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Valuation Theory, the Marshallian
Synthesis and Implications to Mark-toMarket Measurements
Terry V. Grissom
Professor of Real Estate University of
Washington and Lecturer in Real
Estate University of Ulster
Process
• Problem :
Economic Foundation of Valuation
Techniques and Implications to
Theory of Equivalence or Hierarch
of Process
• Theory:
Value
Valuation
Appraisal
• Empirical:
Fit of Model
Equivalence vs. Hierarchy
Comparative & Statistical
mark-to-market
Theory
• Value Theory
[Marhsal (1890/1979) (Friday (1922), Ratcliff
(1961, 1965, 1972),Wendt (1974) Grissom (1981,1985, 1986),
McParland, McGreal and Adair (2000), Odileck and Unsal, (2009)
DeLisle &Grissom (2010)],
• Valuation Theory [Marhsal (1890/1979), Mertzke (1927), Babcock
(1932), Bonbright (1937), Schmutz (1948), Wendt (1956), Ratcliff
(1961, 1965, 1972a), Babcock (1968), Wendt (1974), Graaskamp
(1979), Grissom (1981, 1985, 1986). Grissom et al (1987), Grissom &
Diaz (1991), Moore (1992), Wincott et al (1996), Scott (1996),
Crosby (1999), Crosby and Murdock (1999), Sharpiro et al (2009),
Parli & Fisher (2010), DeLisle &Grissom (2010)],
• Appraisal Theory [Mertzke (1922), Schmutz (1948, 1956), Kinnard
(1966) Ratcliff (1964, 1965, 1972b), Wendt (1974), Graaskamp
(1979), Grissom (1981, 1985, 1986) Diaz (1990), Grissom and Diaz
(1991), Pomykacz (2009), DeLisle and Grissom (2010)
Value Theory
• Value Determinants
• Value Premise/Principles
• Statistical Concepts (Colwell,1979)
(Gini, 1922)
(Kummerow 2002)
(Grissom 1986)
• Equilibrium Concepts (Marshall 1890)
Valuation Theory
Measurement and Base:
• Traditional –Property Base
• Statistical – Data Set or Market Base
(Grissom, Robinson, Wang 1987)
• Equilibrium – Conditioned Set or Market Base
Cannaday and Colwell (1981a, 1981b)
Appraisal Theory
Appraisal Analysis comprised of two general
decision tools (Moore, 1992):
• Methods of standards and measurement; objective
• Decision tools
Standard/Objectives – (subjective/judgment)
Logic:
Theory of Equivalence
Hierarchy
Evaluation Base
Figure 1
Marshallian Valuation Construct and Market Structure
P
SM
SSR
SI
DSR
SL
PM
PI
PSR
DL
DI
DSR’
Q
Market Constructs of Approaches
• Momentary/current price in Short Run Equation:
premised on Supply and Demand
PM   o  qs  Rs | QM
• Price is a function of size/quantity and rent
Where:
 O  QM  RS
PM 

Conditional on and inverse relationship of price and quantity
QM   o   o PM  Rs
Market Constructs of Approaches
• The momentary market is altered by shifts in current
supply considering modifications as per land use
succession conditions:
• This is estimated by the rate of growth in supply based on
the neo-classical theorem as formulated by Robinson
(1962). This theorem influences various long-run impacts
on current expectations across input markets. The
variables per market used in this study are conditioned on
the weighted effects of growth expectations (SR)as
functions of asset market calculus relative to the long-run
normal growth rate:
SSR = h(SM, SR, QSR|PSR, PM)
Market Constructs of Approaches
Short Run Pricing incorporating growth/change
considerations and impacts:
Change/growth rate:
gI
g LR
)gI  (
) g LR ))
 = gSR = h( (
g I  g LR
g I  g LR
Expected Short-Run Price:
 P E|Sm  SR (Qi SR  Sm)  PSR
Market Pricing Constructs of Approaches
Intermediate Valuation Phase:
Hayek: Supply price
/roundabout discounting
affects
VI | PIS   IS  IS Vi|s
Where:
And
Vi
NOI i

Ro i | t
NOI = f(R, Ro|t, GIM)
NOI = net operating income ( rent less all expenses
and deductions)
OER = operating expense ratio, derived from OER = 1-(Ro
X GIM) to derive a market developed operating
expense ratio (OER). See Triece equation
GIM = a gross income multiplier (Price Gross Income/rent).
Market Pricing Constructs of Approaches
Demand Pricing conditioned on price and rent associations:
VI | PI |D   I |D  DVi|D  R
The intermediate equilibrium value (VI|E) occurs where VI|D VI|S = 0; in the equation form where:
[I|D - D VI|D + Ri|D] - [I|S + S VI|S] = 0
Using the relationship VI|D - VI|S = 0; then Equation 5 is restated
as:
[I|D - I|S] + VI|E (S- D) + Ri|D = QVI|E
VI|E
= QVI|E - Ri|D -[I|D - I|S]
(S- D)
Market Pricing Constructs of Approaches
Long Run considerations (distributive theory):
• SLR = f(|R, L|w, K|i, |)|, 
Where:
 = land as a factor of production compensated by rent R, a
market price for the use of land or a cost in the process of
production/construction
L = labor compensated with a wage (w)
K = capital receiving a return of (i) and
 = entrepreneurship, which is compensated with profit, 
which is treated as a cost of production in the creation or
development of an asset.
The factors are conditional on the level of total resources  and the
state of choices of development technology, , efficient, inefficient,
sustainable or traditional.
Market Pricing Constructs of Approaches
• The ability to link long-term normal price and cost
supports the form of the long-run supply and demand
schedules based on Demand and Supply Equations
respectively:
Demand
QLR|D   LR|D   D PLR|D  Ri|LR
Supply
QLR|S  LR|S   S PLR|S
Equilibrium State:
P LR|S - P LR|D = 0
Empirical
• Fit of Theory/Model-Equilibrim: Table 2a/b
and Figures 2-7
• Statistical Distributions- E(V), Ve, Vp: Table 3
relative to Equilibrium values
• Tests of Equality (Marhall’s Time Frames)
Theory of Equivilence
Hierarchy :
Table 4
• Comparative Statics and Marginal
Distributions (Mark-to-Market):
Table 5
Equilibrium Values
Market
Atlanta
Austin
Boston
Moment
ary
ShortRun
$150.00
$142.65
$136.50
$329.00
$275-280 $274
$118.00
$289
Intermediary
$146.30
$123.00
$301.50
Statistical Values
Long
Run
$144.50
$120.00
$295.00
E(V)|M
SR
$144.92
$125.58
$141.31
$153.84
$177.21
$ 72.18
$ 89.21
$128.85
$145.81
$151.65
$243.00
$171.49
$267.01
$313.50
$321.65
LR
$148.57
$144.60
$117.54
$119.62
$263.33
$255.55
Ve|Md
SR
$145.91
$124.82
$141.34
$151.41
$176.77
LR
Vp|Mo
SR
LR
Risk(SR)
SR
$142.74
$149-150
$130-133
$141-142
$140-145
$176-177
$ 72.30 $115.81
$ 85.18
$126.85
$142.76
$151.96 $127.45
$ 72.50
$ 70-75
$110-120
$140-143
$151-153
$ 75
$ 0.46
$16.16
$13.73
$ 6.50
$ 0.85
$243.50
$172.85
$283.55
$309.83
$319.50
$180-190 Bi$200-225 modal
$300-325
$300-305
$310-320 $316
$27.40
$19.85
$44.57
$15.58
$13.56
$148.05
$265.85
$267.70
$147
$144
$109
$3.84
$6.40
$1.36
$0.62
$1.64
LR
$ 2.77
$15.96
$ 7.54
$30.18
$24.19
$60.15
Valuation Theory Model Tests-Empirical
P
220
Atlanta: Marshallian Synthesis of Valuation
Approaches and Market Structure
Sm
S(I)
200
D(I)
D(L)
180
D(sr)
160
Sale
$150.00 Comps
S(L)
Income
$146.30
140
Cost Approach
$144.50
S(I)'
D(I)'
120
S(L)'
D(L)'
D(sr)'
100
90000
110000
130000
150000
170000
Q
190000
Valuation Theory Model Tests
P
240
Austin Marshallian Synthesis of Valuation
Approaches and Market Structure
S(M)
D(I)
200
D(L)
S(I)
D(sr)
S(L)
160
$136.50
120
$123.00
$120.00
D(L)'
80
D(I)'
S(L)'
D(sr)'
40
Q
74000 76000 78000 80000 82000 84000 86000 88000 90000
Valuation Theory Model Tests
P
400
360
320
Boston Marshallian Synthesis of Valuation
Approaches and Market Structure
D(L)
S(m)
S(I)
S(L)
D(I)
D(sr)
$329.00
$301.50
280 $295.00
240
S(L)'
200
D(sr)'
160
D(L)'
S(I)'
D(I)'
120
Q
190000 200000 210000 220000 230000 240000 250000
Valuation Theory Model Tests
Los Angeles Valuation Approaches
and Market Structure
P
360
320
D(L)
D(sr)
S(m)
S(L)
D(I)
S(I)
280
$252.00
240
$237.00
200
$197.00
D(L)'
160
120
80
S(I)'
D(I)'
S(L)'
40
D(sr)'
0
Q
300000 320000 340000 360000 380000 400000 420000
Valuation Theory Model Tests
Nashville Valuation Approaches and Market Structure
P
180
160
D(I)
D(sr)
S(m)
S(I)
140 $135.50
D(L)
S(L)
120 $118.50
$112.50
100
S(I)'
S(L)'
80
D(L)'
D(sr)'
D(I)'
60
Q
24000 26000 28000 30000 32000 34000 36000 38000
Valuation Theory Model Tests
P
500
San Francisco Valuation Approaches
and Market Structure
S(m)
S(I)
D(L)
400
D(I)
S(L)
D(sr)
300$279.00
$259.00
200 $230.00
D(sr)'
D(L)'
100
S(I)'
S(L)'
D(I)'
0
88000 92000 96000 100000
108000
Q
116000
Appraisal Theory: Equivalence vs Hierarchy
• Empirical Analytics suggest Equivalence concept is weaken
• Samuelson and Comparative Statics (1946-1947): offers
statistical critique of comparative statics in relation to marginal
analysis. This offers support for or rejection of observations.
This is achieved in a 3 step process where:
• Samuelson builds on Stigler’s argument that a goods
endogenous attributes are proportional to the quantity of the M
good itself. This allows the price of the goods to be used to
make maximum/minimum decision calculations. Goods can be
specified by unique value determinants and attributes in the
form:
n
M
i 1
1i
Qi  M 1
Appraisal Theory: Equivalence vs Hierarchy
M1 is a minimum aggregated productivity attribute
measurement allowed or acceptable per asset. A1iQi is the
attribute quality measurement observed per unit in the
market.
• The assumptions of the endogenous attributes as defining
the asset or good allows the price or cost estimate to
specified as Pi = C|P1Q1+C|P2Q2…C|PnQn.
• This allows the cost combination in two price situations
to be compared to the extent Pi  Pj and deduce the level
of price changes associated with optimal changes in
quantities associated in each price situation.
Appraisal Theory: Equivalence vs Hierarchy
• In this context the corresponding price and quantity changes in the
momentary market are stated as PM and QM and PSR and QSR in the
short run market.
• The price-quantity pairings in the intermediate and long run
markets are indicated by I and LR. By definition:
Paasche/Laspeyres Indices
 PMQSR   PMQM and  PSRQM   PSRQSR
• Adding these inequalities and rearranging terms produces:
 (PSR-PMR)(QSR-QM) = P1Q1P2Q2…PnQn  0
This equation allows the comparison of the equilibrium positions in a
comparative static format. This enables a direct comparison of the
equilibrium positions as specified for the momentary, short-run,
intermediate and long-run market pricing points.
Appraisal Theory: Equivalence vs Hierarchy
• With the assumption of constant utility (U), the price
differences can be carried further to a dynamic
construct consider the integral format:

t1
t0
[ P I (t )  P SR (t )][Q I (t )  Q SR (t )]dt | U  0
The above equation reflects a Hicksian demand construct, as
such for the equivalence theorem to hold, the Hicksian demand
structure has to hold across market periods, while a hierarchy
format is consistent with the Marshallian construct with additive
utility inferred. The test is determined by the percentage
difference of the value estimate from the current market
standardized as one (1), with the test statistic of 1-.
Conclusions
• Good Fit of Models across Economic phases
• Strong argument for hierarchy of valuation techniques (given the
partial equilibrium construct that underlies the appraisal process
based on the economics of the Marshiallian synthesis.
• though reconciliation process is reasonable, for it to hold significant
procedure and assumptions must be developed in Sharpiro et al
(2009)
• Mark-to-market standards supported if perspectives are designated
as
• Potential to condition pro-cyclical concerns
• Suggest the focus on using market rather than subject as base of
analysis (or integration: See Grissom, Robinson and Wang (1987)
• Further benefits to be gained by employing calculus of variation
construct and error correction models as alternative to structural
equilibrium procedure