Measuring land and other capital inputs

The views expressed are those of the author(s) and should not be attributed to the Economic Research Service or USDA.
Hedonic Analysis of Land
Quality
Richard Nehring*, V. Eldon Ball*, David Marquardt*,
Robert Reinsch**, Paul Reich**, and Jarrett Hart*
SWCS Annual Meetings
Lombard, IL, July 27-29, 2014
The views expressed here are not necessarily those of Economic Research Service
or the U.S. Department of Agriculture.
Affiliations *ERS **NRCS

 Disregarding quality differences generates biased
estimates of the land input and thus of productivity.
 In this PPT we present an example of techniques
and data sets used to quality-adjust values for land
 United States, Canada, Australia, Japan, and 14
European countries using price and quantity data
for 2005.
Objectives

Hedonic Studies of the Effect of Various Characteristics on Farmland
Values
--------------------------------------------------------------------------------------------
Author Year Method Data Key
Characteristics
--------------------------------------------------------------------------------------------
Palmquist et.al. 1989 Box-cox 79-80 Erosion,
tobacco quota
Land Econ
Miranowski et.al.1984 Linear 74-79 Topsoil depth,
PH
AJAE
Maddison 2000 Linear 94 Popden, milk
quota
Land Econ
Roka et. al. 1997 Various 94-95 Popden, prime
farmland
Land Econ
------------------------------------------------------------------------------------------------------------

Hedonic Studies of the Effect of Various Characteristics on Farmland
Values
--------------------------------------------------------------------------------------------
Author Year Method Data Key
Characteristics
--------------------------------------------------------------------------------------------
Nehring 2001 Semi-log 1997 Pop acc, Soil
stress
JPA
Nehring 2003 Semi-log 1997 Pop acc, Soil
stress
Wiebe Book
Nehring et al. 2006 Box-Cox 98-01 Pop acc, Soil
stress
AJAE
Ball et al. 2007 Box-Cox 1992 Pop acc, Soil
stress
Applied Econ
------------------------------------------------------------------------------------------------------------

Land
 To estimate the stock of land in each country, we
construct time series price indexes of land in farms
 The stock of land is then constructed implicitly as the ratio
of the value of land in farms to the time series price index
 Differences in the relative efficiencies of land across
countries prevent the direct comparison of observed
prices
 To account for these differences, indexes of relative prices
of land are constructed using hedonic methods

Methodology
Box-Cox Model
P(1 ) = Xt(2) + D + 
P(1 ) is the Box-Cox transformation of land price
X(2 ) is the Box-Cox transformation of RHS
Continuous variables
D are dummy variables
 is value used to transform continuous variables
 is the error term

 Under the hedonic approach, the price of land is a function
of the characteristics it embodies
 Therefore, the hedonic function may be expressed as
W=W(X,D), where W represents the price of land, X is a
vector of characteristics, and D is a vector of other
variables
 Characteristics include soil acidity, salinity, and moisture
stress, among others
 In areas with moisture stress, agriculture is not possible
without irrigation, hence irrigation is included as a separate
variable
 Because irrigation mitigates the negative impact of acidity
on plant growth, the interaction between irrigation and soil
acidity is also included in the hedonic regression

 In addition to environmental attributes, we also include
a “population accessibility” score for each region in
each country
 These indexes are constructed using a gravity model of
urban development, which provides a measure of
accessibility to population concentrations
 A gravity model accounts for both population density
and distance from that population center
 The index increases as population increases and/or
distance from the population center decreases
 Other variables (denoted by D) include country dummy
variables which capture price effects other than quality

 Most empirical studies adopt the semilog or double-log
form of the hedonic price function
 However, economic theory places few if any restrictions
on the functional form of the hedonic price function
 We adopt a generalized linear form where the dependent
variable and each of the continuous independent
variables are represented by the Box-Cox transformation
 This mathematical expression can assume both linear
and logarithmic forms, as well as intermediate non-linear
forms

Figure 1. Stress Categories in the United States; Data from World
Resources group NRCS

Figure 2. Stress Categories in Europe; World Resources Group NRCS

Table 1. Definition of variables in the data set
Variable Unit Definition
Land price Local currency per
hectare
Price of agricultural land
Land area Hectares Total land area
Population density Index A measure of the size and proximity of nearby population centers
Ice cover Percent of total land
area
Covered by ice
Ocean “ Covered by ocean
Inland water “ Covered by lakes or rivers
Low temperature “ Having soils with mean annual temperature < 0o
C and mean summer temperature < 10o
C
Salinity “ Having soils with pH > 9.0 (i.e. where the salt concentration is so high that it prevents
plant growth)
Acidity “ Having soils with pH < 5.2 (i.e. where soil acidity reduces root growth and prevents
nutrient uptake)
Moisture deficit “ Experiencing soil moisture stress for 4 or more months in a year
Moisture stress “ Experiencing continuous soil moisture stress
Low water storage “ Having soils with low ability to store moisture
Excess water “ Having soils saturated with water during long periods of the year
High organic matter “ Having peats or organic soils
Low nutrients “ Having sandy soils or soils with clays with a low capacity to hold nutrients
High shrink swell “ Having soils dominated by a mineral that causes soils to crack during the dry season
High anion exchange “ Having volcanic soils where phosphate is made unavailable to plants
Irrigation “ Irrigated
Few constraints “ Having soils with few or no major soil-related constraints and a generally temperate
climate
Source: World Soils Group, Natural Resource and Conservation Service.

Table 2. Hedonic regression results for land price as a function of productivity-related characteristics
Variable Coefficient t-statistic Variable Coefficient t-statistic
D1 (United States) 5.929887*** 75.73 Ice cover -0.210585 -0.61
D2 (Canada) 6.223239*** 55.89 Ocean -0.306224 -0.53
D3 (Australia) 4.98466*** 28.6 Inland water -0.612973*** -3.5
D4 (France) 7.935627*** 23.16 Low temperature 0 .
D5 (Finland) 8.644438** 2.27 Salinity 0.458457*** 5.49
D6 (England) 6.587544*** 6.76 High organic matter -0.310311 -0.64
D7 (Ireland) 7.243259*** 3.57 Excess water 0.002775 0.02
D8 (Belgium) 10.69653*** 6.02 Moisture deficit -0.445639*** -3.49
D9 (Denmark) 7.605018*** 3.31 Moisture stress -1.013411*** -4.55
D10 (Luxembourg) 11.216754 0.64 Acidity -0.102152** -2.02
D11 (Netherlands) 8.48386*** 3.37 Low water storage 0.804731*** 2.59
D12 (Japan) 12.040995*** 61.93 High shrink/well -0.287112** -2.11
D13 (Germany) 7.916417*** 19.88 High anion exchange 0.126939 0.26
D14 (Italy) 15.163847*** 15.62 Acidity* irrigation 0.030052*** 2.89
D15 (Spain) 12.104318*** 16.08 Few constraints -0.057805 -1.25
D16 (Greece) 13.188315 1.27 Accessibility 0.196948*** 16.59
D17 (Portugal) 11.01414*** 4.23 Irrigation -0.03737*** -4.36
D18 (Sweden) 6.870508*** 4.48
λ-Moisture deficit 1.148484*** 3.82
Number of observations 1807 λ-Moisture stress 1.326057*** 5.09
Log Likelihood -1404 λ-Acidity* irrigation 0.078327* 1.72
AIC 2889 λ-Acessibility 0.026969 0.55
Schwarz Criterion 3109 λ-Irrigation 0.577739*** 16.15

We find that prices of land of constant
quality in European countries relative
to the United States are significantly
different than what would be derived
by equating land prices with
exchange rates.

Table 3. Land Prices and Purchasing Power Parities 1990
--------------------------------------------------------------------------------------------------
Country Land Price Purchasing Power Paity PPP/EX
Nominal Quality-Adj
---------------------------------------------------------------------------------------------------
U.S 1,650 893 1.00 ----
U.K. 3.673 2,334 2.61 1.46
Ireland 3,709 2,812 3.15 1.90
Belgium 444,616 176,052 197.25 5.90
Denmark 50,000 16,721 18.73 3.02
France 19,883 11,390 12.76 2.34
Germany 33,639 14,495 16.24 10.02
Greece 1,476,553 1,430,450 1,602.66 10.11
Italy 6,894,000 4,370,901 4,897.11 4.09
Netherlands 44,814 6,824 7.65 4.20
----------------------------------------------------------------------------------------------------

Map showing the Harmonized World Soil Database by data Sources
(Source: Nachtergaele et al.,2012)

Table 4. Definition of variables in the data set
Variable Unit Definition
Land price Local currency per
hectare
Price of agricultural land
Land area Hectares Total land area
Population density Index A measure of the size and proximity of nearby population centers
Irrigation Percent of total land
area
Irrigated
Aluminum “ Soils with aluminum toxicity
Calcareous “ Soils with calcareous reactions
Sulfidic “ Sulfidic soils
Moisture stress “ Experiencing continuous soil moisture stress
Aridic torric “ Aridic or torric soil moisture regime too dry to grow a crop without irrigation
Leaching “ High leaching potential
Waterlogging “ Soils experiencing waterlogging
Phosphorus “ High phosphorus fixation
Alkalinity “ Soil alkalinity
Salinity “ Soil salinity
Cryic frigid “ Cryic and frigid (<8jC mean annual), non-iso soil temperature regimes, where management
practices can help warm topsoils for short-term cereal production
Permafrost “ Permafrost with 50cm gelisols; no cropping possingle
Cracking “ Cracking clays
Volcanic “ Volcanic soils
Organic “ Organic soil: >12% organic C to a depth of 50 cm or more (histosols and histic groups)
Clayey top
Loamy top
Clayey sub
Loamy sub
Rock
Sandy top
Sandy sub
“
“
“
“
“
“
“
Clayey topsoil >50% (dummy)
Loamy topsoil >50% (dummy)
Clayey subsoil
Loamy subsoil
Rock or other hard root-restricting layer within 50 cm
Sandy subsoil
Sandy topsoil
Source: World Soils Group, Natural Resource and Conservation Service.

Table 5. Hedonic regression results for land price as a function of productivity‐related characteristics
Variable Coefficient t‐statistic Variable Coefficient t‐statistic
D1 (United States) 8.340205*** 40.56 Aridic/Torric Soil dummy ‐0.854886*** ‐21.98
D2 (Canada) 8.512836*** 48.79 High Leaching Potential dummy ‐0.949345*** ‐3.39
D3 (Australia) 8.661371*** 26.64 Waterlogging dummy 0.042464** 1.98
D4 (France) 10.610257*** 47.15 High Phosphorous Fixation dummy 0.052681 0.49
D5 (Finland) 10.187115*** 11.29 Alkilinity dummy 0.015342 0.40
D6 (England) 8.988770*** 6.94 Cryic/Frigid Soil dummy 0.035078 0.94
D7 (Ireland) 8.861795*** 6.95 Permafrost dummy 0.009510 0.10
D8 (Belgium) 13.677157*** 12.33 Cracking Clays dummy ‐0.028223 ‐0.56
D9 (Denmark) 10.279499*** 9.83 Volcanic Soils dummy ‐0.021171 ‐1.08
D10 (Luxembourg) 15.413769*** 4.31 Loamy Subsoil dummy ‐0.053426 ‐1.54
D11 (Netherlands) 10.989803*** 10.25 Organic Soil dummy ‐0.016017 ‐0.43
D12 (Japan) 13.309955*** 22.14 Rock/Hard‐Root Layer dummy 0.023379 0.97
D13 (Germany) 10.356365*** 15.86 Irrigation Percentage 0.070615*** 6.13
D14 (Italy) 13.064757*** 28.92 Clayey Topsoil 6.719910** 2.07
D15 (Spain) 14.063024*** 15.35 Loamy Topsoil 0.178910** 2.21
D16 (Greece) 9.720294*** 2.73 Population Density 0.378472*** 0.378472
D17 (Portugal) 9.369802*** 6.87 Soil Moisture Stress ‐2.492817 ‐3.74
D18 (Sweden) 10.133151*** 7.95 Clayey Subsoil ‐0.063501 ‐1.35
Aluminum Toxicity dummy 0.190107*** 8.57 Sandy Topsoil 0.002949*** 2.87
Calcareous Reaction dummy 0.366795*** 2.91 λ‐Clayey Topsoil 9.217902** 2.37
Salinity dummy ‐0.051443 ‐0.52 λ‐Loamy Topsoil 0.060192 0.30
Number of Observations 3598 λ‐Irrigation Percentage 1.183951*** 9.21
R‐square 0.9941 λ‐Clayey Subsoil 0.184569 0.55
Adjusted R‐square 0.9941 λ‐Population Density 0.069458*** 3.53
F Value 14350 2 λ‐Soil Moisture Stress 5 748127*** 3 98

Application of Quality-Adjusted
techniques to the U. S.
AJAE 2006

The estimation results as illustrated, figure to
follow,
indicate that the quality adjusted land prices
tend to be highest in a number of eastern
Corn Belt areas
producing high value crops for urban centers
and in Corn Belt states traditionally known to
possess high quality land, ie; Iowa and
Illinois.

Appendix Figure 2. Texture Index By ASD

Application of Quality-
Adjusted techniques to the
U. S. State Files 2004

Most Recent State Estimates
P59 1 -0.00729 0.00893 -0.82 0.4142
p60 1 -0.01400 0.01125 -1.24 0.2134
P61 1 -0.02644 0.02377 -1.11 0.2661
P62 1 -0.00292 0.00883 -0.33 0.7407
p63 1 -0.00271 0.00129 -2.10 0.0356
p64 1 -0.01948 0.04907 -0.40 0.6914
p65 1 -0.00699 0.00133 -5.27 <.0001
P66 1 -0.00230 0.00103 -2.23 0.0260
p67 1 -0.01468 0.00769 -1.91 0.0562
P69 1 -0.00052847 0.00472 -0.11 0.9109
p70 1 0.00648 0.00539 1.20 0.2294
P71 1 -0.00561 0.00517 -1.08 0.2786
P72 1 -0.00015788 0.00121 -0.13 0.8964
P73 1 0.00174 0.00125 1.38 0.1663
P74 1 0.00010266 0.00004012 2.56 0.0106
admk 1 0.10464 0.01053 9.94 <.0001
stress5 1 -0.05533 0.09957 -0.56 0.5784
stress7 1 -1.44228 0.09655 -14.94 <.0001
stress8 1 0.45131 0.10475 4.31 <.0001
stress4 1 -1.66886 0.44044 -3.79 0.0002
TEXTTAV 1 0.20227 0.03346 6.04 <.0001
PHWTAV 1 2.38749 0.41125 5.81 <.0001
SLOPWTAV 1 -0.05802 0.00657 -8.84 <.0001
SALWTAV 1 0.00268 0.03592 0.07 0.9406
PERMWTAV 1 0.09552 0.02186 4.37 <.0001
LAYWTAV 1 0.02884 0.00692 4.17 <.0001
BDWTAV 1 -0.74872 0.12971 -5.77 <.0001
CECWTAV 1 0.01671 0.00719 2.33 0.0201
SARWTAV 1 0.00375 0.01795 0.21 0.8347
POPDEN 1 0.00032526 0.00001306 24.90 <.0001
IRRIPER 1 0.00052728 0.00527 0.10 0.9203

Conclusions and Future Research
• Quality‐adjusted values for land are
estimated for OECD countries.
• These values can be translated into purchasing
power parities providing information on land
prices.
• The quality‐adjusted land input allows an
unbiased estimate of TFP when conducting
international comparisons of agricultural
productivity.

Conclusions and Future Research
• In future work we will add Argentina, Brazil,
China, and India to the land project.

Measuring land and other capital inputs

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