1. Modeling Import Demand for Fruits and Fruit Juices in the U.S. Umesh Bastola Washington State University PNREC-2013 Spokane, WA May 17, 2013

2. 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).

4. 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).

5. Import Share of Some Fruit Commodities in U.S.

6. Import Value of Some Fruit Commodities (1993-2011)

7. 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

8. Objectives Empirically 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.

9. 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.

10. The Model AIDS (Deaton & Muellbauer, 1980) model: S it = expenditure share of good i in period t, P jt = price of good j, M t = total expenditure on all goods, and P t * = aggregate price index (Tornqvist) defined as

11. Theoretical Restrictions For theoretical consistency, the following parameter restrictions must hold:

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

13. 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.

14. ECAIDS The ECAIDS (Karagiannis, Katranidis, & Velentzas, 2000): Where Δ is the difference operator, Δ S it-1 captures consumers habits, μ it-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

15. 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.

16. 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.

17. 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.

18. Results

19. Import Expenditure Shares (Mean ± SD) of Selected Fruit Commodities in the U.S. (1993- 2011)

20. Import Expenditure Share Over Time

21. Results from Time Series Analyses Unit 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).

22. Tests on Theoretical Restrictions Parameter Restriction Calculated χ 2 values Critical χ 2 values (1% level) Degrees of freedom Homogeneity42.6121.679 Homogeneity and symmetry 242.5681.0754 LA-AIDS MODEL EC-AIDS MODEL Parameter Restriction Calculated χ 2 values Critical χ 2 values (1% level) Degrees of freedom Homogeneity26.8621.679 Homogeneity and symmetry 207.6181.0754

23. Parameter Estimates of LA-AIDS Model Para- meters Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Id.(i) 12345678910 γ i1 0.0560.000-0.0790.022-0.0600.0040.0160.0080.0240.008 γ i2 0.0010.0070.0030.005-0.007-0.004-0.001 -0.002-0.001 γ i3 -0.040-0.0120.211-0.0160.014-0.027-0.049-0.014-0.062-0.005 γ i4 -0.003-0.002 0.022-0.0080.000-0.0050.006-0.0070.000 γ i5 0.0120.0020.0080.0010.003-0.001-0.004-0.007-0.012-0.002 γ i6 0.0080.002-0.0560.0040.0180.020-0.008-0.0140.027-0.001 γ i7 0.0020.000-0.0560.003-0.013-0.0020.0750.002-0.0190.008 γ i8 -0.004-0.002-0.0260.0010.014-0.0060.0080.025-0.006-0.005 γ i9 -0.0030.002-0.024-0.006-0.0110.001-0.024-0.0050.073-0.003 γ i10 0.0120.004-0.0040.001-0.0050.014-0.0130.000-0.0400.032 βiβi -0.050-0.004-0.093-0.0180.065-0.014-0.003-0.0170.150-0.016 αiαi 0.949-2.6190.379-1.1620.2350.0770.287-2.8080.359 Red = Significant at 10%, Bold = Significant at 5%

24. Parameter Estimates of LA-AIDS Model Para- meters Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Id.(i) 12345678910 γ i1 0.0560.000-0.0790.022-0.0600.0040.0160.0080.0240.008 γ i2 0.0010.0070.0030.005-0.007-0.004-0.001 -0.002-0.001 γ i3 -0.040-0.0120.211-0.0160.014-0.027-0.049-0.014-0.062-0.005 γ i4 -0.003-0.002 0.022-0.0080.000-0.0050.006-0.0070.000 γ i5 0.0120.0020.0080.0010.003-0.001-0.004-0.007-0.012-0.002 γ i6 0.0080.002-0.0560.0040.0180.020-0.008-0.0140.027-0.001 γ i7 0.0020.000-0.0560.003-0.013-0.0020.0750.002-0.0190.008 γ i8 -0.004-0.002-0.0260.0010.014-0.0060.0080.025-0.006-0.005 γ i9 -0.0030.002-0.024-0.006-0.0110.001-0.024-0.0050.073-0.003 γ i10 0.0120.004-0.0040.001-0.0050.014-0.0130.000-0.0400.032 βiβi -0.050-0.004-0.093-0.0180.065-0.014-0.003-0.0170.150-0.016 αiαi 0.949-2.6190.379-1.1620.2350.0770.287-2.8080.359 Red = Significant at 10%, Bold = Significant at 5%

25. Parameter Estimates of LA-AIDS Model Para- meters Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Id.(i) 12345678910 γ i1 γ i2 γ i3 -0.0160.014-0.027-0.049 γ i4 -0.002-0.0080.000-0.005 γ i5 0.0080.001-0.001-0.004 γ i6 -0.0560.0040.018-0.008 γ i7 -0.0560.003-0.013-0.002 γ i8 γ i9 γ i10 βiβi αiαi Red = Significant at 10%, Bold = Significant at 5%

26. Parameter Estimates of LA-AIDS Model Para- meters Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Id.(i) 12345678910 γ i1 0.0240.008 γ i2 -0.002-0.001 γ i3 -0.062-0.005 γ i4 -0.0070.000 γ i5 -0.012-0.002 γ i6 0.027-0.001 γ i7 -0.0190.008 γ i8 -0.006-0.005 γ i9 -0.0030.002-0.024-0.006-0.0110.001-0.024-0.005-0.003 γ i10 0.0120.004-0.0040.001-0.0050.014-0.0130.000-0.040 βiβi αiαi Red = Significant at 10%, Bold = Significant at 5%

27. Parameter Estimates of LA-AIDS Model Para- meters Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Spring0.008--0.0130.0030.0320.0060.0110.000-0.040-0.005 Summer0.010--0.0140.0010.0400.0050.0000.001-0.028-0.006 Fall0.003-0.026-0.003-0.0070.0010.0050.010-0.028-0.008 Trend0.000--0.0010.000 R2R2 0.438-0.8780.8450.6710.8240.9220.7980.5650.538 Red = Significant at 10%, Bold = Significant at 5%

28. Parameter Estimates of EC-AIDS Model Para- meters Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Id.(i) 12345678910 νiνi 0.071 - 0.0520.0600.107-0.0650.018-0.0570.0540.034 γ i1 γ i2 γ i3 γ i4 γ i5 γ i6 γ i7 γ i8 γ i9 γ i10 βiβi -0.030-0.005-0.105-0.0130.066-0.0040.012-0.0160.115-0.020 λiλi -0.760 - -0.683-0.635-0.656-0.393-0.656-0.604-0.670-0.779

29. Long-Run Price and Expenditure Elasticities Para- meters Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Id.(i) 12345678910 ε i1 -0.367 ε i2 -0.534 ε i3 -0.479 ε i4 -0.312 ε i5 -1.011 ε i6 -0.016 ε i7 -0.109 ε i8 0.056 ε i9 -0.612 ε i10 -0.099 ηiηi 0.4830.7420.8110.4412.0340.3230.9630.3012.1100.540

30. Long-Run Cross-Price Elasticities Fruits Can. olives Dried apricot Fresh banana Fresh lime Fresh mango Fresh papaya Fresh pineap. Frozen bluber. Apple juice Pineap juice Canned Olives 0.746-1.0500.415 Dried Apricot Fresh Banana -0.704-0.946-0.565-1.007 Fresh Lime Fresh Mango Fresh Papaya -0.575 Fresh Pineap. Froz Blueb. Apple Juice Pineapp. Juice 0.692

31. 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.

32. Questions and Suggestions