Do endowments predict the location of production? Evidence from national and international data - by Jeffrey Bernstein, David Weinstein

1
Do endowments predict the location of production?
Evidence from national and international data-
by Jeffrey Bernstein, David Weinstein
2

• Heckscher-Ohlin-Vanek (HOV) model
• relationship b/w factor endowments and the factor
  services that are embodied in goods trade-
  Generates precise predictions of trade in factor
  services
• Countries will Export the services of relatively
  abundant factors and Import the services of
  relatively scarce factorFactor-Endowments-Drive
  n (FED) model of production- Using factor
  endowments to estimate trade flows or outputs-
  Provides the foundation for a common, one-to-one
  mapping of factor endowments into outputs -
  Condition no of goodsno of factors

3
Authors claim

• it is not possible to determine the no of goods
  and factors by counting them
• The observed production patterns suggest a world
  in which the no of goods exceeds the no of
  factors
• Empirical prediction if there are more goods
  than factors, then even in cases where HOV model
  holds, it should not be possible to predict
  output on the basis of endowments i.e. the FED
  model of production should fail for goods traded
  costlessly

4
Theory and tests - Notation

• N no of goods
• F no of factors
• r index regions (from R all regions)
• Xr the (N1) vector of gross output for region
  r
• Vr the (F1) vector of factor endowments
• Br the (NF) matrix of direct factor input
  requirements
• Bcommon technology matrix

5
Theory and tests Heckscher-Ohlin-Vanek (HOV)
model

• Standard assumptions of HOV model
• Technology is identical across regions and
  exhibits constant returns to scale
• Regional endowments are not so divergent as to
  preclude factor price equalization
• Perfectly competitive goods and factor markets
• No of goods is greater or equal to the no of
  factors (NgtF)
• If these are satisfied, then
• Br B (production techniques are identical across
  regions)
• BXr Vr , (F1) for each r, or
• BXV, (FR), or for each f and r Bf Xr
  Vfr
• This equation is the HOV model of production (the
  measured factor content of production should
  equal the actual regional endowment)

6

• The HOV equation
• may fail b/c of technological differences,
  increasing returns, any other reason why
  factor-price-equalization might not obtain.
• If it holds, then any violations of the HOV
  models core assumptions are insufficient to
  undermine the theorys posited relationship b/w
  outputs, inputs, and technology
• Average prediction errors percentage deviation
  b/w the predicted factor content of production
  and the actual factor endowment Dfr Bf Xr /
  Vfr 1
• If the errors are small, then the HOV model
  provides a reasonably accurate description of
  production structure
• If there are substantial errors, there must be
  substantial regional variation in unit input
  requirements, causing the model to be deficient
  in some respects.
• Analyze the average prediction errors and
  distinguish how well the model fits individual
  regions and factors.

7
Theory and tests Factor-Endowments-Driven (FED)
model

• Xr ?Vr ,(N1) output as a linear function of
  factor endowments
• This equation is the FED model of production
• ? matrix is (NF)
• Test if there are equal no of goods and factors
• Only if NltF can output be written as a unique
  function, independent of endowments
• Only if there is factor-price equalization (NgtF)
  will there exist a common technology matrix B
  such that BXr Vr for each r.
• So NF is the condition for both HOV and FED to
  hold.
• Or
• if BXr Vr (the HOV equation holds), a unique ?
  will exist only if B is invertible ( B is of full
  rank, so no of gods no of factors, NF), so
  ?B-1
• If HOV model work and B has full rank, then the
  FED model will fail if there are more goods than
  factors (expect equation HOV to hold and equation
  FED to fail)

8

• Three possible outcomes
• Both HOV and FED models work, then
• endowments do determine the location of
  production
• Both HOV and FED models fail, then
• the world must violate a fundamental tenet of the
  HOV framework
• HOV works but FED fails, then
• the basic assumptions of the HOV model hold, but
  there are more goods than factors

9
The role of trade costs in reducing production
indeterminacy

• Transaction costs of trade direct costs of
  transportation, tariffs, other
• trade barriers, other transaction costs of trade,
  information costs
• These transaction costs of trade can reduce
  production indeterminacy in a world with more
  goods than factors NgtF
• N goods (ltN) are traded at some cost, and N-N
  goods (gtF) traded costlessly
• It is possible to obtain factor-price
  equalization FPE there will be no trade in any
  of the goods with positive transactions costs of
  trade, as each region will produce the amount of
  non-traded goods that exactly satisfies its
  domestic demand
• Homothetic preferences the demand for each good
  is a linear function of endowments, so is the
  output of the N non-traded goods
• For the N-NgtF goods traded costlessly, we will
  not be able to predict the output of these goods

10

• So, endowments should be able to predict the
  output of goods traded at some cost even if they
  cannot predict the output of goods traded
  costlessly.
• Upshot of this analysis trade costs may
  represent an important mechanism for reducing or
  eliminating production determinacy in a HO model
  with more goods than factors.
• Expectation factor endowments should provide
  more accurate predictions of output in
  circumstances where the costs of trade are
  relatively high. (this is the opposite of what
  has been conventionally assumed in empirical work)

11
Empirical test HOV model, regional data

• Data 47 Japanese prefectures, gross output for
  29 sectors/industries for each prefecture, and
  factors workers with less than a college
  education, workers with college education,
  capital
• Test if BXV the model is valid, each region
  employs the same production techniques (BrB for
  each r)
• Calculate the average prediction errors quite
  small (average 13)
• Calculate the average errors over each
  prefecture few exceed 25
• And calculate the average errors over each
  factor
• The model works best for capital and worst for
  non-college-educated labor
• Conclusion
• The small magnitude of prediction errors to the
  extent that economies of scale or technological
  differences exist, they are not significant
  enough to invalidate the production relationship
  specified by the HOV model
• So, the HOV model describes the regional data
  quite well

12
Empirical test FED model, regional data

• Is the regional data supporting a stronger
  relationship b/w factor endowments and
  production? (is NF ?)
• Regressed output on factor endowments for each
  industry i, the regression equation
  Xir?0i??ifVfr?ir , where ? are parameters
  to be estimated and ? are errors.
• Results
• the typical error for FED model (300) is much
  higher than what they got for HOV model (13)
• So, very poor predictions of the FED model
• But it is not clear how to interpret these
  results
• Conclusion
• The FED model fails to hold for the regional data
  as indicated by the enormous indeterminacy in
  production patterns

13

• The HOV equation holds and the FED equation
  fails, so
• either the B matrix is not invertible due to more
  goods than factors, or
• their analysis omitted some very important
  factors
• 1. The possibility of missing factors
• It is impossible to be certain that all relevant
  (production) factors have been included
• Additional variables to be added to the model
• Land (usable land, undeveloped mountain and
  forest land)
• Human capital (finer measured)
• Adding factors to the model yields some
  improvement in R-square, but the average
  prediction errors did not changed much
• So, missing factors cannot explain the poor fit
  of the FED
• model.

14

• 2. Is industry aggregation the solution?
• There is not a sound theoretical justification
  for industry aggregation
• Test again, this time for 7 factors and 7
  industry aggregates (one of the industry
  aggregate was the non-tradable sectors)
• Results
• Smaller average prediction error (for FED) 123,
  but still much larger than for HOV model
• The average error for the tradable aggregates
  vastly exceeds that of non-tradable aggregate
  (but still not good)

15

• Evidence on trade costs and indeterminacy at
  regional level
• Hypothesis in a data set where the no of goods
  traded exceeded the no of factors, and certain
  sectors are traded at cost while others are
  freely traded, the FED model should work better
  for non-traded goods than for tradables.
• Thats what was observed earlier with 7
  aggregated industries and 7 factors.
• The huge divergence b/w the performance of the
  FED in tradable and non-tradable
  sectors/industries is consistent with a world in
  which NgtF and some goods N have positive trade
  costs, while the remaining goods N-NgtF do not.

16
Empirical test HOV and FED models, international
data

• The data production, endowment, same 29
  sectors/industries for a sample of 16 OECD
  countries, same B technology matrix
• Differences b/w cross-country and regional data
• Technology differences, measurement errors and
  other problems are likely to plague the HOV
  framework when applying to intl data (as opposed
  to regional data).
• Expectations worse fit for both HOV and FED
  models
• Higher costs of trade at the intl level.
• Expectations FED may perform better on intl
  data than on regional data, even if the HOV model
  fails at the intl level

17

• The HOV model on intl data
• Calculate the average percentage deviations b/w
  BX and V, using Japans B technology matrix
• Results
• average prediction error is 81
• the fit of the HOV model is far worse at the
  intl level
• The FED model for intl data
• Same set of 29 industries, same factors arable
  land, mineral endowments
• Results
• average prediction error is 67, better
  performance for intl data
• the explanatory power of these regressions
  (adjusted R-square) is much higher than those for
  regional data
• The comparison of the intl and regional results
  is harder to interpret
• factor price equalization does not appear to hold
  in the intl context
• larger and more pervasive trade costs at the
  intl level help eliminate more of the overall
  indeterminacy in the production of tradable goods

18
Conclusions

• Production indeterminacy is substantial in the
  type of real-world data sets typically available
  to empirical trade economists
• The degree of production indeterminacy is
  greatest when trade barriers and trade costs are
  relatively low
• For the regional data, the prediction errors are
  20 times larger for tradable goods than for
  non-tradable services
• Considering a common set of tradable commodities
  prediction errors are 6 times higher for Japanese
  prefectures than for a sample of OCDE nations

19
Implications

• In the context of the endowment and output data
  typically available to empirical researchers,
  observed production patterns appear consistent
  with a world in which no of goods exceeds no of
  factors
• One should exercise great caution in interpreting
  regressions of production (or commodity trade) on
  factor endowments (estimation of trade barriers).
  The standard, factor proportions model of trade
  does an even worse job of explaining production
  patterns for tradable commodities.
• To obtain better descriptions of commodity
  production patterns, empirical researchers should
  try to incorporate technological differences,
  trade costs, and other sources of specialization
  into their analyses.