estimate of the seasonal pattern.

The index was then tested on two local markets, Charlotte,

North Carolina, and Gainesville, Florida, using local multiple

listing services (MLS) data. Both had monthly volume fluctu-

ations similar to the national volume fluctuations. For

both sets of data, the index reduced approximately 60

percent of the monthly differences. The overall variance

was reduced in seven of nine years in Charlotte and eight of

eleven years in Gainesville. The results appear to indicate

the index can be used on the local level.

However it should be pointed out that the local markets

are not always the same as the national market. Some markets

may enjoy a booming business in the summer while others may

boom in winter. Local MLS data should give the local analyst

an indication of any differences from the national market.

It is possible that future seasonal indexes would be provided

on a regional and perhaps even local level to account for

all the market variations.

The information gathered in this study confirms that

prices of existing single-family homes change in the market,

based solely on the month of the year. The seasonal index

derived in this study provides an adjustment which reduces

the monthly price changes. Failure to use a seasonal adjust-

ment may result in a less than accurate appraisal. It could

also allow an additional error term in research data which

use quarterly or monthly housing prices.

While the index derived in this study is by no means

the ultimate seasonal index, it does reduce price fluctu-

ations and is therefore better than using no index at all.

It proves that the industry should recognize the existence

of the seasonal pattern and begin making adjustments for it.

The following chapters present the logic behind the

price changes and the mechanics of the derivation of the



Unger, in building a case for supply and demand forces

in the real estate market, states:

Generally, a market is defined as a sphere within
which price-making forces operate and in which
changes of title tend to be accompanied by actual
movement of the goods affected. . But the term
"market" as used in real estate means something
much different. . In the final analysis, we
find many isolated markets which tend to be connect-
ed with and affected by the overall real estate
cycle. . We do, however, find in these isolated
markets competitive forces at work that do tend to
bring about a uniform price for similar properties.
Those forces are supply and demand.1

Smith agrees that supply and demand determine the value

of real estate, stating:

We may also note that market value is the price
resulting from the forces of supply and demand
operating in the market. Supply is the other side
of the scarcity coin and demand is the market
manifestation of utility. The point of equili-
brium between the supply curve and the demand
curve. . is the marketplace value.

Reasoning for Seasonal Demand

If we concede that the real estate market is affected

by the standard supply and demand theories, then we would

expect prices to change if the demand for housing changed.

Unger states:

The repetitive intra-annual changes are thought
for the most part to be related to climate,
holidays, vacation periods, and even differences
in the number of working days within a month.
These patterns frequently are repetitive because
they are entrenched in custom.3

The United States has a school system based on a nine-

month year, generally the first of September through the end

of May. It is common knowledge that families try to time

moves they make with their children's school year. Thus,

they will delay a move until the summer months to minimize

the effects of a move on the child's life.

There are other factors which influence the time during

the year prospective buyers are more likely to make a purchase.

The weather has been suggested as a possible influencing

factor. Bad weather, as is common during the winter, is

likely to discourage people from moving, while good weather,

as is common from April through fall, would not present the

same obstacles to a move. Additionally, having to disrupt

the family life during special holidays like Thanksgiving,

Christmas, and New Year's would also discourage a move

during November and December.

Given a preference, most people would probably choose

to make their move during June, July, and August, when

school is out and the weather is good. The worst time for a

move would probably be November through February, because

not only does that time interrupt the school year, it is

also the period with the special holidays and the worst


Shifts in Demand


ed data on the volume of sales of existing single-family

houses and determined seasonal indexes to adjust their sales

volume figures. Table 1 shows the NAR volume indexes for


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1966 through 1974.4 Figure 1 plots seasonally adjusted and

unadjusted sales volume figures for the United States for

1968 through 1978.5 The graph, Figure 1, records sharp

increases in sales volume from January through August, then

a sharp decline in sales volume from August to January.

Large changes in the monthly volume of sales are also

evident from the index table. The largest change in volume

for the 1966 to 1974 period appears to have occurred from

January 1967 to August 1967, when the volume index jumped

90.4 percent, from 42 to 80 on an annual monthly average of

62. In other words, the sales of single-family houses

jumped 90 percent from the winter month of January to the

summer month of August. A closer inspection shows most

winter-to-summer volume jumps are in the range of 55 to

65 percent.

Further inspection of the figures and the graph indicate

that the highest volume of sales consistently occurs during

May, June, July, and August. The lowest volume period is

January, November, and December. February, March, and April

appear to be transition months between the low and high

periods, while September and October appear to be the

transition months for the downward movement of sales volume.

If we assume for the moment that the supply curve

remains constant, then we can make some predictions as to

price movements based on the information on volume changes.

Demand begins in the winter months at a given level, the

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base period. As the volume increases, the demand curve

begins shifting to the right, a transition period. The

summer months represent the peak period as the demand curve

stabilizes. The fourth time period begins the shift back to

the winter months and is similar to the earlier transition

period. Thus, with the supply curve remaining stationary,

it is easy to follow the expected resulting price changes.

Prices should be at their lowest in the base period and

their highest in the summer months.

The strength of the shift in demand will, of course,

depend on factors such as personal income, consumer prefer-

ences for moving, interest rates, general market conditions,

and many other factors. The strength of the shift should be

a reflection of the change in the volume from winter to

summer and back again.

Shifts In Supply

The above logic can also be applied to justify an

expected shift in the supply of houses. If people are

buying houses in a greater volume, it follows that there are

probably more houses available for sale.

However, because of the high amount of capital and long

length of time required to create a new house, the real

short-term supply of houses is generally considered to be

fixed. Weimer and Hoyt, in a discussion of the supply of

real estate, state:

Since the supply of properties and even of property
service is relatively fixed, demand is the most important

factor in determining market prices and rents during
short-run periods of a year or two."6

Additionally, even the marginal supply side houses will

be delayed in entering the market. The serious buyers/sellers

generally begin their search for new housing far in advance

of the time they typically list their existing house for

sale. The feeling is they wish to have plenty of time to

find the right place to live, without being under pressure

to move out of their existing home because it was already

sold. This "lag" in adding to the supply should have the

effect of pushing prices upward.


1. Maurice A. Unger, Principles and Practices, 4th ed.
(Cincinnati: South-Western Publishing Co., 1969),
p. 36.

2. Halbert C. Smith, Real Estate Appraiser (Columbus, Ohio:
Grip, Inc., 1976), p. 6.

3. Unger, p. 29.

Division, Existing Home Sales, Annual Report (N.P.:
NAR, 1977), p. 9.

5. Ibid, p. 13.

6. Arthur M. Weimer and Homer Hoyt, Real Estate, 5th ed.
(New York: Ronald Press Co., 1966), p. 115.


Surprisingly, there appears to be little information or

concern about seasonal price changes. A few publications

mention it in passing. In a University of California study

of Multiple Listing Service (MLS) data, which reviewed sales

quarterly from 1953 through 1960, there is mention of a

possible seasonal pattern.

The index of the number of MLS sales shows a
distinct seasonal pattern in which peaks were
registered in the third quarter of five of the
eight years and in the second quarter of the other
years between 1953 and 1960.1

The study goes on to state:

There was no strong seasonal pattern in
average prices during a particular year; however,
in all but 1954, the lowest average price was
registered in the first quarter.2

The sales volume data for this California study are

reported in Table 2 and plotted in Figure 2. A seasonal

pattern is easily discernible. This study is important in

that it substantiates the contention that the seasonal

pattern has been around for longer than just the test period

of this study.

Morton, in an article for The Appraisal Journal,

studied 400 sales of single-family residences in southern

California, using regression analysis. In passing, he


The last variable to enter the regression
equation was the dummy variable representing the
third quarter of each year, and this variable had

Table 2
Total Number of Sales, All Properties,
Reported in Seven Multiple Listing Systems,
Los Angeles County

Quarter 1953 1954 1955 1956 1957 1958 1959 1960

1 3,434 3,179 3,985 4,578 4,077 3,532 4,631 4,532

2 3,359 3,755 4,477 5,215 4,234 3,974 5,099 4,828

3 3,606 4,095 4,896 4,153 4,178 4,672 4,661 4,657

4 3,253 3,425 3,958 3,789 3,511 4,025 3,855 3,440

Annual 13,652 14,454 17,316 17,735 16,000 16,203 18,246 17,457

Index, Total Number of Sales, All Properties,
Reported in Seven Multiple Listing Systems,
Los Angeles County

Quarter 1953 1954 1955 1956 1957 1958 1959 1960

1 85 79 98 113 100 87 114 112

2 83 93 111 129 105 98 126 119

3 89 101 121 102 103 115 115 115

4 80 85 98 94 87 99 95 85

Annual 84 89 107 109 99 100 113 108


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a positive coefficient. The sign of this coeffi-
cient could indicate that, for the sample studied,
the months of July, August, and September had a
high demand in respect to the availability of
properties in relation to the other quarters of
the year.3

Unger, in a discussion of the general economic business

cycles, includes a short paragraph on seasonal variations:

Monthly, quarterly, and weekly data suggest that
there exists a regular recurrence of seasonal
fluctuations. For example, the construction
industry is more active during certain periods of
the year than other periods, and so is the manufac-
ture and production of various goods such as the
manufacture of ladies' handbags.4

In the NAR publication, Existing Homes Sales, they


There is a modest degree of seasonal variation in
reported selling prices. Sales prices tend to
reach a seasonal peak in July, and then decline
moderately over the next three months before
experiencing a seasonal upturn.5

The same publication talks about the number of sales:

Wide monthly fluctuations in sales volume indicate
the high degree of seasonality which characterizes
the existing home market.6

and continues:

For all regions the spring and summer months are
seasonally high volume periods, while January,
November, and December are the lowest.7

All four note an obvious seasonal pattern in the volume

of transactions. But the "wide fluctuations" in sales

volume are masked in the resulting sales prices. This study

attempts to remove that mask so that the seasonal variations

in selling prices will become equally apparent.


1. Frederick E. Case, A Study of Multiple Listing Data
(Los Angeles, California: University of California
Printing Department, 1963), p. 11.

2. Ibid., p. 14

3. T. Gregory Morton, "Factor Analysis, Multicollinearity,
and Regression Appraisal Models," The Appraisal Journal,
(Volume XLV, Number 4, October, 1977), p. 583.

4. Maurice A. Unger, Principles and Practices, 4th ed.
(Cincinnati: South-Western Publishing Co., 1969),
p. 29.

Division, Existing Home Sales, Annual Report (N.P.:
NAR 1977), p. 45.

6. Ibid.

7. Ibid.


A major problem in any research is the availability of

data which are appropriate for the problem. Real estate is

more of a problem because each piece of property is unique.

Therefore, an observation of one parcel may have no relation-

ship to another.

However, as Thompson and Harwood point out:

Although land is nonhomogeneous, there can still
be a high degree of physical and economic similarity.
For example, in a city block containing 20 house
lots of identical size and shape, there will be a
high degree of similarity even though the lots are
still nonhomogeneous. Finding similar properties
is, in fact, the basis for the market-comparison
approach to appraising real estate.l

The real estate problem is no more difficult than the

observation of the stock market. Each company is unique.

But each company, as represented by its stock, is influenced

by business cycles and factors which affect similar companies.

Models can and are constructed which represent the movements

of groups of stocks which contain the individual stock. On

the average, as the group of stocks (the model) moves, so

moves the individual stock. These models are the "average"

or norm from which deviations are measured and changes


If a housing model can be constructed which will function

"on the average," then observations of specific properties

generally comparable to those making up -the model or "average"

can be measured or "adjusted" from the model. The model in


this study is designed to represent the price fluctuations

of the average existing single-family house sold in the

United States. The model is constructed from the observed

prices for sales of existing single-family houses in the

United States from 1968 through 1978, adjusted for inflation,

as measured by the Housing Price Index (HPI), a subcomponent

of the Consumer Price Index.

Using the existing single-family house market for the

United States provides a broad base on which to ensure that

most of the factors which make the individual house unique

are lost or hidden when averaged with all other individual


The Data


ed from 142 Multiple Listing Services (MLS) monthly reports

of existing single-family house sales since 1966. The data

are collected from all over the United States which is

subdivided into four regions (northwest, southwest, northeast,

and southeast) for data collection. Collection of the data

is described in the Existing Home Sales, an NAR annual


Participating MLS's report the number of single
family sales which occurred during the month,
sales prices and number of bedrooms in the unit.
In 1978 data on nearly 650,000 existing single
family home transactions were reviewed and pro-

Participating MLS's are s-ituated in every
region of the country and provide wide geographic

coverage of the existing home market. While all
are located in, or adjacent to, Standard Metropol-
itan Statistical Areas, comparisons of their
reports with Census data from the Annual Housing
Survey show that, as a group, their experience is
representative of the sales activity and prices
that generally prevail in each region of the

The broad base, consistency, and the large number of

sales make these data appropriate for the construction of

the model. NAR reports both median and average prices each

month for the country and for each of the four regions.

Median prices have been collected and reported from January

1966, while average prices have been reported from January

1968. Tables 3 and 4 contain the average and median monthly

sale price of existing single-family homes for the United

States. Both prices have been used in the research for this

study; however, the average price figures have been used for

the model.

Other supporting data have also been collected either

to adjust the NAR data or to test the model. These aata are

contained in various tables in this study, referred to and

explained as they apply in the study.


1. Marvin Thompson and Bruce Harwood, Florida Real Estate
(Reston, Va.: Reston Publishing Co., Inc., 1980),
p. 35

Division, Existing Home Sales, Annual Report (N.P.:
NAR, 1978), p. 45.

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Many variables affect housing prices, including a

change in the mortgage interest rates, a change in consumer

tastes, an increase in the population, and the failure of a

local business. These factors are at work on every level,

from the local market to the national market. These many

variables and their effects on prices are discussed in

detail in basic appraisal and real estate books and do not

need to be discussed in detail in this study.

In order to unmask the seasonal price change and accu-

rately plot its movement, it is desirable and necessary to

eliminate as much of the nonseasonal price fluctuations as

possible. This study's model, using a large number of

observations across the entire nation, has minimized the

effects of most of the local influencing factors, which must

be left to the local appraiser in determining their effects

on the local market. This leaves us with the factors-which

are national in scope and which should be much more easily


We would not expect to see any effect on the national

model of a shut-down of a large government plant in Atlanta.

We would expect to see effects on prices from changes in

consumer tastes in housing which affect the nation, such as

a trend toward larger homes or homes with more amenities.

We would also expect to see changes in prices due to changes

in national mortgage rates.

Most large changes in interest rates have been associated

with business cycles, which contain other influencing

factors such as drops in employment. Such factors affect

the ability of people to buy houses. Thus, on a national

level, influencing factors are often only subcomponents of a

larger more easily identifiable factor which can be used to

explain the observed price changes.

The most obvious factor affecting prices today is

inflation. It probably accounts for the majority of house

price changes. Inflation is also one of the easiest factors

to measure. It is therefore the most logical first step to

take, in adjusting out, unwanted factors. Because of the

indexes published by the government, an adjustment for

inflation can be done with reasonable accuracy.

The first problem, then, is to determine the best

estimate for housing inflation. The three most obvious

indicators are

1. The Consumer Price Index (CPI);

2. The Housing Price Index (HPI), a subcomponent of
the CPI;

3. One of the subcomponents within the HPI.

Since the indexes are available monthly and the HPI is

more directly related to the housing market, the HPI was

selected for use over the CPI.

One potential problem in the use of the HPI is that

housing prices directly affect the HPI and bias its results

more than the CPI. But this is the major reason for select-

ing the HPI. We will be looking at a given level of house

prices (which is already reflected in the HPI). The HPI

will be more sensitive to the changes in house prices from

that given level than would the CPI, and thus should be a

better indicator of market moves. The subcomponents within

the HPI might do as well, particularly the "homeownership"

subcomponent. However, the HPI is a broad index which

should be less sensitive to minor aberrations which could

negatively affect a specific item within the index. The HPI

was therefore considered best for this study.

There has been some criticism of the CPI as not being a

true measure of inflation. One of the major criticisms is

that the interest rate, which is a part of the HPI, reflects

the current market rate of interest to persons buying a

house. It has nothing to do with the vast majority of

people who are renting or who own existing housing. _This

argument adds support to the use of the HPI for this study.

It is the purchase and sale of the existing single-family

house at the time the interest rate contained in HPI affects

the property that the study examines. The current interest

rate affects the housing market at the point where the

marginal buyer and the marginal seller find equilibrium in

their prices. When interest rates change, the cost to one

or the other party changes. Therefore, to represent the

market realistically at the time of the transaction, the


index should contain the interest rate information that

affects the transaction. The HPI figures used to adjust the

NAR sales figures are contained in Table 5.1


1. U.S. Department of Labor, Bureau of Labor Statistics,
Monthly Labor Review (Washington, D.C.: Government
Printing Office, 1965-1979).

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The NAR observed monthly average prices from 1968

through 1978 were adjusted for inflation using the HPI, by

dividing the observed price by the HPI for that particular

month. The resulting adjusted price information is found in

Table 6. The adjusted prices were graphed and are included

in Figure 3.

Had inflation, as measured by the HPI, accounted for

all changes in the price, we would expect to see a flat line

on the graph. This does not occur. Three distinct patterns

become obvious from looking at the NAR graphed data:

1. There is a general upward trend in prices. From
1971 through 1978, the upward trend accelerates.

2. There are distinct movements up and down during
periods of business recessions and expansions.

3. There are sharp increases from the fourth quarter
of each year to the third quarter of the following
year, followed by a decline to the fourth quarter.

This study focuses primarily on the seasonal price

changes noted in the third pattern listed above. But the

general upward trend and the business cycle can influence

seasonal price changes. Their potential influence on any

model using the NAR data needs to be discussed to make this

study complete.

Upward Trend of Prices

It appears from the graph of the NAR data that the HPI

accounted for most of the nonseasonal price changes from

1968 to 1970. There is a slight rise, which becomes much


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more pronounced from 1971 on. The growth appears to be
approximately 2.0 percent per year (depending on when the

rise is calculated as beginning). The next step in this

study was to review the cause for this increase and determine

its effect on the model.

A review of the NAR publication Existing Home Sales,1

or any other publication which reports numbers of bedrooms

or similar differences in amenities, shows that over time

houses are becoming larger on the average and contain more


Since the NAR data report the average of all sales, it

is possible that the "quality" of the average house is

changing over time. A positive change in quality (adding

amenities) would result in higher average prices over time,

as older houses are replaced with new houses. This develop-

ment could explain at least a part of the increase shown in

Pattern 1. This appears to be the case, and is discussed in

a report for the Council on Wage and Price Stability:

Improvements in the quality of new housing
are at least partly responsible for higher housing
prices during 1977 and, more generally, over the
past decade. Buoyed by gains in personal income
since the last recession and by rising housing
values, many current homeowners sold their previous
houses and purchased bigger, fully equipped new
houses on larger lots. Consequently, sales prices
of all houses sold are increasing more rapidly
than sales prices of houses with the average
characteristics of a "fixed-quality house" sold
during 1974.-

Thus the Council's report also recognizes that house

prices are increasing at a rate greater than inflation. It

attributes part of the difference to an increase in the

average quality of housing in the nation.

If the increase in the average quality of housing

accounted for all of the additional price increase, the

"fixed-quality house" price should remain fairly constant

over time. However, this is not the case. A comparison of

the fixed-quality house with both the Consumer Price Index

(CPI) and the Construction Material Index (CMI) shows the

fixed-quality house increasing in price at a faster rate

than justified by both indexes.4 We must conclude that

other factors are contributing to the extra increase.

The Council's report further points out that many new

homes are subject to "frontloading," which requires the

developers to pay for sidewalks, schools, sewer systems,

parks, etc., which are added to the price of the new home

and passed on to the buyer.5 These increased initial costs

have made the new house coming on the market more expensive

than would have otherwise been justified by the increase in

the HPI. It is perhaps these "additional" costs which are

causing a large part of the unexplained growth in sale

prices of both the quality adjusted new houses and existing


These increased initial costs have made the existing

houses more competitive with the new house because the new

houses include these costs in their prices. This is a shift

to the right in the supply curve for new housing. This


would cause marginal new home buyers not to buy a new house,

because of the higher relative price, and to switch into the

existing house market. This switch increases the number of

buyers looking for existing houses. The result is a shift

to the right in the demand curve for existing houses. This

shift results in the sellers being able to command a higher

price for their houses. It is difficult to determine from

the information at hand whether this results in any differ-

ence in the rate of price increase between existing houses

and fixed-quality new houses.

The period of time between the contract date and closing

date is different between the two types of houses. The new

house could have a delay of from one to eight months before

the buyer moves into the house. The average delay is probably

between four and six months, whereas the existing house sale

delay normally does not exceed one month. This time difference

could, if seasonal fluctuations are significant, mean greater

differences in price between the two types of houses. The

time of the year may be significant for the existing home

buyer, because he may be in direct competition with many

buyers during certain months. The buyer of a new house is

not in competition for an existing supply of houses, and

thus has some control over occupancy date, price, and other


There are other logical explanations for the increase

in prices which are greater than the HPI. As suggested in

the Council's report, more and more families can afford to

buy houses. Also, the population has continued to increase,

and the baby boom of the postwar period has added to the

number of people in the market to buy houses. The average

size of a household is decreasing, while the total popula-

tion is increasing. All these factors could represent a

long-term shift in the demand side of the housing market.

Other factors which could help explain the additional

increases above the HPI are better financing terms, FHA and

VA points being passed on to the buyer, increased awareness

by more potential buyers of the inflation hedge provided by

an investment in a house and that the HPI is not the best

cost index for estimating house price increases.

In review, the upward trend in prices appears to be

caused largely by

1. An increase in the quality of homes being sold;

2. An increase in the production cost through front-
loading; and

3. Possible long-term shifts in the demand curve.

A decision whether to adjust the model based on this

information had to be made. With one exception, the model

is designed to represent the "average" sale price of all

existing houses. Since the "average" house is affected by

these factors, and that effect is a part of what the model

is to measure, then eliminating these factors would adversly

affect the model. Therefore no adjustment is desired.

However, the one reason for eliminating these factors is so

that the model can be used to adjust the selling price of

comparable properties in a standard house appraisal. To be

technically accurate, it would be necessary to eliminate any

changes in the data attributable to changes in quality.

This should be the difference between the quality adjusted

percentage price change and the average percentage price

change reported over the same period by the U.S. Department

of Commerce.6 This adjustment would equate the model with

a standard comparable house appraisal by holding constant

the quality (the same amenities) of the house.

Unfortunately, there are several drawbacks to such an


1. It assumes the quality adjustment index is accu-
rate.7 But the Department of Commerce notes:

. houses which are "the same" with regard to
these particular characteristics may vary from one
time period to the next in a number of ways, such
as workmanship, materials, and mechanical equipment.
. The ten characteristics account for approxi-
mately 70 percent of the variation in selling
prices of new one-family houses.

2. The difference between the two rates of change
varies from quarter to quarter and year to year.

3. The model uses monthly data while the quality
figures are available only quarterly and yearly.
The model is not readily compatible with the data,
although interpolation could be used.

4. The quality data are based on new house sales,
while the model is based on existing house sales.

I did not feel that it was critical at this stage of

the research to attempt any additional adjustments to the

model because

1. The frontloading and demand shifts influencing the
upward trend in the model should stay in the model
because they affect all property.

2. A standard house appraisal generally looks only at
comparable sales in a relatively brief time period
(one to six months). The average error factor
introduced by the changes in quality which should
not be in the model would probably be less than
one percent and therefore would not be significant.9

Therefore, no adjustment to the model was made for the

upward trend pattern observed in the graph or for changes in


The Business Cycle

The second pattern observed from the NAR graphed data

was the business cycle. General declines in the graphed

data are apparent in 1970 and in 1974/1975. These declines

are followed by periods of rapid increases in prices.

December 1969 through November 1970, and November 1973

through March 1975 are generally recognized as periods of

recession. The years immediately following the recessions

are considered growth periods.

Unger, in a discussion of real estate cycles, states:

Although comparatively few studies have been
made of the real estate cycle, it is generally
agreed that building activity follows to a degree
the business cycle in a wavelike movement. It is
further indicated that the volume of real estate
activity does not necessarily advance with the
increases in general business, and declines in
real estate activity generally precede general
business declines. It appears that the troughs
and peaks of the real estate cycle go de er and
higher than those of the business cycle.iU

The NAR annual house survey discusses the business

cycle and its effects on house sales:

Like many other types of economic activity,
the existing home market is subject to cyclical
fluctuations. However, home sales generally feel
the impact of cyclical change before many other
sectors. In the last two business cycles the
resale market led the economy at each turning
point. In the 1970 recession existing home sales
began to decline six months before the general
economic downturn was underway. Resale activity
then turned sharply upward in April 1970 a full
seven months before the economy had bottomed out.
A similar pattern was traced out in the longer and
deeper 1973-1975 recession.

In both recessions the drop in resale activity
was much more severe than the decline for the
general economy and the recovery was much more
buoyant. From the peak to the trough of the 1970
recession existing home sales declined 20 percent
compared to just a one percent slump in the general
level of economic activity. Similarly, in the
1973-1975 recession existing home sales slipped
18 percent while the overall economy fell six

From Figure 3, it appears that the general price level

for the HPI adjusted average house price declined during the

winter months in both 1969 and 1970 to below those levels

which would be expected by general observation of previous

years' data. The 1970 summer month price levels also did

not reach expected levels. But, after the 1970 winter,

prices recovered sharply. These price movements appear to

follow closely the 1973/1975 recessionary period.

The 1969/1970 recession was mild compared to the 1973-

1975 recession. The 1974 winter price drop was exceptionally

steep, especially after considering the low 1974 summer

price level. The prices did not appear to fully begin a

strong recovery until early in 1976.

During the 1971/1973 and 1976/1978 business expansion

periods, the NAR house prices increased at rates far in

excess of the inflation rate, recovering not only the ground

lost during the recessions, but moving far above any previous

trend line.

These business phases appear to have marked effects on

prices in the long and short run. While the long-run effect

is not a major concern in this study, the short-run effect

is, if it would distort the seasonal patterns.

By comparing an expansion year of 1977 with a recession

year of 1974, the differences become obvious. In 1977,

prices climbed well above the previous winter months. In

1977 winter prices dipped below the 1977 summer price levels,

but were well above the previous winter prices. On the

other hand, 1974 summer prices barely managed to exceed the

earlier winter months and 1974 winter prices look as if they

had the rug pulled out from underneath them as they plummetted

to 1972 winter levels.

By expanding the visual comparisons, three patterns

began to emerge

1. Growth or expansion period characterized by a
rapid increase in prices from the winter to summer
months, followed by a slight decline to the follow-
ing winter months, establishing a new level well
above the previous year's winter price levels.

2. Recession period characterized by a slight or
modest increase in prices from the winter to
summer months, followed by a sharp decline to the
following winter months.

3. Stable or level period during the period from 1968
through mid-1969 the house market appeared to have
a relatively stable price cycle. The only price
changes not taken care of by the HPI appear to be
the seasonal fluctuations. This period is general-
ly "level" and is characterized by a modest in-
crease in the price level from the winter months
to the summer months, followed by a drop in prices
back to their pre-summer levels.12

Because of the obvious differences which occur in the

various business phases, the first inclination was to divide

the data into the three phases: recession, growth, and

level. The obvious problem with this division into business

phases is that there are only two observations per month for

the recession and level categories. The statistical test

required for these data results in only one degree of freedom

and an almost impossible restriction on the verification of


Fortunately an adjustment in the starting month for

each year, discussed in the next section, reduced the

differences between the phases enough to derive meaningful

results. The appendix discusses the business cycle further

and also provides the derived indexes for the three business

phases. Although the division of the business cycle was not

used in this model for lack of adequate observations, the

refined seasonal index should allow for the division.

The Seasonal Year

While observing the business cycle, another character-

istic of the housing data became apparent. The seasonal

cycle appeared to begin in September and end in August. By

beginning the seasonal year in September and looking at the

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subsequent patterns, the same pattern emerged for all

years. Summer prices were always higher than the previous

winter prices and winter prices were always lower than the

previous summer's prices.

Of course the size of the increase from winter to

summer and the size of the decrease from summer to winter

depends on the phase of the business cycle the year was in.

But, most importantly the direction of the change was always

the same. By beginning the year in September it then became

more precise to average the amount of the seasonal changes

from year to year. Thus the best model for the existing

single-family house price movements is a model which allows

for the business cycle and which also uses a September to

August year.13

Division, Existing Home Sales, Annual Report (N.P.:
NAR, 1979), p. 38.

2. The index of fixed-quality housing costs is constructed
by the Census Bureau by holding constant a specific set
of characteristics believed to measure change in qual-
ity. Executive Office of the President, A Quarterly
Report of the Council on Wage and Price Stability with
a Special Report on Inflation (Washington, D.C.:
Government Printing Office, No. 13, April, 1978),
p. 115.

3. Executive Office of the President, A Quarterly Report
of the Council on Wage and Price Stability with a
Special Report on Inflation (Washington, D.C.:
Government Printing Office, No. 13, April, 1978),
p. 115.

4. Ibid, p. 116.

5. Ibid.

6. Bureau of the Census, Price Index of New One-Family
Houses Sold (Washington, D.C.: U.S. Department of
Commerce, 4th Quarter, 1978), p. 3.

7. Perhaps the accuracy of the index would be improved if
the information were seasonally adjusted.

8. Bureau of the Census, Price Index of New One-Family
Houses Sold (Washington, D.C.: U.S. Department of
Commerce, 4th Quarter, 1978), p. 2.

9. The average difference between the percentage change
of the Fixed-Quality (1974) house index and the Housing
Price Index from the fourth quarter 1967 to the fourth
quarter 1977, is 1.453 percent per year or .121 percent
a month. An error term this small is considered by
the author to be very acceptable in today's real estate

10. Maurice A. Unger, Principles and Practices, 4th ed.
(Cincinnati: South-Western Publishing Co., 1969),
p. 32.

(1979), p. 10.

12. The NAR median sale prices for the United States,
adjusted for inflation, are in Table 7. Fortunately,
information on median sales extends back to 1966.
The earlier prices reflect level prices from 1966
to 1969.

13. The HPI has not accounted for all of the price increases
over the test period. Perhaps a better index to use
in future models would be the Home Purchase Index, a
subcomponent of the HPI.


Several steps in building the model have already been

covered in previous discussions. The monthly sales prices

(P) were divided by the HPI for the corresponding month to

arrive at the adjusted monthly price (AP). The adjusted

prices were then grouped by year, with each year beginning

in September and ending in August.

The Model is an Index

The model constructed is an index which can adjust

sales for the month (season) of the year under observation.

The base of the index is 1.0, representing the average

monthly price for a given year. For example, if there was

no seasonal change, the average price (B) and the observed

price (P) would be equal (P x 1.0 = B).

When the price is subject to seasonal fluctuations, the

observed price and the average price are different. The

seasonal index is the relationship of the two prices to each

other (BMA =B/P), where BMA is the monthly index. The

average price can be determined by multiplying P x BMA.

With the average price then available, the expected price to

be observed in another month can be determined by substituting

the monthly index figure for the appropriate month into the

above equation and solving for P.


The observed monthly prices for the seasonal year

adjusted for inflation are summed and divided by 12 to

arrive at the average monthly sale price for the year. This

average figure is called the base price (B) for that particu-

lar year. The logic is that had the HPI accounted for all

price changes, the price for each month of the year should

equal the other monthly prices within the year (P x 1.0 =

B). Any differences in prices can be measured from the base

price (B). These differences should reflect the seasonal

change. Observing enough of the variations for each month

will allow a reasonable estimation of the expected difference

between the observed price (P) and the base price (B).

The major assumption is that all external factors are

constant except for the seasonal influences. In the short

run of one year used in each period, this assumption seems

reasonable. First, the large population used in the study

minimizes the minor disturbances which might affect specific

cities or local markets. Second, many disturbances such as

changes in tastes and attitudes are gradual, stretching out

over years. The September to August period is a short

enough period not to be materially affected by these variables.

Third, larger disturbances will affect the data, but more

likely not to a major extent within the short period of the

base year. The business cycle is probably an exception.

The monthly adjustment index for each year was then

derived by dividing the adjusted monthly price into the

average monthly price (B/P = MA), where MA equals the monthly

adjustment factor.

A composite base monthly adjustment factor was derived

in a fashion similar to arriving at the base price. The

monthly adjustment factors (MA) were grouped by month, all

April in one group, all Septembers in another, etc. The

sum of the monthly adjustment factors for each month were

then divided by the number of observations of that month to

determine the new base monthly price (BMA) or the monthly
adjustment factor (m=l MAm)/n = BMAm, where n is equal to

the number of observations of a particular month.

Because this factor (BMA) is the average of all the

observed adjustment factors for a given month, it represents

the best estimate of the true adjustment factor for that

particular month.
Summary and Results

In summary the index calculations are

APm = P /HPI

B = (E= APm)/12
y m=l m

MAmy By/APm
my y m
BMA = (E MA )/n
m m=l m


1. P = Observed Sale Price

2. HPI = Housing Price Index (a measure of inflation)

3. AP = Adjusted Price

4. B = Average Adjusted Sale Price for a Specific

5. MA = Monthly Adjustment Factor for a Specific
Month in a Specific Year

6. BMA = Monthly Adjustment Factor for a Specific
Month for all years

7. m = A Specific Month (January, February, etc.)

8. y = A Specific Year (1968, 1969, etc.)

9. n = Number of Observations

Note the 12 BMA's represent the monthly index for all

years. The specific monthly (BMA) indexes are

1.011438 January

1.006715 February

0.999823 March

0.987740 April

0.980343 May

0.976200 June

0.970414 July

0.972055 August

1.018289 September

1.031631 October

1.024754 November

1.029777 December


The base monthly adjustment factor (BMA) when combined

with the BMA's for the other months is the model. It

should accurately represent the seasonal variations from the

base or average price for the NAR national data. But how

good are the results produced by the model? Several tests

were made to help determine whether the model could adjust

out seasonal fluctuations.

Graphed Index Results

The first check was a visual observation of the index

used on the data from which the index was derived. The

solid line in Figures 4a, 4b and 4c depicts the average

national sale prices adjusted for inflation. This is the

same information plotted in Figure 3. The national prices

were then multiplied by the model index. If the index

accounted for all seasonality the graphed data should appear

closer to a straight line.

The dotted line in Figures 4a, 4b and 4c represents the

data seasonally adjusted. Visually it appears that the

fluctuations in the data have been reduced. The business

cycle is still pronounced, and the gradual annual increase

in prices discussed in Chapter VI appears to be more determinabl1

Thus the index appeared to reduce the seasonal fluctuations.

Variance of the Index

Confirmation of the visual observations was the next

step. The monthly difference between the observed price and


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the average price for each seasonal year was calculated for

comparison with the seasonally adjusted data. The variance

was then calculated for each year using

n n
E 2 (il yi)2
i=l Y -

where Yi = the monthly sale price (adjusted for the HPI)

n = the number of observations

The sales figures were then seasonally adjusted using

the seasonal index; the resulting figures are reported in

Table 8. The yearly variances were also calculated.

By comparing Table 8 with Table 3 it can be seen that

of the 120 monthly differences, 92 were reduced when the

seasonal index was used. February and March accounted for

approximately one-third of the errors, suggesting the possibil-

ity that a slight refinement in the index for this transition

period could increase the accuracy of the index. Additionally,

when comparing one year to the next, it is interesting to

note that 10 of the 12 months in 1970 were incorrect. That

year represents about 36 percent of all the errors. That

year was a recessionary year. Another recessionary year,

1974, accounted for an additional 18 percent of the errors.

As noted previously this index was not adjusted for business

cycles. If a business cycle adjusted index were applied, it

appears that an even better adjustment factor might be


The variances for the 10 years showed similar results.

All were reduced except for the years 1970 and 1974. The 80

tCi r o m0 0Lt Ln o tr ) i 6 B-

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percent success rate is considered excellent considering the

volatility of the monthly prices.

The standard deviations for each year were calculated

and are reported in Tables 6 and 8. The coefficient of

variation was determined for each year by dividing the

standard deviation by the mean. The percentage of the mean

represented by the standard deviation (the tightness of the

observations) for the pre-seasonal adjustment figures is

2.54, while after the seasonal adjustment it is 1.25 percent.

A general inference from these results is that the

index has reduced the monthly fluctuations and that the

fluctuations are reduced to a tight range around the mean

price. The results indicate that the index reduces the

monthly fluctuations in the sales data.

Student's t

A final test of the mean is made to determine how much

confidence can be placed in the use of the index. Because

of the small number of observations it is necessary to use

the Student's t test.

To use the Student's t test it is necessary that the

observations on which the BMA are calculated are normally

distributed. Unfortunately, the true distribution of the

observations is not known. However,

. it can be shown that the distribution
of the t statistic is relatively stable for
populations which are non-normal but possess
a mound-shaped probability distribution. This
property of the t statistic and the common
occurrence of mound-shaped distributions of

data in nature enhance the Student's t for use
in statistical inferences.1

The standard deviation for the BMA's was then cal-

culated using

S 2
s' = i=l (y1-y)


n = the number of observations

y = the MA for the month from each year

= the BMA for the year
A 95 percent confidence interval was calculated for

each of the 12 means using the standard formula for finding

a confidence interval for small sample populations:

y = ta/2s/ n


ta/2 = critical value from the student's t table for

.05. All other values are from the previous formula.

The width of the intervals range from a high for the

month of September of .02326, or plus or minus 1.15 percent

of the estimated mean to a low of .01020 for the month of

February. These appear to be reasonably tight confidence


Confidence intervals for the means were calculated

using a confidence coefficient equal to 99 percent (two

tailed). This appeared to increase the confidence interval

by about 0.004, which is still a tight confidence interval.

Table 9 contains the means, standard deviations, and confid-

ence intervals.

Sample Size
A major problem with the study is the lack of a large

sample, which makes the results less reliable. The test

period covers 11 years (1968-1978). However, when the

September-August year was adopted, it meant the loss of one

year's observations. This reduced the number of observations

for each month to only 10. While the above intervals are

considered to be well within a reasonable tolerance for the

purpose of this study, a few more years of data could produce

results having a much smaller interval. Because the NAR has

collected two more years of data on median sale prices, that

information was also tested to determine the tightness of

the confidence interval.

The median data contained 12 observations. A 95 percent

confidence level produced intervals that ranged from a low

of .000895 to a high of .01898. This range equates to a

plus or minus .45 to .98 from the mean. It appeared that

either the median data produce a better estimate of the mean

or the larger number of observations indicates that the

means are in fact very close to the true means. Table 10

contains the means, standard deviations, and confidence

intervals for the NAR median price data. Table 7 contains

the HPI adjusted median data.

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The graphed seasonally adjusted national data (Figure

3) pointed out the obvious need to determine appropriate

adjustment factors for the business cycles and the upward

price trends. However, the graphed seasonally adjusted

data, the reduction in monthly variances from the average

price, and the calculated confidence intervals all confirm

the generated index reduces monthly variations (seasonal

changes) in the national data.

Based on the above information I concluded that the

calculated means were a reasonable estimate of the true

monthly means for the national data and can be used to

seasonally adjust the observed NAR monthly housing prices.

Division, Existing Home Sales, Annual Report (N.P.:
NAR, 1978), p. 46.


The tests thus far indicated the derived index (the

model) is a good model for use with the national data. It

would be a better model if it could be used for localized

markets. However, more external variables add fluctuations

to the local markets that are smoothed over in the national

data. But, because the national market is made up of many

local markets, on the average we should expect to see the

same characteristics in the local markets that we have seen

in the national market data.

Because of problems with small sample populations in

statistical testing, we expect greater fluctuations in local

data compared with the national data. But, if the underlying

assumptions about seasonal demand are valid, then over time,

the seasonal pattern should be observable on the local


There are of course exceptions to most rules. There

will be locations where the seasonal pattern is not the same

as the rest of the country. This model shows a high demand

in the summer months. In places like Vail, Colorado, the

market may be reversed. Miami and other cities in Florida

often experience an influx of people during the winter

months. This could change the seasonal pattern for those

locations. But, on the average, the local markets should

behave as does the national market, of which local markets

are part. Thus several local markets were used to compare

the model's ability to reduce any observed seasonal fluctu-


Using MLS Data

The basic problem with real estate research again comes

up, that of finding representative data. The logical source

is one that is a part of the NAR data but more available to

the local market analyst. This source is the local multiple

listing services (MLS).

Most MLS's publish monthly summaries of local sales

reported by their member offices. This information includes

the gross dollar sales and the total number of sales. If

the MLS data for a local market can be shown to fit the same

seasonal pattern as the national data, a local analyst,

could compare the local MLS sales information with the

national trends to determine whether that market exhibits

the same general characteristics. If it does, a seasonal

adjustment using this study's model may produce a better

representation of the local market. Some markets, as mention-

ed previously, may not exhibit the same seasonal pattern.

But the comparison should give the analyst an idea of the

type of seasonal adjustments warranted in his market.

The California study, noted previously in this paper on

page 12, indicated that MLS data could be used as a good

representative of the total area market. Additionally, in

that California study it was noted that the sales data

appeared to have seasonal characteristics similar to the

national data characteristics. (See Figure 2).

Two local markets were selected for their availability

of information through MLS, Charlotte, North Carolina, and

Gainesville, Florida. Two monthly figures were available

from each area, the total monthly dollar volume and the

total monthly number of sales which make up the dollar

volume. By dividing the first figure by the second, the

average sale price for the month could thus be determined.

Sales in Charlotte, North Carolina

Data from 1966 through 1976 was available for the

number of sales and are shown in Table 11. The total dollar

volume was available from 1966 through 1975. The average

sale price was calculated and shown in Table 12. The

Charlotte data include only house sales. But, in reviewing

the data, an occasional fluctuation was noticed which did

not appear to be consistent with the other data. The expla-

nation offered from the MLS people was that clerical errors

are sometimes made. It might be that a large apartment

complex sale was accidently included in the totals which

would distort the average sale price upward.

This type of problem is typical of problems expected to

be encountered with MLS data especially when the information

has been collected primarily by hand. The greater the

number of observations (sales) the less these errors will

distort the average price.

If the Charlotte price data were to reflect the national

seasonal fluctuations then the volume figures should probably


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have the same tendency to be low in the winter, expand in

the spring and peak during the summer. From Table 11, it

appeared that the volume does follow that pattern. The

highest volume months appeared to be April through August.

The lowest volume months appeared to be October through

December. September, January, February and March are the

transition months.

While the prices in Table 12 had not been adjusted for

inflation it appeared that they experienced the same trend

as the national data. Prices rose in the spring until they

reach a peak in June, July and August. The prices level off

or decline slightly during the winter. This is the same

pattern shown by the national data before it was adjusted

for inflation.

To observe the data further, the prices were adjusted

for inflation using the HPI as was the national data. The

adjusted prices are contained in Table 13. These figures

have been graphed in Figure 5 to show the seasonal patterns.

The initial impression from the data was confirmed by

the adjusted figures and the graph. A distinct seasonal

pattern similar to the national seasonal pattern is apparent.

As mentioned earlier there are abnormalities which appear

from time to time. Because of the previous background

information these abnormalities are believed to be caused by

errors in collecting and reporting the data.

To determine whether the index can-be used on a local

level, the Charlotte prices were manipulated in the same


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fashion as the national prices. The prices were grouped

into seasonal years, from September to August. The adjusted

prices for each month in a year were summed and divided by

12 to obtain the average monthly price for the year. That

average price was compared with each monthly price by

subtracting the monthly price from the mean. If all other

factors are held constant, the difference between the two

prices should be caused by seasonal demand changes.

The variance for the year was then calculated using the

formula described previously. Two comparisons were made,

one to determine how many of the monthly differences were

reduced by the application of the seasonal index and the

other to determine whether the variance was reduced.

To accomplish these comparisons, the national seasonal

index was used to adjust the HPI-adjusted Charlotte prices,

and the same information found above was calculated for the

adjusted data. The results were that 64 of the 108 monthly

observations, or 59.3 percent, resulted in lower differences

between the monthly price and the average price. Additionally,

seven of the nine yearly variances, or 77.8 percent, were

reduced. Table 14 provides a list of the monthly seasonally

adjusted prices and the standard deviations derived from the


There are several interesting features in the results.

First, 23 percent of the wrong adjustments (where the index

did not work) occurred in 1968. Of the 12 monthly adjustments

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in that year 10 were incorrect. In reviewing the raw data

it appears that the volume of sales during that period

increased significantly. It might be that the city experi-

enced a boom in the market that acted to distort the seasonal

pattern. For example a new local industry might have been


Additionally, 40 percent of the wrong adjustments

occurred during February, March, and April. Again, looking

at the raw data, it appears that Charlotte may experience an

earlier upturn in annual sales than does the rest of the

nation. A slight adjustment of the index for this local

market aberration could eliminate most of that problem.

The real test of the index is whether it reduces the

total variance. In this case it does in all but two years.

Those two years were 1967 and 1968. Again, it might be that

a local event distorted the seasonal pattern. The index has

acted to flatten the seasonal pattern in all the other


As with the United States data, the coefficient of

variation (standard deviation divided by the mean) was

reduced on the average for the nine years. However the

percentage reduction was not as great, falling only about

7.5 percent from 5.05 percent to 4.67 percent.

Because of the consistency with which the index reduced

the differences (in effect acted to eliminate the seasonal

changes), I feel that the model is a reasonably good estimate

of the seasonal index for the Charlotte market. A different

index based entirely on the Charlotte market data could be

constructed. But the Charlotte data have errors which are

more pronounced than similar errors in the national data,

and local temporary factors introduce nonrecurring fluctu-

ations in the local data. Thus, the national index is

probably as good, if not a better index, than one derived

from the local data. Certainly it appears that using the

national seasonal index is better than using no index in the

Charlotte market.

Sales in Gainesville, Florida

As with the Charlotte sales data, the Gainesville data

were collected from the local MLS. There are several impor-

tant differences between the two sets of data. First, the

Gainesville volume is less than one-half that of the Charlotte

volume. This will allow the errors to show through more

clearly. Since the sample is smaller, the results are not

as reliable.

The second difference is that the Gainesville MLS only

kept records for total sales. Total sales include vacant

lots, apartment complexes, acreage, and warehouses, as well

as single-family homes. This is a serious deviation from

the national data. However, probably 90 percent of the

reported sales in Gainesville were of single-family houses.

Additionally, monthly summaries showing individual office

sales were available. In an effort to reduce some of the

greater distortions, I reviewed all of the monthly summaries

and eliminated those sales which appeared to be distorted.

For example, in July 1968, office 15 reported a sale of

$1,600. The average sale price for the month was $22,745.

I eliminated the $1,600 sale from the data as probably being

a vacant lot sale. This action has introduced some personal

bias into the data, but hopefully this bias has made the

data more representative of the housing market and is the

type of adjustment which might be used on the local level by

an analyst attempting to establish a local index.

The Gainesville volume data are listed in Table 15.

The average sale price is listed in Table 16 and the average

price adjusted for the HPI is listed in Table 17. Again the

seasonal pattern appears very distinct. Volume is low in

the winter. It increases through the spring, reaching a

high in the summer, before falling through September to the

low winter months.

The prices appear to exhibit the same seasonal vari-

ations as seen in the national and Charlotte data. The HPI

adjusted prices have been graphed in Figure 6. While this

graph is not as smooth as the Charlotte graphed data, neither

were the Charlotte graphed data as smooth as the national

data. It would appear that the larger fluctuations are a

reflection of the smaller number of observations and the

inclusion of nonsingle-family home sales in the data.

The same process used to analyze the Charlotte data was

used on the Gainesville data. The seasonally adjusted and

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M art

HPI adjusted prices are reported in Table 18. The result

was that of the 132 observations, 85, or 64.4 percent, of

the monthly differences were reduced by the seasonal index.

In addition, eight of the eleven years had reduced variances.

15 percent of the wrong adjustments occurred in the month of


A look at the raw data shows that September is still a

transition month, but the amount of the decline from the

summer months to September appears not to be as sharp as the

national average. This could relate somehow to the strong

influence on the area by the University of Florida. While

normal school years begin in late August or early September,

the university school year began in late September; thus,

buying and selling probably continued into September, keeping

prices slightly higher than the national average.

As with the national data and the Charlotte data, the

coefficient of variation (standard deviation divided by the

mean) was reduced on the average for the 11 years. The

reduction from 8.94 percent to 8.27 percent is about 7.5

percent or approximately the same percentage reduction

experienced by the Charlotte data.

The index again reduced the total annual errors and did

better than average on the monthly adjustments. It appears

that the index reflects some seasonal pattern in the Gainesville

market. Additionally, since the national model represents

all the local markets, and the local markets represent all

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sales, it is reasonable to say that on the average the

national model should represent the sale of the average

house within the local market.

Some Observations on Volume

The volume of sales activity has been used throughout

this study as an indication of the expected change in prices.

Table 19 lists the average monthly ranking for the nation,

Charlotte, Gainesville and Los Angeles. There are differences

in monthly rankings from location to location. For example,

June ranks as the month with the second highest volume of

sales for the nation on the average, Charlotte ranks June as

third, and Gainesville ranks the month as fourth. What is

important to note is that the same relative volume is experienced

in all locations for all months. Thus it appears that the

volume builds to the summer months and then falls to the

winter months.

This pattern is based on gross sales. There has been

no adjustment for the number of days in the month, the

number of weekends, or specific days of the week. These

"trading-day" variations have been found to have a signifi-

cant influence on the data.1

The most obvious misrepresentation is for the month of

February. That month generally has only 28 days. When com-

pared with the month before and the month after which have

31 days each, the true demand will be slightly distorted.

For example, if February reports eight sales a day the total


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would be 224 sales for the month. January could report

daily sales of only 7.4 and still be rated higher than

February (7.4 x 31 = 229).

Therefore, any attempt to compare prices directly with

monthly volume should be adjusted for the number of trading

days in the month. However, this problem does not affect

this study's model, since it is concerned only with price

changes; and sale prices are not necessarily affected by

"trading-day" variations.

Test Conclusions

The initial test for the model determined that the

means developed from the national data appeared to represent

the true mean of the data and therefore could reasonably be

used as a seasonal adjustment of national sale prices. The

next two tests applied the seasonal index to two local

markets, Charlotte, North Carolina, and Gainesville, Florida.

The seasonal index reduced the variations in prices which

are believed to be caused by seasonal demand changes in

those markets. The Gainesville test results were significant

by themselves, reducing the monthly price differences for

64.4 percent of the months observed and reducing the monthly

variance in eight out of eleven years. Charlotte's data

produced very similar results with 59.3 percent of the

months showing a reduction in the difference from the average

price. Additionally, in all but two years there was a

reduction in the monthly variance.

The graphed data from both cities also show a close

resemblance to the national data. There are a few months

which vary from the national trend, but those specific

variations are probably caused by errors in reporting the

data. The overall trend of the city data matches that of

the national data.

The model appears to represent a reasonable index with

which to adjust selling prices of the existing single

family house throughout the United States, where those

markets display similar seasonal characteristics. These

characteristics can be found fairly easily by looking at the

MLS sales data for the local market.

The monthly sales volume ranking from the two cities

(Table 19) appears to follow very closely the ranking of the

national data for the same period of time. Quarterly sales

data from Los Angeles from a period 10 to 15 years earlier

than the period covered by this study appear to share

similar characteristics with the national and city data. A

monthly sales volume ranking (Table 19) developed from the

California data and adjusted from the national data, shows

that the California sales volume could have experienced the

same relative volume changes as does the national volume

figures. The implication is that not only does the model

represent the market during the test period but also back to

the beginning of the California study, a span of approximately

25 years.2 Thus, where the sales volume characteristics are

similar, house sales occurring in different months can be

adjusted using this study's index, to obtain an estimate of

the prices that occur during other months.


Division, Existing Home Sales, Annual Report (1978),
p. 46.

2. An additional test was conducted on the California data.
The average quarterly sale prices reported in that
study were grouped into the seasonal years beginning in
the fouth quarter and ending with the third quarter for
1953 through 1960. This produced six seasonal years to
The seasonal index from this study was then grouped
into quarters and averaged for each quarter. This
quarterly index was then applied to the California
seasonal year's data.
Of the 24 quarters, 21 were adjusted so that the
error or difference from that year's average price, was
reduced. It appears that the index might be applicable
to the earlier California data also.
However, it should be noted that the California
data had not been adjusted for inflation (about 5.4
percent annualized for the period). Because of the way
the index and the seasonal year were derived, these
results cannot be used except to note the results with
interest and suggest that further study is needed.


The Formula

The most obvious use for the model will be to adjust an

observed sale price from one month to equate it to a sale

price in another month. This will be useful in appraisal

work and in removing the seasonal variation from research

data. The formula for the model to accomplish this adjust-

ment is
Pi (Pm) r--m+i) (BMA) (1/BMAm+i

Pm = the observed monthly sale price

m+i = the monthly price to be estimated from P

An appraisal example would be to adjust comparable

sales, for the appraiser's estimate of value. Assume a sale

took place in January 1975. That sale is to be used to

determine the value of a subject property being appraised in

April 1975. Inflation increased .021079 from January to

April (1.613 to 1.647 from the HPI). The sale price observ-

ed in January was $36,900. What is April's expected price?

PApr = ($36,900) (1.61) (1.011438) (1/.98034)

PApr = ($37,677.82) (1.031722)
P Apr = $38,873.02
The actual price for April, from the NAR Table 3,

turned out to be $38,800. Using the model, the price was

missed by $73 or only .188 percent. Had the price been

adjusted only for inflation, the estimated price, $37,677.82,

would have been off by $1,122 or 2.892 percent. Had no

adjustment been made in the price, the error would have been

about 5 percent ($36,900 $38,800 = $1,900).

Various comparisons are made using house sales data. If

the analyst is using anything other than annual data, the

information will contain a seasonal bias. By using the

seasonal index, the analyst can reduce the seasonal bias,

creating seasonally adjusted prices with which to work.

This adjustment is simply

PSA = Pm (BMA )

where PSA is equal to the seasonally adjusted price.

An example would be where a researcher is comparing

first quarter 1975 sale prices with third quarter 1980

prices. The first and third quarter prices would be multi-

plied by the seasonal index for that period to obtain the

seasonally adjusted price. (A quarterly index can be deter-

mined at this point by averaging the three monthly index

figures, but this introduces an error factor. This error

will be compounded when a transition month like September is

averaged with July and August, traditionally peak price


Impact on the Appraisal Process

Appraisals of single-family houses, where there are a

reasonable number of recent sales, will use comparable sales

as the most important method of determining the value or

expected selling price of a house. Depending on the avail-

ability of comparable sales, the appraiser will generally

not use sales more than six months old. The appraiser will

generally select from three to six of the more recent sales

felt to best represent the subject property.

Not making a seasonal adjustment in the comparable

house sales may result in a biased value estimate. During

some parts of the year the appraisal accuracy will be

greatly distorted by seasonal price changes. An appraisal

based on four comparable sales with the appraisal work being

done in April (using comparable one to six months old) for

a May 1st appraisal date could have been as indicated in

Table 20.

It is not uncommon to find appraisals which make no

adjustment for time, especially when the comparable sale

takes place within a very few months of the appraisal date.

Had the appraiser made no adjustment for time in the three

examples given in the chart, the appraisal errors would run

from a low of 6.2 percent to a high of 10.5 percent. Obvi-

ously some adjustment, even in the very short term is

required. A professional appraisal error of 10 percent on

a single-family house can hardly be called professional.

Inflation has aggravated the error between comparable

sales and the expected selling price of the existing single-

family house. Many appraisers attempt to adjust for infla-

tion by estimating the amount of inflation which has and

will take place between the time of the comparable sale and


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the expected selling date of the subject house. Since the

Housing Price Index is more a measure of the housing market

at the margin (at the time of the sale), that index is

probably the best inflation estimate of the many available.

Unfortunately, adjustments upward for inflation between

the summer sales and the following winter sales only result

in larger errors because of the actual decline in prices

experienced in the winter months. While the appraiser is

adding one-half to one or more percent per month to the

selling price of the comparable house, by October or November

the price may actually decline one to five percent.

The second part of the chart shows comparable sales

adjusted for inflation using the actual inflation figures

for the time period. While the appraisal error was reduced,

it still ranged from 5 percent to 6.3 percent, a very materi-

al amount of dollar error.

The results of an appraisal during the transition

months without a seasonal adjustment may cause the property

owner either to overprice the house in the winter, causing

it to remain on the market for an extended period of time,

or to underprice the property in the spring. Either way the

property owner has not received his money's worth by having

a professionally accurate appraisal of the property.

The last three lines of the chart show the comparable

sales adjusted not only for inflation but also seasonally

adjusted using this study's seasonal index. In one case the

error was reduced to less than 1.1 percent. The worst the

error was 2.4 percent. This still does not produce results

that are completely accurate, but the results are exception-

ally close when both the inefficiencies in the market are

considered along with the shortcomings of the index previously

discussed. A random sampling of similar seasonal adjustments

produced seasonally adjusted appraisals with errors from as

low as .25 percent up to three percent, with most lying in

the one to two percent range.

Note that the index as designed is a weighted average

between recession data and expansion data. The periods

covered in the chart are expansion periods. The index is

more conservative for expansion periods because of the

inclusion of the recession data. Therefore, the "under"

estimating as experienced in the three examples is to be

expected. Had the example included comparable sales during

a recessionary period, the adjustments would probably over

estimate the subject property. The over estimation should

still not exceed the one to two percent range.

A Counseling Tool

The seasonal index is also a counseling tool for use by

the appraiser. It can be used to show the property owner

that during different periods of the year more or fewer

people are in the market to buy and sell houses, increasing

or decreasing the probability of a sale.

With complete information the buyer (or seller) may

decide to postpone a transaction until market conditions

change. The seasonal index is proof that the change will

occur and of the direction it will take.

The appraiser's information about the seasonal change

could also help a client decide to accept an offer, say in

August, at a lower than desired price, instead of "waiting

to see whether something better comes along". With know-

ledge of the seasonal change the client would know that

because of the drop in the number of buyers in the market

and the expected drop in the average selling price, the

probability of selling the property at the current market

value decreases.

Failing to advise a client of these changing market

conditions could cost that client considerable money and

grief. A seller may not be able to hold off selling for

several months (like over the slow winter months). The

seller might be better off delaying moving or reducing the

price rather than risk holding the property for four to six

months in the winter. Knowledge of the seasonal patterns

will help the client to reduce the risks of home ownership.
Future Regional Indexes

Just as there are now books published with building

costs and standard expense estimates for various regions and

locals, the seasonal index could be further refined not only

to include the obvious adjustments for the business cycle

and quality trends, but also for regional variations in the

seasonal demand.

The NAR publishes its data on a regional basis making

a regional index a reasonable next step. Additionally,

locations with seasonal variations at odds with the national

information could develop their own local index through

correlation of local MLS data of volume and sale prices.

This type of refinement should ultimately lead to a better,

more accurate appraisal for the home owner.

Abnormal Profits

Any time there are predictable changes in prices great

enough to cover transaction costs or holding period losses,

and these price changes are not justified in the long run,

there are abnormal profits available in that market. As

this study has pointed out, there are predictable fluctuations

in the existing single-family house prices which are relative-

ly short term in duration and certainly not justified in the

long run. People with information on these seasonal changes

theoretically could reap abnormal profits by arbitraging

these price differences. It is possible for a person to

option property at the market value in December, pending the

owner's planned move in the summer. The optionee could then

resell the property at the predicted higher price, thereby

obtaining an abnormal profit on the transaction.

However, as more and more people become aware of the

exact nature of the observed monthly price changes, more and

more people should act to eliminate the abnormal profits in

the system, first by offering to pay more for options and

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