L5_gravity_empirics File

International Economic Policy 2014-15
The Gravity Model:
Eempirical issues
Prof. PIERLUIGI MONTALBANO
[email protected]
P. Montalbano - Sapienza Università di Roma
S
Uses and Pitfalls of Gravity Regressions
It looks easy: all you need for a basic specification is data on bilateral trade,
GDP and your favorite explanatory variable
Also it seems practical: you can develop a new proxy for your preferred
policy-related variable and use a really big dataset.
Pitfalls:
• The problem of omitted variables bias (value chain trade, third country
effect, relative costs, market demand or openness)
• Selection bias (heterogeneity, zeroes)
• Dynamics (persistence, sunk costs)
• Interdependence (third country effect and network, clustering)
• Plus, data issues …
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
Step 1: The Left Hand Side
Typology of goods:
• What data: Merchandise trade vs. services, FDI, etc.
• Unilateral flows: Average or sum of imports and exports lead to bias of
the coefficient for the treatment effect, because trade is not balanced!
Conversion:
• Nominal terms and common numeraire: Gravity is a modified
expenditure equation not a demand equation (Baldwin and Taglioni,
JEI 2007)
• Empirically, lack of appropriate deflators: no good price indices for
trade data. Their use risks to be an additional source of biases and
spurious estimations
• CIF vs. FOB: Be aware of what data you are using and interpret the
results accordingly
Firm heterogeneity :
• Not all firms export, and few export to every partner
• Zeroes are a source of information
• Inclusion of zeroes rules out the use of OLS estimations
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
Step 2: right end - Specification Matters!
VARIABLES
limport
limport
limport
lgdp i
0.704***
0.957***
0.803***
lgdp j
0.777***
1.051***
1.003***
ldistance
-0.897***
-1.014***
-1.067***
-1.089***
border
0.406***
0.537***
0.587***
0.564***
FTA
0.146**
-0.172*** -0.632*** -0.717*** 0.266***
Constant
-16.64***
-25.54***
Observations
-19.85***
limport
28.56***
limport
13.02***
10831
10831
10831
10831
10831
0.55
0.732
0.785
0.815
0.928
R-squared
time effects
no
yes
no
no
no
yes
yes
exporter and importer time invariant fe
no
no
no
exporter and importer time-varying fe
no
no
no
yes
no
no
no
no
yes
yes
time invariant pair fe
Note: (*) significant at 10% level; (**) significant at 5% level; (***) significant at 1% level.
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
STEP 3: The Omitted Variables Bias
Add a time dimension and move to panels
• Most typical source of omitted variables bias is country heterogeneity
Include one or more proxies correlated with the omitted
variable
• Trade costs
– Add other trade frictions to distance, including border, common history, language,
doing business indicators, etc.
– Estimated trade frictions (Jacks, Meissner, Novy, AER 2008.)
• Attractors
– Income per capita: higher income countries trade more with each other
– GDP is not enough when trade is driven by value chains (Baldwin and Taglioni,
NBER 2012)
Problems of interdependence: not easy to fix
• The relative costs problem
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
Theoretical underpinnings for
Trade costs
- Anderson (1979): importance of transport costs as well as national
tariffs in each country, both of which are expected to increase with
distance.
- Bergstrand (1985): trade costs differ depending on location, hence
GM must include price indices.
- Anderson and van Wincoop (AVW) (2003): seek to identify trade
costs that give rise to international differences in prices.
P. Montalbano - Sapienza Università di Roma
Trade Costs: Empirical Evidence
1.
2.
Distance variable does not reduce over time. De Menil e Maurel (1994)
calculated for the period 1924-26 in Europe a dist coeff. = –70, less than in
many current estimations (it reinforces the idea that distance is not only
shipping costs but something more – e.g. cultural unfamiliarity and it keeps
matter nowadays!);
The so-called border effect. Mc Callum (1995) and Helliwell (1996) find that,
after controlling for market size and distance, trade among Canada provinces
is 22 times larger than trade between Canada provinces and U.S. states.
It is referred to as the “Mc Callum Border Puzzle”, one of the 6 main
puzzles of open economy macroeconomics (Obstfeld e Rogoff, 2001)
since the actual distance among the Canada provinces is much more than
that before Canada and USA and about 85% of the Canadian population
leave less than 100 miles from the USA border.;
However, more recently Anderson and van Wincoop (2003) show a
reduced border effect by controlling for the “Multilateral Resistance Term”
(MRT).
© P. Montalbano, 2011
P. Montalbano - Sapienza Università di Roma
MRT and the «Border Effect»
•
Bilateral trade between country i and j depends on the specific bilateral trade barrier as
well as their multilateral resistance terms
This means that for a given bilateral trade barrier, higher trade barriers between j and all its
other trade partners will reduce the relative price of country i’s exports to j and thereby
cause a raise of i’s exports to j.
High multilateral resistance of i and j with regard to the rest of the world raises bilateral
trade between i and j.
Example: Australia and New Zealand should experience relatively high bilateral trade, as
both countries face relatively high multilateral resistance due to their geographical
remoteness with respect to the rest of the world.
ATT: It solves the McCullogh border puzzle between USA and Canada (being Canada
relatively open overseas, USA and Canada face relatively low bilateral trade (There isn’t any
Border Effect!)
P. Montalbano - Sapienza Università di Roma
The Relative Costs Problem
Implications of a world with many countries
• 3rd countries mass and distance matters
• 2-way effect
Rest of the World
Country A
Country B
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
The Relative Costs Problem
Theory helps:
• The gravity equation is an expenditure function (and not a demand
equation) and as such it depends on relative and not absolute prices.
• On the side of the exporter, the price pi that will clear the market is a
function of nation i’s sales over all markets, including its own market
Hence we end up with the relative costs problem:
• Multilateral resistance (MR) terms (Anderson and van Wincoop AER,
2003 and JEL, 2004)
• In a multi-period setting, with unbalanced trade better to look at the
individual components of multilateral resistance (Baldwin and
Taglioni, REI 2007):
– Price index of importing country
– Market potential of exporting country
X ij = φij
1−σ
M j Mi
Pj1−σ Ω i
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
Accounting For The Relative Costs Problem
Empirically
Standard price indices (CPI, PPI, etc.) are not aggregated in
the way implied by theory:
• Poor proxy for the true (ideal) price indices (weighted averages of
bilateral trade costs)
Ignoring them is not an option:
• This would lead to omitted variables bias unless the MR terms have
zero correlation with exports and trade costs (or GDP)
Common empirical fixes
• Fixed effects model
• Random effects model
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
A GENERALISED GRAVITY MODEL
Normal trade with resistances (in ln)
Xij = a0 + a1 (Yi) + a2 (Yj) + a3 (yi) + a4(yj) + a5 (TCij) + a6 (MRTi) + a7 (MRTj) + uij
Trade costs (TC) are usually proxied by:
• Distance
• Adjacency
• Common language
• Colonial links
• Common currency
• Island
• Trade policy
• Bilateral tariff barriers often missing!
While Multilateral Resistance Terms (MRT) are not observable (function of transport / trade
costs and consumer prices, not only pecuniary costs)
P. Montalbano - Sapienza Università di Roma
Cross-section ⇒ panel
Natural to extend the above from cross section to panel regressions
In a panel regression you now have data for your cross-section but also
over time.
The standard panel regression typically involves “fixed” effects, where for
each variable you take the difference for each year, from the mean for that
variable.
• Hence the interpretation of the panel estimation is quite different from the
cross-section.
– Cross section is a static comparison across countries
– Panel typically has much more of dynamic interpretation ie. you are
looking at the impact of changes in the explanatory variables on changes in
trade flows
What form should these fixed effects take:
• Country pair fixed effects – standard
• Country fixed effects à la Anderson & Wincoop.
P. Montalbano - Sapienza Università di Roma
A GENERALISED GRAVITY MODEL
•
Cross-section ⇒ panel estimation
In a panel context (data for your cross-section but also over time), multilateral resistance
terms are estimated using country fixed effects (dummy variables)
•
3 possible sets of fixed effects in the « full model »:
1. Country effects (exporter-specific effects and importer-specific effects): unobserved
factors such as geographical, political, cultural, institutional factors
2. Time specific effects
3. Interactions (exporter–importer interactions, exporter–time interactions and
importer–time interactions)
• Hence you now have bilateral trade depending on income levels in importing and
exporting countries + transport costs + country specific fixed effects.
• However… if you are including country specific fixed effects these are then perfectly
collinear with the GDP variables.
• The solution is therefore to take the GDP variables over to the left hand side (but then
what are we left with?)
P. Montalbano - Sapienza Università di Roma
Preferred Fixed Effects’ Specification
Xijt = ϕ ijt1−σ FEjt FEit FEij
• Fixed effects specification
– Constant and time-varying dummies for each exporter and importer
– Time invariant pair dummy
• Pros:
– Very simple to estimate
– Proper account of the relative costs problem
– Produces unbiased estimates for the policy variable
• Cons:
– Dimensionality quickly becomes an issue with sectoral models: N+N can be in
the hundreds, or thousands
– Because of collinearity constraints, we cannot identify separate effects due to
factors that vary in the exporter or importer dimensions
– Only factors varying bilaterally can be identified, and even here avoidance of
collinearity is not warranted
P. Montalbano - Sapienza Università di Roma
STEP 4: Selecting The Appropriate
Functional Form
Non-linearities
Selection bias and zeroes
Dynamics
Interdependence and networks
P. Montalbano - Sapienza Università di Roma
Selection Bias And Zeroes
Heckman 2-stages least squared estimation (Heckman, 1979)
• It introduces in the specification the inverse of the so-called Mills ratio
• Crucially, computation of Mills ratio requires variables that may explain the
•
selection (zero or positive trade) but not the value of traded good, when this is
positive.
If the variable included in the selection equation also affects the outcome
variable, it can lead to the researcher preferring simple OLS to the Heckman
procedure (Puhani 2000).
Non-linear estimators (Santos-Silva and Tenreyro, 2006)
• Poisson Pseudo Maximum-Likelihood (PPML) estimator, using a log-linear
•
function instead of log-log one: easy-to-implement strategy to deal with
heteroskedasticity and zero trade flows.
Need to pay attention to the structure of the data, the level of overdispersion
and the assumptions one is willing to impose on the data.
No easy choices.
• Need to take seriously the exclusion restriction to make correct choice
• Need convincing answer to question: where are all those zeros coming from?
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
Dynamics
Persistence and sunk costs call for attention to
dynamics
Literature at its infancy and still exploratory in nature
• Blundell-Bond system GMM estimator (De Benedictis
and Vicarelli 2005; De Benedictis et al. 2005; Olivero
& Yotov, 2012)
• Full set of panel cointegration estimators (i.e. the Fully
Modified OLS estimator or the Dynamic OLS) that
control for the endogeneity of dependent variables
(Fidrmuc 2009).
P. Montalbano - Sapienza Università di Roma
The Global trade network
Fonte: De Benedictis et al., (GEJ, 2014)
19
P. Montalbano - Sapienza Università di Roma
Interdependence
Relative costs problem is one aspect of a more general problem of
interdependence
• If i and j are part of a group g, assumption of an i.i.d. stochastic error
term eij is violated (Lindgren 2010).
• Traditional robust standard errors procedure may lead to biased
estimated errors and erroneous statistical inference.
• When a cluster g is identified, standard errors need to be clustered
around g (Cameron et al. 2010) .
In the gravity equation, several choices for clustering, e.g.:
• By country: if we believe that countries have a memory of their past
decisions and project it onto the future.
• By FTA: if two countries belong to the same preferential trade
agreement .
• If a hierarchical structure exists, need to nest the level of clustering
choosing the most aggregate level.
• Caveat: number of clusters should be large and balanced.
Solution: two-way or multi-way clustering, clearly discussing the
adopted clustering structure
Source: De Benedictis & Taglioni (2011)
P. Montalbano - Sapienza Università di Roma
STEP 5: Testing for Policy
Dummies vs. continuous variables
• Francois et al, 2006, De Benedictis and Salvatici 2011 book
Aggregate vs. disaggregated data
Exogeneity of trade policy
• Baier and Bergstrand, 2007
• Heckman-type approaches
Propensity score matching techniques
• Millimet and Tchernis, 2009, B-B 2009, De Benedictis and Nenci, 2013
Models of interdependence and network
• Formation of an FTA given the existence of previous FTA (Egger and Larch,
•
•
2008 and Chen and Joshi, 2012)
The role played by third countries is fundamental in understanding the
formation of FTA
MR term not sufficient in explaining interdependences (De Benedictis et al,
2010)
P. Montalbano - Sapienza Università di Roma
How to address “ex post” the policy effect in
the gravity model?
3 subsequent strategies :
Dummy strategy: standard strategy in log linear gravity
equations with panels’ time series dimension to estimate the
causal ATE on trade volumes of FTAs;
Continuous variables strategy: i.e., measuring the
“treatment” more appropriately by quantifying the
“preferential margin” guaranteed by the preferential
agreements;
Non parametric Matching econometrics: i.e., to estimate the
treatment effects without imposing a functional relationship &
addressing the “non random selection bias”.
© P. Montalbano, S. Nenci, 2011
P. Montalbano - Sapienza Università di Roma
Dummy strategy
Main drawbacks
of each strategy
Source: Montalbano & Nenci, 2014
Continuous variable
Matching strategy
strategy
It implies that all
Aggregation problem
X dimensionality
countries in the
(a proper aggregation
Selection bias in
treatment group are
would take into
observables;
assumed to be subject
account that imports
Selection bias in
to the same dose of
of some goods are
unobservables(selfmore responsive to
treatment
selection);
changes in prices than
It cannot distinguish
No- Overlap
between the
others)
assumption
The risk of
No multiple versions
treatment and any
of the treatment and
other event specific to
endogeneity btw trade
the country pair and
flows and trade policy
“non-interference”
contemporaneous to
Omitted nonassumption
the treatment (OV
linearities: if the
bias)
relationships btw the
It is unable to catch
FTA “treatment”
gradualism in the
and the other tradeimplementation
flows determinants
process (trade policy
are non linear , the
does not switch from 0
OLS ATE will differ
to 1)
from the ATT
The more control for
(Persson, 2001)
heterogeneity and
Selection bias:
trade costs, the less
country pairs that
we are able to capture
share preferences
the policy effect of
tend to share similar
interest (i.e., trade off
economic
btw method’s
characteristics that
accuracy& policy
gravity eq. uses to
relevance)
explain their trade
flows (i.e., the fact
that country pairs with
FTA trade more does
not imply FTA actually
causes trade).
P. Montalbano - Sapienza Università di Roma