SEASONAL FLUCTUATIONS IN THE PRICE
OF EXISTING SINGLE FAMILY HOUSES
BY
KENNETH R. McGURN
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1981
Copyright 1981
by
Kenneth R. McGurn
ACKNOWLEDGEMENT
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.
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
LIST OF FIGURES
LIST OF TABLES
ABSTRACT ......
CHAPTER
T TMT'DncT
(,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 ...................................
FACTORS AFFECTING PRICES ..................
RESULTS OF ADJUSTING FOR INFLATION ........
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 .................................
PAGE
iii
vi
vii
ix
II
III
IV
V
VI
VII
VIII
. .... .... ....... . 57
........................
.........................
.........................
.........................
CHAPTER PAGE
IX TESTING IN THE LOCAL MARKET ............... 58
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
LIST OF FIGURES
PAGE
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
LIST OF TABLES
PAGE
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
vii
PAGE
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
viii
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
SEASONAL FLUCTUATIONS IN THE PRICE
OF EXISTING SINGLE FAMILY HOUSES
By
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.
CHAPTER I
INTRODUCTION
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
index.
CHAPTER II
SUPPLY AND DEMAND
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
weather.
Shifts in Demand
The NATIONAL ASSOCIATION OF REALTORS@ (NAR) has collect-
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.
Notes
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.
4. NATIONAL ASSOCIATION OF REALTORS@, Economics and Research
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.
CHAPTER III
REVIEW OF THE LITERATURE
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
noted:
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
Total
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
Average
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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
report:
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.
Notes
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.
5. NATIONAL ASSOCIATION OF REALTORS@, Economics and Research
Division, Existing Home Sales, Annual Report (N.P.:
NAR 1977), p. 45.
6. Ibid.
7. Ibid.
CHAPTER IV
THE MODEL
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
noted.
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
17
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
houses.
The Data
The NATIONAL ASSOCIATION OF REALTORS@ (NAR) has collect-
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
publication:
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-
cessed.
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
country.2
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.
Notes
1. Marvin Thompson and Bruce Harwood, Florida Real Estate
(Reston, Va.: Reston Publishing Co., Inc., 1980),
p. 35
2. NATIONAL ASSOCIATION OF REALTORS@, Economics and Research
Division, Existing Home Sales, Annual Report (N.P.:
NAR, 1978), p. 45.
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CHAPTER V
FACTORS AFFECTING PRICES
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
identified.
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
25
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
Note
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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CHAPTER VI
RESULTS OF ADJUSTING FOR INFLATION
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
27
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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
amenities.
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
houses.
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
32
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
factors.
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
adjustment:
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
quality.
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
percent.11
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
success.
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
Notes
1. NATIONAL ASSOCIATION OF REALTORS@, Economics and Research
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
market.
10. Maurice A. Unger, Principles and Practices, 4th ed.
(Cincinnati: South-Western Publishing Co., 1969),
p. 32.
11. NATIONAL ASSOCIATION OF REALTORS@, Existing Home Sales
(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.
CHAPTER VII
BUILDING THE MODEL
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.
Methodology
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
12
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
12
B = (E= APm)/12
y m=l m
MAmy By/APm
my y m
12
BMA = (E MA )/n
m m=l m
where
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
Year
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
CHAPTER VIII
VALIDITY OF THE MODEL
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
46
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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
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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
derived.
The variances for the 10 years showed similar results.
All were reduced except for the years 1970 and 1974. The 80
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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
n
S 2
s' = i=l (y1-y)
n-1
where
n = the number of observations
y = the MA for the month from each year
= the BMA for the year
y
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
where
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
intervals.
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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Conclusion
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.
Note
1. NATIONAL ASSOCIATION OF REALTORS@, Economics and Research
Division, Existing Home Sales, Annual Report (N.P.:
NAR, 1978), p. 46.
CHAPTER IX
TESTING IN THE LOCAL MARKET
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
levels.
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-
ation.
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
64
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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
variances.
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
responsible.
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
years.
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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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
September.
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.
Notes
1. NATIONAL ASSOCIATION OF REALTORS, Economics and Research
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
adjust.
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.
CHAPTER X
WORKING WITH THE MODEL
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
HPI
Pi (Pm) r--m+i) (BMA) (1/BMAm+i
m
where.
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
months).
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
