Readers’ Appendix to accompany “Specification and Estimation of Regular Inverse Demand Systems” by Gary K K Wong and Keith R McLaren (to appear in American Journal of Agricultural Economics)
This appendix provides more detailed information on parameter estimates and elasticities than was made available in the published version of the paper.
Table BI:
Parameter Estimates for the LIDS (Asymptotic
T-Ratios in Parentheses)
|
a1 |
0.2518 |
(80.5893) |
a3 |
0.0827 |
(17.2042) |
a5 |
0.1324 |
(13.6580) |
|
a2 |
0.3207 |
(63.0230) |
a4 |
0.0938 |
(5.2116) |
a6 |
0.1186 |
(8.8561) |
|
b1 |
-0.0520 |
(3.1623) |
b3 |
-0.0431 |
(2.6546) |
b5 |
0.0039 |
(-0.1551) |
|
b2 |
0.0595 |
(-2.5944) |
b4 |
0.0202 |
(-0.8155) |
b6 |
0.0115 |
(-0.4869) |
|
g11 |
0.0000 |
(-0.0319) |
g31 |
-0.0001 |
(-0.0643) |
g51 |
0.0002 |
(0.0633) |
|
g12 |
0.0002 |
(0.0639) |
g32 |
0.0031 |
(1.0967) |
g52 |
-0.0097 |
(-1.4335) |
|
g13 |
-0.0001 |
(-0.0643) |
g33 |
-0.0010 |
(-0.6222) |
g53 |
0.0031 |
(0.9246) |
|
g14 |
-0.0002 |
(-0.0642) |
g34 |
-0.0029 |
(-1.1124) |
g54 |
0.0091 |
(1.3932) |
|
g15 |
0.0002 |
(0.0633) |
g35 |
0.0031 |
(0.9246) |
g55 |
-0.0097 |
(-0.8984) |
|
g16 |
-0.0001 |
(-0.0645) |
g36 |
-0.0053 |
(-0.9612) |
g56 |
0.0071 |
(0.7298) |
|
g21 |
0.0002 |
(0.0639) |
g41 |
-0.0002 |
(-0.0642) |
g61 |
-0.0001 |
(-0.0645) |
|
g22 |
-0.0097 |
(-0.9991) |
g42 |
0.0091 |
(1.3497) |
g62 |
0.0071 |
(0.7489) |
|
g23 |
0.0031 |
(1.0967) |
g43 |
-0.0029 |
(-1.1124) |
g63 |
-0.0053 |
(-0.9612) |
|
g24 |
0.0091 |
(1.3497) |
g44 |
-0.0085 |
(-1.0832) |
g64 |
-0.0066 |
(-1.0826) |
|
g25 |
-0.0097 |
(-1.4335) |
g45 |
0.0091 |
(1.3932) |
g65 |
0.0071 |
(0.7298) |
|
g26 |
0.0071 |
(0.7489) |
g46 |
-0.0066 |
(-1.0826) |
g66 |
-0.0020 |
(-0.1910) |
Table
BII: Parameter Estimates for the CLIDS and AISIDS (Asymptotic T-Ratios in Parentheses)
|
CLIDSa
& b |
AISIDS |
|||||||||||
|
a1 |
0.247 |
(5.655) |
g1 |
0.123 |
(5.988) |
|
0.370 |
(16.273) |
|
0.270 |
(7.409) |
|
|
a2 |
0.315 |
(10.744) |
g2 |
0.133 |
(7.474) |
|
0.438 |
(19.305) |
|
0.391 |
(5.320) |
|
|
a3 |
0.181 |
(11.959) |
g3 |
0.013 |
(2.996) |
|
0.192 |
(104.656) |
|
0.339 |
(5.060) |
|
|
a4 |
0.051 |
(1.588) |
g4 |
0.000 |
¾ |
|
0.398 |
(28.154) |
|
0.271 |
(5.882) |
|
|
a5 |
0.106 |
(2.541) |
g5 |
0.000 |
¾ |
|
0.556 |
(39.560) |
|
0.401 |
(10.805) |
|
|
a6 |
0.099 |
(3.620) |
g6 |
0.013 |
(2.735) |
|
0.046 |
(5.153) |
|
0.328 |
(9.996) |
|
|
b1 |
0.129 |
(2.583) |
|
|
|
k1 |
0.014 |
(3.929) |
k2 |
-0.024 |
(-1.449) |
|
|
b2 |
0.244 |
(4.614) |
|
|
|
h1 |
0.212 |
(8.978) |
h2 |
0.521 |
(7.589) |
|
|
b3 |
0.020 |
(1.504) |
|
|
|
|
|
|
k0 |
0.400 |
(6.590) |
|
|
b4 |
0.164 |
(4.404) |
|
|
|
|
|
|
|
|
|
|
|
b5 |
0.299 |
(8.328) |
|
|
|
|
|
|
|
|
|
|
|
b6 |
0.145 |
(4.569) |
|
|
|
|
|
|
|
|
|
|
Note: aFor the CLIDS, the estimated
standard error must be interpreted with care since the standard asymptotic
theory is inapplicable when parameters are subject to inequality constraints.
bThe constraints g4 ³ 0 and g5 ³ 0 were binding, and hence
no estimated standard errors are reported.
Detailed Table 3: Comparison of Quantity and Scale Elasticities
(With asymptotic
T-Ratios in Parentheses)
|
Compensated Quantity
Elasticities |
|||||||
|
Commodity |
f |
f |
f |
f |
f |
f |
|
|
LIDS |
|||||||
|
High |
-0.756 |
0.241 |
0.247 |
0.239 |
0.243 |
0.239 |
|
|
|
(-145.762) |
(30.960) |
(106.296) |
(29.943) |
(35.439) |
(33.219) |
|
|
Medium |
0.333 |
-0.694 |
0.375 |
0.411 |
0.261 |
0.406 |
|
|
|
(30.803) |
(-44.417) |
(37.061) |
(16.257) |
(16.315) |
(40.287) |
|
|
Low
|
0.070 |
0.075 |
-0.938 |
0.042 |
0.091 |
0.044 |
|
|
|
(12.666) |
(9.114) |
(-258.903) |
(4.108) |
(11.044) |
(6.133) |
|
|
Cuttlefish
|
0.115 |
0.157 |
0.058 |
-0.943 |
0.192 |
0.060 |
|
|
|
(7.299) |
(6.821) |
(4.468) |
(-28.907) |
(8.437) |
(4.021) |
|
|
Lobster
|
0.135 |
0.103 |
0.182 |
0.209 |
-0.940 |
0.205 |
|
|
|
(17.657) |
(9.469) |
(20.096) |
(10.181) |
(-66.020) |
(23.957) |
|
|
Shellfish |
0.102 |
0.118 |
0.076 |
0.043 |
0.153 |
-0.954 |
|
|
|
(13.234) |
(9.872) |
(22.737) |
(8.136) |
(16.835) |
(-54.939) |
|
|
CLIDS |
|||||||
|
High |
-0.416 |
0.070 |
0.127 |
0.223 |
0.208 |
0.136 |
|
|
|
(-19.880) |
(5.204) |
(6.629) |
(25.953) |
(22.552) |
(9.001) |
|
|
Medium |
0.096 |
-0.413 |
0.199 |
0.316 |
0.305 |
0.211 |
|
|
|
(7.428) |
(-12.155) |
(7.393) |
(26.472) |
(20.284) |
(10.205) |
|
|
Low
|
0.039 |
0.043 |
-0.681 |
0.068 |
0.068 |
0.055 |
|
|
|
(4.626) |
(4.347) |
(-10.502) |
(7.739) |
(6.894) |
(5.334) |
|
|
Cuttlefish
|
0.096 |
0.107 |
0.137 |
-0.851 |
0.168 |
0.140 |
|
|
|
(10.526) |
(6.443) |
(4.659) |
(-38.544) |
(5.180) |
(4.727) |
|
|
Lobster
|
0.124 |
0.127 |
0.138 |
0.144 |
-0.849 |
0.139 |
|
|
|
(15.472) |
(18.167) |
(15.814) |
(11.211) |
(-70.307) |
(15.421) |
|
|
Shellfish |
0.060 |
0.065 |
0.080 |
0.100 |
0.101 |
-0.681 |
|
|
|
(18.808) |
(18.761) |
(14.371) |
(9.066) |
(8.719) |
(-11.000) |
|
|
AISIDS |
|||||||
|
High |
-0.377 |
0.298 |
0.076 |
0.001 |
0.001 |
0.001 |
|
|
|
(-35.677) |
(35.182) |
(14.597) |
(1.496) |
(1.504) |
(1.483) |
|
|
Medium |
0.223 |
-0.302 |
0.076 |
0.001 |
0.001 |
0.001 |
|
|
|
(21.134) |
(-35.559) |
(14.597) |
(1.496) |
(1.504) |
(1.483) |
|
|
Low
|
0.223 |
0.298 |
-0.524 |
0.001 |
0.001 |
0.001 |
|
|
|
(21.134) |
(35.182) |
(-100.611) |
(1.496) |
(1.504) |
(1.483) |
|
|
Cuttlefish
|
0.367 |
0.491 |
0.125 |
-1.013 |
0.016 |
0.013 |
|
|
|
(20.731) |
(36.242) |
(14.746) |
(-2384.999) |
(28.721) |
(22.078) |
|
|
Lobster
|
0.367 |
0.491 |
0.125 |
0.011 |
-1.008 |
0.013 |
|
|
|
(20.731) |
(36.242) |
(14.746) |
(25.689) |
(-1798.469) |
(22.078) |
|
|
Shellfish |
0.367 |
0.491 |
0.125 |
0.011 |
0.016 |
-1.010 |
|
|
|
(20.731) |
(36.242) |
(14.746) |
(25.689) |
(28.721) |
(-1667.222) |
|
Table 3: (Continued)
|
|
Uncompensated Quantity Elasticities
|
Scale Elasticities |
||||||||||
Commodity
|
f |
f |
f |
f |
f |
f |
si |
|||||
|
LIDS |
||||||||||||
|
High |
-0.946 |
-0.044 |
0.159 |
-0.044 |
-0.006 |
-0.031 |
-0.786 |
|||||
|
|
(-653.635) |
(-24.914) |
(9.642) |
(-6.143) |
(-14.779) |
(-9.462) |
(-134.827) |
|||||
|
Medium |
0.071 |
-1.087 |
0.255 |
0.021 |
-0.083 |
0.034 |
-1.178 |
|||||
|
|
(26.794) |
(-380.207) |
(9.237) |
(7.023) |
(-15.010) |
(8.579) |
(-166.506) |
|||||
|
Low
|
0.017 |
-0.005 |
-0.963 |
-0.038 |
0.021 |
-0.032 |
-0.361 |
|||||
|
|
(59.726) |
(-12.340) |
(-269.880) |
(-6.275) |
(15.048) |
(-9.175) |
(-5.431) |
|||||
|
Cuttlefish
|
0.018 |
0.012 |
0.013 |
-1.086 |
0.066 |
-0.077 |
-1.169 |
|||||
|
|
(40.414) |
(33.760) |
(6.326) |
(-79.409) |
(15.038) |
(-9.104) |
(-42.347) |
|||||
|
Lobster
|
0.031 |
-0.054 |
0.135 |
0.052 |
-1.077 |
0.056 |
-1.028 |
|||||
|
|
(19.344) |
(-34.901) |
(8.872) |
(6.468) |
(-210.050) |
(8.924) |
(-539.098) |
|||||
|
Shellfish |
0.024 |
0.001 |
0.040 |
-0.074 |
0.050 |
-1.065 |
-1.116 |
|||||
|
|
(65.833) |
(1.850) |
(10.623) |
(-6.300) |
(15.039) |
(-149.700) |
(-91.591) |
|||||
|
CLIDS |
||||||||||||
|
High |
-0.735 |
-0.215 |
-0.345 |
0.115 |
0.167 |
-0.047 |
-1.323 |
|||||
|
|
(-62.524) |
(-7.526) |
(-7.067) |
(1.960) |
(2.522) |
(-4.611) |
(-9.676) |
|||||
|
Medium |
-0.347 |
-0.808 |
-0.453 |
0.173 |
0.253 |
-0.040 |
-1.182 |
|||||
|
|
(-4.879) |
(-57.695) |
(-4.795) |
(2.056) |
(2.794) |
(-3.106) |
(-13.249) |
|||||
|
Low
|
-0.050 |
-0.037 |
-0.813 |
0.037 |
0.056 |
0.003 |
-1.951 |
|||||
|
|
(-3.868) |
(-3.291) |
(-12.742) |
(2.496) |
(3.695) |
(1.193) |
(-12.351) |
|||||
|
Cuttlefish
|
-0.064 |
-0.037 |
-0.101 |
-0.909 |
0.145 |
0.046 |
-0.439 |
|||||
|
|
(-5.253) |
(-4.024) |
(-4.956) |
(-44.755) |
(5.522) |
(4.475) |
(-1.799) |
|||||
|
Lobster
|
-0.054 |
-0.031 |
-0.123 |
0.087 |
-0.870 |
0.039 |
-0.163 |
|||||
|
|
(-2.661) |
(-2.143) |
(-4.189) |
(2.150) |
(-21.896) |
(4.204) |
(-0.652) |
|||||
|
Shellfish |
-0.073 |
-0.053 |
-0.116 |
0.059 |
0.086 |
-0.756 |
-0.754 |
|||||
|
|
(-2.863) |
(-2.523) |
(-3.735) |
(1.967) |
(2.789) |
(-12.375) |
(-11.326) |
|||||
|
AISIDS |
||||||||||||
|
High |
-0.612 |
-0.026 |
0.010 |
-0.119 |
-0.129 |
-0.096 |
-0.972 |
|||||
|
|
(-110.147) |
(-3.258) |
(1.126) |
(-6.517) |
(-14.235) |
(-9.475) |
(-302.038) |
|||||
|
Medium |
0.001 |
-0.607 |
0.014 |
-0.112 |
-0.121 |
-0.091 |
-0.916 |
|||||
|
|
(0.259) |
(-82.741) |
(1.633) |
(-6.539) |
(-14.150) |
(-9.415) |
(-353.218) |
|||||
|
Low
|
-0.118 |
-0.172 |
-0.620 |
-0.173 |
-0.187 |
-0.140 |
-1.411 |
|||||
|
|
(-16.560) |
(-12.862) |
(-53.195) |
(-6.421) |
(-14.606) |
(-9.752) |
(-179.876) |
|||||
|
Cuttlefish
|
0.124 |
0.156 |
0.057 |
-1.136 |
-0.118 |
-0.087 |
-1.005 |
|||||
|
|
(10.932) |
(20.820) |
(5.247) |
(-60.804) |
(-12.565) |
(-8.134) |
(-6887.169) |
|||||
|
Lobster
|
0.126 |
0.158 |
0.057 |
-0.112 |
-1.141 |
-0.086 |
-0.997 |
|||||
|
|
(11.056) |
(21.321) |
(5.321) |
(-6.029) |
(-122.378) |
(-8.117) |
(-12354.435) |
|||||
|
Shellfish |
0.121 |
0.152 |
0.056 |
-0.114 |
-0.120 |
-1.112 |
-1.017 |
|||||
|
|
(10.755) |
(20.116) |
(5.143) |
(-6.033) |
(-12.599) |
(-102.771) |
(-3765.662) |
|||||
Note: 
,
and si are the point estimates of
the elasticity equations 
,
and Si respectively.
Restrictions on AISIDS Compensated Elasticities due to Implicit Separability
Let the set of indices of the
quantities x be I = {1, 2,……, N}, and order these quantities in M separable groups
defined by the mutually exclusive and exhaustive partition I0 = {I1,…,
Im, …, IM} (M £ N)
of the set I. Then preferences are
said to be implicitly separable in the partition I0 if the distance function has the structure:
D(x, u) =
D0[u, D1(x1, u),…, Dm(xm,
u),…, DM(xM, u)],
where xm is a vector of quantities in the partition I0,
and the Dm are quasi-distance functions depending only on group
quantities xm and utility level u.
Let
denote the compensated cross quantity elasticities between two goods in different
groups. It is shown that the compensated elasticity equations corresponding to are given by:
= 
= 
= 
= 
which suggests that the signs and
size of 
should be the same for all 
.