Estimating an Import Demand Systems using the Generalized Maximum Entropy Method Santosh R. Joshi *,1,2 , Kevin Hanrahan 2 , Eithne Murphy 1 , and Hugh Kelley 1 1 Department of Economics, National University of Ireland, Galway. 2 Rural Economy Research Center, TEAGASC, Athenry Abstract The Generalized Maximum Entropy (GME) method is used to esti- mate import demand systems with many equations. The GME method allows for estimation of models, which due to paucity of data, are ill- posed (when the number of unknown parameters exceeds the number of data points) and/or ill-conditioned (where, for example, there are linear dependencies among the set of explanatory variables used in estimation). Such problems are common when estimating the parameters of trade mod- els. This paper uses the GME method to estimate the parameters of an Almost Ideal Demand System (AIDS) specification of import demand sys- tems. The regularity conditions required by microeconomic theory, i.e. adding up, homogeneity, symmetry and concavity conditions are all ex- plicitly imposed in the estimation the model parameters. These economic regularity conditions have to be satisfied if the parameters estimates are to be used in the parameterisation of an applied general equilibrium (AGE) model. The AIDS import demand systems are estimated for two very differ- ent types of products, electronic goods and cereals. The choice of such contrasting goods was deliberate as it reveals the advantages of adopting a flexible functional form specification, such as the AIDS, over more re- strictive traditional trade specifications such as the CES based Armington * Correspondence Author, email: [email protected]1
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Estimating an Import Demand Systems using the
Generalized Maximum Entropy Method
Santosh R. Joshi∗,1,2, Kevin Hanrahan2, Eithne Murphy1, and
Hugh Kelley1
1Department of Economics, National University of Ireland, Galway.
2Rural Economy Research Center, TEAGASC, Athenry
Abstract
The Generalized Maximum Entropy (GME) method is used to esti-
mate import demand systems with many equations. The GME method
allows for estimation of models, which due to paucity of data, are ill-
posed (when the number of unknown parameters exceeds the number of
data points) and/or ill-conditioned (where, for example, there are linear
dependencies among the set of explanatory variables used in estimation).
Such problems are common when estimating the parameters of trade mod-
els. This paper uses the GME method to estimate the parameters of an
Almost Ideal Demand System (AIDS) specification of import demand sys-
tems. The regularity conditions required by microeconomic theory, i.e.
adding up, homogeneity, symmetry and concavity conditions are all ex-
plicitly imposed in the estimation the model parameters. These economic
regularity conditions have to be satisfied if the parameters estimates are to
be used in the parameterisation of an applied general equilibrium (AGE)
model.
The AIDS import demand systems are estimated for two very differ-
ent types of products, electronic goods and cereals. The choice of such
contrasting goods was deliberate as it reveals the advantages of adopting
a flexible functional form specification, such as the AIDS, over more re-
strictive traditional trade specifications such as the CES based Armington
It is necessary to have estimated functional forms used in the applied general
equilibrium models should satisfy curvature conditions. Jorgenson and Frau-
meni (1981) applied their version of Lau’s (1978b) method of imposing curva-
ture conditions in their 36 industry translog study of U.S. industries, they ended
up setting 204 out of 360 second order parameters equal to zero. Moreover, al-
though their method imposes curvature conditions globally, it does so at the
cost of flexibility (Diewert and Wales, 1987). Concavity plays an important role
when predicting future consumption patterns when price levels are expected to
change and when conducting policy analysis that depends on price elasticities.
The growth in the use of applied general equilibrium models (e.g. GTAP) and
partial equilibrium models (e.g. CAPRI or FAPRI) to analyse the trade poli-
cies, it needs to be ensured that price and income elasticities are estimated in a
theoretically consistent manner (Cranfield and Pellow, 2004).
Elasticities
The parameters of the AIDS cannot be used for useful economic interpretations.
So, it is required to calculate the expenditure and price elasticities from those
parameters. The expenditure elasticities at the sample mean is
εki = 1 +βkiski. (10)
7
Marshallian price elasticities at the sample mean is
ηkij = −δij +γkijski− βkiski
(αkj +∑k
γkjklogPkk ) (11)
where δij = 0 for i 6= j and δij = 1fori = j.
Hicksian price elasticities is given by
εkij = ηkij + εiskj (12)
3 Generalized Maximum Entropy method
The traditional maximum entropy (ME) method is based on the information
theory developed by Shannon(1948). Shannon defined entropy as the measure
of uncertainty (state of knowledge) of a collection of events. Let x be a random
variable with possible outcomes xs, s = 1, 2,...N, with probabilities qs such that∑s qs = 1. Shannon defined the entropy of the distribution q = (q1, q2, ...qs), as
H(q) = −∑s
qslnqs (13)
when, qs = 0 then H(q) = 0 and when q1 = q2 = .... = qs = 1/N then H(q) is
maximum. To determine the probability assigned, Jaynes (1957a, 1957b) pro-
posed maximum entropy principle which is to maximize entropy subject to the
available sample moment information and the requirement that the probablili-
ties be proper (added to one).
Golan et al. (1996) proposed Generalized Maximum Entropy by specifying
error term in maximum entropy framework. The GME method uses a flexible,
dual loss objective function: a weight average of the entropy of the deterministic
part of the model and the entropy from the disturbance or stochastic part (Golan
et. al 1996). Different weight could be given to deterministic and stochastic
part of the model. Intuitively, giving the higher weight to deterministic part
will allow data to speak more. Balanced approach is used in this paper where
equal weight is given to both objectives. ME is special case of the GME where
no weight is placed on the entropy of the error terms and where the data are
represented in terms of exact moments.
8
In generalized maximum entropy formulations, we define ill-posed pure in-
verse problem as
y = Xβ + e (14)
where y is a T- dimensional vector of observables, β is a (K > T )-dimensional
vector of coordinates that reflects the unknown and unobservable coefficients,
and X is a linear operator that is a known (T x K) non-invertible matrix. e is
T- dimensional vector of unobserved disturbance.
β is defined by support space Z and probability q. Consistent with this
specification, rewrite β as
β = Zq (15)
where Z is a (K ×KM) matrix and q is a KM dimensional vector of weights.
For each βk, there exists a discrete probability distribution that is defined
over the parameter space [0,1] by a set of equally distanced discrete points
z = [z1, z2, ...., zM ] with corresponding probabilities qk = [qk1, qk2, ....., qkM ]
and with M ≥ 2. So, βk can be expressed as convex combination of M- dimen-
sional vector of support points of zk and M- dimensional positive weights qk
that sums to one.
β = Zq =
z′
1 0 . . 0
0 z′
2 . . 0
. . . . .
. . . . .
0 . . . z′
k
q1
q2
.
.
qk
z′
kqk =∑m
zmqkm = βk (16)
for k = 1,2 ,...,K, m = 1,2,...,M
Similarly, the vector of disturbance e can be defined as
e = Vw (17)
where V is a (T x TJ) matrix and w is a TJ dimentional vector of weights.
For each et is convex combinations of J-dimensional vector of support space
vT and J-dimensional positive weights wT that sums to one. The T unknown
9
disturbance e may be written in matrix form as
e = Vw =
v′
1 0 . . 0
0 v′
2 . . 0
. . . . .
. . . . .
0 . . . v′
T
w1
w2
.
.
wT
eT = v′TwT =
∑J
vtJwt (18)
The natural support vector for the error term v = (−1, 0, 1) because all the
dependent variables are shares that lie between 0 and 1.
Using reparameterized unknowns β = Zq and e = Vw,
y = Xβ + e = XZq + Vw (19)
The objective of the generalized entropy problem is to recover the unknown
parameters through the sets of probabilities, q and w. At the optimal solution,
the probabilities must satisfy the model or consistency constraints additivity
constraints. Accordingly, Golan et. al (1997) propose a generalized maximum
entropy solution to the linear inverse problem with noise that selects q, w >> 0
to maximize
H(q,w) = −q′lnq−w
′lnw (20)
subject to
y = XZq + Vw (21)
1k = (IK ⊗ 1′M)q (22)
1T = (IT ⊗ 1′J)w (23)
The Generalized Maximum Entropy objective is strictly concave on the in-
terior of the additivity constraints set, and a unique solution exists if the inter-
section of the consistency and additivity constraints sets is non-empty. GME
selects probabilities on supports Z and V that are most uniform (i.e. uncertain)
and satisfy the observed information. The optimal probability vectors, q and w,
may be used to form point estimates of the unknown parameter vector, β = Zq,
and the unknown disturbances, e = Vw.
10
The choice and dimension of the support space on the parameters and error
term is discussed in Golan et al. 1996 (chapter 8). The choice of support
space on the parameters i.e. the restrictions imposed on the parameter space
through Z reflect prior knowledge about the unknown parameters. However,
such knowledge is not always available, and researchers may want to entertain
a variety of plausible bounds on β . Wide bounds may be used without extreme
risk consequences if our knowledge is minimal and we want to ensure that Z
contains β . Intuitively, increasing the bounds increases the impact of the data
and decreases the impact of support. The dimension of the support space on the
parameters and error. The increase in the number of points in the support and
allocate them in the equidistant fashion, the variance of the uniform distribution
decreases. The greatest improvement in precision comes from using the M and
J to be 5.
The computation of asymptotic standard errors for estimated coefficients is
also possible and may facilitate a more conventional inference apporach. The
assumptions and calculation of asymptotic standard error is described in the
Appendix I.
Substituting these reparameterized terms in the AIDS specification,
Skit =∑b
akibckib +
∑j
∑d
zkijdqkijdlogP
kjt + zkdq
kidlog(
µktP kt
) +∑h
vhwith (24)
Here, b, d and h is dimensions of the support space c, q and w respectively.
GME adding up conditions,∑d
qkijd =∑d
qkid =∑h
wkith = 1 (25)
So GME estimator for AIDS is to maximize
H(q,w) = −q′lnq−w′lnw (26)
subject to import share equations (equation 24 ), GME adding up condition
(equation 25) and constraints from consumer demand theory (equations 5, 6,
7 and 9). Forming the Lagrangean and solving for the first order conditions
yields the optimal solution qhat and what. Then estimates of the AIDS can be
determined by
αki =∑b
akibckib (27)
11
γkij =∑d
zkijdqkijd (28)
βki =∑d
zkidqkid (29)
ekit =∑d
vkithwkith (30)
These estimates are then used to calculate the expenditure elasticities and
Hicksian own and cross price elasticities using equations 10 and 12 respectively.
4 Data
More heterogenous goods (electronics) and relatively homogenous goods (cere-
als) are chosen for the estimation in view of capturing both complementary and
substitution relationships that may exists in complex trading pattern. Cere-
als sector used in this paper is the aggregation of GTAP sectoral Classification
(GSC2) No. 1, 2 and 3. Electronic goods used in this paper is GTAP Sectoral
Classification (GSC2) No. 40 with the view of using these estimates in GTAP
model. Data used in this paper is taken from UN COMTRADE database of
the classification Standard International Trade Commodity (SITC) Rev3 data
at 4 digit level and aggregated to map at GTAP Sectoral Classification level.
Yearly data of import from the period 1988 - 2008 are used to estimate for both
the sectors. Eleven regions are chosen for electronic sector are Brazil, China,
DEDC (Group of Developed Countries), India, Ireland, LDC (Group of Least
Developed Countries), REU15 (Rest of the EU 15), REU27 (Rest of EU 27),
RWorld (Rest of the World), UK and USA 1. It would have been better to
compare between electronic goods and cereals if trade data of cereals for all
the eleven regions was available but unfortunately, it seems there is no bilateral
trade between some of the regions for cereals. So, only five regions chosen for
cereals sector are Ireland, UK, DEDC, REU15, and RWorld. Data are in terms
of Values (dollars) and Quantities (kg). Price are calculated as the ratio of val-
ues to quantities at SITC Rev3 4-digit level. Then the price at the aggregation
level of GTAP is calculated using the weighted average at the price level of SITC
Rev3 4-digit level.1This aggregation of different region is followed from the Horridge and Labrode (2008) for
their TASTE program
12
In this paper, we estimate with the assumption of the separability between
domestic and imported products. Eventhough, this assumption of separability
between domestic and imported products have already been questioned (Win-
ters, 1984), domestic product could not be included in the estimation typically
because data for domestic product is not available in the same classification as
SITC Rev3.
5 Results
GME estimates are estimated by maximizing the entropy function subject to
constraints of AIDS specification, GME adding up condition for probabilities
and consumer demand theory restrictions of adding up, homogeneity, symme-
try and concavity. The AIDS parameters are calculated using equations 27,
28 and 29. The parameters estimated for the AIDS model have no economic
meaning in themselves. So, the Hicksian own and cross price elasticities and
expendtiture elasticites (refer Table 1 for cereals and Table 2 electronics goods)
are calculated at the sample mean . With the concavity imposed, all the own
price elasticites are negative for both the cereals and electronics goods as ex-
pected. In the import of cereals and electronics goods by different countries,
both complementary and substitution between the pair of countries are seen.
More complementary pair of countries are found in electronic goods than in
cereals (only 7 pairs of countries are complementary out of 30 pairs in cereals
and 420 pairs of countries are complementary out of 990 pairs of countries in
electronics goods). Parameters estimated are shown in tables of Appendix II.
About one third of the parameter estimated are statistically significantly differ-
ent from zero on the basis of asymptotic t-statistics (refer tables in appendix
II). Asymptotic standard errors are calculated as described in Appendix I and
have to interpreted with cautious in the GME context.
It is found that estimated parameters are sensitive to support vector chosen
to parameters. This in turn has an impact on the other calculated values of
expenditure, own and cross price elasticities showing changes sign as well as
magnitude. Sensivity of support vector to the parameter estimated is done
in this paper. First, support vector for α is selected as [-1,-0.5,0,0.5,1] and
13
Figure 1: Hicksian Own and Cross Price Elasticities Cereals
support vector for both γ and β are chosen as [-1,-0.5,0,0.5,1], [-5,-2.5,0, 2.5,5],
[-20,-10,0,10,20] and [-100,-50,0,50, 100] consecutively to see the effect on the
estimated parameter. It is found that there is only some changes in estimated
parameter. Then, support vector for α is chosen as [-100,-50,0,50, 100] and for
both γ and β is selected as [-1,-0.5,0,0.5,1], [-5,-2.5,0, 2.5,5], [-20,-10,0,10,20] and
[-100,-50,0,50, 100] consecutively. It is found that at the higher support vector
of α, estimated parameter differ widely in first two support vector of γ and β
in both magnitude and direction but for later two support vectors, difference
in estimated parameter is very less. It would appear therefore that the selected
support vectors clearly influence on the estimated values. So,the results in the
estimation shown are estimated using wider support vector of [-100,-50,0,50,
100] for α, γ and β. If no prior information about the parameter, it is also
suggested that to chose the wider support vectors such that it is wide enough
to include all the possible outcomes (Golan et al. 2001). The natural support
vector for the error terms is [-1,-0.5,0,0.5,1] as all the dependable variable is
shares that lies between 0 and 1 in our model.
All of the own price estimates of cereals have a negative sign and appear to
be sensible in terms of magnitude of the estimates. The cross price estimates
for cereals have both negative and positive signs implying complementary and
substitution relationships. Most of the cross price elasticity are positive. The
results shows that there are only few negative cross price elasticities. Further-
14
Figure 2: Hicksian Own and Cross Price Elasticities for Electronic goods
15
more, negative cross price elasticities are mostly low except at very low import
shares. (refer fig 1 and table 1). In DEDC, cross price elasticities are all posi-
tive. In REU15 and UK, there is only one pair of countries that have negative
cross price elasticities. In RWorld and USA, there are two and three pairs of
countries that are complementary respectively. These cross price elasticities are
asymmetric meaning that the change in price of US cereals in import demand
of UK cereals in DEDC is different than the change in price of UK cereals in
import demand of USA cereals in DEDC.
Own, cross and expenditure elasticities for electronics goods of 11 importing
countries are shown in table 2. The results show that cross price elasticities
are in very diverse range. At low import shares from 0 to 0.001, the cross
price elasticities are on the very high range, at import shares from 0.01 to 0.001
cross price elasticities are on high range, at import shares from 0.1 to 0.01 and
0.1 to 0.8 cross price elasticities range is moderate (refer figure 2). Own price
elasticities are all negative as expected. The own price elasticities at low import
shares below 0.02 starts to decrease exponentially. Above the 0.02 import share,
own price elasticities is usually within -2. It can be clearly seen from the results
that import shares have a huge affect on the own and cross price elasticities of
electronic goods.
Expenditure elasticities of cereals and electronic goods are in all the three
categories (refer table 1), above 1 (superior goods), between is 0 to 1 (normal
goods) and below 0 (inferior goods). For DEDC as importing countries for ce-
reals, expenditure elasticities are all negative except for USA . And for REU15,
it is all positive and above 1 for DEDC, RWorld and UK and below 1 for USA
cereals. Refer table 1 and table 2 for expenditure elasticites for cereals and
electronic goods respectively. The result shows that the superior goods in one
country could be inferior in the other country. For instance, LDC product may
be considered to be inferior in Brazil while superior in China. It is possible that
different quality of goods is imported by different countries. Clearly, import
shares have influence in the expenditure elasticies of electronic goods as well.
16
Table 1: Hicksian Own and Cross Price Elasticities for Cereals
Importing Country: DEDC
Price Elasticities Expenditure
Elasticities
REU15 RWorld UK USA
REU15 -1.747 0.050 0.086 1.611 -2.718
RWorld 0.070 -2.180 0.020 2.090 -0.095
UK 1.737 0.291 -4.141 2.114 -7.791
USA 0.081 0.075 0.005 -0.162 1.249
Importing Country:REU15
DEDC RWorld UK USA
DEDC -1.296 0.134 -0.390 1.552 1.378
RWorld 0.071 -3.337 1.997 1.270 1.560
UK -0.250 2.434 -2.185 0.001 1.040
USA 0.768 1.195 0.001 -1.964 0.255
Importing Country:RWorld
DEDC REU15 UK USA
DEDC -1.280 -0.014 -0.011 1.305 1.403
REU15 -0.024 -0.235 0.226 0.032 0.235
UK -0.157 2.018 -1.952 0.091 -0.391
USA 0.577 0.009 0.003 -0.589 1.071
Importing Country:UK
DEDC REU15 RWorld USA
DEDC -0.393 0.385 0.158 -0.269 1.293
REU15 0.076 -0.400 0.005 0.198 1.054
RWorld 0.430 0.072 -1.846 1.224 4.335
USA -0.556 2.066 0.927 -2.557 -2.697
Importing Country:USA
DEDC REU15 RWorld UK
DEDC -0.240 0.179 -0.014 0.075 1.206
REU15 1.406 -1.698 0.417 -0.124 -0.685
RWorld -0.105 0.392 -0.167 -0.119 1.263
UK 26.510 -5.598 -5.710 -15.202 -8.644
17
Table
2:
Hic
ksi
an
Ow
nand
Cro
ssP
rice
Ela
stic
itie
sfo
rE
lectr
onic
pro
duct
Importin
gC
ountry:
Brazil
Pric
eEla
stic
itie
sExpendit
ure
Ela
stic
itie
s
Chin
aD
ED
CIn
dia
Irela
nd
LD
CR
EU
15
REU
27
RW
orld
UK
USA
Chin
a-1
.780
-0.0
63
-0.1
03
-0.4
62
-0.1
21
-0.1
62
-0.4
27
-0.9
42
0.8
89
1.0
75
2.0
96
DED
C0.1
70
-1.5
94
0.0
99
0.0
50
-0.0
49
0.1
37
0.0
42
0.7
13
-0.5
86
1.1
37
-0.1
20
India
-12.0
64
42.8
93
-4.4
06
-5.4
84
0.0
92
7.9
35
-7.1
87
8.6
45
20.8
77
24.2
67
-75.5
69
Irela
nd
-8.5
46
2.2
76
-0.6
16
-6.0
75
-0.7
24
-0.2
81
-3.5
58
7.1
18
5.8
26
8.6
44
-4.0
64
LD
C-2
72.3
75
-120.1
48
1.6
61
-97.9
93
-67.4
90
66.2
33
-54.6
06
-166.6
16
-113.5
32
1493.2
43
-668.3
76
REU
15
-0.0
50
-0.0
11
-0.0
03
-0.0
37
-0.0
03
-0.9
41
0.1
75
0.1
01
0.0
71
-0.4
82
1.1
79
REU
27
-7.0
54
1.0
73
-0.6
88
-3.0
59
-0.3
57
3.5
88
-3.3
78
0.2
80
4.5
55
4.4
83
0.5
56
RW
orld
-0.3
11
0.0
57
-0.0
23
0.0
91
-0.0
43
-0.0
58
-0.0
03
-1.8
88
-0.2
90
0.4
07
2.0
60
UK
5.5
57
-9.7
45
0.8
01
2.1
42
-0.3
34
-0.8
52
1.9
65
-10.1
01
-11.3
83
7.3
36
14.6
15
USA
0.4
92
0.5
08
-0.0
02
0.1
03
0.1
28
-0.0
32
0.0
77
0.9
09
0.4
50
-2.6
65
0.0
32
Importin
gC
ountry:
Chin
a
Brazil
DED
CIn
dia
Irela
nd
LD
CR
EU
15
REU
27
RW
orld
UK
USA
Brazil
-14.8
53
-42.4
20
0.7
41
1.7
13
10.2
89
47.4
29
9.6
74
-4.3
04
10.2
91
11.4
97
-30.0
57
DED
C-0
.041
-1.0
30
-0.0
36
0.0
91
-0.0
63
-0.0
77
-0.1
01
0.9
73
0.0
58
-0.0
61
0.2
87
India
0.7
47
-27.9
07
-10.8
21
11.2
84
0.2
28
-15.7
95
-3.0
61
127.0
29
-5.4
17
-17.0
55
-59.2
33
Irela
nd
0.1
02
3.9
61
0.7
21
-3.0
50
-0.6
87
1.5
79
-0.0
96
-16.6
80
0.8
82
0.8
83
12.3
85
LD
C89.4
33
-886.4
76
1.7
99
-94.2
48
-363.1
32
-402.7
95
-311.2
07
1292.3
53
127.4
98
-221.9
40
768.7
24
REU
15
0.1
10
-0.1
54
-0.0
52
0.1
02
-0.0
94
-0.7
90
-0.1
56
0.9
67
0.0
40
0.0
26
0.0
02
REU
27
0.7
69
-10.8
02
-0.2
60
-0.0
88
-2.8
50
-5.4
04
-3.5
46
18.3
23
2.1
59
-1.7
67
3.4
66
RW
orld
-0.0
09
0.1
40
0.0
40
-0.0
72
0.0
82
0.0
20
0.1
02
-1.8
66
-0.0
56
-0.0
13
1.6
31
UK
0.2
11
1.8
30
-0.1
27
0.3
30
0.3
29
0.4
23
0.5
80
-1.4
92
-1.6
18
0.4
10
-0.8
75
USA
0.0
19
-0.1
64
-0.0
52
0.0
72
-0.0
38
0.0
00
-0.0
41
0.6
47
0.0
32
-0.7
42
0.2
67
18
Importin
gC
ountry:
DED
C
Brazil
Chin
aIn
dia
Irela
nd
LD
CR
EU
15
REU
27
RW
orld
UK
USA
Brazil
-22.1
66
25.3
27
-19.7
41
-7.0
92
9.0
86
24.2
72
2.2
87
-15.5
79
10.7
60
41.9
98
-49.1
53
Chin
a0.1
64
-0.6
40
0.1
55
-0.0
26
-0.0
89
-0.4
29
-0.0
41
-1.0
76
-0.2
06
-1.5
10
3.6
98
India
-57.6
26
86.1
30
-125.7
05
-52.8
69
52.8
60
68.4
92
6.2
46
90.8
13
31.1
48
171.5
04
-270.9
94
Irela
nd
-0.6
09
0.3
56
-1.5
16
-2.4
88
0.5
45
1.5
01
0.1
54
1.8
83
0.5
91
0.5
84
-1.0
03
LD
C103.7
59
-159.3
04
206.5
55
74.9
08
-260.7
89
-29.7
89
-12.6
50
-382.7
21
-101.7
31
217.3
71
344.3
91
REU
15
0.1
84
-0.1
58
0.1
28
0.1
59
0.0
07
-1.0
36
-0.0
34
-0.1
96
-0.2
34
0.0
55
1.1
22
REU
27
0.3
93
-1.4
31
0.3
20
0.2
68
-0.1
87
-1.4
25
-2.0
44
-3.3
76
-0.1
17
-0.1
54
7.7
54
RW
orld
-0.1
02
-0.0
64
-0.0
10
0.0
39
-0.0
67
-0.0
79
-0.0
15
-1.0
11
0.0
85
-0.0
72
1.2
96
UK
0.3
02
-0.4
42
0.2
51
0.2
23
-0.2
62
-0.7
74
0.0
18
1.0
46
-1.9
34
0.5
57
1.0
15
USA
0.0
83
-0.0
94
0.0
90
0.0
11
0.0
95
0.1
47
0.0
41
0.4
12
0.0
90
-0.8
45
-0.0
30
Importin
gC
ountry:
India
Brazil
Chin
aD
ED
CIr
ela
nd
LD
CR
EU
15
REU
27
RW
orld
UK
USA
Brazil
-3.9
30
0.7
55
-6.5
24
-2.8
76
2.0
41
-5.2
28
0.1
46
17.6
28
-2.4
06
-1.4
20
1.8
13
Chin
a0.0
03
-2.4
01
0.0
38
-0.3
70
-0.0
58
-0.3
39
-0.2
15
-0.3
19
0.1
98
0.2
32
3.2
30
DED
C-0
.030
0.4
19
-1.0
93
-0.0
43
0.1
34
-0.0
12
-0.0
92
0.2
55
0.0
26
0.3
41
0.0
95
Irela
nd
-0.5
20
-11.8
39
-2.9
24
-3.7
96
0.5
44
-0.2
27
-2.4
78
11.4
29
1.6
34
-0.8
29
9.0
07
LD
C12.0
08
-52.6
76
167.1
72
18.0
15
-38.5
71
-36.7
62
-2.0
35
-9.8
31
-30.8
83
5.1
07
-31.5
44
REU
15
-0.0
33
-0.0
87
-0.1
54
0.0
25
-0.0
44
-0.7
36
-0.0
25
0.0
18
0.0
36
-0.0
09
1.0
10
REU
27
0.0
32
-10.6
11
-6.7
72
-3.6
96
-0.0
98
-2.2
81
-4.2
10
14.8
31
0.4
39
0.8
57
11.5
09
RW
orld
0.0
33
0.1
92
-0.0
21
0.1
51
-0.0
07
0.0
21
0.1
32
-1.2
55
-0.0
66
-0.0
56
0.8
75
UK
-0.0
52
1.1
21
0.1
16
0.2
39
-0.1
20
0.2
31
0.0
68
-0.4
76
-0.8
84
-0.3
41
0.0
98
USA
-0.0
05
0.5
31
0.2
73
0.0
16
0.0
00
0.0
76
0.0
45
0.0
96
-0.0
74
-1.2
61
0.3
03
Importin
gC
ountry:
Irela
nd
Brazil
Chin
aD
ED
CIn
dia
LD
CR
EU
15
REU
27
RW
orld
UK
USA
Brazil
-87.4
75
81.5
58
-14.5
42
-4.0
93
-44.4
16
-53.8
56
65.9
29
-38.0
77
-61.4
78
219.3
75
-62.9
24
19
Chin
a0.2
11
-2.7
04
1.0
16
-0.0
71
0.6
57
-1.2
57
-0.3
73
-2.5
53
-0.0
67
0.5
40
4.6
01
DED
C-0
.036
1.0
11
-0.8
83
0.1
02
-0.1
66
0.0
05
0.3
32
1.2
00
-0.0
29
-0.2
31
-1.3
06
India
-1.0
89
-7.0
95
14.4
97
-10.6
00
6.4
29
-11.1
84
-6.5
21
12.8
92
-32.1
05
26.2
39
8.5
37
LD
C-6
.600
37.5
00
-11.9
04
3.6
47
-17.6
63
31.4
47
6.9
14
-1.1
39
10.9
04
-28.1
86
-24.9
21
REU
15
-0.0
71
-0.3
08
-0.2
49
-0.0
43
0.2
08
-1.3
18
-0.0
08
0.0
30
-0.3
91
0.8
96
1.2
53
REU
27
0.8
74
-1.8
60
1.9
53
-0.3
31
0.5
91
-0.6
66
-2.3
64
-1.6
42
0.2
00
-1.8
00
5.0
45
RW
orld
-0.0
38
-0.5
07
0.1
55
0.0
39
-0.0
36
-0.1
12
-0.0
49
-1.2
43
0.0
41
-0.3
61
2.1
13
UK
-0.0
61
0.1
96
-0.2
54
-0.0
95
0.0
30
-0.2
67
0.0
62
0.2
84
-0.9
68
-0.0
56
1.1
28
USA
0.1
56
0.4
71
-0.1
77
0.0
82
-0.1
72
0.8
78
-0.0
31
0.2
51
0.2
94
-1.2
12
-0.5
39
Importin
gC
ountry:
LD
C
Brazil
Chin
aD
ED
CIn
dia
Irela
nd
REU
15
REU
27
RW
orld
UK
USA
Brazil
-11.9
99
25.7
53
-24.1
69
4.9
38
-11.9
41
3.7
32
18.4
87
23.0
00
-5.7
19
0.9
29
-27.5
85
Chin
a0.7
84
-2.5
49
1.5
82
-0.6
79
0.3
86
-0.3
59
-3.4
92
-1.9
29
0.3
58
0.3
05
6.4
70
DED
C-0
.309
0.9
12
-1.6
86
0.1
24
0.1
63
0.2
31
1.3
61
0.7
58
-0.2
06
-0.2
60
-1.4
87
India
8.4
47
-38.0
65
13.0
15
-21.5
84
17.6
89
-8.1
54
-40.0
09
-25.8
74
32.5
96
24.1
49
44.7
98
Irela
nd
-0.3
07
0.4
87
-0.0
95
0.2
63
-1.0
45
0.0
74
-0.3
93
0.1
35
-0.4
88
-0.1
58
1.6
27
REU
15
42.4
37
-126.7
82
232.9
40
-53.5
89
37.1
24
-64.8
67
-254.2
78
-81.3
06
110.6
78
140.9
33
19.7
03
REU
27
0.0
28
-0.1
83
0.0
75
-0.0
51
-0.0
57
-0.0
84
-1.1
06
0.0
08
-0.0
14
0.0
04
1.4
53
RW
orld
1.2
14
-3.3
27
2.5
33
-0.7
90
-0.0
64
-0.3
92
-2.2
53
-4.4
36
1.1
02
-0.0
69
7.5
27
UK
-0.1
39
0.5
29
-0.4
10
0.3
66
-0.2
17
0.1
71
0.8
24
0.5
75
-1.0
68
-0.1
01
-0.8
21
USA
-0.0
24
0.5
00
-0.4
97
0.2
82
0.0
41
0.2
18
0.8
94
0.2
05
-0.1
03
-1.0
02
-0.8
00
Importin
gC
ountry:
REU
15
Brazil
Chin
aD
ED
CIn
dia
Irela
nd
LD
CR
EU
27
RW
orld
UK
USA
Brazil
-12.7
80
-5.8
25
32.0
75
-6.9
23
1.5
05
-5.9
17
2.4
85
6.9
80
-18.6
14
-7.7
89
14.8
03
Chin
a-0
.063
-0.6
71
-0.9
17
-0.1
15
-0.1
04
0.0
37
-0.3
21
-1.0
64
-0.8
09
-0.0
76
4.1
03
DED
C0.2
60
-0.0
64
-1.4
54
0.1
04
0.0
63
0.2
37
0.2
53
-0.0
40
0.1
78
0.6
44
-0.1
81
India
-11.0
76
-9.9
65
28.5
70
-49.4
22
24.7
93
6.5
67
-10.7
69
10.0
68
-1.3
41
45.4
39
-32.8
65
Irela
nd
0.0
71
-0.0
35
-0.0
82
0.5
08
-0.8
71
-0.0
22
-0.1
54
0.8
67
-0.5
97
-1.5
27
1.8
42
20
LD
C-9
6.5
25
47.8
45
523.5
23
66.6
06
-9.2
07
-143.9
79
4.0
92
-124.4
55
-40.0
11
-201.5
89
-26.3
01
REU
27
0.0
84
-0.7
15
0.0
69
-0.2
20
-0.2
31
0.0
04
-1.6
72
-1.4
27
-0.4
87
0.0
62
4.5
33
RW
orld
0.0
51
-0.0
63
-0.2
79
0.0
00
0.1
42
-0.0
38
-0.0
69
-0.9
94
0.1
02
-0.0
29
1.1
76
UK
-0.1
65
-0.1
77
0.2
03
-0.0
37
-0.0
98
-0.0
27
0.0
51
0.5
72
-0.4
37
0.1
04
0.0
10
USA
-0.0
41
0.4
03
0.6
85
0.1
94
-0.2
63
-0.1
00
0.2
53
0.3
67
0.1
12
-1.4
06
-0.2
05
Importin
gC
ountry:
REU
27
Brazil
Chin
aD
ED
CIn
dia
Irela
nd
LD
CR
EU
15
RW
orld
UK
USA
Brazil
-6.2
16
-8.4
41
-11.0
10
-5.2
24
14.5
93
1.2
80
19.1
28
-25.7
93
-0.4
81
15.9
79
6.1
84
Chin
a-0
.075
-1.2
46
-0.1
61
-0.2
24
-0.2
19
-0.2
69
-0.0
34
-1.6
70
0.3
69
0.3
47
3.1
84
DED
C-0
.098
0.0
77
-0.6
58
0.0
04
0.2
78
0.0
83
0.1
11
-0.2
64
0.0
31
-0.0
38
0.4
74
India
-6.9
68
-37.9
93
-5.3
48
-12.9
28
3.0
62
-4.8
60
18.8
32
-62.5
24
17.7
01
23.4
91
67.5
36
Irela
nd
0.9
78
-1.7
61
1.6
01
0.1
93
-7.5
88
-0.8
71
0.4
46
1.1
30
1.5
99
-0.7
85
5.0
58
LD
C8.6
00
-216.7
93
43.9
43
-25.1
88
-91.2
97
-158.5
43
-133.4
34
-95.7
32
195.6
61
278.4
44
194.3
41
REU
15
0.0
41
0.2
32
0.0
22
0.0
68
0.0
68
-0.0
14
-0.9
86
0.2
20
-0.0
91
-0.0
41
0.4
79
RW
orld
-0.0
80
-0.4
41
-0.1
85
-0.1
12
0.0
97
-0.0
22
-0.0
83
-0.8
59
0.0
25
0.1
17
1.5
43
UK
-0.0
02
0.9
00
0.1
29
0.2
34
0.4
11
0.4
35
-0.2
91
0.6
14
-1.4
66
-0.5
17
-0.4
48
USA
0.1
87
0.7
41
0.0
25
0.2
44
-0.0
68
0.4
86
0.1
07
0.8
86
-0.4
15
-1.8
54
-0.3
40
Importin
gC
ountry:
RW
orld
Brazil
Chin
aD
ED
CIn
dia
Irela
nd
LD
CR
EU
15
REU
27
UK
USA
Brazil
-5.9
84
4.5
02
23.1
98
-1.1
16
-0.1
01
0.1
60
-4.1
16
4.8
20
-0.1
83
-5.9
75
-15.2
05
Chin
a0.0
13
-0.8
31
-1.1
87
0.0
58
-0.0
77
0.1
00
-0.3
77
-0.0
23
-0.0
92
-0.7
10
3.1
25
DED
C0.1
56
-0.1
89
-0.9
83
-0.0
22
0.0
28
0.1
23
0.1
50
-0.0
42
0.2
24
0.4
09
0.1
46
India
-1.4
59
10.9
58
3.5
64
-5.0
48
2.2
84
-0.1
25
-1.4
26
3.8
58
6.6
29
4.0
07
-23.2
41
Irela
nd
-0.0
72
-1.5
83
-0.8
45
0.2
91
-2.4
83
0.1
05
-3.4
05
0.4
82
-0.6
11
2.8
90
5.2
34
LD
C2.8
28
127.4
39
250.8
08
-2.2
40
8.7
50
-124.8
79
-96.5
21
-13.7
27
-106.5
61
-198.9
09
153.0
12
REU
15
-0.1
11
0.0
12
0.2
19
-0.0
64
-0.2
36
-0.0
64
-0.6
75
0.2
52
0.1
05
0.1
11
0.4
51
REU
27
1.0
78
-1.4
23
-3.6
29
0.6
27
0.5
29
-0.1
42
2.2
75
-3.3
77
1.0
31
-5.3
14
8.3
45
UK
-0.0
54
-0.1
11
1.6
51
0.3
15
-0.1
68
-0.3
61
0.3
47
0.3
93
-4.4
85
1.4
11
1.0
62
21
USA
-0.0
89
0.0
44
0.2
93
-0.0
20
0.1
80
-0.0
63
0.0
42
-0.1
05
0.1
82
-0.9
95
0.5
32
Importin
gC
ountry:
UK
Brazil
Chin
aD
ED
CIn
dia
Irela
nd
LD
CR
EU
15
REU
27
RW
orld
USA
Brazil
-21.9
53
-10.3
63
9.8
09
-4.5
97
-5.4
77
0.6
61
-46.5
83
-3.9
60
-9.1
48
18.3
85
73.2
26
Chin
a-0
.244
-1.0
04
-1.0
89
-0.3
03
0.1
17
0.0
48
-2.0
16
0.0
59
-0.2
24
-0.6
35
5.2
91
DED
C0.2
14
-0.1
18
-1.8
16
0.1
25
0.3
33
-0.0
50
1.3
34
0.1
81
0.3
77
0.1
80
-0.7
60
India
-8.0
12
-17.5
86
14.8
90
-18.5
65
6.8
27
5.3
78
-57.7
76
-8.3
76
10.9
96
35.5
87
36.6
37
Irela
nd
-0.0
22
0.2
70
0.4
63
0.1
16
-0.8
70
0.0
72
-0.4
56
-0.1
61
0.2
99
-0.5
59
0.8
50
LD
C8.0
87
26.5
27
-24.4
25
35.8
29
50.7
09
-24.0
01
234.3
01
7.8
72
-60.4
08
-37.7
08
-216.7
81
REU
15
-0.0
81
-0.0
69
0.2
10
-0.1
00
-0.1
06
0.0
52
-1.0
56
-0.0
18
-0.2
09
0.1
01
1.2
75
REU
27
-0.1
25
0.0
94
0.1
21
-0.2
40
-0.6
85
0.0
11
-1.7
54
-1.2
29
-1.8
44
0.2
01
5.4
50
RW
orld
0.0
45
0.1
42
-0.0
12
0.0
67
0.0
73
-0.0
58
-0.2
23
-0.0
91
-0.8
55
-0.0
74
0.9
87
USA
0.2
65
0.0
84
0.1
32
0.2
09
-0.1
25
-0.0
55
0.9
31
0.1
86
0.2
76
-1.2
17
-0.6
86
Importin
gC
ountry:
USA
Brazil
Chin
aD
ED
CIn
dia
Irela
nd
LD
CR
EU
15
REU
27
RW
orld
UK
Brazil
-8.7
00
-16.2
19
28.5
88
1.0
27
3.1
76
-2.2
64
-1.8
09
1.7
34
-11.5
19
3.1
21
2.8
66
Chin
a-0
.308
-1.9
49
-0.0
96
0.1
25
0.3
08
-0.3
53
0.1
32
0.0
60
-2.0
98
-0.0
31
4.2
11
DED
C0.2
88
0.6
13
-1.0
31
-0.0
31
-0.0
54
0.0
67
0.0
28
-0.0
67
0.5
78
-0.0
03
-0.3
87
India
3.6
76
27.1
16
-5.1
16
-8.5
62
-6.4
27
10.0
64
-0.7
01
2.4
12
-1.3
63
0.7
95
-21.8
93
Irela
nd
1.0
77
5.8
13
-2.6
40
-0.6
38
-4.0
38
3.7
78
1.7
96
-0.4
09
-6.0
19
-1.0
96
2.3
77
LD
C-1
79.2
93
-1341.9
50
880.9
74
231.7
86
909.3
02
-1100.1
80
-504.4
28
159.7
15
2038.2
14
104.9
81
-1199.1
10
REU
15
-0.1
14
1.3
30
0.5
39
-0.0
30
0.4
02
-0.4
77
-2.0
20
0.0
76
1.6
29
0.2
83
-1.6
18
REU
27
1.0
15
2.2
26
-4.6
10
0.3
82
-0.6
99
1.1
16
0.5
07
-1.1
01
-0.0
05
-0.5
58
1.7
28
RW
orld
-0.0
57
-0.1
47
-0.0
95
-0.0
20
-0.0
85
0.0
94
0.0
19
0.0
03
-0.8
05
-0.0
05
1.0
97
UK
0.5
11
0.0
92
-0.6
35
0.0
19
-0.5
22
0.1
72
0.5
29
-0.1
56
-0.4
81
-1.2
60
1.7
30
22
6 Conclusions
The generalized maximum entropy estimation method is a technique that is
useful when estimating import demand systems with limited trade data and