Bayesian Inference in the Seemingly Unrelated Regressions Model
Bayesian Inference in the Seemingly Unrelated Regressions Model
Bayesian Inference in the Seemingly Unrelated Regressions Model
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26<br />
σ<br />
ij<br />
=<br />
β<br />
i<br />
ij<br />
S S<br />
j<br />
+ 1<br />
i ≠ j<br />
and <strong>in</strong>put demand elasticities<br />
ii<br />
ηii<br />
= + Si<br />
−1<br />
Si<br />
η<br />
ij<br />
β<br />
β<br />
=<br />
S<br />
ij<br />
i<br />
+ S<br />
j<br />
C. Expenditure Functions<br />
Our third example <strong>in</strong>volves two expenditure functions estimated from a sample of<br />
1,834 Bangkok households, and deflated by an “equivalence scale” measure of<br />
household size (Griffiths and Chotikapanich 1997). For <strong>the</strong> t-th observation, <strong>the</strong><br />
functions are<br />
α m<br />
β m<br />
( x<br />
− α m<br />
− α<br />
− α m<br />
1 1t<br />
1 1t<br />
t 1 1t<br />
2 2t<br />
3 3t<br />
w1<br />
t<br />
= +<br />
e1<br />
t<br />
xt<br />
xt<br />
( β1m1<br />
t<br />
+ β2m2t<br />
+ β3m3t<br />
)<br />
m<br />
)<br />
+<br />
α<br />
m<br />
β<br />
m<br />
( x − α m<br />
− α<br />
− α m<br />
2 2t<br />
2 2t<br />
t 1 1t<br />
2 2t<br />
3 3t<br />
w2t<br />
= +<br />
+ e2t<br />
xt<br />
xt<br />
( β1m1<br />
t<br />
+ β2m2t<br />
+ β3m3<br />
t<br />
)<br />
m<br />
)<br />
m = 1+δ n +δ n<br />
1t 21 2t 31 3t<br />
m = 1+δ n +δ n<br />
2t 22 2t 32 3t<br />
m = 1+δ n +δ n<br />
3t 23 2t 33 3t<br />
where<br />
w jt = expenditure proportion for commodity j,<br />
x t = total expenditure,<br />
m jt = equivalence scale for commodity j,