Estimating the Gravity Model When Zero Trade Flows are Frequent and Economically Determined
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World Bank, Washington, DC
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This paper evaluates the performance of
alternative estimators of the gravity equation when zero
trade flows result from economically-based data-generating
processes with heteroscedastic residuals and
potentially-omitted variables. In a standard Monte Carlo
analysis, the paper finds that this combination can create
seriously biased estimates in gravity models with
frequencies of zero frequently observed in real-world data,
and that Poisson Pseudo-Maximum-Likelihood models can be
important in solving this problem. Standard threshold–Tobit
estimators perform well in a Tobit-based data-generating
process only if the analysis deals with the
heteroscedasticity problem. When the data are generated by a
Heckman sample selection model, the Zero-Inflated Poisson
model appears to have the lowest bias. When the data are
generated by a Helpman, Melitz, and Rubinstein-type model
with heterogeneous firms, a Zero-Inflated Poisson estimator
including firm numbers appears to provide the best results.
Testing on real-world data for total trade throws up
additional puzzles with truncated Poisson
Pseudo-Maximum-Likelihood and Poisson
Pseudo-Maximum-Likelihood estimators being very similar, and
Zero-Inflated Poisson and truncated Poisson
Pseudo-Maximum-Likelihood identical. Repeating the Monte
Carlo analysis taking into account the high frequency of
very small predicted trade flows in real-world data
reconciles these findings and leads to specific
recommendations for estimators.
Palabras clave
PANEL DATA, VARIABILITY, REGRESSION MODEL, MINIMIZATION, ERRORS, BINOMIAL DISTRIBUTION, COEFFICIENTS, LIMITED DEPENDENT VARIABLE, NORMAL DISTRIBUTION, DUMMY VARIABLES, GDP PER CAPITA, INFORMATION, LINEAR FUNCTION, EXPORTS, ELASTICITY, TRADE FLOWS, LOGARITHMS, DISTRIBUTION, GRAVITY MODEL, VARIABLES, DEGREES OF FREEDOM, ECONOMETRIC METHODS, NONLINEARITY, EXOGENOUS REGRESSORS, NONLINEAR MODELS, DUMMY VARIABLE, NUMBER OF OBSERVATIONS, PROBABILITIES, PREFERENTIAL ACCESS, INDEPENDENT VARIABLES, CLASSIFICATIONS, VARIABLE ESTIMATION, KNOWLEDGE, EMPIRICAL ANALYSIS, BIASES, MONTE CARLO SIMULATION, GOODNESS OF FIT, STANDARD DEVIATION, DATA, MAXIMUM LIKELIHOOD, STEP ESTIMATOR, LAY OUT, EXOGENOUS VARIABLES, TRADE BLOCS, DECISION TREE, PROBABILITY, NOTATION, LINEAR MODELS, ECONOMETRICS, CLUSTERING, STANDARD ERRORS, CASES, CRITERIA, LINEAR PROBABILITY, MATRIX, EXPLANATORY VARIABLES, POSITIVE OBSERVATIONS, ACCESS, INDICATORS, RESEARCH, ARTICLE, LIKELIHOOD FUNCTION, ECONOMETRIC PROBLEMS, LARGE NUMBER, VOLUME OF TRADE, RANDOM VARIABLES, GRAVITY EQUATION, ECONOMIC RESEARCH, ERROR VARIANCE, SELECTION MODEL, LIMITED DEPENDENT VARIABLES, MODEL RESULTS, ECONOMIC SURVEYS, INTERNATIONAL TRADE, ECONOMETRIC ANALYSIS, VALIDITY, DESCRIPTION, VALUE, DEPENDENT VARIABLE, POISSON DISTRIBUTION, DISTRIBUTION FUNCTION, LIKELIHOOD RATIO, ERROR TERMS, GAMMA DISTRIBUTION, INDEX, COEFFICIENT VECTOR, EXPECTED VALUE, DEPENDENT VARIABLES, RESEARCHERS, AGRICULTURE, CORRELATION, EQUATIONS, STANDARD NORMAL DISTRIBUTION, SAMPLES, ERROR TERM, MEASUREMENT, ECONOMIC THEORY, CONSTANT VARIANCE, ASYMPTOTICALLY EQUIVALENT, SURVEYS, ECONOMICS, ECONOMIC MODELS, CASE, LOG-LIKELIHOOD FUNCTION, HETEROSCEDASTICITY, INTEGER VALUES, FIXED EFFECTS, FUNCTIONAL FORMS, JOURNAL OF ECONOMETRICS, TRADE, GDP, THEORY, BILATERAL TRADE, STATISTICS, EVALUATION, STATA, TRADE THEORIES, PRECISION, STANDARD, ERROR, WEBSITE, SAMPLE SELECTION, MAXIMUM LIKELIHOOD ESTIMATOR, HOMOSCEDASTICITY, LINEAR PROBABILITY MODEL, RANDOM VARIABLE, LINEAR REGRESSION, ECONOMIC STATISTICS, DEVELOPMENT POLICY