i ional Agricultural Trade and Policy Center
VALUING CATASTROPHIC LOSSES FOR PERENNIAL
Damian C. Adams, Richard L. Kilmer, Charles B. Moss, and Andrew Schmitz
PBTC 03-8 August 2003
POLICY BRIEF SERIES
Institute of Food and Agricultural Sciences
INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
MISSION AND SCOPE: The International Agricultural Trade and Policy Center
(IATPC) was established in 1990 in the Food and Resource Economics Department
(FRED) of the Institute of Food and Agricultural Sciences (IFAS) at the University of
Florida. Its mission is to provide information, education, and research directed to
immediate and long-term enhancement and sustainability of international trade and
natural resource use. Its scope includes not only trade and related policy issues, but also
agricultural, rural, resource, environmental, food, state, national and international
policies, regulations, and issues that influence trade and development.
The Center's objectives are to:
Serve as a university-wide focal point and resource base for research on
international agricultural trade and trade policy issues
Facilitate dissemination of agricultural trade related research results and
Encourage interaction between researchers, business and industry groups,
state and federal agencies, and policymakers in the examination and
discussion of agricultural trade policy questions
Provide support to initiatives that enable a better understanding of trade and
policy issues that impact the competitiveness of Florida and southeastern
agriculture specialty crops and livestock in the U.S. and international markets
VALUING CATASTROPHIC LOSSES FOR PERENNIAL AGRICULTURAL
Damian C. Adams, Richard L. Kilmer, Charles B. Moss, and Andrew Schmitz
Department of Food and Resource Economics, IFAS, UF, Gainesville, FL 32611
Key Words: Citrus, perennial crops, catastrophic loss, damages, freeze
Abstract. Courts are often required to estimate changes in welfare to agricultural
operations from catastrophic events. For example, courts must assign damages in
lawsuits, such as with pesticide drift cases, or determine "just compensation" when the
government takes private land for public use, as with the removal of dairy farms from
environmentally sensitive land or destruction of canker-contaminated citrus trees. In
economics, the traditional method of estimating changes in producer welfare is the
computation of lost producer surplus, but courts rarely use this method. Instead, they turn
to substitute valuation methods that may not fully capture welfare change, such as
changes in land value, tree replacement value, and total revenue. This study examines
various measures for valuing the back-to-back catastrophic freezes that occurred in the
Florida citrus industry in the 1980s. We first use the traditional method to determine the
welfare change due to a freeze (1) for a citrus grove that loses one crop and is able to
return to full production the next year (simulating destruction of annual crops), and (2)
the lower measure of welfare loss due to a citrus grove that loses all of its trees and is
abandoned or is replanted. The lower measure is used to simulate the legal doctrine of
avoidable consequences. These measures are then compared to substitute valuation
measures that have been used by courts to determine welfare changes. For case 1, total
revenue overestimated losses by 35.6%. For case 2, total revenue overestimates losses by
55.3%, tree replacement value underestimates losses by 93.6%, and changes in land value
underestimates losses by 13.2%.
VALUING CATASTROPHIC LOSSES FOR PERENNIAL AGRICULTURAL
One cornerstone of applied economic analysis is the valuation of dramatic events
for policy analysis. For example, economists may estimate the effect of a disease
outbreak on the beef industry, as in the case of "Mad Cow Disease" or ecoli
contamination of packing facilities, or the effect of changes in agricultural or trade
policy, as in the case of FAIR or NAFTA. Courts, too, are often required to estimate
changes in welfare to agricultural operations from catastrophic events. For example,
courts must assign damages in lawsuits, such as with pesticide drift cases, or determine
"just compensation" when government takes private land for public use, as with the
removal of dairy farms from environmentally sensitive land or destruction of healthy
citrus trees within range of canker-contaminated trees.
In economics, the traditional method of estimating the effects of a catastrophic
event is the computation of lost producer surplus as developed in Just, Hueth, and
Schmitz (1982), but courts rarely use this method. Instead, they turn to substitute
valuation methods that may not fully capture producer losses, such as changes in land
value, replacement value, and total revenue.
This study examines various approaches for valuing catastrophic losses for
annual1 and perennial agricultural crops. One such catastrophic event was the back-to-
1 Although citrus crops are perennial crops, we simulate losses to annual crops, like corn, soybeans, and
wheat, by considering a grove that loses its fruit only following a light freeze, which results in the loss of
the current year's crop, but the grove can return to full production the following year.
back freezes that occurred in the Florida citrus industry in the 1980s. Following these
events, citrus in Florida retreated further to the south.2
We first calculate lost producer surplus, or change in producer welfare (AW) due
to the freeze events. AW is a function of the age of the original grove. Assuming a 30-
year planning horizon, price expectations based on market information available prior to
the 1983-84 marketing period, and using an age distribution assuming that the average
tree age structure for Lake County holds for the individual grower, the value of the loss
with and without tree replacement is computed using
(1) AW = (-) ((TRWo TVCW -Iw) -(TRt TVC I))
where AW is the value of the freeze loss in dollars; S'= (1/(1+.0465))tis the factor used
to discount future dollars back to current dollars at an interest rate of 4.65 percent as
suggested by Moss, Weldon, and Muraro (1991); TR, denotes total revenue in time t;
TVC, is the total variable cost in time t; I, is costs associated with tree replacement and
care in time t; and superscripts w and wo indicate, respectively, with and without the
freeze events, which are assumed to occur in time t=0.
For a typical 100-acre grove, a tree-age profile for Lake County is constructed
from the Florida Agricultural Statistics Service Commercial Citrus Inventories (1982-
1986) that implies a loss of 90.1% of trees and a lost yield of 24,927 boxes of oranges in
the freeze year. We estimate a second order autoregressive function to project expected
2 The citrus industry essentially shut down in the traditional northern groves around Orlando and
moved to the flatwood areas to the south.
future orange prices before the 1983-84 freezes3. Averaging over a projected 30-year
planning horizon yields an average orange price of $7.54/box with an expected price in
the 1983-84 marketing period of $7.99/box. A TVC, of $2.10 per box4 is assumed. AWis
calculated for the freeze year and over a 30-year planning horizon both without and with
tree replacement for a typical 100-acre grove (Table 1).
AW for annual crops is simulated by computing losses to the citrus producers in
the freeze year only (and thus assuming that the grove will produce a crop next year
because the bloom was not frozen). Investment is assumed to be unaffected. In this case,
AW = $-136,694 for the freeze year only.
When trees are lost, but not replaced, the AW must similarly be calculated over
the expected life of the grove and must consider differences in tree yields for trees of
different ages. We use tree age yield information from Zanzig, Moss, and Schmitz
(1997). When calculating yield differences over time, one must also consider grove age
distribution and attrition rates. Maintaining a citrus grove includes replacing under-
producing trees-those that produce less than 50% of their expected yield. Muraro and
Fairchild (1985) have stated that citrus trees have an age-dependent probability of
permanently under-producing, which for Lake County is 2.3% of citrus trees aged 0 to 3,
1.3% of those aged 4 to 10, and 3% of those aged 11 or more. Given a grove age
distribution at the time of a freeze, one can predict what that grove's age distribution and
3 Typical assumptions of welfare analysis as discussed in Just, Hueth and Schmitz (1982) are based on ex
4Based on Muraro (1983a), and Muraro (1983b). This paper assumes that pick and haul costs remain
nominally fixed over the 30-year planning horizon.
number of trees would be both with and without the freeze, and with and without
replacement. Future grove yield is found by multiplying the grove tree age distribution by
the average yield per tree for a tree of each age. AW= $-930,654 million without
replacement. AW= $-748,623 with tree replacement. The legal doctrine of avoidable
consequences would require a producer to take steps to minimize losses following a
tortious act or state land taking. In this case, to simulate this doctrine, we would only
compensate the producer using the lower of the two welfare measures.
We will now compare the change in producer welfare based on welfare theory
with the measures used in the market place and by courts. These include tree replacement
value, the change in land values, and total revenue.
Tree replacement includes buying new citrus trees, preparing the land for trees,
and planting the new trees. For the Lake County tree age distribution, in year 2000
dollars, tree replacement cost is $482.70 per acre for trees and land work (Muraro, 1983),
or $48,270 for a 100-acre grove (Table 1). This is significantly less than the $930,654
welfare loss without tree replacement and the $748,623 loss with tree replacement (Table
Change in Land Values
Another approach to valuing the cost of the catastrophic event is the change in
land values. Under traditional asset valuation concepts, the land value of a grove reflects
the normal profit from citrus production. Accordingly, after the freeze, rational investors
would incorporate the effect of the lost land use alternative (i.e. loss of economically-
viable orange production) into their bids for farmland in the area. The post-freeze value
of the citrus land should be equal to the land's pre-freeze next best use value. For
example, if the pre-freeze next best use were as a cattle ranch, then the change in land
values approach would measure damages as the difference between the net present value
of the land as a citrus operation and the net present value of the land as a cattle operation.
We assume that Lake County citrus land had no economically viable next best use. Under
these assumptions, the change in the land value between pre-freeze years and the post
freeze years provides an estimate of the economic loss of the shutdown.
According to the Lake County property register5, before the 1983 freeze event,
orange grove land in Lake County sold for about $10,376 per acre in year 2000 dollars.
After the freeze, land in the same area sold for almost $3,881 per acre. Thus, about
$6,495 per acre was lost due to the freeze. Multiplying this by 100 acres yields an
estimated economic loss of $649,500 in year 2000 dollars (Table 1). Figure 1 shows the
changes in average per acre land values for Lake County between 1981 and 1986.
Total Revenue Approach
A related methodology that is sometimes used to quantify the economic loss is the
total revenue approach. The total revenue approach overstates AW because total variable
costs and total investment costs are not included in the valuation. Following this
procedure, the total revenue loss on the 100-acre grove using Lake County is $1.16
million with tree replacement, and $3.70 million without replacement (Table 1).
5 Lake County land values were accessed using the Florida Deed Transfers and Tax Assessor Records
database from www.lexis.com/research.
Results and Discussion
The alternative measures of economic loss due to the freezes of the 1980s for the
typical 100-acre orange producer in Lake County, Florida using the estimated Lake
County tree replacement distribution are presented in Table 1.
Catastrophic events that permanently damage perennial crops pose a more
difficult problem than annual crops. Much more data is needed to calculate AW using
traditional economic measures and courts must also consider contingencies. In the case of
the freezes of the early 1980's, AW must be calculated with and without tree
replacement. It is the lower of the two loss calculations that should be used to simulate
courts' use of the doctrine of avoidable consequences. In our case, AW with tree
replacement is the lower measure by $182,031 (Table 1).
If a court needs to use alternative measures, it is important to know which method
performs best. For the typical 100-acre orange grove in Lake County, the AW is most
closely approximated by the change in land values, with total revenue and cost of tree
replacement providing much worse estimations.
The total revenue measure overestimates economic loss as compared to the
AW measures both with and without tree replacement. This is expected because the total
revenue concept pays the grove owner for variable costs that the grove owner did not
experience (e.g., pick and haul costs). Total revenue is an imprecise measure of economic
loss. For the typical 100-acre grove in Lake County, the total revenue measure with tree
replacement overestimates economic losses by $414,302, or 55.3% when compared to
AW with tree replacement (computed from Table 1).
The cost of tree replacement measure also does not perform well. It does not
consider the lost revenue from current or future income that will result from the
increasing tree yield as the tree gets older, so it severely understates the economic loss
experienced by the grove owner. Cost of tree replacement is a very imprecise measure of
economic loss. In this case, when compared to AWwith tree replacement, it
underestimates producer losses by almost $700,353, or over 93.6% (computed from
Finally, change in land value performs the best when compared with AWwith
tree replacement, but it underestimates producer loss. Here, the change in land value
when compared to AW with tree replacement, underestimates producer loss by $99,123
or 13.2% (computed from Table 1). Change in land values may not be a good estimate of
producer losses, especially when urban development pressures are strong.
In theory, successful lawsuits are meant to make the complaining party "whole"
or as well off with the court-awarded compensation as they were before the catastrophic
event. This is equally true for personal injury awards as it is for government takings
awards. In economics, the traditional method for determining the amount needed to make
the party "whole" is a AW estimation based on compensating variation (also known as
Ricardian rent and producer surplus). While the most accurate, this method requires
complicated calculations and an understanding of economics and statistics to make
appropriate estimations. As such, courts often turn to alternative measures, like change in
total revenue, change in land value, or cost of tree replacement. These measures may not
fully capture producer losses due to a catastrophic event. Our estimates suggest that this
is the case for the back-to-back freezes of the early 1980's.
Florida Agricultural Statistics Service. 1982 1986. Commercial citrus inventory. Fl.
Agr. Stat. Serv.
Just, R. E., D. L. Hueth, and A. Schmitz. 1982. Applied Welfare Economics and Public
Policy. Englewood Cliffs: Prentice-Hall.
Moss, C. B., R. N. Weldon, and R. P. Muraro. 1991. The Impact of Risk on the
Discount Rate for Different Citrus Varieties. Agribusiness: An International
Journal 7(4): 327-38. (Abstr.)
Muraro, R. P. 1983a. Budgeting Costs and Returns: Central Florida Citrus Production,
1982-3. Univ. Fla., Inst. Food Agr. Sci., Econ. Info. Rpt. 185.
Muraro, R.P. and G. Fairchild. 1985. Economic Factors Affecting Postfreeze Production
Decisions in the Florida Citrus Industry. Proc. Fla. State Hort. Soc. 98:91-96.
Zanzig, B., C. B. Moss, and A. Schmitz. 1997. Natural Disasters and the Yield
Curve of Florida Valencias. J. Agr. & Resource Econ. 22: 402.
Lake County Grove Land Values
6000 --Avg. Per Acre
o Land Value
1980 1981 1982 1983 1984 1985 1986 1987
Year of Grove Sale
Figure 1. Average per acre land values for Lake County orange groves before and after
the 1983 freeze event.
Table 1. Alternative measures of freeze loss for a
100-acre citrus grove in Lake County, Florida.
AW without tree replacement $-930,654
AW with tree replacement -748,623
Tree replacement cost only -48,270
Lost land value -649,500
Total revenue w/out tree replacement -3,700,000
Total revenue with tree replacement
a Loss over life of grove (30 Years)