Welcome to The Log of Gravity page.
Reference (now with open access):
Santos Silva, J.M.C. and Tenreyro, Silvana (2006), The Log of Gravity, The Review of Economics and Statistics, 88(4), pp. 641-658.
An early version of the paper can be found at CEP/LSE (and an even earlier version at Boston Fed).
In this page you can find the data set used in the paper, codes to extend some of the results in the paper, and other useful information on the implementation of the PPML estimator.
If you cannot find here the answer to your question about The Log of Gravity, please do not hesitate to contact the authors; we will be only too pleased to help.
The dataset (in xls and dta formats) is available here.
Convergence problems:
Incidental parameters:
Charbonneau (2012, p. 41)
claimed that "a Poisson model with two fixed effects does suffer from the incidental parameter problem", and this
claim has recently been echoed by other researchers. However, Charbonneau's claim is based on an example with N = T = 2,
which cannot be informative about the existence of an incidental parameter
problem because this problem is asymptotic in nature. In contrast,
Fernández-Val and Weidner (2014, example 2, p. 16)
have recently proved that a Poisson model with two fixed effects does not suffer from the incidental parameter
problem as long as the regressors are strictly exogenous (a requirement that is also needed for the consistency of
the fixed effects estimator in liner models). Therefore, under very general conditions, inference based on the
estimation by ppml of gravity equations including both importer and exporter fixed effects will not be affected by
an incidental parameter problem.
Testing competing models for non-negative data with many zeros:
We have developed a simple test to choose between competing models for non-negative data with many zeros. The paper is
forthcoming in the Journal of Econometric Methods and is
available here
(an earlier version is here).
Stata code to implement the test is available here; the
code and data used in the applications are available here.
Instrumental Variables:
We have written a crude Stata command (recently updated) to estimate the
IV version of PPML. This estimator
was originally described in Windmeijer, F. and Santos Silva, J.M.C. (1997),
"Estimation
of Count Data Models with Endogenous regressors: An Application to Demand for Health Care," Journal of Applied Econometrics,
12(3), pp. 281-294. Here is an example of how to use the command.
UPDATE: This estimator is now implemented in Stata 13;
see the ivpoisson command and the add option (the default).
RESET test:
Here is a
sample of the code to perform the test.
R-squared:
If you want to compute the R-squared for a
model estimated by PPML, you can used the method implemented
here.
PPML performance with many zeros:
Simulation evidence on the excellent performance of the PPML estimator
when the data has many zeros can be found in this
Economics Letters
paper.
Warning:
Be advised that there are several papers purporting to introduce estimators that improve on the PPML. While it
is of course possible to find estimators that outperform PPML in specific conditions, to our knowledge all the newly proposed
alternatives to PPML are either simply invalid, or valid only under implausibly strong distributional assumptions. Therefore we
stand by the claim that PPML has all the characteristics needed to be the workhorse for the estimation of constant-elasticity
models such as the gravity equation. If you believe to have evidence that another estimator generally outperforms PPML in this
context please do let us know; we would be delighted to acknowledge that.
We have written a short reply to "The log of gravity revisited".
If you want to compute 'undertrading' and 'overtrading' after fixed-effects regressions with panel data, you need to obtain a set of residuals with zero mean. Here is how to do it.
In this Annual Review of Economics paper we use PPML and panel data to estimate the trade effect of the euro; an earlier version is available here.
Related work by other authors:
Eight FAQ's & myths about the Log of Gravity
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Last updated on 2 October 2014