We currently assume that goods/services making up government consumption expenditures are produced from just one industry (namely, industry $M$).
However, given data from an input/output table, it would be trivial to find demand for output from any sector $m$ that results from gov't consumption expenditures.
Analogous to how we model differentiated consumption goods, we can have a unit of gov't expenditures be made up of outputs from different sectors using a fixed-coefficient matrix. E.g., demand for industry $m$ output from gov't consumption will be given as:
$$
G{m,t} = \pi{gov, m} G_{t}
$$
where $\pi_{gov, m}$ is the fraction of a unit of gov't spending that comes from industry $m$.
The price of a unit of gov't consumption will then be:
$$
p{gov,t} = \sum{m=1}^M \pi{gov, m} p{m}
$$
Government spending in the government's budget constraint, currently $G{t}$ will be replaced by $p{gov,t}G_{t}$ since this change will mean that gov't expenditures are not only on the numeraire good (which is the current assumption in OG-Core).
We currently assume that goods/services making up government consumption expenditures are produced from just one industry (namely, industry $M$).
However, given data from an input/output table, it would be trivial to find demand for output from any sector $m$ that results from gov't consumption expenditures.
Analogous to how we model differentiated consumption goods, we can have a unit of gov't expenditures be made up of outputs from different sectors using a fixed-coefficient matrix. E.g., demand for industry $m$ output from gov't consumption will be given as:
$$ G{m,t} = \pi{gov, m} G_{t} $$
where $\pi_{gov, m}$ is the fraction of a unit of gov't spending that comes from industry $m$.
The price of a unit of gov't consumption will then be:
$$ p{gov,t} = \sum{m=1}^M \pi{gov, m} p{m} $$
Government spending in the government's budget constraint, currently $G{t}$ will be replaced by $p{gov,t}G_{t}$ since this change will mean that gov't expenditures are not only on the numeraire good (which is the current assumption in OG-Core).