Modeling Import Demand for Fruits and Fruit Juices in the U.S.

Umesh BastolaWashington State University

PNREC-2013 Spokane, WA

May 17, 2013

Motivation• In the last two decades, the U.S. has been

experiencing a substantial growth in imports of fruits and fruit juices.

• Reasons - Rising consumer income, consumer awareness on health benefits of fruits, easier trade flows, and technological improvements (Huang & Huang, 2007; Pollack, 2001).

• The growing ethnic diversity of the immigrant U.S. population who are accustomed to fresh produced diets has also contributed to the increased demand for imported fruits, especially the tropical fresh fruits (Fonsah et al., 2007).

Motivation• Domestic production, although increasing, has not

been able to satisfy the increasing demand, primarily due to: – the less favorable U.S. continental climate, – seasonality in production, and – high domestic farm labor costs (Nzaku et al. 2010).

• As a result, the U.S. has increasingly become a net fruit importer (Huang & Huang, 2007), particularly in most of the tropical fruits of all forms including fresh, dried, canned, and juices (USDA ERS, 2012).

Import Share of Some Fruit Commodities in U.S.

Canned

Olive

Dried Apric

ot

Banan

a Fres

h

Limes

Fresh

Mango

Fresh

Papay

a Fres

h

Pineapple

Fresh

Blueberr

y Frozen

Apple Juice

Pineapple

Juice0

20

40

60

80

100

120

-100

0

100

200

300

400

500

600

700

Average (1993 - 2011) 2011 Growth rate (1993-2011), %

Impo

rt S

hare

, %

Grow

th ra

te (1

993

- 201

1), %

Import Value of Some Fruit Commodities (1993-2011)

0200400600800

100012001400160018002000

0

5

10

15

20

25

Average Import Value ($M) 2011 Import Value ($M) Avg. ann. growth rate (%)

Impo

rt V

alue

, $M

Grow

th ra

te,%

Previous Studies on Fruit Demand• Most of the studies in fruit demand in the U.S. have

focused in either domestic or export markets (You et al. 1998; Pollack, 2001; Cook, 2003; Seale et al. 1992; Durham & Eales, 2010).

• Available studies on import demand for fruits and fruit juice are limited to a single fruit commodity or a narrow range of fruits (e.g., Fonsah & Muhammad, 2008; Nzaku et al. 2010).

• Study focusing on a broader range of fruits (tropical and temperate) and their forms (fresh, frozen, dried, canned/preserved, and fruit juices) in one analytical framework is still lacking.

• Methodological issues

ObjectivesEmpirically estimate demand relationships among major imported fruit commodities in the U.S.

Specifically, to

1. Test theoretical restrictions for the import demand model of fruit commodities .

2. Assess the price and income characteristics of imported fruit commodities such as necessities or luxuries, and complements or substitutes.

3. Explore price and income elasticities for imported fruits and juices.

Empirical Model• Almost Ideal Demand System (Deaton &

Muellbauer, 1980):– Flexible functional form demand system– Provides perfect aggregation over consumers – Allows statistical testing of theoretical

restrictions– Its linear approximation is simple to estimate

• It assumes that consumers allocate total expenditure among group of goods, the imported fruit and fruit juices being one.

The Model• AIDS (Deaton & Muellbauer, 1980)

model:

Sit = expenditure share of good i in period t,

Pjt = price of good j, Mt = total expenditure on all goods, and Pt

* = aggregate price index (Tornqvist) defined as

1

(1) ln lnn

tit i ij jt i it

j t

MS PP

*, 1

1 , 1

1(2) ln ln2

nit

t it i ti i t

PP S SP

Theoretical Restrictions• For theoretical consistency, the

following parameter restrictions must hold:

1 1 1

(3) 1, 0, 0, (Adding-up)n n n

i ij ii i i

j

1

(4) 0, (Homogeneity)n

ijj

i

(5) (Symmetry)ij ji

Price and expenditure elasticities

• Price (6) and expenditure elasticities (7), calculated at sample means (Green & Alston, 1990) are given by:

(6) ,

where is the Kronecker delta ( 1 for and

0 for )

(7) 1

ij jMij ij i

i i

ij

ij

ii

i

SS S

i j

i j

S

Time Series Analysis• It is necessary to examine time series property of

data to identify if any dynamic equilibrium relationships are meaningful or merely spurious.

• ADF (Dickey & Fuller, 1979) test for unit roots

• If the variables are I(1), we can test for cointegration

• If the dependent and a series of independent variables are cointegrated, error correction version of the AIDS (ECAIDS) model can be estimated.

ECAIDS• The ECAIDS (Karagiannis, Katranidis, & Velentzas,

2000):

Where Δ is the difference operator, Δ Sit-1 captures consumers habits, μit-1 are the lagged estimated residuals

from the cointegration equations, and λ < 0, is the speed of adjustment.

• This equation is estimated using Engle and Granger (1987) two-step procedure where the estimated residuals are obtained from the LAAIDS model.

• Iterated seemingly unrelated regression (ISUR) method

1 11

(8) ln lnn

tit i it ij jt i i it it

j t

MS S P

P

Testing Restrictions• The homogeneity and symmetry restrictions are

tested rather than taking as maintained hypotheses.

• Hence, the LA-AIDS and EC-AIDS are estimated as: – without imposing restrictions on homogeneity

and symmetry (unrestricted) and testing for joint restriction; and

– testing for the homogeneity restriction with symmetry maintained.

• Wald test is used for testing the above restrictions.

• If these restrictions are rejected, then an unrestricted model is estimated for further analysis.

Data• Five fruit forms most commonly imported to the U.S

are selected – fresh, frozen, canned/preserved, dried, and juice.

• In order to control for domestic production, only those fruits and juice are selected of which the import share constitutes more than 50% of its total consumption in the U.S. (USDA –ERS, Fruit and Tree Nuts Yearbook, 2012)

• A total of 10 fruit commodities are selected and are listed by categories as follows: a) fresh - banana, mango, papaya, pineapple, and lime; b) frozen - blueberry; c) canned/preserved - olives; d) dried - apricot; and e) juice – apple and pineapple.

Data• Monthly data on import quantity, value, and unit

prices are available from Jan-1993 to Dec-2011 for all the selected fruit commodities (USDA ERS, 2012).

• Sum of monthly import value of all the selected fruit commodities gives the monthly total expenditure.

• Monthly expenditure shares of each fruit commodity are then obtained by dividing the monthly expenditures by the monthly total expenditures.

• To control for potential trend and seasonality, a time trend and three seasonal dummies are also included in the model.

Results

Import Expenditure Shares (Mean ± SD) of Selected Fruit Commodities in the U.S.

(1993-2011)

Canned Oliv

es

Dried Apric

ot

Fresh Ban

ana

Fresh Lim

e

Fresh M

ango

Fresh Pap

aya

Fresh Pineap

ple

Frozen Bluberry

Apple Juice

Pineapple Ju

ice0%

10%

20%

30%

40%

50%

60%

Import Expenditure Share Over Time19

93-1

1993

-819

94-3

1994

-10

1995

-519

95-1

219

96-7

1997

-219

97-9

1998

-419

98-1

119

99-6

2000

-120

00-8

2001

-320

01-1

020

02-5

2002

-12

2003

-720

04-2

2004

-920

05-4

2005

-11

2006

-620

07-1

2007

-820

08-3

2008

-10

2009

-520

09-1

220

10-7

2011

-220

11-9

0%

10%

20%

30%

40%

50%

60%

70%

80%

Canned Olive Fresh Banana Fresh LimesFresh Mango Apple Juice

Results from Time Series AnalysesUnit root tests• All data series including prices, income, and

expenditure shares were non-stationary and contained unit root.

Cointegration tests• Each of the demand equation was found to

be cointegrated implying a long-run relationship among the variables (prices and expenditure shares).

Tests on Theoretical Restrictions

Parameter Restriction

Calculated χ2

valuesCritical χ2 values

(1% level)Degrees of freedom

Homogeneity 42.61 21.67 9

Homogeneity and symmetry

242.56 81.07 54

LA-AIDS MODEL

EC-AIDS MODELParameter Restriction

Calculated χ2

valuesCritical χ2 values

(1% level)Degrees of freedom

Homogeneity 26.86 21.67 9

Homogeneity and symmetry

207.61 81.07 54

Parameter Estimates of LA-AIDS ModelPara-

metersCan.

olivesDried

apricotFresh

bananaFresh lime

Fresh mango

Fresh papaya

Fresh pineap.

Frozen bluber.

Apple juice

Pineap juice

Id.(i) 1 2 3 4 5 6 7 8 9 10γi1 0.056 0.000 -0.079 0.022 -0.060 0.004 0.016 0.008 0.024 0.008γi2 0.001 0.007 0.003 0.005 -0.007 -0.004 -0.001 -0.001 -0.002 -0.001γi3 -0.040 -0.012 0.211 -0.016 0.014 -0.027 -0.049 -0.014 -0.062 -0.005γi4 -0.003 -0.002 -0.002 0.022 -0.008 0.000 -0.005 0.006 -0.007 0.000γi5 0.012 0.002 0.008 0.001 0.003 -0.001 -0.004 -0.007 -0.012 -0.002γi6 0.008 0.002 -0.056 0.004 0.018 0.020 -0.008 -0.014 0.027 -0.001γi7 0.002 0.000 -0.056 0.003 -0.013 -0.002 0.075 0.002 -0.019 0.008γi8 -0.004 -0.002 -0.026 0.001 0.014 -0.006 0.008 0.025 -0.006 -0.005γi9 -0.003 0.002 -0.024 -0.006 -0.011 0.001 -0.024 -0.005 0.073 -0.003γi10 0.012 0.004 -0.004 0.001 -0.005 0.014 -0.013 0.000 -0.040 0.032βi -0.050 -0.004 -0.093 -0.018 0.065 -0.014 -0.003 -0.017 0.150 -0.016αi 0.949 - 2.619 0.379 -1.162 0.235 0.077 0.287 -2.808 0.359

Red = Significant at 10%, Bold = Significant at 5%

Parameter Estimates of LA-AIDS ModelPara-

metersCan.

olivesDried

apricotFresh

bananaFresh lime

Fresh mango

Fresh papaya

Fresh pineap.

Frozen bluber.

Apple juice

Pineap juice

Id.(i) 1 2 3 4 5 6 7 8 9 10γi1 0.056 0.000 -0.079 0.022 -0.060 0.004 0.016 0.008 0.024 0.008γi2 0.001 0.007 0.003 0.005 -0.007 -0.004 -0.001 -0.001 -0.002 -0.001γi3 -0.040 -0.012 0.211 -0.016 0.014 -0.027 -0.049 -0.014 -0.062 -0.005γi4 -0.003 -0.002 -0.002 0.022 -0.008 0.000 -0.005 0.006 -0.007 0.000γi5 0.012 0.002 0.008 0.001 0.003 -0.001 -0.004 -0.007 -0.012 -0.002γi6 0.008 0.002 -0.056 0.004 0.018 0.020 -0.008 -0.014 0.027 -0.001γi7 0.002 0.000 -0.056 0.003 -0.013 -0.002 0.075 0.002 -0.019 0.008γi8 -0.004 -0.002 -0.026 0.001 0.014 -0.006 0.008 0.025 -0.006 -0.005γi9 -0.003 0.002 -0.024 -0.006 -0.011 0.001 -0.024 -0.005 0.073 -0.003γi10 0.012 0.004 -0.004 0.001 -0.005 0.014 -0.013 0.000 -0.040 0.032βi -0.050 -0.004 -0.093 -0.018 0.065 -0.014 -0.003 -0.017 0.150 -0.016αi 0.949 - 2.619 0.379 -1.162 0.235 0.077 0.287 -2.808 0.359

Red = Significant at 10%, Bold = Significant at 5%

Parameter Estimates of LA-AIDS ModelPara-

metersCan.

olivesDried

apricotFresh

bananaFresh lime

Fresh mango

Fresh papaya

Fresh pineap.

Frozen bluber.

Apple juice

Pineap juice

Id.(i) 1 2 3 4 5 6 7 8 9 10γi1

γi2

γi3 -0.016 0.014 -0.027 -0.049γi4 -0.002 -0.008 0.000 -0.005γi5 0.008 0.001 -0.001 -0.004γi6 -0.056 0.004 0.018 -0.008γi7 -0.056 0.003 -0.013 -0.002γi8

γi9

γi10

βi

αi

Red = Significant at 10%, Bold = Significant at 5%

Parameter Estimates of LA-AIDS ModelPara-

metersCan.

olivesDried

apricotFresh

bananaFresh lime

Fresh mango

Fresh papaya

Fresh pineap.

Frozen bluber.

Apple juice

Pineap juice

Id.(i) 1 2 3 4 5 6 7 8 9 10γi1 0.024 0.008γi2 -0.002 -0.001γi3 -0.062 -0.005γi4 -0.007 0.000γi5 -0.012 -0.002γi6 0.027 -0.001γi7 -0.019 0.008γi8 -0.006 -0.005γi9 -0.003 0.002 -0.024 -0.006 -0.011 0.001 -0.024 -0.005 -0.003γi10 0.012 0.004 -0.004 0.001 -0.005 0.014 -0.013 0.000 -0.040βi

αi

Red = Significant at 10%, Bold = Significant at 5%

Parameter Estimates of LA-AIDS ModelPara-meter

sCan.

olivesDried aprico

tFresh

bananaFresh lime

Fresh mang

o

Fresh papay

a

Fresh pinea

p.

Frozen bluber

.Apple juice

Pineap juice

Spring 0.008 - -0.013 0.003 0.032 0.006 0.011 0.000 -0.040 -0.005Summer 0.010 - -0.014 0.001 0.040 0.005 0.000 0.001 -0.028 -0.006

Fall 0.003 - 0.026 -0.003 -0.007 0.001 0.005 0.010 -0.028 -0.008

Trend 0.000 - -0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000

R2 0.438 - 0.878 0.845 0.671 0.824 0.922 0.798 0.565 0.538Red = Significant at 10%, Bold = Significant at 5%

Parameter Estimates of EC-AIDS ModelPara-

metersCan.

olivesDried

apricotFresh

bananaFresh lime

Fresh mango

Fresh papaya

Fresh pineap.

Frozen bluber.

Apple juice

Pineap juice

Id.(i) 1 2 3 4 5 6 7 8 9 10νi 0.071 - 0.052 0.060 0.107 -0.065 0.018 -0.057 0.054 0.034γi1

γi2

γi3

γi4

γi5

γi6

γi7

γi8

γi9

γi10

βi -0.030 -0.005 -0.105 -0.013 0.066 -0.004 0.012 -0.016 0.115 -0.020λi -0.760 - -0.683 -0.635 -0.656 -0.393 -0.656 -0.604 -0.670 -0.779

Long-Run Price and Expenditure ElasticitiesPara-

metersCan.

olivesDried

apricotFresh

bananaFresh lime

Fresh mango

Fresh papaya

Fresh pineap.

Frozen bluber.

Apple juice

Pineap juice

Id.(i) 1 2 3 4 5 6 7 8 9 10εi1 -0.367εi2 -0.534εi3 -0.479εi4 -0.312εi5 -1.011εi6 -0.016εi7 -0.109εi8 0.056εi9 -0.612εi10 -0.099ηi 0.483 0.742 0.811 0.441 2.034 0.323 0.963 0.301 2.110 0.540

Long-Run Cross-Price Elasticities

FruitsCan.

olivesDried

apricotFresh

bananaFresh lime

Fresh mango

Fresh papaya

Fresh pineap.

Frozen bluber.

Apple juice

Pineap juice

Canned Olives 0.746 -1.050 0.415Dried Apricot

Fresh Banana -0.704 -0.946 -0.565 -1.007Fresh Lime

Fresh Mango

Fresh Papaya -0.575Fresh Pineap.

Froz Blueb.

Apple Juice

Pineapp. Juice 0.692

Conclusions• Imposing theoretical restrictions would result in biased

estimates.

• In general, the imported fresh fruits are complements and all are normal goods.

• Mango and apple juice are luxuries while all other fruits are necessities.

• Mango and apple juice are both price and income elastic while most of other fruits are inelastic.

• Effects of seasonality and habit persistence are observed.

• Any deviations in the long-run equilibrium demand relationships are corrected in the short-run to bring back to the equilibrium.

Questions and Suggestions