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A Case for Flexibility in Explaining Agricultural Trade Distortions?
Pravin Trivedi and Will Martin
1 June 2011
A Case for Flexibility in Explaining Agricultural Trade Distortions?
A number of recent studies use the Grossman and Helpman (1994) and other political-economy
models such as the median-voter approach (Mayer 1984) to explain patterns of agricultural
protection across countries and over time. A key feature of this literature is the use of theoretical
models to derive simple estimating equations that can be confronted with data on key economic
features such as the level of income, the degree of economic inequality and measures of political
ideology. An excellent set of studies in Anderson (2010) apply the latest techniques to the data
on rates of agricultural protection collected in the course of a large World Bank sponsored study
of agricultural distortions.
The typical approach used in this literature involves the use of standard regression
techniques for cross-sectional or pooled time-series, cross-sectional data. One potential problem
with this approach is the risk of distortions in statistical inference resulting from the very skewed
nature of the dependent variable. If we focus on the key Relative Rate of Assistance to
Agriculture (RRA) variable in the agricultural distortions database, we see in Figure 1 that this is
extremely skewed in its distribution. Around 90 percent of the observations on RRA are between
-1 and +1 but the remaining 10 percent are between 1 and 3. One concern is that these "outliers"
may have large leverage on some coefficients of the regression models given that the widelyused OLS estimator is known to be sensitive to large outliers.
There are a priori reasons for considering more flexible specifications and estimators.
Dutt and Mitra begin with pooled ordinary least squares (OLS) as their estimator of the panel
model, but they also consider random and fixed effect estimators. However, all their
specifications assume that the parameters are constant throughout the population. It is more
flexible, and potentially more informative, to consider models which permit unobserved
heterogeneity in the relationship between RRA and its determinants. Countries could be
characterized as falling in different latent groups or classes, and coefficients of regressions could
vary systematically according to these classes. For example, in a model with (say) two latent
classes the relationship between RRA and per capita GDP may be stronger in one group than the
other, or the role of some political variables may be negligible in one case but not the other.
Investigation along these lines requires specification of a latent class or finite mixture model
(FMM). A specific example is a mixture of normals, which is quite flexible.
Figure 1. The distribution of the Relative Rate of Assistance to Agriculture
Source: www.worldbank.org/agdistortions
The purpose of this paper is to relax the assumption that the coefficients on key
explanatory variables are constant throughout the population when the endogenous variable is
distributed in such a skewed manner. To do this, we focus on the Dutt and Mitra (2010) model
because it builds on a wide range of contributions to this literature, ingeniously nesting several
key political economy models, including the median-voter model, political-economy models and
key variables from the earlier literature on the political-economy of agricultural protection, such
as the share of agriculture in the economy identified as potentially important by Anderson ( ).
We examine the potential implications of using two flexible modeling approaches: the Finite
Mixture Model (FMM) introduced by Deb and Trivedi (1997) and quantile regression ( ). We
ask particularly whether it result in different estimates for different groups of countries, and
whether it is superior in terms of its ability to explain the patterns in the data.
The Model
Dutt and Mitra (2010) put forward several potential frameworks for testing hypotheses about the
inter-country and inter-temporal variation and evolution of agricultural protection. Their first
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model involves the level of per capita income and the reported ideology of the government.
They find that both the political ideology of the government and the degree of inequality are
important determinants of agricultural protection. If labor is assumed to be mobile across sectors,
the model generates a potentially testable hypothesis that the leftist ideology variable will have a
positive coefficient and the interaction will have a negative coefficient under the HeckscherOhlin model, where labor is mobile between agriculture and other sectors. If, by contrast, labor is
immobile, the coefficient on leftist ideology will be negative and that on the interaction term
positive.
Dutt and Mitra's analysis begins with the following regression model:
agprotct  1(percapita
income)ct  2 (Ideology)
 3 (percapita
income* Ideology)
 ct (1)
As set out in Table 1, the dependent variable is the relative rate of protection (RRA). This is
derived from the nominal rate of assistance (NRA) as follows: RRA =
100*[(100+NRAag)/(100+NRAnonag ) - 1]. The ideology variable refers to the political ideology
of the chief executive and is taken from the Database of Political Institutions. In addition to
ideology, the authors try several other political variables: gini (a measure of inequality in land
ownership); rural (a dummy = 1 if the chief executive's party can be classified as rural); a
measure of the share of agriculture in employment; system - a measure of extent of
institutionalized constraints on the decision-making powers of chief executives.
One practical issue in estimation and model comparison comes from having non-uniform
data coverage across countries. The Dutt-Mitra data set is constructed by merging data from
other sources with those from Anderson et al. But some variables, such as the inequality variable
gini, are only available for a handful of countries. Consequently, depending on whether such
variables are retained in the estimation sample, the number of available observations can vary
substantially across specifications, causing loss of precision and difficulties in model
comparison.
The first step in the analysis reported in this paper was to replicate the Dutt and Mitra
(2010) analysis. This was done successfully and the detailed results are presented in Appendix 2.
In DM's analysis the variable lpcgdp (log of per capita GDP) is a consistent and robust
performer. Results indicate a robust positive association between per capita GDP and RRA, with
the coefficient estimate being between around 0.56 in the OLS regressions based on Model 1.
The ideology variable is positive, and the interaction term between ideology and income is
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negative, consistent with immobility of labor. When country and year fixed effects are
introduced, this coefficient falls to approximately 0. 35, as is the case when a random effects
model is used. In the latter cases, the ideology variables become insignificant.
Political variables like rural and system2 and have rather patchy performance. This
overall feature persists even when random effects models are estimated in place of pooled OLS.
In their fixed effect specification, however, there is some support for rural (a dummy for a
rural party in power) and system 2 (a dummy for a presidential system) having a positive impact
on RRA.
Finite Mixture Models
This specification uses a discrete representation of unobserved (neglected) heterogeneity. This
generates a class of models called finite mixture models (FMM) -- a particular subclass of latent
class models. This model, introduced by Deb and Trivedi (1997), is related to the two-part
models involving some zero observations and some with non-zero observations whose value is to
be explained. However, they make a less sharp distinction into different components of the
sample distinguished by the distributions characterizing them.
A two-component FMM specifies that the density of the dependent variable y is a linear
combination of two different densities, where the j th density is f j ( y |  j ) , j  1, 2,...,m .
Thus an m -component finite mixture is distributed according to:
f ( y | , )   j 1  j f j ( y |  j ),
2
0   j  1,

m
j 1
 j  1.
A simple example is a mixture of two normals, N ( 1 (x), 12 ) and N (2 (x),  22 ). This may
reflect the possibility that the sampled population contains two types of cases, whose y
outcomes are characterized by distributions f1 ( y | x, 1 ) and f 2 ( y | x, 2 ) that are assumed to
have different moments. The mixing fraction  1 is in general an unknown parameter to be
estimated in the analysis. In a more general formulation it too can be parameterized in terms of
observed variable(s) z.
Quantile Regression
Another flexible framework is quantile regression (QR). QR accommodates the possibility that
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the response of RRA to its determinants varies at different points in the conditional of RRA.
Thus QR can also handle the case in which RRA is more sensitively related to explanatory
variables such as per capita GDP or political variables at different levels of the dependent
variable. While the two approaches are quite distinct, they both imply a non-additive form of
heterogeneity—that is they both allow different responses to determinants in different parts of
the distribution of RRA.
The standard linear regression is a useful tool for summarizing the average relationship
between the outcome variable of interest and a set of regressors, based on the conditional mean
function E [ y | x] . This provides only a partial view of the relationship. A more complete picture
would provide information about the relationship between outcome y and regressors x at
different points in the conditional distribution of y. Quantile regression (QR) is a statistical tool
for building just such a picture.
Results from FMM Analysis
If we begin with a model like equation (1), we can use the full sample, and compare the results
with those from Dutt and Mitra. In this case, the sample is divided into two components—one
accounting for 21 percent of the sample and another accounting for 79 percent of the sample. In
the smaller component, the coefficient on income is very high, at 0.875. Those on ideology and
the ideology have the same sign and order of magnitude as in the Dutt-Mitra OLS results, but are
only significant at the 0.15 percent level. In the larger sample of Component 2, only the real
income variable is significant and the coefficient on this variable is only 0.256.
A two-component FMM specification that including gini ("comprehensive model") was
estimated using a rather small sample only (417 observations). This model also supports the
inference hypothesis that the population data are a mixture of two components, in this case with
one comprising 89% of the sample and the remaining about 11%. In the larger group, the RRA
is less sensitively associated with per capita GDP than in the smaller; but it is negatively
associated with gini and the share of agriculture in employment ( agempshare ) . The larger
group shows a negative association between RRA and gini , and RRA and agempshare , and
RRA and system 2 (presidential system). The smaller group by contrast shows no significant
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relation with gini , agempshare, and a significant positive relationship with system 2. This
illustrates how potential diversity may camouflage or mitigate the impact of a variable when
parameter variation is not modelled.
A parsimonious version of the FMM model was estimated for a sample of 1203
. In this case the
observations with just three regressors: ( lpcgdp, agempshare, ideology 
estimates split the population into two groups with about 21 percent in the first group and the
rest in the second. In the first group, lpcgdp has a coefficient of 1.49 compared with that of
0.20 in the second. The coefficient of agempshare in the first group is 4.23 and highly
significant, compared with  .18 in the second group. The variable ideology is statistically
insignificant in both groups. These results again highlight the diversity in the role of both
political and economic variables.
What do the two groups correspond to? Can we attach some sort of label to the two
groups to improve our understanding of the results? This is indeed possible by doing an analysis
of posterior probabilities. But preliminary analysis suggests that the small group is characterized
by high average RRA (greater than 1) and the large one by a much lower average RRA (less than
0.2). In this sense we could label the small group as more protectionist than the large group.
Results from QR
The application of QR to the RRA analysis is very preliminary and is restricted to just two
specifications. In the first case, the specification is parsimonious with just two regressors (
lpcgdp, and agempshare); in the second case we added two more regressors ( rural and
system2). The regressions were estimated at 4 separate quantiles q  .25, .50, .75, and .90.
The sample size is 1662 for the first specification and 1650 for the second.
The results show significant parameter variation across conditional quantiles of RRA.
The coefficient of the most robust regressor, lpcgdp , is nearly 4 times smaller at the q  .25
quantile compared with q  .90. That is, the sensitivity of RRA to per capita GDP is much
lower at low values of RRA than at higher values. At all quantiles, a higher share of agricultural
employment ( agempshare ) is associated with a lower RRA. Having a ruling rural party is
associated with higher RRA except in the highest quantile, and having a presidential system (
system 2 ) is associated with a lower RRA especially at the lowest quantiles. These results are
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broadly consistent with those from the FMM specification with the same regressors. They are
also broadly consistent with the analysis of Dutt and Mitra, with the qualification that the results
of FMM and QR are more nuanced and capture a greater diversity in the response of RRA to its
determinants. These results also warn us that greater care should be exercised in interpreting
results from least squares regressions that do not attempt to control for heterogeneity of behavior.
Conclusions
There are a priori reasons for considering more flexible specifications and estimators. DM use
pooled OLS as their estimator of the panel model, but they also consider random and fixed effect
estimators. However, all their specifications assume that the parameters are constant in the
population. It is more flexible, and potentially more informative, to consider models which
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permit unobserved heterogeneity in the relationship between RRA and its determinants.
Countries could be characterized as falling in different latent groups or classes, and coefficients
of regressions could vary systematically according to these classes. For example, in a model with
(say) two latent classes the relationship between RRA and per capita GDP may be stronger in
one group than the other, or the role of some political variables may be negligible in one case but
not the other. Investigation along these lines requires specification of a latent class or finite
mixture model (FMM). A specific example is a mixture of normals, which is quite flexible. Both
this model and the quantile regression model reveal a great deal of important heterogeneity in the
response of agricultural protection rates to the income level in the country, and key politicaleconomy explanators of protection.
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References
Anderson, K., M. Kurzweil, W. Martin, D. Sandri and E. Valenzuela (2008), “Measuring
Distortions to Agricultural Incentives, Revisited”, World Trade Review 7(4): 1-30.
Anderson, K. and E. Valenzuela (2008), ‘Global Estimates of Distortions to Agricultural
Incentives, 1955 to 2007’, database available at www.worldbank.org/agdistortions.
Beck, T., G. Clarke, A. Groff and P. Keefer (2001), ‘New Tools in Comparative Political
Economy: The Database of Political Institutions’ World Bank Economic Review 15(1):
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Deb,P. and Trivedi, P. (1997), ‘Demand for Medical Care by the Elderly: A Finite Mixture
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Deininger, K. and L. Squire (1996), ‘A New Data Set Measuring Income Inequality’,World Bank
Economic Review 10(3): 565-91.
Dutt, P. and Mitra, D. (2010), ‘Explaining Agricultural Distortion Patterns: The Roles of
Ideology, Inequality, Lobbying and Public Finance’ in Anderson, K. ed. The Political
Economy of Agricultural Protection, Cambridge University Press, Cambridge.
Findlay, R. and Wellisz , D.(1982), ‘Endogenous Tariffs, the Political Economy of Trade
Restrictions, and Welfare’, in J. Bhagwati (ed.), Import Competition and Response,
Chicago and London: University of Chicago Press.
Grossman, G.M. and Helpman, E. (1994), ‘Protection for Sale’ American Economic Review 84:
833–50.
Li, H., L. Squire and H. Zou (1998), ‘Explaining International and Intertemporal Variations in
Income Inequality’ Economic Journal 108(446): 26–43.
Marshall, M.G., K. Jaggers and T.R. Gurr (2000), ‘Political Regime Characteristics and
Transitions, 1800-2002’, Polity IV Project, Center for International Development and
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Mayer, W. (1984), ‘Endogenous Tariff Formation’ American Economic Review 74: 970–85.
World Bank (2007), World Development Indicators 2007, World Bank, Washington DC.
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Appendix 1: Data Sources for the Analysis
Variable
Relative Rate of Assistance
to agriculture (RRA)
Nominal Rate of Assistance
to agriculture (NRA)
Political Ideology
Income Inequality
Land Inequality
Per capita GDP
Share of agriculture in
employment
Comparative Disadvantage
in Agriculture
Direct taxes (% of total
taxes)
Constraints on Executive
Rural party
Years
Description
1955-2007 Anderson and Valenzuela (2008). (Methodology in Anderson
et al. 2008.)
1955-2007 Anderson and Valenzuela (2008). (Methodology in Anderson
et al. 2008.)
1975-2000 Political Ideology of chief executive (the President for
Presidential systems and largest ruling party for Parliamentary
system). Source: Database of Political Institutions 2004
(update of Beck et al. 2001).
1960-1999 Gini coefficients from Dollar and Kraay (2002) and Deininger
and Squire (1996, 1998). Data for the latter at
www.worldbank.org/research/inequality/data.htm
One year
Land Gini from Li, Squire and Zou (1998).
1960-2000 GDP per capita on a PPP basis. Source: World Bank (2007).
1960-2000 Total workers employed in agriculture as a proportion of labor
force. Source: World Bank (2007).
1960-2000 Measured as (X-M)/(X+M) where X is exports of agricultural
products and M is the imports of agricultural products.
1970-2000 Direct taxes include income taxes, profits and capital gains
tax. Source: World Bank (2007).
1960-2000 Extent of institutionalized constraints on the decision-making
powers of chief executives, whether individuals or
collectivities. Source: Polity IV Project, (Marshall, Jaggers
and Gurr 2000).
1975-2000 Dummy equals 1 if chief executive’s party can be classified as
rural. Source: Database of Political Institutions 2004 (update
of Beck et al. 2001).
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Appendix Table 2. Replicating the results of Dutt and Mitra
h
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Appendix Table 3. Estimating the Finite Mixture Model
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