Welcome to The Log of Gravity page.
Reference (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. These and other issues are also discussed in this short review. 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.
Summary: Researchers often have to model nonnegative dependent variables (potentially with many zeros), and different approaches have been used to estimate models for this kind of data. Typical approaches include using log-linearized models and Tobit-type estimators. In the Log of Gravity, we challenged these long-established practices and proposed as an alternative the use of the Poisson pseudo maximum likelihood (PPML) estimator of Gourieroux et al. (1984). The PPML estimator is easy to implement and is extraordinarily well suited for the estimation of models for this kind of data and is especially suitable for the estimation of gravity equations..
The dataset (in xls and dta formats) is available here.
Google Scholar Classic papers in Economics:
The Log of Gravity tops the list of Google Scholar's Classic papers in Economics.
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 proved that a Poisson model with two fixed effects does not suffer from the incidental parameter
problem as long as the sizes of the two sets of fixed effects grow at the same rate and the regressors are strictly
exogenous or predetermined. 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. Remarkably, Martin Weidner and Tom Zylkin have shown
that PPML is also largely immune to the incidental parameter problem when the model contains three sets of fixed effects.
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.
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
available here.
Stata code to implement the test is available, type "ssc install hpc"; the
code and data used in the paper are available here.
Instrumental Variables:
We have written a crude Stata command 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.
This estimator is now implemented in Stata; 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 use the method implemented
here.
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:
FAQs & myths about the Log of Gravity
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