European Unon Import Demand for In-Shell Peanuts: The Source Dfferentated AIDS Model 1 Tullaya Boonsaeng Post Doctoral Assocate Department of Agrcultural and Appled Economcs Unversty of Georga E-mal: tullaya@uga.edu Stanley M. Fletcher Professor Department of Agrcultural and Appled Economcs Unversty of Georga May 31, 2007 Abstract Ths research estmates mport demand elastctes for n-shell peanuts n the European Unon from four dfferent sources: Chna, the Unted States, South Amerca, and Afrca. The null hypothess of aggregaton over product sources s rejected at conventonal levels of sgnfcance suggestng that peanuts from dfferent sources are dfferentated by EU consumers whch mght attrbuted to ther dfferent qualty characterstcs. Condtonal expendture elastctes for U.S. n-shell peanuts are larger than expendture elastctes for Latn Amercan, Chnese and Afrcan peanuts. Keyword: In-Shell Peanuts, Nonlnear SAIDS, the European Unon Selected Paper/Poster Amercan Agrcultural Economcs Assocaton Portland, Oregon, July 29 August 1, 2007 Copyrght 2007 by Tullaya Boonsaeng and Stanley Fletcher. All rght reserved. Readers must may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copy rght notce appears on all such copes. 1 Workng paper please do not cte.
Introducton The European Unon (EU 2 ) s the largest mporter of peanuts n the world. In 2005, ts peanuts mports accounted for around 40 percent of the world mports of ths commodty (FAOSTAT database 2007). However, lttle economc research has been done on the EU markets for peanuts. To the best of our knowledge, our paper s the frst study analyzng the EU mport demand for peanuts dfferentated by source of producton. The EU countres mport peanuts manly from Chna, the US, Latn Amerca and Afrca. Whereas the demand for peanuts n Europe has been steady, the export shares among exportng countres have changed. In the last decade, the U.S. share of the total mport quantty of n-shell peanuts n the EU has declned whereas Chna, Afrca and Latn Amerca have ncreased ther export shares. Chna has replaced the US as the man exporter of n-shelled peanuts to the regon. The prncpal objectve of ths study s to analyze the EU demand for mported peanuts and to estmate prce and expendture elastctes that can be used for polcy analyss. The second objectve of ths study s to test product aggregaton to see whether U.S. peanuts are dfferentated from other countres because peanuts from dfferent sources may be dfferent qualty characterstcs. We hypothesze that EU mport demand for peanuts s dfferentated by regon of orgn. The study of European Unon (EU) markets for peanuts mght be useful to peanut exporters, but especally the U.S. The recent US farm polcy changes n 2002 that 2 The countres ncluded n the European Unon members are Austra, Belgum, Germany, Denmark, Span, Fnland, France, Unted Kngdom, Greece, Ireland, Italy, Luxemburg, Netherlands, Portugal, and Sweden. It can be called EU15. 1
replaced the quota system by the Marketng Loan Program have affected not only US peanut producton but also US export peanut supply. Therefore, the results from ths study can be used to better understand the changes n the demand for peanuts n the world market. Polcy makers and economsts could also use these results, for example, to analyze and quantfy the potental mpacts of federal promoton programs on the EU demand for U.S. peanuts. The EU countres mport two types of peanuts: 1) n-shell peanuts and 2) shelled peanuts. Both types are completely dfferent because n-shell peanuts are consumed drectly by consumers but shelled peanuts are mported by processors to produce peanut butter, candy, snacks, etc. In ths study, we only focus on the mported demand for nshell peanuts. General Informaton on the U.S. Peanut Markets Peanuts n the Unted Sates can be classfed nto four basc types: Runner, Vrgna, Spansh, and Valenca. Each of type of peanuts can be dstngushed by ts sze, flavor, and nutrtonal composton and purpose of use. Vrgna peanuts are manly used for roasted peanuts or to be sold as peanuts n shell. Spansh peanuts are prmarly utlzed to make peanut candy and peanut ol. Valenca peanuts are sweet and excellent to make fresh make fresh boled peanuts whch are sold n the shell. Vrgna peanuts are the man source of n shell peanuts for domestc use and export. Vrgna peanuts are grown manly n southeastern Vrgna and northeastern North Carolna. After the elmnaton of the peanut quota program n 2002 and due to 2
hgh cost of productons, there has been a sgnfcant move away from peanut producton n Vrgna and North Carolna. Peanuts acreage n these two states has declned over tme from 197.5 thousand acres n 2001 to 118 thousand acres n 2005 and the producton has decreased from 591,225 thousand pounds n 2001 to 354,000 thousand pounds n 2005 (NASS 3 database). Peanut producton has begnnng to move to the Southeast where farms are more productve, have hgher yelds and where Runner peanuts are manly planted. The volume of peanut exports n the U.S. depends on the U.S. producton because ther producton has to match wth domestc consumpton frst before exports. The declne n producton of Vrgna peanuts n favor of Runner peanuts has also weaken export of n shell peanuts n U.S. Moreover, changes to the peanut program n the 2002 may have further dmnshed export ncentves, as domestc producers who formerly produced addtonal peanuts for export can now market ther peanuts domestcally. Background Informaton on World Peanut Trade Accordng to the Producton, Supply, and Dstrbuton (PSD onlne) database of the Foregn Agrcultural Servce of the USDA, the man supplers of peanuts to the world peanut market are Argentna, Chna and U.S. whch account for 70 percent of total quantty exports. In 2005, the world total quantty export of peanuts was 2,005 thousand metrc tons. Out of ths total amount, Argentna exported 400 thousand metrc tons, Chna exported 784 thousand metrc tons, and the U.S. exported 223 thousand metrc tons. 3 Natonal Agrcultural Statstcs Servce, Unted States Department of Agrcultural 3
The man mporters of peanuts n the world are Canada, the EU, Japan and Mexco. These four mporters account for more than 60 percent of total mports. In 2005, Canada, Japan and Mexco each accounted for about 7 percent of total world mport quanttes and the EU accounted for around 40 percent. Hence, the EU s the largest mporter of peanuts by quantty and value. Chna, the U.S., Latn Amerca, and Afrca are the major exporters of n-shell peanuts to the EU. They accounted for more than 96% of the total value and quantty of EU n-shell peanut mports between 1995 and 2005 (EUROSTAT). Whereas the demand for peanuts n Europe has been steady, the competton among exporters has changed. Chna s stll the man domnant exporter of peanuts. Both Afrca and Latn Amercan countres have ncreased ther export share whle the US export share for peanuts has decreased over tme (Fgure 1). In the early 90s, the U.S. and Chna were the man exporters of n-shell peanuts to the EU. For example, n 1991 the US and Chne exported to the EU 35.62 and 40.90 mllon klograms (kg) of n-shelled peanuts, respectvely. The U.S. exports of peanuts peak n 1995 reachng a level of exports of 70.53 mllon kg followed by Chna (29.75 mllon kg), Latn Amercan (2.54 mllon kg), and Afrca (2.52 mllon kg). In 1996, Chna became the most domnant exporter of n-shell peanuts to the EU markets exportng 36.51 mllon kg, followed by the US (21.77 mllon kg), Afrca (2.73 mllon kg), and Latn Amerca (1.96 mllon kg). The U.S. share of the total mport quantty of n-shell peanuts n the EU declned from 66.66% n 1995 to 13.91% n 2005. The Chnese share of total mport quantty 4
ncreased from 28.12% n 1995 to 57.40% n 2005. The South Amerca s share of total mport quantty ncreased from 2.40% n 1995 to 11.38% n 2005 and the Afrca s share of total mport quantty also ncreased from 2.36% n 1995 to 14.84% n 2005. Fgure 1: EU15 Imports of In-Shell Peanut by Dfferent Sources 80 Quantty (1,000,000 kg) 70 60 50 40 30 20 10 0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 Source: EUROSTAT database Chna US Latn Amerca Afrca The Source Dfferentated AIDS Model The Source-dfferentated AIDS Model (SAIDS) was frst specfed by Yang and Koo (1994). The SAIDS model allows for source dfferentaton and t closely follows the dervaton of the AIDS model proposed by Deaton and Muellbauer (1980). Ths model has been prevously used n Yang and Koo (1994), and Carew, Florkowsk and He (2004). The SAIDS model also allows dsaggregatng and dfferentatng products by source. 5
The SAIDS model s derved from a prce ndependent generalzed logarthmc expendture functon whch accounts for the mporter s behavor that dfferentates goods from dfferent orgns. Even though tarff and quota on mport peanuts and peanut products have become neglgble n the EU, food safety ssues are stll a concern among EU consumers, especally the level of aflatoxns. Gven ths concern, the degree of food safety could become, to some extent, a source of product dfferentaton. Snce peanuts from dfferent sources have dfferent qualty attrbutes (Blss, 2005), t s mportant to recognze qualty dfferences among peanut exporters when analyzng the EU peanut mport demand. Applyng Shephard s lemma to the expendture functon, the source-dfferentated AIDS for one product (n shell peanuts from dfferent orgns n ths case) can be wrtten as: (1) w = α + γ ln p j + β ln( xg Pg ) j g where ln Pg = α 0 + α k ln pk + 1 2( γ kl ln pk ln pl ) s a prce ndex, g represents g k g k g l g the group, xg (= p q ) s total expendture on n shell peanuts from countres g (= Chna, U.S., Latn Amerca, Afrca or ROW), p and q are the prce and quantty of shelled peanuts from countres, w = p q x g s the condtonal budget share of shelled peanuts from all the mported sources. Prevous studes usng the SAIDS have used the Stone prce ndex as a proxy for the prce ndex derved analytcally from the AIDS cost functon; however, several 6
studes on consumer demand have showed that the Lnear Almost Ideal Demand System could produce based estmates of demand elastctes (Buse, 1994; Moschn, 1995; Chen, 1998). Therefore, the SAIDS model should be estmated as a nonlnear model (NLSAIDS) nstead of usng ts lnear approxmaton because polcy evaluatons and smulatons requre relable estmates of demand responsveness to prces and expendture. Consstent wth demand theory, the demand restrctons are addng up ( g α = 1 = 1, g = 1 γ = 0, β = 0 ), homogenety ( g = 1 j g γ = 0 ), and symmetry ( γ = γ j,, j g ). To test the hypothess of product aggregaton, the AIDS model whch does not dfferentate the product by orgns can be estmated. Estmaton of the AIDS model corresponds to the followng restrctons on the SAIDS model (Hayes, Wahl and Wllams, 1990): α = α g, g, γ = γ,, j g, g β = β g, g. These restrctons mply that the prce and expendture coeffcents from the dfferent sources are equal. The estmated parameters from equaton (1) are utlzed to compute ncome, ownprce, and cross-prce elastctes. The formulas of ncome elastctes, Marshallan prce elastctes, and Hcksan prce elastctes for the nonlnear SAIDS model are presented as equatons (2), (3) and (4), respectvely. 7
(2) η = + ( β w ) 1 (3) ε = δ + ( γ β ln(x g Pg )) w * (4) ε = ε + w η, where δ = 1 f = j and δ = 0 f j. j To dentfy whether the goods are substtutes or complements, the Morshma elastctes were calculated usng the followng equaton (Blackorby and Russell, 1989): (5) M = ε ε * * These elastctes measure the percentage change n the consumpton rato h ( p, u) h j ( p, u) due to a one percent change n the correspondng rato p p j. Morshma elastctes of substtuton are very natural measure of substtutablty, because by focusng on prce and quantty ratos they reflect the curvature of ndfference curves. If the Morshma elastctes are postve, the goods are consdered to be substtutes. The estmaton of the standard errors of the elastctes n the non-lnear SAIDS s complcated by the fact that these elastctes are non-lnear functon of several parameter estmates. To conduct statstcal tests on the elastctes, two types of approaches can be appled to obtan the standard errors. The frst method s the delta method whch s based on a Taylor seres approxmaton (Greene, 2003). The second approach s the blocks movng bootstrap method for tme seres data as outlned n Goncalves and Whte (2005). Both methods are utlzed and compared n ths paper. 8
Data and Procedures The data used to estmate the model are quarterly data from 1991 to 2005 provdng a total of 60 observatons. The sources of orgn of the EU mports of n-shell peanut consdered n ths study are Chna, U.S., Latn Amerca, Afrca, and rest of the world. The data were obtaned from the EUROSTAT database. The quantty of mports from each source s measured n 100,000 kg, and the value of mports s measured n 1,000 EUROS. Snce mport prce data s dffcult to obtan, unt prces 4 are used as approxmate of mport prce. The EU countres grow a trval amount of peanut plant because the weather n Europe s unsutable to grow peanuts. Ther peanut producton s nfntesmal relatve to the amount of ther peanut mported 5. Peanut consumpton n the EU manly depends on peanut mports from dfferent sources. Therefore, domestc producton can be gnored. Emprcal Estmaton The estmated system of equatons s condtonal on the EU total expendture on mported n-shell peanuts. To make the estmaton manageable, we assume that the EU consumers allocate total expendture among groups of goods, n-shell peanuts beng one. Preferences among these groups are weakly separable. For the allocaton of expendture for the n-shell peanut group, the EU consumers select mported n-shell peanuts from dfferent sources (Chna, U.S., Latn Amerca, Afrca, and ROW). 4 Unt prces of mported n-shell peanut from each country are computed by dvdng total value by total quantty of mports. 5 The EU producton s less than 0.0001 percent of total world producton and s less than 0.01 percent of total EU mport of peanuts. The data of EU and world peanut producton are avalable at Producton, Supply and Dstrbuton (PSD onlne) from the FAS, USDA. 9
The condtonal demand system contans fve equatons. The ROW equaton for n-shell peanut s dropped to avod sngularty problems snce the expendture shares n the condtonal demand system sum to one. The parameters of the unrestrcted condtonal demand system are estmated by usng the terated seemngly unrelated regresson (ITSUR) method. The parameters of the restrcted condtonal demand system were estmated by the seemngly unrelated regresson method (SUR) n order to take nto account the cross-prce effects on source-dfferentated wthn a product. Tests of homogenety and symmetry were conducted n the unrestrcted demand system, takng nto account that cross prce effects are source-dfferentated wthn a product. The test of product aggregaton was performed n the restrcted demand system (Carew, Florkowsk, and He, 2004). The MODEL procedure from SAS was used for estmaton proposes. Results The null hypothess of no autocorrelaton was rejected n all of the models ndcatng that the data s serally correlated. The systems of demand equatons were estmated and corrected for frst-order autocorrelaton. Snce the model s a sngular equaton system, we follow the frst-order autocorrelaton correcton procedure proposed by Berndt and Savn (1975). Ths approach assumes a constant autocorrelaton coeffcent n all the equatons of the system of equatons and zero cross equaton autocorrelaton. The estmated value of the frst autocorrelaton coeffcent s 0.3092 whch was sgnfcant at the 5 percent statstcal level. 10
The results of the tests of the homogenety and symmetry restrctons n the SAIDS model after correcton for the frst autocorrelaton are presented n table 1. The null hypothess that symmetry or homogenety or symmetry and homogenety restrctons are satsfed s not rejected. Lkelhood rato tests were used to test the restrctons. The results of the test of product aggregaton are showed n table 1. A Wald F-test was used for ths purpose. The null hypothess of product aggregaton whch mantans that n-shell peanuts from dfferent producton sources are perfect substtutes s rejected. These results suggest that n-shell peanuts from dfferent sources are dfferentated by EU consumers whch mght be attrbuted to ther dfferent qualty characterstcs. Results of Parameter Estmates Estmaton results of the nonlnear SAIDS model after the correcton of autocorrelaton are shown n table 2. Dummy varables measurng the effects of seasonalty show that mported demand for U.S. and Afrcan n-shell peanuts s hgh durng the October-December season whch concdes wth the harvestng season of peanuts n the U.S. and the hgher consumpton demand of the product durng the holday season. The seasonal dummy varables also show that mported demand for Chnese nshell peanuts does not concde wth the harvestng season. Ths ndcates that n Chna some n-shell peanuts are stored and sold durng off season. All of the seasonal dummy varables are sgnfcant for Chna and U.S. but they are not sgnfcant for Latn Amerca. The dummy varable ncluded to capture the 2002 Farm bll whch elmnated the marketng quota system for peanuts was found to have a sgnfcant and negatve effect 11
on mported demand for US n shell peanuts as expected snce the declne n the producton of Vrgna peanuts n the U.S. has weaken the export of n shell peanuts from the U.S. due to ts hgh cost of producton. Ths dummy varable also captures Ncaragua export of n shell peanuts sgnfcantly rsng n the last three years. It has sgnfcant and a postve effect on mported demand for Latn Amercan n shell peanuts. The change n farm polcy n U.S. has not had any effect on n shell peanuts exported from Chna and Afrca. Result of Elastctes Condtonal expendture elastctes are reported n table 3. Imported n shell peanuts from Chna, Latn Amercan, and Afrca are condtonally expendture nelastc whle mported n shell peanuts from the U.S. are condtonally elastc. These results suggest that, as peanuts mports ncrease, the EU mports more peanuts from the US than form other sources. Ths mght be due to the fact that U.S. peanuts have better qualty. The condtonal expendture elastcty from rest of the world s negatve because most of n shell peanuts mported to the EU are mostly low qualty peanuts from Inda. Mashallan prce elastctes showed n table 3 ndcates that all condtonal own prce elastctes for n-shell peanuts from dfferent sources are negatve correspondng to the law of demand. The Marshallan own prce elastctes of demand for U.S. n shell peanuts are -2.2952 and that for Chnese n shell peanuts -1.7787. They are condtonally hghly elastc and sgnfcant. These results suggest that EU consumers respond more to prce reductons for n shell peanuts mported from Chna and the US. 12
Latn Amercan n shell peanuts are much less own prce elastc. Ths ndcates that EU consumers demand for Latn Amercan n shell peanuts s not that senstve to own prce changes. The Marshallan own prce elastctes are only -0.4720. The Marshallan own prce elastctes of n shell peanuts from Afrca and the rest of the world are more elastc than Latn Amercan n-shell peanuts but less elastc than US and Chnese n-shell peanuts. Afrcan n-shell peanuts have a Marshallan own prce elastcty of -1.4935 whch s very close to the own prce elastcty of the rest of the world whch s -1.4851. Somethng that s mportant to pont out s the fact that only the own and cross prce elastctes correspondng to the US and Chna were statstcally sgnfcant. The Morshma elastctes of substtuton are utlzed to dentfy whether goods are substtutes or complements and they are shown n table 3. The Morshma elastctes ndcate that n-shell peanuts from Chna, Latn Amerca, Afrca, and the rest of the world are substtutes for U.S. n-shell peanuts. The Morshma elastctes also ndcate that peanuts from Chna and the U.S. have a hgher degree of substtutablty than other countres probably because Chna and U.S. are the man exporters of n-shell peanuts to the EU markets. Chna has a lower degree of substtutablty for n-shell peanuts from Latn Amercan. The U.S. has lower substtutablty for n-shell peanuts from Afrca and Latn Amercan. The estmated standard errors of elastctes are also shown n table 3. Standard errors of elastctes are the values n parentheses. The frst row of values n parentheses corresponds to standard errors calculated usng the delta method and the second row of values n parentheses correspond to standard errors calculated usng bootstrappng. 13
Statstcal tests conducted usng bootstrappng standard errors yelded a hgher number of statstcal sgnfcant elastcty estmates. Summary and Conclusons Ths research estmates mport demand elastctes for n-shell peanuts n the European Unon from four dfferent sources: Chna, the Unted States, South Amerca, and Afrca. A source dfferentated AIDS model was used for estmaton of the demand parameters. The null hypothess of aggregaton over product sources s rejected at conventonal levels of sgnfcance suggestng that peanuts from dfferent sources are dfferentated by EU consumers whch mght attrbuted to ther dfferent qualty characterstcs. The expendture elastcty s elastc for U.S. n-shell peanuts whch mght be assocated wth ther hgher qualty. The results also ndcate that own prce elastctes for n shell peanuts from dfferent sources are negatve. The own prce elastctes of demand for U.S. and Chnese n shell peanuts are more elastc than Latn Amercan, Afrcan and the rest of the world n shell peanuts. These results suggest that EU consumers respond more to prce reductons for n shell peanuts mported from Chna and the US. The Morshma elastcty results ndcate that n shell peanuts from Chna, Latn Amerca, Afrca, and rest of the world are substtutes for U.S. n shell peanuts and also ndcate that Chna and U.S. countres have a hgher degree of substtutablty than other countres. 14
Demand for peanuts n Europe has been steady, whle competton among exporters has changed. The results of expendture and prce elastctes may help to evaluate polces that can be used by the US peanut exporters to mantan exstng export markets n the face of ncreasng global competton. Mantanng strong export markets s an mportant prorty for the U.S. peanut ndustry. For example, a polcy ssue that may be addressed wth ths research s the queston n regards to allocatng federal dollars for peanut export promoton nto the EU. Promoton and advertsng program wll help boost the demand for U.S. n shell peanuts so that U.S. peanut ndustry can reman strong n a compettve market for peanuts. 15
Table 1: Test Results for Demand Restrctons and Product Aggregaton Nonlnear SAIDS L.R. statstc Pr>Chsq System tests for homogenety 8.86 0.0646 System tests for symmetry 7.24 0.2994 System tests for homogenety 10.06 0.4352 and symmetry Product aggregaton Wald F-value 408.19 <.0001 16
Table 2: Parameter Estmates for the Restrcted Condtonal SAIDS Model of EU Import Demand for In-Shell Peanuts (Homogenety and Symmetry mposed) Chna U.S. Prce effects ( γ ) Chna -0.4406 ** (0.1201) U.S. 0.4075 ** -0.5447 ** Latn Amercan Afrca (0.1351) (0.1958) Latn Amercan -0.0331 0.0525 0.0306 (0.0403) (0.0438) (0.0291) Afrca 0.0685 0.0641-0.0519 * -0.0701 (0.0726) (0.0893) (0.0304) (0.0736) Rest of the World -0.0023 0.0206 0.0019-0.0106 (0.0210) (0.0225) (0.0103) (0.0152) Expendture effects -0.0299 0.0960-0.0086-0.0441 (0.0719) (0.0700) (0.0272) (0.0432) Trends 0.0006-0.0022 * -0.0001 0.0018 ** (0.0013) (0.0013) (0.0005) (0.0007) Seasonal effects Quarter 1 0.1083 ** -0.0771 * 0.0003-0.0354 (0.0457) (0.0438) (0.0172) (0.0278) Quarter 2 0.1472 ** -0.0976 ** 0.0244-0.0731 ** (0.0459) (0.0435) (0.0174) (0.0278) Quarter 3 0.2370 ** -0.1351 ** 0.0036-0.1035 ** (0.0498) (0.0466) (0.0187) (0.0305) Farm Bll 2002-0.0154-0.1381 ** 0.0848 * 0.0529 0.0508 (0.0508) (0.0192) 0.0318 R 2 0.6410 0.7565 0.5625 0.4895 Adjusted R 2 0.5772 0.7133 0.4847 0.3988 DW 2.0710 1.7377 1.6200 2.0405 Sgnfcance levels of 0.05 and 0.10 are ndcated by ** and *, respectvely 17
Table 3: Income Elastctes for the SAIDS model of In-Shell Peanuts Income Elastcty 0.9433 ** Chna (0.1365) (0.1326) 1.2929 ** U.S. (0.2135) (0.2671) 0.8604 * LA (0.4436) (0.4738) 0.3781 Afrca (0.6091) (0.4849) RW -0.0274 Chna U.S. LA Afrca Marshallan Elastctes Chna U.S. LA Afrca RW -1.7787 ** 0.7026 ** -0.0514 0.1751 0.0090 (0.2817) (0.3152) (0.2882) (0.2794) (0.2893) (0.3062) (0.0663) (0.1340) 0.9450 ** (0.4209) (0.4921) -0.3982 (0.9334) (0.5698) 1.5986 * (1.3095) (0.9956) -2.2952 ** (0.5219) (0.5310) 0.6820 (1.0023) (0.7781) 0.1261 (1.4071) (0.7841) 0.1010 (0.4488) (0.1455) -0.4720 (0.9377) (0.7837) -0.6062 * (1.2902) (0.4419) -0.0376 (0.4310) (0.1696) -0.7353 * (0.9079) (0.5111) -1.4935 * (1.1963) (0.9611) -0.0061 0.0630-0.0031 RW 0.8720 0.2796 0.3486 0.0122-1.4851 Morshma Elastctes CN US LA AF RW CN - 2.29 1.35 1.52 1.30 US 3.50-2.05 1.93 1.88 LA 0.47 1.38 - -0.26 0.49 AF 3.26 1.72 0.88-1.49 RW 2.43 1.57 1.83 1.50 - Sgnfcance levels of 0.05 and 0.10 are ndcated by ** and *, respectvely The frst row of values n parentheses corresponds to standard errors calculated usng the delta method and the second row of values n parentheses correspond to standard errors calculated usng bootstrappng. 18
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