session 1: counterfactual simulations using the gravity model

IntroductionSimulations and the AvW Model

Additional Issues in Counterfactual SimulationsSummary

Session 1: Counterfactual Simulations Usingthe Gravity Model

Ben Shepherd

Principal, Developing Trade Consultants Ltd.

ARTNeT/RIS Capacity Building Workshop on the Use ofGravity Modeling

Friday, November 11, 2011

Ben Shepherd Session 1: Counterfactual Simulations Using the Gravity Model

1



Outline

1 Introduction

2 Simulations and the AvW Model

3 Additional Issues in Counterfactual Simulations

4 Summary


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Introduction

Thus far, we have focused on using the gravity model toobtain estimates of the sensitivity of trade to changes inparticular geographical or policy factors.We have been interested in measuring the strength ofthese effects through parameters such as elasticities,focusing on estimated sign, magnitude, and statisticalsignificance.That is not the only way to interpret gravity model results...


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Introduction

Counterfactual simulations are an alternative way ofpresenting results from the gravity model.We take observed data and estimated elasticities, and usethem to map a “shock” to some independent variable ontoprojected trade effects:

ln

(X̃ij

Xij

)= b̂ ln

(τ̃ij

τij

)

Gravity is a very crude method for performing suchsimulations, and should only ever be used for “back of theenvelope” numbers. For a rigorous analysis (includingeconomic welfare), a CGE model is really required.


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Introduction

The AvW model has serious implications for the way inwhich we estimate gravity models.It turns out also to have serious implications for the way inwhich we conduct counterfactual simulations.Because of the computational complexity of the problemsinvolved, we will only consider an approximate approachhere. For more details, see AvW (2003, 2004).


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Simulations and the AvW Model

The AvW Gravity Model–Aggregate Data

ln(Xij)

= ln(Yi) + ln(

Ej

)− ln(Y ) + (1−σ)

[lnτij + lnΠi + lnPj

]As we have seen, the MR terms play a crucial role insetting up and estimating gravity models.One motivation for going back to theory was that we didn’tbelieve that trade costs elsewhere could not influencetrade on a particular bilateral route.An alternative motivation is that it is unlikely that changesto trade costs on one bilateral route do not influence tradeelsewhere.These effects need to be picked up properly when weconduct counterfactual simulations.


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Recall the definitions of inward and outward MR:(Πk

i)1−σk = ∑

Cj=1

{τk

ij

Pkj

}1−σk Ekj

Y k and(Pk

j

)1−σk= ∑

Cj=1

{τk

ij

Πki

}1−σkY k

iY k

From a simulation standpoint, the important thing to note isthat both MR terms are functions of all bilateral trade costs.Thus, any counterfactual simulation based on a shock totrade costs needs to account for two effects:

A direct trade impact through the trade costs function in themain gravity model; andAn indirect trade impact through the MR terms.


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The fixed effects AvW model takes account of the MRterms at the estimation stage.However, if we conduct counterfactual simulations basedon a fixed effects model, we can only obtain the first-order(direct) effect.The fixed effects do not tell us anything about howchanges in trade costs translate into changes in MR, andhow changes in MR map to changes in trade flows.


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To see this more clearly, take the AvW model:

ln(Xij)

= ln(Yi)+ ln(

Ej

)− ln(Y )+(1−σ)

[lnτij + lnΠi + lnPj

]and

(Πk

i)1−σk = ∑

Cj=1

{τk

ij

Pkj

}1−σk Ekj

Y k ;(Pk

j

)1−σk= ∑

Cj=1

{τk

ij

Πki

}1−σkY k

iY k

Clearly, 1Xij

∂Xij∂τij

= 1−σ

τij+ 1−σ

Πi

∂Πi∂τij

+ 1−σ

Pj

∂Pj∂τij


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However, for the fixed effects model:

ln(Xij)

= c + ai + aj + (1−σ) lnτij

And so in practice, 1Xij

∂Xij∂τij

= 1−σ

τijbecause we have no way

of evaluating the MR terms.

The problem is even more acute for ∂Xij∂τkl

, because that termappears in the MR terms but not at all in the FE model.


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To deal with this problem, we need to use an empiricalmodel that includes the MR terms more directly than doesFE.Two possible solutions, neither of which is (yet) widelyused in the literature:

Direct estimation as per AvW;Baier-Bergstrand estimation via a Taylor seriesapproximation.

The first solution is difficult to implement. The secondgives a relatively good approximation, and is much simpler.


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The Baier-Bergstrand Model

Recall that the BB Taylor expansion gives a gravity modelthat looks like this:

ln(

X kij

)= ln

(Y k

i

)+ ln

(Ek

j

)− ln

(Y k)

+

(1−σk )

[lnτ

kij −∑

iθi lnτij −∑

jθj lnτij +∑

i∑j

θiθj lnτij

]

The correction introduced by the approximate MR termsmeans that just as the estimates take account of MR, sotoo do simulation results based on the BB model.


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1 Calculate the MR adjustment term∑i θi lnτij + ∑j θj lnτij −∑i ∑j θiθj lnτij for each trade costvariable, and transform the original variable by subtractingthe adjustment term. Thus,τ∗

ij = lnτij −1N ∑i lnτij − 1

N ∑j lnτij + 1N2 ∑i ∑j lnτij .

2 Estimate a gravity model using the transformed trade costvariables.


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1 Design a policy simulation, and create a new trade costvariable τ̃ij that represents the counterfactual value of tradecosts you are interested in.

2 Calculate the MR adjustment term for the counterfactualtrade cost variable, and transform the counterfactualvariable by subtracting the counterfactual adjustment termto produce τ̃∗

ij .3 Calculate the percentage change in the transformed trade

cost variable (counterfactual relative to baseline), then mapthe percentage change to trade using the estimatedelasticity.


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More formally:

ln

(X̃ij

Xij

)= b̂ ln

(τ̃∗

ij

τ∗ij

)where ~ indicates counterfactual variables, and * indicatestrade costs transformed according to BB’s procedure fortaking account of the MR terms.


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Additional Issues in Counterfactual SimulationsChoice of Counterfactual Scenario

It is important to choose a policy-relevant counterfactual.“What if” Swaziland turns into Switzerland is not relevant.WMO look at regional averages: this can represent areasonable and achievable benchmark, so counterfactualresults can be meaningful.Be aware that technically, counterfactuals involving largeshocks are unlikely to be valid: parameters might change,or linear approximations break down.


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Additional Issues in Counterfactual SimulationsPresentation of Counterfactuals

Particularly in the context of trade facilitation, independentvariables in the gravity model can tend to be stronglycorrelated.Econometric techniques can help us identify independenteffects of particular variables.But when we perform variable-by-variable counterfactuals,we are implicitly assuming that it is possible to shock onevariable without shocking the others.Conversely, if we add together variable-by-variable shocks,the total effect may well be overstated due to the fact thatthings tend to move together in practice.


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Additional Issues in Counterfactual SimulationsBinding Constraints

Gravity models often do not include data onNTBs–including binding quotas–due to lack ofcross-country data.Thus, counterfactuals can grossly overstate trade effects insituations where NTBs are binding, and effectively inhibitexport expansion.When working in regions and sectors where NTBs are anissue, it is important to be clear about this.More generally, be skeptical of overly large counterfactualresults!


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Additional Issues in Counterfactual SimulationsUncertainty and Sampling Error

The gravity model does not give us certain values for theelasticity of trade with respect to trade costs.It only gives us estimated values, which are subject tosampling error and, thus, to uncertainty.By choosing only the core estimate for counterfactuals, wecan give an impression of undue precision to an audiencethat does not appreciate the mechanics of this approach.


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Additional Issues in Counterfactual SimulationsUncertainty and Sampling Error

One way to deal with this is to provide a measure ofuncertainty for the counterfactual results too.Calculate the counterfactual results using the corecoefficient estimate.Then repeat the calculation twice more using:

The core estimate + 1 standard deviation;The core estimate - 1 standard deviation.

This is a very approximate approach, but it gets the pointacross: counterfactuals produce a zone of results, ratherthan just a single number.


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Summary

Gravity counterfactuals can be a good way of explainingmodel results to a policy audience.However, it is important to make the caveats clear:

Gravity models trade effects, not welfare;Results are indicative only, subject to uncertainty, and donot take account of constraints that may be binding inpractice;Counterfactual results lose validity as the shock becomeslarger.


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Summary

A FE gravity model can be a starting point forcounterfactuals, but it misses out on indirect effectsthrough the MR terms.BB is a better way of taking account of such indirect effects.In general, treat gravity counterfactuals as a “back of theenvelope” calculation. If quantification is important, theyshould be backed up with CGE results.


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session 1: counterfactual simulations using the gravity model

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