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14.581 International Trade
Class notes on 2/25/2013^1
Testing the Ricardian Model
- Given that Ricardo’s model of trade is the first and simplest model of international trade it’s surprising to learn that very little has been done to confront its predictions with the data
- As Deardorff (1984) points out, this is actually doubly puzzling:
- As he puts it, a major challenge in empirical trade is to go from the Deardorff (1980) correlation (pA.T ≤ 0) based on unobservable autarky prices pA^ to some relationship based on observables.
- So the name of the game is modeling p^ A as a function of primitives (technology and tastes).
- Doing so is trivial in a Ricardian model: relative prices are equal to relative labor costs, both in autarky and when trading.
1.1 What Has Inhibited Ricardian Empirics?
- Complete specialization: If the model is right then there are some goods that a trading country doesn’t make at all. - Problem 1: this doesn’t appear to be true in the data, at least at the level for which we usually have output or price data. (Though some frontier data sources offer exceptions.) - Problem 2: if you did find a good that a country didn’t produce (as the theory predicts you should), you then have a ‘latent variable’ problem: if a good isn’t produced then you can’t know what that good’s relative labor cost of production is.
- A fear that relative labor costs, as recorded in international data, are not really comparable across countries. - See Bernard and Jones (1996) and later comment/reply.
- A fear that relative labor costs are endogenous (to trade flows). (^1) The notes are based on lecture slides with inclusion of important insights emphasized during the class.
- Leamer and Levinsohn (1995): “the one-factor model is a very poor setting in which to study the impacts of technologies on trade flows, because the one-factor model is jut too simple.” - Put another way, we know that labor’s share is not always and every where one, so why would you ignore the other factors of production? (Though as we shall see next week, for an interesting two-factor model to drive the pattern of trade we need: sectors to utilize more than one factor, and for these sectors to differ in their factor intensities.) - One possible reply: perhaps the other factors of production are very tradable and labor is not.
- A sense that the Ricardian model is incomplete because it doesn’t say where relative labor costs come from.
- Probably the fundamental inhibition: Hard to know what is the right test or specification to estimate without being “ad-hoc”: - As discussed in lecture 2, generalizing the theoretical insights of a 2-country Ricardian model to a realistic multi-country world is hard (and has only been done to limited success). - As we will see shortly, many researchers have run regressions that take the intuition of a 2-country Ricardian model and translate this into a multi-country regression. - But because these regressions didn’t follow directly from any general Ricardian model they couldn’t be considered as a true test of the Ricardian model.
2 ’Ad-hoc’ tests
2.1 Early Tests of the Ricardian Model
- MacDougall (1951) made use of newly available comparative productiv ity measures (for the UK and the USA in 1937) to ‘test’ the intuitive prediction of Ricardian (aka: “comparative costs”) theory: - If there are 2 countries in the world (eg UK an USA) then each country will “export those goods for which the ratio of its output per worker to that of the other country exceeds the ratio of its money wage rate to that of the other country.”
2.2 Golub and Hsieh (2000) I
- An update of MacDougall (1951)—or Stern (1962) or Balassa (1963)—to modern data.
- To fix ideas, suppose we are interested in testing the Ricardian model by comparing the US to the UK, as MacDougall did. (GH also compare the US to 6 other big OECD countries.)
- Suppose also (for now) that we only have one year of data (as MacDougall did).
13 12 42
1
2420 21
9 14 (^10 11 ) 18
2 3 4 5 6 7 10 1 0.01 0.02 0.03 0.04 0.06 0.08 0.1 0.2 0.3 0.4 0.6 0.8 1
U.S Tariffs
U.K Tariffs
39 35 41 42
27
6
47 48
46
37
26
19 17 23
38
3331 (^4344 )
49
40
30 32 29 28 36 34
25
22
16
8 75
Quantity of Exports, U.S.: U.K. Productivity, Exports, and Tariffs, 1950
Output per worker, U.S.:U.K.
2
3
4
5
6
7
8
9 10
(^1) .5 1 2 4 6 810
20
40
60
80
100
200
300
400
(In Hundreds) Labor Productivity
Exports
U.S./U.K. Export and Productivity Ratios 1950 and 1951 (Logarithmic Scale)
Image by MIT OpenCourseWare.
Image by MIT OpenCourseWare.
- GH run regressions of the following form across industries k:
Xk U S k log = α 1 + β 1 log(aU S /akU K^ ) + ε 1 k , Xk U K Xk U S→U K k log = α 2 + β 2 log(aU S /akU K^ ) + ε 2 k. M (^) U Sk ←U K
- GH run regressions of the following form across industries k:
Xk U S k k log = α 1 + β 1 log(aU S /aU K ) + εk 1 , Xk U K Xk U S→U K k k log = α 2 + β 2 log(aU S /aU K ) + εk 2. M (^) U Sk ←U K
- Here XU Sk^ is the US’s total exports of good k, whereas XU Sk^ →U Kis US exports to the UK in good k (and US imports from UK are M (^) U Sk^ ←U K).
- The coefficient of interest is β.
- The intuition of the Ricardian model suggests that β 1 > 0 and β 2 > 0.
- But there is no explicit multi-country Ricardian model that would generate this estimating equation. So it is hard to know how to interpret this test.
Comments:
- They also have a time series of this data for many years (from 1972-91):
- So they run this regression separately for each year, restricting the coefficients α and β to be the same across each year’s regression.
- They also apply a SUR technique to improve efficiency.
- Measuring a^ k and ak is harder than it sounds: U S U K
- One is in Dollars per hour and the other is in Sterling per hour.
- Market exchange rates are likely to be misleading (failure of PPP in short-run).
- So ‘PPP exchange rates’ are used instead. This is where international agencies collect price data for supposedly identical products (eg Big Macs) across countries and use these price observations to try to get things in real units (eg Big Macs per hour).
- GH use three different PPP measures: ‘Unadjusted’ (same PPP in each sector) is surely wrong. ‘ICP’ (the Penn World Tables’s PPP) is better, but has problem that these are expenditure PPPs. ‘ICOP PPP’ is probably best.
- Harrigan (2003): Simple partial equilibrium supply-and-demand mod els predict this relationship too. “A truly GE prediction of Ricardian models is that a productivity advantage in one sector can actually hurt export success in another sector, but GH do not investigate this prediction [and nor has anyone since.]”
- Harrigan (2003): A test of a trade model needs to have a plausible alternative hypothesis built in which can be explicitly tested (and perhaps rejected).
- Subsequent work (which we will discuss shortly) has tackled ‘Problem 1’, but not ‘Problems 2-4.’
2.3 Nunn (2007)
- Open question in Ricardian model: where do labor cost (ie productivity) differences come from? - Relatedly, in an empirical setting: are we prepared to assume that productivity differences are exogenous with respect to trade flows?
- Nunn (2007) took an innovative take on this problem.
- (But this paper does not try to tackle the fundamental ‘Problems 1-4’ of Ricardian model-based empirical work highlighted above.)
- Nunn (2007) is an influential paper in the ‘Trade and Institutions’ liter ature (really: How Institutions ⇒ Trade; a separate literature considers the reverse). - As we saw in the previous lecture, this literature argues that institu tional differences across countries do not just have aggregate produc tivity consequences (as in AJR 2001), but may also have differential productivity differences across industries within countries (industries may differ in their ‘institutional intensity’). - If that is true, institutional differences should generate scope for com parative advantage, and hence trade.
2.3.1 Set-up
- The key intuition was seen in Lecture 2:
- With imperfect contract enforcement (‘bad courts’) input suppliers who make relationship-specific inputs will under-invest ex ante in fear of ex post hold-up.
- This harms productivity. And it is worse in industries that are particularly-dependent on relationship-specific inputs, and in coun tries with bad courts.
- Suppose further that productivity (in country i and industry k) is the simple product of the ‘relationship-specific input intensity’ of the industry, zk, and the quality of the country’s legal system, Qi.
- Then we have an institutional microfoundation for each country and industry’s productivity level: a^ k = zk^ × Qi. i
2.3.2 Empirical specification
- Based on this logic, Nunn (2007) estimates the following regression, which is similar to Golub and Hseih (2000)’s regression 1:
ln x^ k = αk^ + α i +^ β 1 z^ kQ i +^ β 2 h kH i +^ β 3 k kK i +^ ε k i i
- x is total exports and αk^ and αi are industry and country fixed effects.
- The inclusion of αk is the same thing as taking differences across countries (like the US-UK comparison that GH did) and pooling all of these pairwise comparisons.
- While the regressor of interest is zkQi, Nunn controls for Heckscher Ohlin-style effects by including an interaction between industry-level skill- intensity (hk) and country-level skill endowments (Hi), and similarly for capital.
2.3.3 Is this regression justified by theory?
- Nunn appeals to Romalis (AER, 2004) which derived an expression like this from theory. - Romalis (2004) is a Heckscher-Ohlin model with monopolistic com petition and trade costs, so FPE is broken. - One problem with that is that Romalis doesn’t explicitly have ‘tech nology’ terms (like zkQi) in his regression, though Morrow (2008) derives a version with these included.
2.3.5 Comments
- Interpreting the results:
- Regression coefficients are standardized, so they can be compared directly with one another. Hence institution-driven comparative ad vantage appears to explain more of the world than HO CA.
- But the partial R^2 in these regressions is very low (3 % of the non- fixed effects variation can be explained by all regressors combined).
Least Contract intensive: lowest z (^) irs1^ Most Contract intensive: highest z (^) irs
Poultry processing Flour milling Petroleum refineries Wet corn milling Aluminum sheet, plate and foil manufacturing Primary aluminum production Nitrogenous fertilizer manufacturing Rice milling Prim. nonferrous metal excl. copper and alum. Tobacco stemming and redrying Other oilseed processing Other gas extraction Coffee and tea manufacturing Fiber, yarn, and thread mills
Synthetic rubber manufacturing
Synthetic dye and pigmentmanufacturing
Plastic material and resinmanufacturing Phosphatic fertilizer manufacturing Ferroalloy and related products manufacturing Frozen food manufacturing
Photographic and photocopying equip. manufacturing Air and gas compressor manufacturing Analytical laboratory instr. manufacturing Other engine equipment manufacturing Other electronic component manufacturing Packaging machinery manufacturing Book publishers Breweries Musical instrument manufacturing Aircraft engine and engine parts manufacturing Electricity and signal testing instr. manufacturing Telephone apparatus manufacturing Search, detection, and navig. instr.manufacturing Broadcast and wireless comm. equip. manufacturing Aircraft manufacturing Other computer peripheral equip. manufacturing Audio and video equip. manufacturing Electronic computer manufacturing Heavy duty truck manufacturing Automobile and light truck manufacturing
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . The contract intensity measures reported are rounded from seven digits to three digits.
The Twenty Least and Twenty Most Contract Intensive Industries
zrs1i^ Industry Description z (^) irs1 Industry Description
Judicial quality interaction: z (^) i Q (^) c
Capital interaction: k (^) i Kc
Log income x intra-industry trade: iit (^) i ln yc
Log income x input variety: (1 - hii ) ln yc
Log income x value added: vai ln yc
Log credit/GDP x capital: ki CR (^) c
Skill interaction: hi H (^) c
R 2
Industry fixed effects Number of observations
Country fixed effects
.289** (.013)
Yes
_ _
_ _
_ _
_
Yes . 22,
.318** (.020)
Yes Yes . 10,
.326** (.023) .085** (.017) .105** (.031)
Yes Yes . 10,
.235** (.017)
-.117* (.047) (.041) .576** . (.033) . (.012) .446** (.075) Yes
_
_
Yes . 15,
.296** (.024) (.017)
.063** . (.041) -.137* .546**
(.067) (.056) -. .
(.049) (.018) .522** (.103) Yes Yes . 10, Dependent variable is lncountry c to all other countries. In all regressions the measure of contract intensity used is z xic. The regressions are estimates of (1). The dependent variable is the natural log of exports in industryrs1 (^). Standardized beta coefficients are i by reported, with robust standard errors in brackets, * and ** indicate significance at the 5 and 1 percent levels.^ i
(1) (2) (3) (4) (5)
The Determinants of Comparative Advantage
Image by MIT OpenCourseWare.
Image by MIT OpenCourseWare.
So there is lots more to do on explaining export specialization! (Or the specification was wrong and/or there is big time measurement error.)
- Nunn (2007) pursues a number of nice extensions:
- Worry about endogeneity of Qi so IV for it with legal origin (La Porta et al, 1997/1998).
- Propensity score matching: restrict attention to British and French legal origin countries only. Then do matching on them (to control non-parametrically for observed confounders...but note that match ing never helps to obviate concerns about omitted variable bias due to unobserved confounders).
2.3.6 Similar Ricardian-style Exercises
- A number of other papers pursue similar empirical set-ups to that in Nunn (2007): - Cunat-Melitz: industry-level volatility × country-level labor market institutions. - Costinot (JIE, 2009): industry-level job complexity × country-level human capital. - Levchenko (ReStud, 2007): industry-level complexity × country-level contracting institutions.
Judicial quality interaction: z (^) i Q (^) c Skill interaction: hi H (^) c
British legal origin: z (^) i Bc French legal origin: z (^) i Fc German legal origin: z (^) i G (^) c Socialist legal origin: z (^) i Sc
Capital interaction: ki Kc Full set of control variables Country fixed effects Industry fixed effects Number of observations
R 2
F-test Hausman test ( p- value) Over-id test ( p- value)
.289**(.013)
No Yes Yes . 22, First stage IV estimates: Dependent variable is z (^) iQ (^) c****.
OLS and second stage IV estimates: Dependent variable is ln xic****. .385**(.022)
No Yes Yes . 22, -.295** (.033) -.405(.025) -. (.045) -.477(.035)
. .
.326(.023) .085(.017) .105** (.031) No Yes Yes . 10,
.539(.044) .042(.019) .183* (.035) No Yes Yes . 10, -.210** (.038) -.304**(.030) -. (.051)
. .
.296(.024) .063(.017) . (.041) Yes Yes Yes . 10,
.520** (.046) (.019). .114** (.043) Yes Yes Yes . 10, -.215** (.036) -.298**(.028) -. (.049)
. . In the second stage standardized beta coefficients are reported, with robust standard errors in brackets. The dependent variable is the natural log of exports in industry i bycountry c to all other countries. In the first stage I report regular coefficients, with robust standard errors clustered at the country level reported in brackets. The dependent variable is the judicial quality interaction zstage, to conserve space I do not report the first stage coefficients for these variables. The omitted legal origin category is Scandinavian. Because there are no Socialist legali Q (^) c. The measure of contract intensity used is z rs1. Although all explanatory variables in the second stage are also included in the first origin countries in the smaller samples of columns (3)null hypothesis that the coefficients for the interaction terms are jointly equal to zero, * and ** indicate significance at the 5 and 1 percent levels.(5), the Socialist interaction term does not appear as an instrument in these specifications. The reported F-test is for the_
i
OLS (1) IV (2) OLS (3) IV (4) OLS (5) IV (6)
IV Estimates Using Legal Origins as Instruments
Image by MIT OpenCourseWare.
- Explicit GE model allows proper quantification: How important is Ricardian CA for welfare (given the state of the productivity differ ences and trade costs in the world we live in)?
3.1 A Ricardian Environment
- Essentially: a multi-industry Eaton and Kortum (2002) model.
- Many countries indexed by i.
- Many goods indexed by k.
- Each comprised of infinite number of varieties, ω.
- One factor (‘labor’):
- Freely mobile across industries but not countries.
- In fixed supply Li.
- Paid wage wi.
3.1.1 Assumption 1: Technology
- Productivity zki (ω) is a random variable drawn independently for each triplet (i, k, ω)
- Drawn from a Fr´echet distribution F (^) ik (·):
k^ −θ i
k F (z) = exp[− z/zi ]
- Where: k
- zi > 0 is location parameter we refer to as ‘fundamental productiv k ity’. Heterogeneity in zi generates scope for cross-industry Ricardian comparative advantage. This ‘level’ of CA is the focus of CDK (2011).
- θ > 1 is intra-industry heteroegeneity. Generates scope for intra-industry Ricardian comparative advantage. This ‘level’ of CA is the focus of EK (2002).
3.1.2 Assumption 2: Trade Costs
- Standard iceberg formulation:
- For each unit of good k shipped from country i to country j, only 1 /dk ij ≤ 1 units arrive.
- Normalize dk ii = 1
- Assume: dk il^ ≤ dkij^ · dkjl
3.1.3 Assumption 3: Market Structure
- Perfect competition:
- In any country j price p^ k (ω) paid by buyers of variety ω of good k j is: pk^ k j (ω) = min i^ cij (ω)
k dkij wi
- Where c (^) ij (ω) = (^) zk (ω)is the cost of producing and delivering one unit i of this variety from country i to country j.
- Comment: paper also develops case or Bertrand competition.
- This builds on the work of Bernard, Eaton, Jensen and Kortum (2003)
- Here, the price paid is the second -lowest price (but the identity of the seller is the seller with the lowest price).
- This alteration doesn’t change any of the results that follow, because the distribution of markups is fixed in BEJK (2003).
3.1.4 Assumption 4: Preferences
- Cobb-Douglas upper-tier (across goods), CES lower-tier (across varieties within goods): - Expenditure given by:
k k �^ k 1 −σj k x^ k j (ω) =^ pj (ω)^ pj ·^ αj wj^ Lj
- Where 0 ≤ αk^ ≤ 1, σ^ k j j <^ 1 +^ θ
]
3.3 Cross-Sectional Predictions
Lemma 1. Suppose that Assumptions A1-A4 hold. Let x^ k ij be^ the^ value^ of^ trade from i to j in industry k. Then for any importer, j, any pair of exporters, i and i , and any pair of goods, k and k ,
x^ k^ k^ k^ k^ dk ij xi j zi zi ij di j k ln (^) k k = θ ln (^) k k − θ ln. x (^) ij xi j z (^) i z (^) i dkij^ dki j
where θ > 0.
- Proof: model delivers a ‘gravity equation’ for trade flows and pair of countries i,j.in each industry k. Take differences twice.
- Difficulty of t
- ‘Fundamental Productivity’ (z^ k i )^ is^ not^ observed^ (except^ in^ autarky). This is z^ k = E[zk (ω)]. i i
- Instead we can only hope to observe ‘Observed Productivity’, z^ k ≡ w i E zik (ω)w^ Ωki , where Ωki^ is set of varieties of k that i actually pro- duces.
- This is Deardorff’s (1984) selection problem working at the level of varieties, ω.
- CDK show that: k −^1 /θ zi zki πkii k =^ k · zi zi πi ik
- Intuition: more open economies (lower πii^ k^ ’s) are able to avoid using their low productivity draws by importing these varieties.
- This solves the selection problem, but only by extrapolation due to a functional form assumption.
Theorem 2. Suppose that Assumptions A1-A4 hold. Then for any importer, j, any pair of exporters, i and i , and any pair of goods, k and k ,
where xij ≡ xij πii.
[ ]
k ∑
(w (^) idk/z θ xk^ ij^ i^
)− k ij =^ k − ·^ αj wj^ Lj i ′^ (wi′^ di′j /z k (^) ) θ i′
aking Lemma 1 to data:
x˜ij ln
( (^) k ˜
′ xki′j
k′ i′
θ ln
dkij d = θ ln
˜ zki z˜ k
′ − i
′j
xk ij′ xki j′^ z ik ′zki ′ dkij′ dki′j
k k k
- Note that (if trade costs take the form dkij^ = dij dk j) then this has a very similar feel to the standard 2 × 2 Ricardian intuition. - But standard 2 × 2 Ricardian model doesn’t usually specify trade quantities like Theorem 3 does. - And the Ricardian model here makes this same 2 × 2 prediction for each export destination j.
- Can also write this in ‘gravity equation’ form:
- This derivation answers a lot of questions implicitly left unanswered in the previous Ricardian literature: - Should the dependent variable be x^ k or something else? i - How do we average over multiple country-pair comparisons (ie what to do with the j’s)? - How do we interpret the regression structurally (ie, What parameter is being estimated)? - What fixed effects should be included? - Should we estimate the relationship in levels, logs, semi-log? - What is in the error term? (Answer here: the error term is ln dk ij plus measurement error in trade flows.)
- However, this specification is effectively a gravity equation (which we will see many variants of throughout this course) so this cannot be seen as a test of Ricardo vs some other gravity model.
- In the above specification, note that δij and δj^ k^ are fixed-effects. Comments about these: - These absorb a bunch of economic variables that are important to the model (eg e^ k is in δ j k) but which are unknown to us. This is good j and bad. - The good: we don’t have to collect data on the e^ k variables—they j are perfectly controlled for by δ^ k j.^ (And^ similarly^ for^ other^ variables like wages and the price indices.) Even if we did have data on these variables such that we could control for them, they would be endoge nous and their presence in the regression would bias the results. The fixed effects correct for this endogeneity as well. - The bad: The usual problem with fixed-effect regressions is that the types of counterfactual statements you can make are much more lim ited. However, in this instance, because of the particular structure of this model, there are a surprising number of counterfactual state ments that can be made with fixed effects estimates only.
ln ˜xkij = γij + γjk + θ ln z˜ik − θ ln dkij
- 13 (2-digit) manufacturing industries.
- As Bernard, Eaton, Jensen and Kortum (2003) point out, in Ricardian world relative productivity is entirely reflected in relative (inverse) pro ducer prices.
- This is always true in a Ricardian model (since wages cancel).
- But further impetus here:
- It might be tempting to use measures of ‘real output per worker’ instead as a measure of productivity.
- But statistical agencies rarely observe physical output. Instead they observe revenues (Rki ≡ Qki P (^) ik ) and deflate them by some price index ki i^ k (P k) to try to construct ‘real output’ (≡^ R i (^) P ). R^ ki /Pi^ k wiL P L
- So again wages cancel. In a Ricardian world, statistical agencies’ measures of relative ‘real output per worker’ are just relative inverse producer prices.
ki i^ k
3.6 Final Specification
- With all of the above comments included the final specification used by CDK (2010) is:
ln x^ k^ k ij −^ ln^ π k (^) = δij + δ j k (^) − θ ln p + εk ii i ij
- OLS requires the orthogonality restriction that E[ln P (^) ik |dkij^ , δij , δkj] = 0.
- CDK can’t just control for trade costs, because the full measure of trade costs dk ij is not observable (trade costs are hard to observe, as we’ll discuss in Week 8).
- Recall that εkij^ includes the component of trade costs that is not country-pair or importer-industry specific.
- This orthogonality restriction is probably not believable. So also present IV specifications in which ln P (^) ik^ is instrumented with log R&D expenditure (in i and k in 1997). - In a Ricardian world, then, ‘real output per worker’ = (^) L = = wi. ki Pik
ki
- That is, ˜zki ˜z ik′′ zik′ zk i′^ =
[
E[pki (ω)|Ωki ]E
[ pk i′′ (ω)|Ωk i′′
]
E[pki′ (ω)|Ωki′ ]E[pk i ′(ω)|Ωk i ′]
]− 1
3.7 Results
log(corrected
Dependent variable: log(exports)
exports)
log (productivity, 1.123 1.
based on producer prices) (0.099)*** (0.103)***
Observations 5,652 5,
R-squared 0.856 0.
Notes: Regressions include exporter-times-importer fixed effects and importer-times- industry fixed effects. Robust standard errors in parentheses.
Endogeneity Concerns
- Concerns about OLS results:
- Measurement error in relative observed productivity levels: attenua tion bias.
- Simultaneity: act of exporting raises fundamental productivity.
- OVB: eg endogenous protection (relative trade costs are a function of relative productivity)
- Move to IV analysis:
- Use 1997 R&D expenditure as instrument for productivity (inverse producer prices).
- This follows Eaton and Kortum (2002), and Griffith, Redding and van Reenen (2004).
- Also cut sample: pairs for which dkij^ = dij · dkj^ is more likely.
IV Results
