Trade Flows and Trade Policy Analysis. October 2013 Dhaka, Bangladesh

Transcription

1 Trade Flows and Trade Polcy Analyss October 2013 Dhaka, Bangladesh Wtada Anukoonwattaka (ESCAP) Cosmo Beverell (WTO) 1

2 The gravty model n nternatonal trade 2

3 Content a. What s t? b. Naïve gravty estmaton c. Theoretcal foundatons d. Mstakes to avod e. Estmatng theoretcally-founded gravty equaton f. Recent theoretcal developments g. References 3

4 a. What s t? Econometrc model (ex-post analyss) Models many socal nteractons (mgraton, toursm, trade, FDI) For decades, socal scentsts have been usng a modfed verson of Isaac Newton's Law of Gravtaton to predct movement of people, nformaton, and commodtes between ctes and even contnents The gravty model takes nto account the populaton sze of two places and ther dstance. Snce larger places attract people, deas, and commodtes more than smaller places and places closer together have a greater attracton, the gravty model ncorporates these two features Intally, no theoretcal foundatons Why so popular? Hgh explanatory power (R 2 between 0.65 and 0.95) Easy access to relevant data Estmaton standards and benchmarks clearly establshed 4

5 Newton s unversal law of gravtaton and the gravty specfcaton n trade Newton F G M D M 2 Where F s the attracton force, G s the gravtatonal constant, M s mass, D s dstance, and ndex pont masses Gravty X G Y T Y Where X = exports from country to or total trade; Y=economc sze (GDP, POP) and T= Trade costs 5

6 The effects of sze and dstance More blateral trade the larger the countres Less blateral trade the more the dstance between them A and B are predcted to trade more than C and D C A D B 6

7 Proxes for trade costs Dstance Contguty Common language Colonal lnks Common currency Island, landlocked country Insttutons, nfrastructure, mgraton flows, Surprsngly enough, tarffs are very often omtted Man reason: endogenety ssue Do tarffs reduce trade or does more trade nduce tarff reductons? (reverse causalty problem) 7

8 b. Naïve gravty estmaton Naïve estmaton of the gravty regresson s ln( Trade ) ln( GPD ) ln( GPD ) ln( dst ) Ths regresson fts the data very well R-squared of 0.7 n cross-secton data ( dataset) However ths naïve verson can lead to very based results Serous omtted varable bas: any - or - characterstc that correlates both wth trade and GDP ends up n the error term. The basc OLS assumpton of orthogonalty between the error term and the explanatory varables s volated 8

9 c. Theoretcal foundatons Deardorff (1998) I suspect that ust about any plausble model of trade would yeld somethng very lke the gravty equaton Baldwn and Taglon (2006) The emergency of the new trade theory n the late 1970s and early 1980s started a trend where the gravty model passed from havng too few theoretcal foundatons to havng too many 9

10 Maor contrbutons Anderson (1979) Armngton hypothess (goods dfferentated by country of orgn) Bergstrand (1990) Monopolstc competton Prce ndces are those used n practce, not suggested by the theory Anderson and Van Wncoop (2003) Monopolstc competton No complete account of prce ndces => practcal way to estmate gravty coeffcents n cross country Helpman et al. (2008) Trade model wth heterogeneous frms: structural treatment of zeros See also Head and Mayer (2013) 10

11 Dervng the gravty equaton a. Step 1: the (Dxt-Stgltz) demand functon x Y p P 1 (1) Where ndexes exporter, ndexes mporter LHS = nomnal demand by s consumers for s goods Y s s nomnal ncome p s mports prce P p (2) s the deal CES prce ndex n, σ > 1 s the elastcty of substtuton across varetes 11

12 Dervng the gravty equaton (ct d) (1) can be rewrtten n terms of value: p x T Y p P 1 (3) Equaton (3) could be estmated drectly, but researchers often lack good data on trade prces b. Step 2: addng the pass-through equaton p p t (4) Where p s the producer prce n country and t are all trade costs 12

13 Dervng the gravty equaton (ct d) c. Step 3: Market clearng condton (aggregate supply equals aggregate demand) to elmnate the nomnal prce (5) Where Y W s world nomnal ncome and θ Y /Y W s the share of s nomnal ncome n world nomnal ncome Usng (3) and (4) nto (5) we obtan: (6) In ths expresson, (7) s the multlateral resstance (openness of s exports to world markets) 13 W W Y T Y Y T Y 1 1 p P t

14 Dervng the gravty equaton (ct d) We now want to get rd of producer prces Substtute (6) back nto (3) and use (4) to obtan: T Y Y Y W P 1 (8) Theoretcally-founded gravty equaton Maor contrbuton of Anderson and Van Wncoop (2003): blateral trade s determned by relatve trade costs Usng (6) nto (2), one can derve the prce ndex as: P Equatons (7) and (9) can be solved for all P s and Ω s (9) 14

15 Dervng the gravty equaton (ct d) Anderson and Van Wncoop (2003) show that f trade costs are symmetrc (τ = τ ), Ω = P and the gravty equaton (9) becomes: X Y Y Y W t P P 1 (10) Takng dst as proxy for t, rewrte (10) to look lke as Newton s physcal law of gravty: blateral trade G Y Y ( dst ) 1 Where G (1/P P ) 1-σ s not a constant as t s n the physcal world, but rather specfc (also t f we have tme varaton) 15

16 Dervng the gravty equaton (ct d) In the gravty lterature t s n general assumed that trade costs take the form: t d 1 exp cont lang ccol col llock RTA Where d s blateral dstance, and cont, lang, ccol, col, llock, RTA are dummy varables denotng respectvely whether the two countres have a common border, common language, common colonzer, whether one was a colony of the other at some pont n tme, whether one of the two s a landlocked country, whether the two countres are member of and RTA 16

17 d. Mstakes to avod Standard estmatng procedure ln( x ) ln( Y ) ln( Y ) ln( dst ) Gold medal mstake: omttng the un-constant term G Omtted varable bas, snce Ω and P (n error term) nclude t (n matrx of explanatory varables) Other common mstakes nclude: Slver medal mstake: averagng the recprocal trade flows (exports from to and exports from to ) before takng logs (theory tells that one should take the average of logs, not the log of the average, of X and X ) Bronze medal mstake: deflatng the nomnal flows by US prce ndex Gravty s an expendture functon allocatng nomnal GDP nto nomnal mports. If use US GDP deflator, need to nclude tme dummes to control for nflaton 17

18 e. Estmatng theoretcally-founded gravty equaton Normal trade wth resstances ln( x ) ln( Y ) ln( Y ) ln( dst ) MTR MTR MTR s the multlateral trade resstance term t s unobservable Three ways to take MTR nto account: 1. Use an teratve method to solve MTR as functon of observables (see Anderson and Van Wncoop, 2003) or lnear approxmaton of MTR (Baer and Bergstrand, 2009) 2. Proxy MTR usng remoteness REM (trade/gdp weghted average dstances from the rest of the world) 3. Fxed Effects (FE) REM GDP dst /GDP W 18

19 Fxed effects estmaton Importer (exporter) fxed effect s a (0, 1) dummy that denotes the mporter (exporter) Fxed effects control for unobserved characterstcs of a country,.e. any country characterstc that affect ts propensty to mport (export) They are used to proxy each country remoteness They do not control for unobserved characterstcs of par of countres, e.g. f they have a RTA n place (need country-par fxed effects for ths) Cross secton vs. panel datasets 19

20 a. Fxed effects estmaton n a cross secton In cross country analyss MTR are fxed. Therefore, usng country fxed effects yelds consstent estmaton Where ln( x ) 1 ln( ) τ s blateral trade cost (e.g. dstance) D are country specfc dummes There are 2n dummes Total observatons = n(n-1) D D It s mpossble to estmate the coeffcent for GDP and other countryspecfc varables (they are perfectly collnear wth the country fxed effect) 20

21 b. Fxed effects estmaton n a panel It s now possble to estmate the coeffcent for GDP and other countryspecfc varables ln( x ) ln( Y ) ln( Y ) t 1 t 2 t 3 ln( t ) D D Where There are 2n country-specfc dummes Total observatons = n(n-1)t It s stll not possble to estmate tme-nvarant country-specfc characterstcs (e.g. sland, landlockedness ) There may be a bas due to the varaton over tme of MTRs 21

22 b. Fxed effects estmaton n a panel (ct d) In the case of a panel, MTRs may change over tme (varaton n transport costs or composton of trade) ln( x ) t 1 ln( ) t t D t t D t t K t t Where D are tme-varyng country-specfc dummes K s a tme dummy (to take global nflaton trends, busness cycles and the lke nto account) There are 2nT+T dummes, where T denotes the tme perod Impossble to estmate the coeffcent of GDP (perfectly collnear wth country-tme dummy) 22

23 b. Fxed effects estmaton n a panel (ct d) Address the bas due to the correlaton between the blateral trade barrers and the MTRs ln( x ) ln( Y ) ln( Y ) t 1 t 2 t 3 ln( t ) D Where I= are country-par dummes There are n(n-1)/2 such dummes Dsadvantage: coeffcents of blateral varables are estmated on the tme dmenson of the panel and cannot estmate coeffcent for dstance, common border, common language (they do not vary over tme) A soluton: Use random effects and the Hausman test (xtoverd n Stata) to choose between random and fxed effect estmaton 23

24 How to proceed? Senstvty analyss, test the robustness of the results to alternatve specfcatons of the gravty equatons Report the results for the dfferent equatons estmated 24

25 Interpretaton of results Most of the varables are expressed n natural logarthms, so coeffcents obtaned from lnear estmaton can be read drectly as elastctes The elastcty of trade to dstance, for nstance, s usually between -1 and - 1.5, so a 10 per cent ncrease n dstance between two countres cuts ther trade, on average, by 10 to 15 per cent Elastctes wth respect to mportng-country GDPs are also typcally untary, suggestng untary ncome elastctes of mports at the aggregate level 25

26 Interpretaton of results (ct d) The coeffcents for the dummes (e.g. common border) are not elastctes They need to be transformed as follows to be nterpreted as elastctes: p exp( ) 1 where p s the % change n the dependent varable and δ s the estmated coeffcent of the dummy varable To derve ths formula: Consder that lnx (1) s the predcted value of trade when the dummy = 1 whle lnx (0) s the value of trade when dummy = 0 The dfference lnx (1) - lnx (0) = δ X (1) / X (0) =exp(δ), whch n turn mples that the percentage change n trade value due to the dummy swtchng from 0 to 1 s: X (1) -X (0) / X (0) = exp(δ)-1 You can do better and estmate p = exp [δ] and (almost) unbased exp [ 1 2 var δ ] 1, whch s consstent 26

27 f. Recent theoretcal developments Recently, Helpman et al. (2008) (HMR) derve a gravty equaton from an heterogeneous frms model of trade The mportance of ths dervaton relates to three ssues that prevous models of trade could not explan Zero-trade observatons Asymmetrc trade flows The extensve margn of trade: more countres trade over tme 27

28 Incdence of zero trade 28

29 Extensve margn of trade Trade growth n the extensve margn s mnor 29

30 How to handle zero trade data? a. Tradtonally When takng logs, zero observatons are dropped from the sample. Then, the OLS estmaton s run on postve values Take the log(1+x ), but then use Tobt estmaton as the OLS would provde based results (dstrbuton s censored at zero: all observatons possbly negatve are dentfed as equal to zero) b. More recently The probablty of havng postve (non-zero) trade between two countres s lkely correlated wth unobserved characterstcs of that country par A selecton model à la Heckman s called for. In ths context, zero trade flows result from the frm decsons not to export n a certan market The approprate estmaton procedure s therefore that to model these decsons, and correct the estmaton on the volume of trade for ths selecton bas 30

31 How to handle zero trade data? (ct d) b. More recently (ct d) HMR clam: the standard approach produces based results In ther model, dfferences n trade costs across countres and frms heterogenety account for both asymmetrc trade flows and zero trade Zero trade occurs when the productvty of all frms n country s below the threshold that would make exportng to proftable Problem: the probablty of havng postve trade between 2 countres s correlated wth unobserved characterstcs of that country par These characterstcs also affect the volume of ther blateral trade, gven that they trade 31

32 How to handle zero trade data? (ct d) Selecton bas and omtted varable problem HMR provde the followng soluton: 2 stage estmaton 1. Probt on the lkelhood that 2 countres trade (.e. probablty that frms enter the export market) 2. Gravty model on postve trade values, where The results of the frst stage are use to correct for the sample selecton bas ntroduced by omttng zero trade flows (the standard Heckman correcton term, the nverse of the Mll's rato) An estmate of the (unobserved) share of frms selectng nto the export market s added to the equaton to control for frm heterogenety 32

33 Helpman et al. (HMR) (2008) model 1. Frst-stage Probt regresson T 1 d Pr 0 Where the probablty of where the probablty of a postve trade flows between and, ρ, depends on the mporter and exporter dummes (ξ and ζ ) and blateral trade costs, where d denotes varable trade costs and φ denotes blateral fxed costs of entry 2. Second-stage gravty regresson x exp z d ln 1 0 Where λ and χ are mporter and exporter fxed effects and the term n the curly brackets s the estmator for the share of frms that export to ; z are the ftted varable for the latent varable from the fst-stage Probt and η s the nverse Mll's rato Notce that the last equaton has to be estmated by non-lnear least squares (NLLS) 33

34 How to handle zero trade data? (ct d) b. More recently (ct d) An alternatve approach s to use (Pseudo) Posson maxmum lkelhood (ML) estmator. Ths method can be appled on the levels of trade, thus estmatng drectly the non-lnear form of the gravty model and avodng droppng zero trade Santos Slva and Tenreyro (2006) hghlght that, n the presence of heteroskedastcty (as usual n trade data), the PPML s a robust approach Ths approach has been used n a number of estmaton of gravty equatons See the log of gravty webpage for detals, FAQs, Stata codes and references 34

35 g. Applcaton: Gravty estmaton of AVE of NTBs The gravty equaton can be used n reverse to measure blateral trade costs and to decompose trade costs nto a tarff and non-tarff component (see for nstance Jacks et al., 2011 and ESCAP/WB database) a. Theoretcal approach Take expresson (8) and wrte t down for X, X, X and X, where X and X are the expressons for ntra-natonal trade Rearrange trade costs Tarff equvalent of blateral trade costs relatve to domestc trade costs can then be expressed as geometrc average of trade barrers n both drectons t t t t t t t t 1 X X X X X X X X (11) (12) 35

36 a. Theoretcal approach (ct d) Expresson (11) s a dervaton of overall trade costs from the gravty equaton wthout mposng a cost functon It s nether assumed that domestc trade costs are zero, nor that they are the same across countres (t may dffer from t ) nor that blateral trade costs are symmetrc (t may dffer from t ) Under the specfc assumpton that domestc trade costs are zero and blateral trade costs symmetrc (as mpled by takng the geometrc average as measure of blateral trade costs), t s also possble to decompose overall trade costs n ther varous cost components by assumng an arbtrary trade cost functon (see slde 18) 36

37 a. Theoretcal approach (ct d) For example, t s possble to decompose overall trade costs n ther tarff and non-tarff component by smply estmatng ln( ) ln( dst ) ln( tarff ) ln( NTB ) where NTB s a dummy To compute the tarff equvalent of a quota, we only need to calculate what s the percentage change n tarff that has the same mpact on trade costs as a quota Tarff equvalent = exp(δ 3 /δ 2 )

38 b. Emprcal mplementaton The dffculty n calculatng (11) s to get fgures for ntra-natonal trade One approach s to estmate these fgures as the dfference between producton and exports (see for nstance Novy 2012) The use of GDP nstead of producton data tends to overstate ntra-natonal trade, and therefore trade costs, because a growng share of trade s servces (largely non-tradable) One can use the TPP datasets (World Bank or CEPII) See Exercse 2 of Chapter 3 of the Practcal Gude to Trade Polcy Analyss 38