On predictability in the neoclassical trade model

1
On predictability in the neoclassical trade model

• Daniel M. Bernhofen
• School of Economics and GEP
• University of Nottingham

2
Motivation/Background

• Choi and Krishnas (2004, JPE) test of Helpmans
  (1984, EJ) Heckscher-Ohlin type prediction on the
  bilateral factor content of trade.
• Attractive features of Helpmans prediction
• bilateral prediction gt allows an empirical
  investigation for a subset of trading countries
  for which high quality data is available.
• (ii) requires no specific assumption about
  preferences.
• (iii) Multi-cone model framework doesnt
  require the (empirically embarrassing) factor
  price equalisation property.
• gt Choi and Krishnas test of Heckscher-Ohlin is
  viewed as a major advancement in the empirical
  trade literature. (Feenstra (2004))

3
A forgotten theoretical general equilibrium
trade literature

• McKenzies classic (1954,1955) papers
• Investigate the central role of factor price
  equalization in a general trading equilibrium.
• Multi-cone models of international specialization
  using (Koopmans) activity analysis.
• Mc Kenzie (1954, p.180) The deficiency of the
  classical methods...of comparative labour
  costsis their dependence on bilateral
  comparisonsIt is not possible through merely
  bilateral comparisons to develop a complete
  theory of efficient multilateral specialization
• Mc Kenzie (1955, p. 245) In the set of goods
  price vectors which do not permit equalization of
  factor prices no assured statement about
  specialization can be made without stronger
  assumptions (about demand)
• gt raises suspicion about Helpmans prediction

4
Three contributions

• 1) I claim that Helpmans (1984) well-cited
  bilateral Heckscher-Ohlin prediction is not a
  prediction about international specialization. I
  provide several arguments for this claim.
• 2)(i) I suggest a conceptual framework for
  thinking about the predictability/testability of
  a theory. I apply this framework to the
  neoclassical trade model and suggest a taxonomy
  of pattern of trade predictions.
• (ii) The taxonomy leads to the following key
  insight The formulation of a refutable pattern
  of trade prediction is closely related to the
  gains from trade.
• 3) Building on Ruffins (2002) recent
  reinterpretation of Ricardos (1817) four magic
  numbers, I reconstruct Ricardos proof and show
  that his logic is a special case of the general
  framework developed in part 2.

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Part I Revisiting Helpman (1984)

• Literature background to Helpman
• It builds on Deardorffs (1979, JIE) chain of
  comparative advantage paper.
• It claims to generalize Brecher and Choudhris
  (1982, JIE) n-good, 2-factor, 2-country
  formulation to multiple countries and factors.
• Key assumptions
• Countries possess identical linear technologies
• Because of factor endowment dissimilarity,
  countries produce different goods in a free trade
  equilibrium (multi-cone model).
• It investigates the property of a free trade
  equilibrium.
• Key claim no assumptions about demand are
  necessary.
• Clue Deardorff (1979) and Brecher and Choudhri
  (1982) rely mostly on
• on the Lerner-Pearce diagram.

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Multi-cone graph (3 countries, 6 goods)
country ranking (K/L)1gt(K/L)2gt(K/L)3?(w/r)1gt(w/r)
2gt(w/r)3
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Model specification

• m countries, n goods, l factors, common
  technology matrix A(.)lta(.)gt.
• underlying framework (i) we are in a competitive
  trading equilibrium,
• (ii) all variables are endogenous.
• Tij denotes the n-good gross bilateral exports
  from country i to country j.
• Fij denotes the factor content of Tij
  FijA(wi)Tij (wi factor price vector of the
  exporting country i).
• Helpmans set of restrictions/predictions
• (i) (wj-wi)Fij 0.
• (ii) (wj-wi)Fji 0,
• (iii) (wj-wi)'(Fij-Fji) 0, (Note (i) and
  (ii) imply (iii)).
• Interpretation (Helpman (1984), Helpman and
  Krugman (1985), Choi and Krishna (2004), Feenstra
  (2004))
• Factors embodied in trade should flow, on
  average, towards the country with the higher
  factor price. If factor k has a higher price in
  country j than in country i, i.e. wkj-wkigt0, then
  country j should, on average, be a net importer
  of that factor, i.e. Fkij-Fkjigt0.

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2 countries, 2 factors, n goods

• Helpmans prediction

Heckscher-Ohlin prediction (Brecher and
Choudhri)

Heckscher-Ohlin theorem If country 1 is
relatively capital abundant, i.e. (w1/r1)gt(w2/r2),
then it will be a net exporter of capital
(K12-K21gt0) and a net importer of labour
(L12-L21lt0). Helpman is a prediction based on
country-specific differences in absolute factor
prices. However, in competitive trade theory
the direction of international specialization is
governed by differences in relative not absolute
factor prices.
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Helpmans proof

• Claim (wj-wi)Fij 0.
• Notation p vector of equilibrium trading
  prices,
• Vj endowment vector, Yj production vector,
• GDP function G(p,Vj) p'Yjwj'Vj. (j is the
  importer)
• Reminder FijA(wi)Xij
• Proof
• 3-steps
• (i) p'Tijwi'Fij (constant returns to scale)
• (ii) G(p,Vj)p'Tijp'Yj p'Tij G(p,VjFij),
• (iii) G(p,VjFij) G(p,Vj)?G(p,Vj)/?Vj'Fij
  p'Yj wj'Fij.
• gt wi'Fijp'Tij wj'Fij or (wj-wi)Fij 0.
• Problem with step (ii) is that it applies to any
  subvector Fi of Vi
• gt (ii) generates many predictions/restrictions
  .
• () (wj-wi)Fik 0 for any third country k.
• Interpretation factor price difference between
  country pair j and i predicts the factor content
  flow between country i and any third country k
  ??

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What do we make of Choi and Krishna (2004) ?

• Country sample 8 countries (US, Canada,
  Denmark, France, Germany, UK, Netherlands, Korea)
  gt 28 observations or country pairs
• (i) (wj-wi)'(Fij-Fji) 0 (Choi and Krishna
  (22-24)/28 satisfy (i))
• (ii ) (wj-wi)'(Fik-Fjl) 0 for all i, j, k,
• gt for each country pair (i, j) we have 49 third
  country configurations
• gt total number of predictions 28x491372 (!)
• Conclusions
• (i) Choi and Krishna (2004) provide incomplete
  support for an implication of the concavity
  property of the production property of the model.
  
• (ii) Evidence for Heckscher-Ohlin? No

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PART II On predictability

• Motivation
• (i) Helpman (1984, p. 84) It is therefore
  valuable to identify restrictions on permissible
  vectors of trade which necessarily hold in
  equilibrium. If certain restrictions are
  empirically testable they can be used for
  preliminary testing of the theory before a more
  thorough examination is undertaken, or they can
  be used to reject the theory.
• (ii) How can we reconcile Helpmans idea of
  identifying restrictions on permissible vectors
  with the comparative statics framework?
• (iii) In a 2-good framework, the neoclassical
  model is thought to make exact predictions while
  in higher dimensions the model is thought to have
  only weak or average predictions. The meaning
  of average is also somewhat vague.
• (iv) What about an alternative hypothesis?

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Defining predictability

• Key idea instead of taking the theory as a
  given, we take real world observables as a given
  and then relate the theory to the observables.
  
• Formal definition of predictability
• Given a set O of outcomes that are either
  directly observed or estimated. A theory T is
  said to make a prediction on the set of
  observables by identifying a subset OP of O. OP
  is called the prediction set and OA O/OP is
  called the alternative.
• (i) If OA is associated with an alternative
  theory TA, then the theories T and TA can be
  distinguished by whether the observed/estimated
  outcomes fall either in OP or OA.
• (ii) If there is no alternative theory that
  restricts O, then we can postulate chance as
  the alternative hypothesis.

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2 simple illustrations

• 1) We are interested how an excise tax will
  affect the volume of sales in any market.
  Denoting sales with x and the excise tax with t,
  the set of possible outcomes is O?x/?tgt0,
  ?x/?tlt0, ?x/?t0.
• Given the standard ceteris paribus assumptions,
  partial equilibrium market theory predicts that
  OP?x/?tlt0.
• Empirical IO literature has been interested in
  estimating a market conduct parameter ? gt
  O0?1, OT0, OA0lt?1, T perfect
  competition, A imperfectly competition.
• Comparative statics (a special case)
• A theory T is often characterized by f(x,a)0 or
  a fixed-point equation xg(x,a) (x is the
  equilibrium variable and a is a parameter of the
  model).
• In comparative statics we consider the
  functional relationship x(a).
• Assume now that T predicts that x is increasing
  in a, we define
• O?eR ??x/?agt0 or ?x/?a 0 and OP?
  ?x/?agt0.
• Shortcomings of the comparative statics
  framework
• (i) one-dimensional,
• (ii) assumes a unique equilibrium.

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A taxonomy of pattern of trade predictions

• (i) 2-good formulation of comparative advantage
  (small open economy)
• Exogenous to the prediction autarky prices
  (p1a,p2a) and world prices (p1fp2f)
• observables (T1, T2) if Ti gt(lt)0 good i is
  imported (exported)
• Common formulation of the law (two conditional
  if statements)
• (i) If p1a/p2a lt p1f/p2f, then T1lt0 and T2gt0,
  (good 1 is exported),
• (ii) p1a/p2a gt p1f/p2f, then T1gt0 and T2lt0,
  (good 1 is imported),
• O(T1,T2)eR2 p1f T1 p2fT20 (BOT condition)
• OP(T1,T2)eR2 p1f T1p2fT20 and p1aT1
  p2aT2gt0.
• 1st key point the exogenous autarky vector
  (p1a,p2a) imposes a restriction on O by cutting
  the set of possible outcomes into half gt the
  theory implies a probability statement about the
  alternative hypothesis chance
• H0 Te OP H1Pr(Te OP) 0.5.

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2nd key point Te OP ltgt T generates gains from
trade Graph 2-good case
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(ii) n-good formulation of comparative advantage
Deardorff (1980)O(TeRn pfT0 (BOT
condition)OP(TeRn pfT0 and paTgt0. (the
n-good prediction has the same underlying
structure as the 2-good prediction, pa restricts
O)
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(iii) Predicting the factor content of trade the
general case reformulation of Deardorff
(1982)

• Definition (Factor content of trade)
• Given a countrys net import vector T and any
  technology matrix A, the factor content of trade
  F is defined as FAT.
• Trade in factor services allows the economy to
  reach the new endowment point Vcons VF.
• gains from trade in factor space waVconsgtwaV
  ltgt waFgt0.
• OFeRl FAT,
• OPFeRl waFgt0.
• Key insights
• (i) wa restricts O,
• (ii) Fe OP ltgt F generates gains from trade,

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Factor content of trade prediction the general
case


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(iv) Heckscher-Ohlin theorem (using Ohlins price
definition of factor scarcity for
the 2 factor case).

• Ohlins (price) definition of relative factor
  abundance (1labor, 2capital)If
  w1a/w2altw1f/w2f, then the home economy is labour
  abundant relative to the rest of the world,
  otherwise it is capital abundant.
• Heckscher-Ohlin prediction
• If w1a/w2altw1f/w2f gt F1lt0 and F2 gt0,
• If w1a/w2agtw1f/w2f gt F1gt0 and F2lt0.
• ltgt
• O (F1,F2)eR2 w1fF1 w2fF20 (BOT condition
  in factor trade)
• OP(F1,F2)eR2 w1fF1w2fF20 and
  w1aF1w2aF2gt0.

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Heckscher-Ohlin prediction in the 2-factor case
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(v) Nature of the prediction that does not rely
on autarky data

• Heckscher-Ohlin-Vanek (HOV)
• additional assumption identical
  homothetic preferences gt
• VconssVw (Vw worlds endowment vector
• s countrys share in world
  income)
• gt FV-sVw (Heckscher-Ohlin-Vanek
  equationFactor balance of trade equation),
• HOV is not a prediction on F, but it generates
  sign relationships on
• Fi Fi(sViw-Vi)gt0 for all i1,,l
• Comparison
• (i)-(iv) exogenous pa (wa) restrict O to OP
  gt refutable predictions
• (v) Balance of trade condition gt nonrefutable
  regarding the general equilibrium relationship.

Fi(sViw-Vi)gt0 for all i1,,l
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Summary

• The evaluation of permissible equilibrium trading
  vectors (in goods or factor space) requires
  information from outside the trading
  equilibrium. In neoclassical trade theory the
  outside information stems from the state of
  autarky.
• The restriction of permissible trading vectors is
  directly related to the gains from trade (in
  goods or factor space). The theory excludes
  trading outcomes that are Pareto inferior to a
  state without international trade.
• Implications
• Autarky information is essential for a refutable
  general equilibrium prediction.
• Bilateral comparisons are irrelevant for the
  direction of specialization
• (see also Anderson and van Wincoop (AER 2003) on
  bilateral volume of trade predictions in a
  multi-lateral trade)

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PART III Ricardos (1817) four magic numbers

• The quantity of wine which she Portugal shall
  give in exchange for the cloth of England, is not
  determined by the respective quantities of labour
  devoted to the production of each, as it would
  be, if both commodities were manufactured in
  England, or both in Portugal. England may be so
  circumstanced, that to produce the cloth may
  require the labour of 100 men if she attempted to
  make the wine, it might require the labour of 120
  men for the same time. England would therefore
  find it her interest to import wine, and to
  purchase it by the exportation of cloth.
• To produce the wine in Portugal, might require
  only the labour of 80 men for one year, and to
  produce the cloth in the same country, might
  require the labour of 90 men for the same time,
  It would therefore be advantageous for her to
  export wine in exchange for cloth.
• Mills reading of Ricardo acE /awE100/120 lt
  acP/awP90/80 gt England exports cloth.
• ( the pattern of trade is determined by the
  comparison of labor costs)
• Historical puzzles
• Ricardo jumps to his conclusion before he
  states Portugals costs.
• Logical inconsistency by the 19thcentury
  master logician of political economy .
• (Some historians have argued that Torrens
  should be given credit for the discovery of
• the doctrine)

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A reconstruction of Ricardos proof

• Background Sraffa (1930) and Ruffin (2002)
  suggest that the 4 numbers are
• not labour input coefficients but the labour
  needed to produce the wine and
• cloth actually traded.
• gt Ricardos logic in light of what we have
  discussed before.
• (i) Ricardo took the terms of trade as given
  Tc/Tw.
• (ii) 2 possible trading outcomes for England
• (a) Tcgt0,Twlt0 or (b) Tclt0,Twgt0 gt O(,-),
  (-,)
• (iii) The direction of trade is dictated by the
  gains from trade, where the gains are measured in
  terms of gains measured in labour units.
• His numbers are then the factor content trade
  100TcacE and 120TwawE.
• If Tcgt0,Twlt0 gt Englands net gain from trade is
  TcacE-TwawE100-120-20lt0
• If Tclt0,Twgt0 gt Englands net gain from trade is
  TwawE-TcacE120-10020gt0
• gt Ricardos numbers predict OP (-,)
• gt England will export cloth and import wine
  because this trading pattern generates gains. The
  pattern of trade is determined by the gains from
  trade.