The equations comes in two flavors, long-term and short-term. Salient fact about the long-term ones is that most of them are imposed (singly or jointly) rather than estimated. For instance, the elasticities of consumption with respect to income and wealth are constrained to sum to one. The elasticity of employment with respect to real wages is constrained to be negative one. (Oh, that one makes me mad.) The elasticities of exports and imports with respect to their respective market sizes are constrained to be one. And so on. Meanwhile, the short-term (one- and two-year) equations are allowed to be determined by the data.
There's a couple reasons for this, at least one of which is reasonable. The reasonable one is that they want the long-run behavior of the model to converge to an equilibrium. If, let's say, the long-run elasticity of imports with respect to income was anything but 1, the share of imports in consumption would rise without limit over time. I'm not sure how I feel about this. (Bad blogger!) On the one hand, it's obviously true that that imports or consumption relative to GDP, or the wage share, or relative prices among trading patterns, don't diverge to infinity. On the other hand, time doesn't pass to infinity either. The practical relevance of the long-run conditions is only for a period long enough that exogenous fluctuations have canceled out, yet short enough that the parameters of the model remain unchanged. It's not at all clear to me that the set of such periods is not empty. On the other hand, there may be reasons why postulating a long-run equilibrium is useful, even if we recognize that no such equilibrium is ever reached.
The other reason for the long-run restrictions is less defensible -- or, since really who cares about my opinion, let's say it's substantive rather than methodological. The model "combines short-term Keynesian-type dynamics with a consistent neoclassical supply-side in the long run." (Interestingly, mainstream macro has this in common with a major strand of Marxist economics, in contrast with the (post-)Keynesians who allow a role for demand even in the long run.) So some of the long-run restrictions are imposed not simply to get an equilibrium, but to get a particular, tastes-endowments-and-technology equilibrium. There's no reason in principle that practical macroeconomics should exclude the possibility of changes in real wages changing income shares in the long run. That the OECD does, tells you something.
On to the substance:
A couple interesting things here, which unlike the thumbsucking above, one can actually use. These are hardly gospel, of course; but enshrined in the OECD macro model they can be taken as stylized facts, in the sense that in many contexts they don't, qualitatively, have to be explicitly argued for.
1. Wealth effects (on consumption) are largest for the US, smallest for Japan.
2. The effect of import prices on the domestic price level is negligible in the US and Japan, but substantial in Europe.
3. Trade flows are much more responsive to income changes than to relative prices. Estimated export elasticities are two to three times higher for income than for "competitiveness" ; estimated import elasticities are two to four times higher.
4. US export prices move with domestic prices essentially one for one; US import prices move with foreign prices only slightly. For most other countries, export pass-through is lower and import pass-through is greater.
The last two are particularly interesting.
Eventually, one would like to think through the conceptual basis, and limits, of these sorts of models. There's that never-realized long-term. Meanwhile here in the short-term, when you're making heterodox arguments it's nice to get empirical backup from some place impeccably orthodox.