Page 10

1.

12.

retailers. The variable-parameter structure of the de-
mand model is arbitrary, but it suits our purpose. [See
Rausser et al. (1982) for how variable-parameter speci-
fications are routinely used to model structural change.]
Consider it a linear approximation of a demand model
derived from a utility function with preferences indi-
cated and aggregated over consumers. With the pas-
sage of time, quantity demanded increases.

The reduced-form equations can be determined by
setting demand equal to supply, solving for P*, and then
substituting the solution for P* into the demand model
in order to solve for Q*:

P* = [(at + ctM) - (e - gW)I/LF + (b/t))

Q* = (at + ctM){1- [by/(tf + b)}}
+ bl(e - gWy/i(tf + b))

First consider P*. The term (at + ctM) must be positive
in order for quantity demanded to be positive, and the
numerator must be positive [i.e., (at + ctM) > (e- gW)]
in order for demand and supply to intersect. Thus, ast
increases, P* increases--just what one should expect if
preferences strengthened.

What happens to Q* as t increases can be seen by taking
its limit as t goes to infinity. Accordingly, the last term
goes to zero, the second multiplicand of the first term
goes to 1, and the first multiplicand of the first term goes
to infinity. Thus,.Q* increases with time--again, what
one should expect if preferences strengthened.

Because I do not presume to know the utility and
production functions that underlay the structural model,
itis important for me to emphasize that what I estimated
are linear approximations to unknown reduced-form
models. Nevertheless, positive coefficients on the time
trends in my models are consistent with the above
tesults. Thus, it is unnecessary to try to recover any
structural coefficients or to know elasticities of demand
to test for evidence of preference change.

Implicit here is the assumption that food comprises a
subutility function in a multistage budgeting process.
This is a common assumption in the food-demand
literature (e.g., Choi and Sosin 1990). Also, strictly
speaking, seafood should have been excluded from the
CPI for all foods when the relative price of seafood was
calculated. However, because seafood is such a negli-
gible part of total food expenditures, this adjustment
was not made.

For example, when estimating structural models of
specific seafood markets (e.g., groundfish in New En-
gland), researchers have had to specify price linkages
between market levels instead of retail supply relation-

13.
14.

15.

ships (e.g., Bockstael 1976; Crutchfield 1985; Felixson
et al. 1987).

Solow (1987) shows that such data dredging results in
a threefold increase in the test statistic.

Solow (1987) explains that the t-test on a, or b, should
not be used to test for a change-point because estimates
of these parameters are positively biased.

None of the determinants of individual household ex-
penditures on seafood reported by Cheng and Capps
(1988)--race, coupon value, household size, geographic
region, urbanization, and seasonality--were specified
in my analysis. Except for racial composition, these
factors are not congruous to a time-series analysis of
nationwide aggregate consumption patterns. When
racial composition was added to the models reported in
Table 1, the change-point results did not change appre-
ciably, but the severe multicollinearity among it, the
time period, and per capita income became apparent
from changes in coefficient estimates on these regres-
sors. Regardless, although according to Cheng and
Capps (1988) nonwhites spend about eight percent
more than whites on seafood, the small increase in the
relative size of the non-white population during the
study period--about five percent--combined with this
difference in expenditures falls far short of accounting

"for the 50-percent increase in per capita consumption.

16.

17.

I considered two other demographic trends. Even if
coastal residents eat more seafood, the tiny increase in
the relative size of the coastal population from 52 to 53
percent since 1960 could not account for much of the
observed increase in seafood consumption. Finally, the
interrelated trends of more women in the workforce and
eating away from home more often could not account
for increased per capita consumption of seafood at
higher relative prices.

Seeing two minima as in Figure 3a may suggest to you
that a three-phase regression procedure would be ap-
propriate. However, choosing a three-phase model
after having seen the results from the two-phase analy-
sis is data dredging too (Solow 1987). Consequently,
kept to the two-phase models, understanding that the
local minima may, in fact, be statistically significant as
well as noteworthy.

A comparison of the results from estimating models
with only t and (t - A)Dyy with the results reported in
Table 1 underscored the severe collinearity between t
and M. In each “pure” time-series model, the coeffi-
cients on t were positive and significant. However, the
change-point results (i.e., estimates of a,, b,, and d)
were very stable regardless of specification or range of
data. The additional models are available upon request.



Page 1

. : ABSTRACT

The results from graphical and regression analyses of time-series data on seafood consumption and prices
suggest that preferences for seafood strengthened in response to medical evidence that seafood promotes nutrition
and health. The graphical analysis reveals steady increases in per capita consumption of seafood since the 1960s
despite concurrent increases in the relative prices of seafood. The two-phase regression analyses of per capita

consumption of generic seafood products

, fresh or frozen seafood, canned seafood, and cured seafood) and of

the relative price of seafood identify the mid- 1960s and early 1980s as times of change. These results, which match
those reported for red meats and poultry, have important implications for modeling ex-vessel demand, estimating
economic welfare, managing fishing effort, and allocating fish stocks._ 2}

INTRODUCTION

Since discovering the relationships between fat intake
and nutrition and health, the medical profession has urged
dietary changes (Clancy 1986). Infact, since the early 1980s,
eating seafood at least twice a week has been recommended
in order for one to benefit from the ability of omega-3 fatty
acids to reduce heart disease and certain other ailments such
as arthritis and various metabolic and neurological disorders
(Lees 1988). Yet, despite these admonitions and Jones and
Weimer’s (1981) survey results on the changing American
diet, economists have mostly ignored consumer demand for
seafood, focusing instead on apparent structural changes in
preferences forred meats and poultry since the 1960s (Chavas
1983; Choi and Sosin 1990; Dahlgran 1987; Eales and
Unnevehr 1988; Goodwin 1989; Moschini and Meilke 1989;
Nyankori and Miller 1982; Purcell 1989; Thurman 1987)'.
Inthis paper, I begin to fill this gap with evidence of structural
changes in preferences for seafood.

Inaddition to the relatively small amount of money that
consumers spend on seafood (about 10 percent of the total
meat budget, but growing), consistently dubious results
probably have caused researchers to omit seafood from
focused study’, In particular, positive own-price coefficients
and complementarity between seafood and red meats and
poultry are common results when the demand for seafood is
estimated as part of a structural system (Goodwin 1989;
Huang 1988; Pope etal. 1980; Wohlgenant 1985). However,
such “dubious” results could be due to structural shifts in
preferences for seafood. Positive own-price coefficients
would result from simultaneous-equations bias if demand
“traced” a relatively stable supply. Also, negative cross-
price coefficients, which at face value indicate a curious
complementarity, would result from omitted-variable bias
when structural changes in preferences are not modeled.
That is, stronger preferences for seafood would lead to both
higher seafood prices and reduced preferences for red meats.

Because of the failure of structural models such as the
oft-used almost-ideal-demand system (AIDS) to generate
credible estimates of seafood demand, I have chosen a
different approach to analyze for structural changes in pref-
erences for seafood. Part of my analysis follows Purcell’s
(1989) admonition to utilize graphical analyses when exam-
ining the evidence of structural changes in demands for

foods’. Accordingly, in the Graphical Analysis section of
this report, plots of time-series data of relative prices and per
capita consumption have been inspected for signs of pref-
erence change. The trends suggest that preferences for
seafood strengthened since 1960, particularly during the
mid-1960s and then again during the early 1980s.

In addition, two-phase regression has been used in the
Two-phase Regression section of this report to test and
quantify the apparent trends. However, due to the above-
mentioned poor performance of previous structural models,
Thave used reduced-form models. The regression results
corroborate the conclusions drawn from the graphical analy-
sis.

Finally, three implications of the results for economic
research and fishery management are highlighted in the
Implications section of this report. A Summary and Con-
clusions section completes this report.

GRAPHICAL ANALYSIS

The 50-percent increase in annual consumption of
seafood from about 10 pounds per capita in 1935 to about
15 pounds in 1988--despite steady increases in the relative
prices of seafood--constitutes important evidence that pref-
erences for seafood have strengthened (Figure 1)‘. The near
doubling of consumption of fresh or frozen fish and shell-
fish since 1935 to about 10 pounds in 1988 comprised most
of this increase. Consumption of canned fish and shellfish
also rose, but only slightly to about five pounds per capita
in 1988. Incontrast, consumption of cured fish and shellfish
(e.g., smoked fish and salted fish) declined 50 percent
between 1935 and 1988 to only 0.3 pounds.

On average, the U.S. population increased its con-
sumption of seafood by 50 percent-even though seafood
steadily became more expensive than other meats and
foods. This isapparent from the ratios of the consumer price
index (CPI) for all fish and shellfish products (the only
available national timeseries of retail prices*) tothe CPIs for
poultry, beef & veal, pork, and all foods (Figure 1b)*. Also,
during the late 1940s, much of the 1970s, and the late 1980s,
annual per capita consumption of seafood increased despite
concurrent increases in the price of seafood relative to per
capita income.




Page 6

Table 1.. Regression results for per capita consumption of fresh or frozen seafood, canned seafood, and cured seafood, and for

seafood price, over two ranges of years: 1935-88 and 1958-88

Coefficient Estimates (t-Statistic) Change-Points
Range R ~ Intercept t 4D, M Optimal U Local
® (95% CD Minimum
Fresh or Frozen Seafood
1935-88 0.91 5.073 0.004 0.126 0.010 1967 26.22" -
(54) (12.85) ~ 0.25) (10.04) (1.04) (1963-69)
1958-88 0.94 3.526 -0.047 0.140 0.031 1966 4.36" 1982
G1) (3.53) (1.00) (4.53) (2.13) (1962-70)
Canned Seafood
1935-88 0.61 7.307 -0.180 0.277 0.038 1943 16.74" -
(54) (10.70) (3.71) (4.96) 3.23) (1942-44)
1958-88 0.61 2.425 -0.064 0.052 0.026 1967 1.32 -
G1) (2.83) (1.78) (2.34) (2.14) NS?
Cured Seafood
1935-88 0.87 0.832_ -0.002 -0.005 -0.002 1955 1.49 -
(54) (8.96) 1.05) 1.71) 1.26) NS?
1958-88 0.82 0.477 -0.034 0.020 0.002 1961 0.64 -
G1) (3.37) (-4.09) (3.04) (1.21) NS?
Seafood Price
1935-88 0.87 44.916 0.397 0.694 0.126 1969 3.74" 1944
(54) (7.06) (1.77) @.57) (0.91) (1963-76)
1958-88 0.94 72.933 0.462 1.183 -0.121 1966 3.60" 1985¢
(1) (8.45) (1.22) (4.58) (0.98) (1962-70)

* Significant at the 95-percent level of confidence (i.e., U > Fry.soasa)
© NS - not significant.

* The residual sums of squares for the optimal and local minima were virtually identical.

ever, in the same study, income was not a significant
determinant of expenditures on shrimp, total shellfish, and,
curiously, any finfish product when examined separately
(cod, flounder, haddock, perch, snapper).

The regression models for canned seafood are notice-
ably different from the models for fresh or frozen seafood.
First, the coefficients on tare negative and significant in both
ranges, although the high degree of collinearity between t
and M should still be kept in mind.. The positive and
significant change-point within range I probably shows the
impact of WWII on production and trade, not preferences.
Finally, the change-point during range II is positive and
identical to that for fresh or frozen seafood, but it is insignifi-
cant judging from the test on the likelihood ratio statistic,
ut"

Turning to consumption of cured seafood, a negative
trend in consumption may have been picked up by the
regression model, however, no significant change-point is
apparent. These results are not surprising given the appar-
ently linear, negative trend in per capita consumption of
cured seafood (Figure 1a).

Finally, the qualitative results from modeling the rela-
tive price of seafood are very similar to the models for fresh
or frozen seafood, as one would expect, because the majority
of seafood is marketed in these forms. Once again, it is
difficult to draw firm conclusions from the empirical esti-
mates of the coefficients on t because of the collinearity with
M. However, the optimal change-points are virtually the
same as for consumption of fresh or frozen seafood (Figure
3b). In addition, a local minimum appears during WWII in



Page 3

o Relative price index
1996
100
80 }—
1989
60 $$$ + +
7 8 9 0 nH 2 19 4 8 16
A Total per capita consumption (pounds)
Relative price index
100 4 - - —|
4989
80 7— =
60 }~ on
° ce!
204—
1995
ot—
7 8 98 © HH 2 8 4 68 4
B Total per capita consumption (pounds)
Relative price index
20
100 —
1989
80 {$$ a
60
1995
40
20
°
7 8 8 0 2° 8 4 6° 6
Total per capita consumption (pounds)

Figure 2. Historical relationships between annual per capita consumption of total seafood and the CPI of seafood relative to: (a) per
capita income (x10,000); (b) the CPI of poultry (x100); and (c) the CPI of beef (x100).


Page 2

Consumption (pounds per capita)”
1935 1940 1945 1950 1955 1960°1965 1970 1975 1980 1985 1990
. Year
A —— Fresh or frozen Canned “~~ Cured —— Total
Relative price index
oO rn rn n 1. 1 1 _t in an n
1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990
° Year
B —Alltood — Poultry Beet ~ Pork

Figure 1. Historical data on seafood demand: (a) U.S. annual per capita consumption of commercial fish and shellfish (Fisheries
Statistics Division, National Marine Fisheries Service 1989); and (b) relative prices (1988=100; Putnam 1989).

Graphs of the relative prices of seafood against total per
capita consumption yield even more compelling insights
into the. possibility of preference change. In Figure 2, the
jagged lines trace how seafood consumption and relative
prices changed together over time. The last two digits of
every fifth calendar year and the arrowheads mark the paths.

In Figure 2a, the price of seafood relative to per capita
income is plotted against total annual per capita consump-
tion. The influences of the Great Depression and World War
Il (WWID are apparent: from wide swings of per capita
consumption during the late 1930s and the 1940s. Since the
mid-1960s, however, per capita consumption: generally

increased, except during the late 1970s to early 1980s.
Indeed, throughout the late 1960s, most of the 1970s, and the
late 1980s, consumption increased despite increases in the
price of seafood relative to income.

The mid-1960s and early 1980s also seemed to mark a
change in the relationships between seafood consumption
and the prices of seafood relative to other meats. In Figure
2b, the price of seafood relative to poultry is plotted against
per capita consumption. During the 1950s and early 1960s
‘consumption vacillated while the relative price of seafood
increased, suggesting, perhaps, that consumers habitually
ate seafood during particular days or holidays’. Subse-



is the time period when these lines intersect, i.e.,d = (a,-a,')/
(a/-a,) or (, - b,V(b,- b,). In addition, a, = a,'-a,, and b,
=b/-b,.

‘ A maximum likelihood procedure is used to search the
interval (3,T-2) for the value of d which minimizes the
model's residual sum of squares (see Solow 1987). Because
the change-point is not selected a priori, “data dredging” is
avoided’.

For any value of the change-point, model (2) is a linear
regression model with regressors t, (t- d)D,,, and z. The
parameters are estimated by fitting model (2) with the
optimal value of d. Subsequently, a,’, a,’, b,’, and b,’ can be
derived from these estimates.

The test of the null hypothesis of no change-point
(against the two-sided alternative)--which is tantamount to
testing whether there is no difference between the trend
coefficients before and after the hypothesized change-point-
-uses the likelihood ratio statistic’*:

U = [(S, - S3V/IS/N - 4)]

where S, is the residual sum of squares from fitting the null
models:
4,7 a) + att az, +e, (t=1,...7] (4a)
or
p= b,+bt+bz, +n, [t= 1..,T] 4b)
Also, S is the residual sum of squares from fitting the
alternative model at the optimal value of d, and N is the
number of observations. When U > F, nosey the null
hypothesis is rejected at the 95-percent level of significance.
A significant change-point is consistent with a structural
change in preferences for seafood.
Finally, the 95-percent confidence interval for the opti-
mal change-point is the time period which satisfies
(S, - SYISH(N - 49] $F, x soos
where S, is the residual sum of squares from an alternative
model with a non-optimal change-point. See Solow (1987)
fora clear discussion of the two-phase regression model and
its test statistics.

RESULTS

Model Specification and Data

Model (2) for the three generic types of seafood and the
seafood CPI (relative to the CPI for all foods) has been
estimated with the above two-phase regression procedure.
Inaddition tot and (t-d)D, yr €ach model has been specified
as a function of real per capita income (nominal income
divided by the CPI for all foods), M, which is representative
of z in model (1).

Page 5

In addition, each model has been estimated from two
ranges of the data. Range I encompasses the years 1935-88
(t = 1,...,54), including, therefore, the end of the Great
Depression and WWII. Range II encompasses the years
1958-88 (t = 1,....31). Range II has been selected because it
corresponds to data bases used to model derived demand at
the harvesting level (e.g., Bell 1968; Felixson et al. 1987),
and, therefore, should be most relevant to fishery econo-
mists.

As noted in Figure 1, data on per capita consumption of
seafood have been reported by the Fisheries Statistics Divi-
sion, National Marine Fisheries Service (1989). Also, per
capita income and the CPIs for seafood and for all foods
have been provided by the U.S. Bureau of Labor Statistics
(Putnam 1989).

Regression Models

The regression results are reported in Table 1.
SHAZAM'’s procedure to adjust automatically the covari-
ance matrix for unknown sources of heteroskedasticity has
been used to estimate these models (White 1987).

First consider the results from modeling per capita
consumption of fresh or frozen seafood. Although the linear
time trends are insignificant (95-percent level of confi-
dence), the change-point results are positive and signifi-
cantly different from zero in both ranges of data. The year
1967 corresponds to the change-point in both models.

The residual sum of squares from estimating the model
for fresh or frozen seafood from data in range II is presented
in Figure 3a. The 95-percent confidence interval around the
optimal change-point is from 1962 to 1970. However, the
local minimum corresponding to the year 1983 is also
important because it is virtually identical to the “global”
minimum. Also, it coincides with when the health benefits
of omega-3 fatty acids from seafood began to be widely
publicized by the popular press as well as by physicians'®.

Although the estimated coefficients on per capita in-
come, M, are positive in both models of consumption of
fresh or frozen seafood, the estimates are not robust. This
appears to be due in large part to the high correlation (0.97)
between t and M’’. Nevertheless, the effect of income on
consumption of seafood also is ambiguous. For example,
both Bockstael (1976) and Crutchfield (1985) reported per
capita income to be a significant determinant of the aggre-
gate demand for fresh groundfish in retail markets, but it
was not a significant determinant of the demand for frozen
groundfish products in their studies. This result is important
tomy study because frozen seafood constitutes about 60-70
percent of total fresh or frozen seafood products. Cheng and
Capps (1988) also reported mixed results of how income
affected a household’s expenditures on seafood. In their
microeconomic study, household income was a significant
determinant of expenditures on crabs, oysters, and total
finfish (they used the 90-percent level of confidence). How-


oP 50
Tetbitiinn

NOAA Technical Memorandum NMFS-F/NEC-87

Evidence of Structural Change

in Preferences for Seafood

U. S. DEPARTMENT OF COMMERCE
National Oceanic and Atmospheric Administration
National Marine Fisheries Service
Northeast Region
Northeast Fisheries Science Center
Woods Hole, Massachusetts

January 1992

SEPRODUCED BY

US DEPARTMENT OF COMMERCE
NATIONAL TECHNICAL INFORMATION SERVICE
SPRINGFIELD, VA 22161

ne nen

|


Page 8

demand, and b, isa matrix of parameters, the values of which
vary across time periods’. If, instead, derived demand is
estimated with a constant-parameter model,

Pa, 7 DX

then the estimates of the true parameters, b,, will be biased.
Specifically, estimates of the constant-parameter vector, b.,
will be the weighted average of the individual b, (Rausser et
al. 1982). Thus, with increasing preferences for seafood, a
constant-parameter model would underestimate quantity
demanded at all prices, including forecasts of demand”,

A second, related implication concerns benefit estima-
tion. If overlooking stronger preferences for seafood leads
to underestimates of current and future demand, then it
follows that changes in surplus benefits for consumers and
the seafood sector will be underestimated, too, if a constant-
parameter model is specified”. Furthermore, in the context
of benefit-cost analyses of fishery management plans which
are intended to protect or rebuild fish stocks, or, of increas-
ing importance, to allocate fish among commercial and
recreational fishermen, the degree of underestimation will
worsen to the extent that future shifts in demand due to
structural changes in preferences for seafood are not fore-
casted.

Finally, a host of issues concerns the prospect of even
greater fishing effort on stocks of marine fish and shellfish,
many of which are already subjected to growth overfishing
and even recruitment overfishing”. Depending on the
degree of monopsonistic power in landings markets and on
future supplies from trade and aquaculture, increases in
retail prices could bring the fishing industry higher ex-vessel
prices, causing effort to increase in the longer run. This was
illustrated in dramatic fashion recently in the red drum
fishery in the Gulf of Mexico following rapid acceptance of
blackened redfish by consumers, but the same communica-
tion between retail and landings markets probably functions
in other fisheries too.

Ifrecenthistory portends future events, continued growth.
in preferences for fresh or frozen seafood will further
increase fishing effort on already overfished stocks in order
to satisfy Americans’ growing appetite for fish. And with
the continuation of virtual open-access conditions in the
majority of U.S. fisheries, of ineffective controls on effort
and harvest, and of average or less-than-average stock
recruitment, incteased fishing effort will, in turn, further
lower the yield of fish resources and, in a negative feedback,
decrease the net benefits that the nation derives from its
publicly owned fish stocks.

The public sector's role in resolving multiple-use con-
flicts should not be overlooked either: Conflicts among
incompatible fishing practices and between commercial
fishing and both sport fishing and marine mammal protec-
tion should grow in direct proportion to increased prefer-
ences for seafood and higher ex-vessel prices. Many current
events seem to support this statement. For example, in New
England, the use of otter trawls to catch lobsters in tradi-

tional pot fisheries is steadily increasing. Concerning con-
flicts with sport fishing, the regional fishery management
councils in the eastern United States recently conferred
virtual gamefish status on billfish in order to eliminate the
small but growing commercial fishery (South Atlantic Fish-
ery Management Council 1988). Ongoing efforts to seques-
ter other gamefish species such as bluefish and sharks are
being justified, in part, on similar grounds. Finally, the
incidental killing of turtles, dolphins, whales, and seals
trapped in fishing gear, such as gillnets and purse seines,
more and more elicits a storm of protest from proponents of
marine mammal protection.

SUMMARY AND CONCLUSIONS

The Graphical Analysis section provides strong evi-
dence of structural changes in preferences for seafood,
probably in response to medical evidence about both the
nutritional value of fish and shellfish and the health benefits
of omega-3 fatty acids. Per capita consumption of seafood
has increased since the early 1960s despite concurrent
increases in the relative prices of seafood. Also, the mid-
1960s and early 1980s appear to mark periods of accelerated
change.

Attempts to quantify and test apparent trends in seafood
consumption yielded mixed results. Severe collinearity
between per capita income and the time period undermined
most tests of a linear time trend in per capita consumption
and price. However, the robust change-point results in the
reduced-form models for price and consumption of fresh or
frozen seafood suggest that preferences accelerated during
the mid-1960s and early 1980s. I do not know why similar
change-points were not identified for consumption of canned
seafood, although it may be due to the fact that most
consumption of seafood still takes place in restaurants and
other types of eateries where canned fish and shellfish
generally are not sold. Also, the absence of a negative
change-point for salted, smoked, and other types of cured
fish would have been consistent with concems about nutri-
tion and health. Nevertheless, the steady decline in per
capita consumption of cured seafood since 1935 has at least
been reflected by the negative coefficient on the linear time
trend.

It is also interesting to note that the change-points
identified for fresh or frozen seafood and for price match
times of structural change in demands reported for red meats
and poultry (Chavas 1983; Choi and Sosin 1990; Dahigran
1987; Eales and Unnevehr 1988; Goodwin 1989; Moschini
and Meilke 1989; Nyankori and Miller 1982; Purcell 1989;
Thurman 1987). Thus, my study helps to complete the
general picture of how consumers have responded to nutri-
tion and health messages from the medical profession.

Stronger consumer preferences for fresh or frozen
seafood have important implications for economic research
and fishery management. Fishery economists should begin
to test variable-parameter structures in derived, ex-vessel


Page 7

Sum of squared residuals
34
24-- - -
14 - wes ae —
i) T T T T T T
1955 1960 1965 1970 1975 1980 1985 1990
Year
A
Sum of squared residuals
320
240 4-—
ee ae - -
BO fam es aoe
Cy ; — —— ; r r
1955 1960 1965 1970 1975 1980 1985 1990
B Year .

Figure 3, Residual sum of squares from regressions of: (a) per capita consumption of fresh or frozen seafood; and (b) price during the

years 1958-88.

the data from range I. The local minimum from range IT is
1984, although the value of the residual sum of squares is
virtually identical to that for the optimal change-point.

IMPLICATIONS

The evidence of structural changes in preferences for
seafood--particularly fresh or frozen seafood--has implica-
tions for fishery research and management. Three implica-
tions are highlighted here.

Although time-series data on retail sales of particular
species to consumers do not exist, ignoring strengthened
preferences for fresh or frozen seafood products could lead
to biased estimation of derived demand models in landings
markets. To see this, let the short run ex-vesse] demand
model be:

Pa,7 bX

where p,, is ex-vessel price during time period t, x, is a
matrix of regressors, including determinants of consumer


Page 4

quently, however, consumption increased despite continued
increases in relative price, except between the late 1970s and
early 1980s when consumption was somewhat stable.

The relationships between seafood consumption and
the price of seafood relative to beef & veal (Figure 2c), to
pork, and to “all foods” (available upon request) are similar
to those for poultry.

TWO-PHASE REGRESSION

Although structural changes in preferences for seafood
are apparent from Figure 2, additional insights can be gained
by quantifying and testing for significance of the apparent
trends. Accordingly, note that the trends in Figure 2 include
upward-sloping portions that are punctuated by periods of
telatively less change in annual per capita consumption
Prior to the mid- 1960s and then again during the late 1970s
to early 1980s. The functional form selected to test for
evidence of structural changes in preferences for seafood
should accommodate such “change-points.”

I emphasized in the introduction that the consistently
dubious estimates of the parameters of seafood demand
models seem to preclude further use of structural models,
such as the AIDS model, to test for evidence of structural
changes in consumers’ preferences for seafood when aggre-
gate data are used. Consequently, I have chosen a reduced-
form specification that can be understood in terms of the
following conceptual model:

4,7 QP ob2)
4," 40.4)

where 4%, and q, are per capita demand and supply, respec-_

tively, during time period t, and where Pis price and z, and
w, ate exogenous determinants of demand and supply. The
variables in this system could be partitioned to accommo-
date a system of substitutes (e.g., seafood, poultry, beef).
Also, Rausser et al. (1982) have already explained how the
time period, t, can be specified to pick up changes in
preferences over time’.

In order for average per capita consumption to have any
behavioral meaning, the conceptual model must be inter-
preted as aggregate demand and aggregate supply divided
by population size’. Accordingly, the reduced-form models
are:

4g, = Ut2,W,)
P, = PLZ).

Accordingly, neither own-price nor the prices of substitutes
are part of the reduced-form specification of q,.

A test of the significance of t is consistent with a test of
possible structural changes in preferences for seafood. If
preferences for seafood strengthened over time, then one

should expect increases in t to be associated with increases
in q, and p, in the reduced-form models (as well as in the
elusive structural models)"°. Thus, it has not been necessary
to recover the underlying structural models to test for
possible structural changes in preferences for seafood.

Based on this derivation (and the need for an alternative
to structural models), the following general reduced-form
specifications have been estimated:

9 = 4,462) Gi = 1,2,3] (la)
P, = P(tz,) (1b)

where q, ,, is annual per capita consumption of the i* generic
seafood product (i.e., of fresh or frozen seafood, canned
seafood, or cured seafood) in the U.S. during year t, P,is the
CPI of seafood relative to the CPI of all foods'!, and. zis
defined as above. Unfortunately, data on exogenous deter-
minants of supply (i.e., w,) cannot be specified, but this isnot
unusual for economic studies of seafood markets'?,. For
convenience, the subscript i has been omitted from the
remainder of the report.

TWO-PHASE REGRESSION MODEL

Hinkley (1971) described a two-stage regression proce-
dure that tests for the location ofa structural change ina time-
series process--i.e., a change-point. When applied to this
study, the empirical version of equations (1a) and (1b)
become:

q, =a, + a,t + a(t - AD yy t+azte, (2a)

=b,+bt+dt- AD, + by, +, (2b)
where a, and b, are parameters, e, and n, are residual pro-
cesses, and d is a change-point in the relationships between
tand q, or between t and p, such that Dyy equals 0 if t is less
than or equal to d, and equals | if t is greater than d. The
change may be either instantaneous or gradual, occurring
over several years. If gradual, the model actually selects a
point within the interval of change.

The nature of a change-pointis clarified when equations
(2a) and (2b) are decomposed into two phases:

a tat+az+e  [t=1,...,1] (3a)

q-
ajtas‘ttaz+e [t= (rtl),...,.T] Ga)
b, +bt +bz + na [t= 1,...,1] (3b)

P=
"bre bte btn, [t= (1)..T] — @b9

where T is the terminal time period, and the change-point
lies inthe interval (r,r+ 1). Mathematically, the change-point





18. The apparent contradiction between the likelihood ratio
test on U and the t-test on a, in this. model and in the
regression for cured seafood from data in range II is
probably due to the positive bias in a, See Solow
(1987). .

19. Most ex-vesse] demand models are estimated with
monthly or seasonal data. Within these time frames,
landings are usually assumed to be independent of ex-
vessel price. This assumption would not be valid,
though, over the longer run as prices and stock abun-
dance change.

20. See Rausser et al. (1982) fora summary of the literature
on how to model structural changes in consumer pref-
erences (and production technology), and for a synthe-
sis of the various types of variable-parameter struc-
tures.

21. Ifproperly specified, anex-vessel demand model would
capture consumer surplus and all producer surpluses in
the seafood sector except for harvesters. See chapter 6
in Just et al. (1982) for the theory of welfare estimation
with general equilibrium models.

22. In the Northwest Atlantic Ocean, fishing effort on
groundfish species long favored by consumers (¢.g.,
cod, halibut, flounders) increased recently despite de-
creases in stock abundance and reduced catch per unit
of effort (Conservation & Utilization Division, North-
east Fisheries Center 1988).

ACKNOWLEDGMENTS

Phil Logan, David Terkla, Stanley Wang, Andrew
Solow, and Richard Raulerson made helpful comments.
The two anonymous reviewers helped me clarify several
points of confusion.

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Page 11

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Maddala, G.S. 1984. Limited-dependent and qualitative
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Moschini, G.,and K.D. Meilke. 1989. Modeling the pattern
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Nyankori, J.C.O., and G.H. Miller. 1982. Some evidence
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(continued from inside front cover)

68. MARMAP Surveys of the Continental Shelf from Cape Hatteras, North Carolina, to Cape Sable, Nova Scotia
(1984-87). Atlas No. 3. Summary of Operations. By John D. Sibunka and Myron J. Silverman. July 1989. iv + 197
p., 36 figs., 2 tables. NTIS Access. No. PB90-160656/AS.

69. The 1988 Experimental Whiting Fishery: A NMFS/Industry Cooperative Program. By Frank P. Almeida,
Thurston S. Burns, and Sukwoo Chang. August 1989. v + 16 p., 9 figs., 11 tables, 1 app. NTIS Access. No. PB90-
160664/AS.

70. Summer Distribution of Regulated Species on Georges Bank with Reference to the 1988 Experimental
Whiting Fishery. By Frank P. Almeida, Sukwoo Chang, and Thurston S. Burns. September 1989. v+ 25 p., 74 figs.,
1 table. NTIS Access. No. PB90-206525/AS.

71. Allocation of Statewide-Reported MRFSS Catch and Landings Statistics between Areas: Application to
Winter Flounder. By Frank P. Almeida. September 1989. v + 18 p., 5 figs., 6 tables, 2 app. NTIS Access. No. PB90-
246745.

72. Status of the Fishery Resources off the Northeastern United States for 1989. By Conservation and Utilization
Division, Northeast Fisheries Center. December 1989. iv + 110p., 50 figs., 93 tables. NTIS Access. No. PB90-170622/
AS.

73. Surface and Bottom Temperature Distribution for the Northeast Continental Shelf. By David G. Mountain
_ and Tamara J. Holzwarth. December 1989. iii + 32 p., 31 figs. NTIS Access. No. PB90-252172/AS.

74, Shell Disease of Crustaceans in the New York Bight. By C.J. Sindermann (chair.), F. Csulak (EPA coord.), TK.
Sawyer (rapp.), R.A. Bullis, D.W. Engel, B.T. Estrella, E.J. Noga, J.B. Pearce, J.C. Rugg, R. Runyon, J.A. Tiedemann,
and R-R. Young. December 1989. vii + 47 p., 7 figs., 4 tables, 4 app. NTIS Access. No. PB90-195058/AS.

75. An Indexed Bibliography of Northeast Fisheries Center Publications and Reports for 1988. By Jon A. Gibson.
December 1989. iii + 32 p. NTIS Access. No. PB91-112912.

16. Finfish Maturity Sampling and Classification Schemes Used during Northeast. Fisheries Center Bottom
Trawl Surveys, 1963-89. By Jay Burnett, Loretta O’Brien, Ralph K. Mayo, Jeffrey A. Darde, and Margot L. Bohan.
December 1989. iii+14 p., 11 tables, 1 app. NTIS Access. No. PB91-128389/AS.

77, Shell Disease among Red Crabs Inhabiting Submarine Canyons of the New York Bight. By Randall R. Young.
December 1989. iii+9 p., 18 figs., 5 tables. NTIS Access. No. PB90-194762/AS.

78. Seasonal Distribution Patterns of Commercial Landings of 45 Species off the Northeastern United States
during 1977-88. By Sukwoo Chang. October 1990. v+130 p., 246 figs. NTIS Access. No. PB91-160846.

79. Contaminants in Sediment and Fish Tissue from Estuarine and Coastal Sites of the Northeastern United
States: Data Summary for the Baseline Phase of the National Status and Trends Program Benthic Surveillance
Project, 1984-1986. By Vincent S. Zdanowicz and Donald F. Gadbois. December 1990. x + 138p., 67 figs., 21 tables.
NTIS Access. No. PB92-147453/AS.

80. Distribution of Sexually Immature Components of 10 Northwest Atlantic Groundfish Species Based on
Northeast Fisheries Center Bottom Trawl Surveys, 1968-86. By Susan E. Wigley and Wendy L. Gabriel. January
1991. iv + 17 p., 23 figs., 3 tables. NTIS Access. No. PB92-101617.

81. Status of the Fishery Resources Off the Northeastern United States for 1990, By Conservation and Utilization
Division, Northeast Fisheries Center. January 1991. iv + 130 p., 50 figs., 82 tables. NTIS Access. No. PB91-213785.

82. Response of the Habitat and Biota of the Inner New York Bight to Abatement of Sewage Sludge Dumping:
Third Annual Progress Report-1989. By Anne L. Studholme, Merton C. Ingham, and Anthony Pacheco, eds.
February 1991. vi + 57 p., 74 figs., 20 tables, 1 app. NTIS Access. No. PB91-208199.


Page iii

TABLE OF CONTENTS

Abstract ....
Introductior
Graphical Analysis .
Two-phase Regression
Implications .....
Summary and Conclusions
Notes .
Acknowledgments
References Cited .

FE oma ke ee

LIST OF TABLES

Table 1. Regression results for per capita consumption of fresh or frozen seafood, canned seafood, .....
and cured seafood, and for seafood price, over two ranges of years--1935-88 and 1958-88

LIST OF FIGURES

Figure 1. Historical data on seafood demand: (a) U.S. annual per capita consumption of ....
commercial fish and shellfish; and (b) relative prices
Figure 2. Historical relationships between annual per capita consumption of total seafood ...
and the CPI of seafood relative to: (a) per capita income; (b) the CPI of poultry;
and (c) the CPI of beef and veal
Figure 3. Residual sum of squares from regressions of: (a) per capita consumption of fresh........
or frozen seafood; and (b) price during the years 1958-88



Recent issues in this series

53. Contaminants in Hudson-Raritan Estuary Water and Influence of Cold Storage upon Its Chemical
Composition. By Anthony Calabrese, Lawrence J. Buckley, and J. Christopher Powell. May 1988. vii + 37 p., 10 figs.,
11 tables. NTIS Access. No. PB88-225628/AS.

54. Epizootic Ulcerative Syndromes in Coastal/Estuarine Fish. By Car! J. Sindermann. June 1988. v + 37 p., 8 figs.,
1 table. NTIS Access. No. PB89-110803/AS.

55. A Plan for Study: Response of the Habitat and Biota of the Inner New York Bight to Abatement of Sewage
Sludge Dumping. By Environmental Processes Division, Northeast Fisheries Center. June 1988. iii + 34 p., 5 figs., 3
tables, 4 app. NTIS Access. No. PB89-100903/AS.

56. Characterization of the Middle Atlantic Water Management Unit of the Northeast Regional Action Plan. By
Anthony L. Pacheco, ed. July 1988. v + 322 p., 136 figs., 21 tables. NTIS Access. No. PB89-145262/AS.

57. An Analysis and Evaluation of Ichthyoplankton Survey Data from the Northeast Continental Shelf
Ecosystem. By Wallace G. Smith, ed. August 1988. xiii + 132 p., 53 figs., 12 tables, 1 app. NTIS Access. No. PB89-
122501/AS.

58. An Indexed Bibliography of Northeast Fisheries Center Publications and Reports for 1987. By Jon A. Gibson.
August 1988. iii + 20 p. NTIS Access. No. PB89-113013/AS.

59. Surveys of Breeding Penguins and Other Seabirds in the South Shetland Islands, Antarctica, January-
February 1987. By W. David Shuford and Larry B. Spear. September 1988. vii + 27 p., 14 figs., 1 table. NTIS Access.
No. PB89-141311/AS.

60. Survey of Antarctic Fur Seals in the South Shetland Islands, Antarctica, during the 1986-1987 Austral
Summer. By John L. Bengtson, Lisa M. Ferm, Tero J. Harkonen, Everett G. Schaner, and Brent S. Stewart. September
1988. vii + 8 p., 1 fig., 3 tables. NTIS Access. No. PB89-141303/AS.

61. Fish as Sentinels of Environmental Health. By Robert A. Murchelano. September 1988. iii + 16 p., 4 figs. NTIS
Access. No. PB89-139737/AS.

62. The Effects of Density Dependent Population Mechanisms on Assessment Advice for the Northwest Atlantic
Mackerel Stock. By W. J. Overholtz, S.A. Murawski, W.L. Michaels, and L.M. Dery. October 1988. v + 49 p., 7 figs.,
20 tables. NTIS Access. No. PB89-151948/AS.

63. Status of the Fishery Resources Off the Northeastern United States for 1988. By Conservation and Utilization
Division. October 1988. iii + 135 p., 51 figs., 52 tables. NTIS Access. No. PB89-130819/AS.

64. The Shell Disease Syndrome in Marine Crustaceans. By Carl J. Sindermann. February 1989. v + 43 p., 5 figs.,
2 tables. NTIS Access. No. PB89-162523/AS.

65. Stock Assessment Information for Pollock, Pollachius virens (L.), in the Scotian Shelf, Georges Bank, and Gulf
of Maine Regions. By Ralph K. Mayo, Stephen H. Clark, and M. Christina ‘Annand. April 1989. vi + 14 p., 6 figs.,
14 tables. NTIS Access. No. PB90-120676/AS.

66. Guidelines for Estimating Lengths at Age for 18 Northwest Atlantic Finfish and Shellfish Species. By Judith
A. Pentilla, Gary A. Nelson, and John M. Burnett, III. May 1989. iii + 39 p., 18 figs., 19 tables. NTIS Access. No., PB90-
120675/AS.

67. Response of the Habitat and Biota of the Inner New York Bight to Abatement of Sewage Sludge Dumping.

Second Annual Progress Report -- 1988. By Environmental Processes Division, Northeast Fisheries Center. July
1989. vii + 47 p., 39 figs., 11 tables, 3 app. NTIS Access. No. PB90-125444/AS.

(continued on inside back cover)

u


demand models in order to control for possible preference
change among consumers. Otherwise, we will continue to
risk estimating biased models and underestimating welfare.
In addition, fishery managers are well-advised to anticipate
both greater fishing effort on already overfished stocks and
anera of allocating stocks among commercial fishing, sport
fishing, and marine mammal protection. Indeed, the na-
tional advertising campaign to induce consumers to “eat fish
and seafood twice a week” and proposed federal legislation
for seafood inspection should further stimulate preferences
and exacerbate management.

NOTES

1, Respondents to Jones and Weimer’s (1981) survey of
the American diet reported the following net changes in
meat consumption during the late 1970s: (a) a 15-
percent and 3-percent increase in consumption of fish
and shellfish, respectively; (b) a 16-percent increase in
consumption of poultry; (c) a 14-percent decrease in
consumption of beef; (d) a 14-percent decrease in
consumption of fresh pork; and (e) a 21-percent de-
crease in consumption of bacon and sausage. These
changes were attributed to concerns about nutrition and
health.

2. Often, seafood demand is either omitted from a system
of structural equations, such as the almost-ideal-de-
mand system, (e.g., Choi and Sosin 1990), or is lumped
in with all other foods (e.g., Chavas 1983; Eales and
Unnevehr 1988).

3. Purcell (1989) used only a graphical analysis of time-
series data to show that preferences for beef declined
during at least the first half of the 1980s. This conclu-
sion conflicts with results reached from AIDS models
(e.g., Wohlgenant 1985) and from nonparametric stud-
ies of expenditures (Chalfant and Alston 1988). Yet,
Purcell (1989) is adamant when he scolds economists
about “...looking at the data again. ...[W]e have to get
reacquainted with theoretical and conceptual rigor in
dealing with phenomena we cannot effectively quan-
tify. And we need to stop substituting technique for
thinking.” (p. 19).

4. These seafood consumption data are for edible meat
from domestically-caught and imported fish and shell-
fish entering U.S. markets (Fisheries Statistics Divi-
sion, National Marine Fisheries Service 1989). They
are adjusted for beginning and ending inventories and
trade, but they exclude unknown consumption of sport-
caught fish, negligible amounts of cultured catfish prior
to 1973, and recent surimi production. For comparison,
Icelanders and Japanese consume four-to-five-times
more fish than Americans currently consume (Fisheries

10.

Page 9

Statistics Division, National Marine Fisheries Service
1989), Also for comparison, annual per capita con-
sumption of poultry and red meat in the United States in
1988 was 57.3 and 114.8 pounds (boneless-equivalent
weights), respectively (Putnam 1989). The discussion
is limited to the post-1935 period for comparison with
relative prices. In addition, per capita consumption
prior to the 1930s is only approximated by the National
Marine Fisheries Service.

The CPI for seafood includes prices of a wide variety of
fresh, frozen, canned, and cured products. I have used
the CPI for total seafood because separate indices for
canned seafood and for fresh and frozen seafood were
not reported until 1978.

The prices of seafood relative to pork andtoall foods are
not shown because they closely overlap that for beef
and veal.

For example, prior to 1967, Catholics were forbidden
from eating meat on non-Lent Fridays (Bell 1968).

In the Implications section, I briefly convey Rausser et
al.'s (1982) explanation for how the time period can be
used in a variable-parameter specification to test for
structural changes in preferences. Nevertheless, you
should consult their survey and synthesis for details on
how to model structural change.

I should at least acknowledge that this behavioral
interpretation raises the specter of heterogeneous pref-
erences and a censored population of seafood consum-
ers. These have implications for estimating models
based on average, or per capita, consumption. How-
ever, I wish to point out that the many published studies
of AIDS models in the food-demand literature suffer
the same deficiencies. These issues should be re-
searched in the near future. For example, see Maddala
(1984) for a discussion of estimation procedures for
censored data.

The following exercise illustrates my point. Let the
structural demand model be

Q = a(t) - b(L)P + c(t)M
= at - (b/t)P + ctM
and the structural supply model be
Qz=e+fP-gW
where t is the time period, the other lower case letters are
parameters (those in the demand model are variable

parameters which are a function of time), Q is quantity,
P is price, M is income, and W is input price for the


Page 12

Purcell, W.D. 1989. The case of beef demand: a failure by
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Rausser, G.C., Y. Mundlak, and S.R. Johnson. 1982.
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South Atlantic Fishery Management Council. 1988. Fish-
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ment, regulatory impact review, and initial regulatory
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Atlantic Fishery Management Council, Charleston, S.C.
149 pp.

Solow, A.R. 1987. Testing for climate change: an applica-
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Thurman, W.N. 1987. The poultry market: demand stability
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Wohlgenant, M.K. 1985. Estimating cross elasticities of

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GY U.S. GOVERMENT PRINTING CFFICE: 1962--600-051--60003,