Institutional governance and endowment management
17 May 2021Good institutional governance involves good management of institutional wealth. For some institutions a lot of that wealth is in an endowment. “Endowment rules” governing the proportion of wealth consumed today vs saved for tomorrow encode a lot of information about the institution’s values, goals, and constraints.
Maximization is probably not a desirable framework for designing governance
For a broad class of institutional objective functions, endowment rules which maximize the objective ought to be Euler-like. They should equate marginal utilities and shadow prices today with their discounted counterparts tomorrow. (If the objective does not involve the future then those tomorrow components can be set to zero, but let’s suppose we’re in the class of objectives that presume continuation into the indefinite future.)
Let’s suppose the institution uses a market discount rate. The longer the impact of a new project stretches, the more the lowest possible discount rate ought to be used. Regardless, any maximizing endowment draw rate \(c_t\) ought to satisfy something like
\[u'(c_t) + \lambda_{t} f'(K_{t}, c_t) = \beta E_t[u'(c_{t+1}) + \lambda_{t+1} f'(K_{t+1}, c_{t+1})],\]in all periods, where $u$ is the utility function which encodes the institution’s values and goals, \(\beta\) is the discount factor, \(K_{t}\) is the stock of wealth, $f’$ is the marginal growth of the institution’s wealth, and $\lambda_t$ is the shadow price of that wealth. \(E_t\) on the right hand side indicates the need for forecasts of how things might look tomorrow. This can be generalized to multiple types of wealth and consumption if necessary, but it already gives us a lot of information. For example, \(u'\) and the \(\lambda\)s tell the institution’s managers how to value marginal fundraising or new projects.
A lot of institutional governance can be expressed as struggles over the components of equations like this one. What’s the $u$ we’ll use, and who gets more or less voice in that? Which \(\lambda\)s should be considered, and how should their value be assessed? Which discount rate is relevant? In actual practice, the components of equations like these change over time as different factions become ascendant, constraints from previous decisions bind, and constraints on future decisions (perhaps to limit some new faction’s ascendancy) are introduced. Getting an institution to commit to following any explicit stationary maximization rule is probably hard and likely to raise a lot of unpleasant political battles. Maximization takes us to the Pareto frontier (defined appropriately relative to the objective being maximized), and the Pareto frontier tends to force uncomfortable tradeoffs. It’s not obvious to me that any generation’s preferred maximization rule can really be time consistent when current members exit and new members enter. Part of the appeal to turn-taking modes of politics is the chance to change the components guiding decision-making eventually, so the battle to make a stationary rule could be quite ugly even without raising the prospect of future generations with intrinsically different goals or constraints.
Sustainability and guaranteeing capabilities to future generations might be a better approach
It’s probably a lot easier and less contentious to have some sort of heuristic which acts as a safeguard against “bad” decisions rather than a rule which forces “good” decisions. I think a good one for long-lived institutions involves ensuring some notion of sustainability. Fortunately, smart folks have thought about this. An equivalence result in the linked paper establishes that changes in intergenerational well-being map to changes in “comprehensive” wealth. In the institutional context, that “intergenerational well-being” is simply the intertemporal objective. “Comprehensive” wealth includes machine and financial (“reproducible”) capital, human capital, and natural resource capital. Endowments are not the same as “comprehensive” wealth, since many institutions have at least substantial human capital if not natural resource capital, but suppose we take it as such for now. This suggests a simple rule to use for ensuring an institution’s wealth is governed sustainably: make sure the real value of the endowment (before gifts) doesn’t fall.
This approach gives the current generation a lot of flexibility to exercise their capabilities and look after their own interests without harming future generations. Large negative shocks to permanent income (e.g., a pandemic with a large recessionary impact) would reduce future comprehensive wealth, giving current generations a bit more room to draw on capital and smooth over the shock. There are probably more nuanced and smarter things to be said about sustainability over the business cycle. But the bigger appeal, to me, is that it allows us to abstract from the specific utility function (and avoid encoding maximization goals) to focus on wealth instead.
Gifts could perhaps be included in the value being maintained, but I think there are two reasons to exclude gifts. First, to the extent that gifts are random and hard to forecast, forecast errors can lead to unsustainable paths. If the goal is to be sustainable for as much of the future as possible, excluding gifts can support the objective but including them can only harm it. This is a sort of “conservative management” principle. Second, to the extent that gifts come with additional obligations, the short-run gains they provide may not net out with the long-run costs they impose. This is a really unpleasant effect, since endowment managers can end up having to starve other line items being funded in order to preserve the real value of the gift. The fact that gift contracts include these kinds of terms seems to me a signal that people have found value in rules like this. The entire endowment is effectively a gift from previous generations to current ones, with current generations acting as stewards for future generations, so applying the rule to the endowment as a whole (rather than some parts only) seems like a natural extension.
A sustainability rule like this one requires institutional managers to accept new projects with caution even if they come with funding sources. If new projects create future obligations which could reduce wealth eventually, they may be unsustainable despite guaranteed current funding. Austerity measures which reduce future flows into wealth (e.g., by reducing the long-run prestige of the institution) are similarly unsustainable. These conclusions follow from purely financial considerations, since we are treating “comprehensive” wealth as only the financial wealth in an endowment.
For institutions like colleges and universities adding some measure of “accessible knowledge capital” seems sensible as well. It’s not obvious how to value it (“what’s the shadow price?”) but changes in library scope or quality could form a useful metric for investment in said capital. Arrow and co manage to assess sustainability using only changes in comprehensive wealth (“comprehensive investment”), so the measurement problem here is really only to track and value flows. Endowment flows are easy to track and value, at least in principle.
The most interesting issue to me is how to think about human capital in this framework. Arrow and co think about this as education and health, which maybe makes sense for nations. Health capital seems like a reasonable component for any kind of institution that employs people, especially under the American system of employer-provided healthcare. Perhaps some metric like “proportion of claims filled” so as to avoid selection against those with pre-existing conditions, is a useful way to track the flows of health capital. There’s still a problem of figuring out the right shadow price. Supposing the measurement challenge is resolvable, adding a health capital metric to comprehensive wealth offers an even more stringent (conservative) test for the sustainability of austerity measures.
I don’t think “education” forms a desirable metric for human capital. Institutions often need employees with a wide range of skills, representing different types and degrees of formal and informal education. Appropriately measuring such capital/investment and valuing it with respect to institutional goals seems quite hard and like a recipe for bitter internecine fights. Perhaps there’s some other metric that better gets at the end goal of having different mixes of employees, but I still see unpleasant politics ahead when trying to incorporate human capital.
A sustainability approach delivers a bunch of things
Properly defined, sustainability and guaranteeing capabilities for the future requires relatively simple heuristics for wealth management. These principles will generally not be of the form “only draw \(x\%\) per year”, no matter what \(x\) is chosen. They do not provide a guide to what a “good” decision is, only guardrails against “bad” decisions. A “bad” decision in this framework is anything which reduces comprehensive wealth along future paths. “Bad” decisions can include projects with funding not guaranteed beyond a few years, austerity measures, and direct reductions in institutional capital stocks (e.g., libraries). Sustainability rules create a need for forecasts and some further rules on how to handle uncertain impacts in the future. The rules to handle uncertainty seem tricky: it’s not obvious what the right level of risk tolerance ought to be. But some state-dependent sustainability guardrails seem better than none.