Content
Introduction and Course Overview
In this lecture, we pick up where we left off in the previous class and dive into inclusive wealth. You might recall that we talked about discounting, and it turns out that thinking about well-being over time is critical to understanding what sustainability looks like because we are fundamentally concerned with the well-being of future generations.
Where We Are in the Course
To remind ourselves of the course structure, we started with an introduction to the big picture, talking about planetary donuts. Then we put forth the economic theory of decision making and how that builds up almost like the moral and ethical case for what it is that we care about. This framework is what we will use extensively in our inclusive wealth definition.
After that, we talked about market failures of many different types and how to solve them, but we pretty quickly switched back to the macro scale, thinking about limits to growth. We discussed sustainable development and examined GDP as a flawed metric. Then we arrived at where we were last time, thinking about not just markets and macroeconomic scale indicators, but what happens when we think about it over time. We covered discounting and thought about equity in the context of having future generations that, depending on how good of a person you are, you care more or less about.
Where We Are Going
Now we are going to use everything we have covered to build out inclusive wealth. Once we have inclusive wealth established, we will be able to dive into a new set of topics that are very frequently included in a standard natural resources course, specifically how to properly manage non-renewable resources and renewable resources. We will examine the optimal way of extracting oil or minerals from the ground. While it might not seem relevant to ordinary life, it is actually a really cool way of thinking about sustainability over time. It becomes even more interesting when we think about renewable resources, like fisheries, and how they grow and how we can try to get value from them.
Following that, we will shift to climate change, and then a big part of the course will focus on natural capital and ecosystem services. We will actually be running models and using GIS (geographic information systems) to plot maps for that section. Starting with climate change is also where we will begin to dive into the country reports, which serve as the final product. That will comprise the bulk of the second half of the course, and then we will end with thinking about how all of this changes under future scenarios, culminating in a comprehensive modeling approach to combine all of these elements.
The Alphabet Soup of GDP Replacements
We talked through inclusive wealth and why GDP is not a good metric, then we discussed discounting. Now we have all the pieces to combine into the question of not just whether GDP is bad, but whether there are better metrics available.
The short answer is yes—there are much better metrics. In fact, we almost have a problem of too many metrics, which can be described as the alphabet soup of GDP replacements. We are not the first people to recognize that GDP is a flawed metric, and there exists a whole bunch of alternatives that fall into many different categories.
Categories of Alternative Metrics
Adjusted Flow Metrics
A lot of alternative metrics start by thinking about whether we can adjust flow metrics like GDP by adding things in, like features that address the quality or sustainability of economic welfare. This category includes approaches such as gross ecosystem product, which essentially tries to complete the picture of GDP by adding extra elements.
Intangible Measures
Another category is less focused on adjusting flow metrics and more focused on capturing intangibles, like the Human Development Index or the Multidimensional Poverty Index. These incorporate non-production variables like health or education level.
Sustainability and Planetary Boundaries
The third category covers sustainability and planetary boundaries. The donut model is one example that has been highlighted for this course. These approaches typically combine a bunch of indicators on planetary health or sustainability. A big one in this space is the SDGs, or Sustainable Development Goals, which are something the United Nations and a whole bunch of countries have agreed to. The SDGs consist of literally a list of 169 different indicators on things we think we care about, so they can be very detailed.
Capital-Based or Wealth Measures
The focus of this lecture is the last category: capital-based or wealth measures. You might recall when we talked about GDP that one of its flaws is that it is a flow. So not too surprisingly, we are not going to highlight the flow values but instead talk about wealth-based measures. This is important for a basic reason we discussed: your income is nice, but when it comes to making an emergency medical payment or something, the size of your paycheck does not matter—the contents of your bank account, your wealth, is what matters. That is often more closely tied to whether or not you get that life-saving medical treatment.
There are lots of options in this alphabet soup, and people will debate endlessly about which one is best. We are going to focus on one particular contender, and a detailed argument will be made about why this is a particularly good one.
Defining Inclusive Wealth
What Is Inclusive Wealth?
Inclusive wealth is the metric this lecture has been building towards. It requires understanding a whole lot of different things—economic growth, discounting, and all those other concepts we have covered. That is why it can be hard to explain sometimes, but we are now ready to understand it. It is a metric that diverges from traditional indicators that look at GDP or other flow things, towards understanding the value of the assets, or the wealth, that generates our well-being.
The definition of inclusive wealth is going to be the total value of society’s productive assets.
That might not sound like a very interesting definition because it is a little too vague. So we are going to be more specific, and that is where we will see that it becomes a really powerful concept. We are going to define it in a way that economists like, using numbers.
The Three Types of Capital
We are going to build from the intuition we have already seen—like with the circular flow diagram—that capital is what creates consumption in future periods, and thereby happiness. But we are going to extend it so there is not just one type of capital.
Produced Capital
The first component is produced capital, which we will subscript with P. The value of produced capital, V_P, is multiplied by K_P, which is the quantity of produced capital. This one is straightforward: capital would be something like the number of tractors we have available—produced capital to help us grow food. And the value of produced capital would be the price of that capital stock, the price of those tractors.
Much of standard economic growth theory has focused on produced capital.
Human Capital
There is an important extension to consider: the value of human capital also matters to economic productivity. So we also have the value of human capital, V_H, times the stock of human capital, K_H. Where do we produce human capital? Colleges and universities are a primary source. Students pay to increase their human capital, and it will help their income because now their capital is worth more. From a society-wide perspective, much of modern economic growth has diverged to be not just about the total capital stock, but about how much we can educate our workers. That is becoming ever more important in this information society.
Natural Capital
Critically, especially for this class, is the value of natural capital. We will subscript that with N for natural capital, which encompasses ecosystems, land, soil, resources, minerals, oil, climate, and all those things.
The Inclusive Wealth Equation
The argument is that inclusive wealth is the value of all of these things together, and that differs from what people often use in non-inclusive wealth approaches, which would only capture the ones that have easy market values—like tractors. It gets harder when we are dealing with V_N, the value of natural things.
In short, but with much more to break down, inclusive wealth is just the value of this now more inclusive set of capital. Other people will add even more types—some argue that social capital matters too. If you have a society where everybody trusts each other and cooperates, it tends to produce more economic output than one constantly dealing with cheating, fraud, and so on. But we will leave that out for now and focus on the three main types.
The Production Function with Multiple Capital Types
Extending the Standard Model
We are going to borrow heavily from what we have done in the past. Before, our production function Y—the production of the economy, which leads to GDP—was a function of just capital K in the standard case. But now we are going to say that at a given time step T, there is some production function across all of society that takes not just one type of capital, but all of the capitals: produced capital, human capital, and natural capital.
Production over time is going to depend on how much of each type of capital gets plugged into this production function.
Capital Stocks Over Time
One thing to note is that different societies will have very different levels of each type, and so we are going to keep track of the levels of each of the different capital stocks—just K at time t across all types.
For visualization purposes, let us say orange represents natural capital and dark blue represents produced capital. We are going to keep track of the relative shares.
The reason we like this structure is that we want to tie it back to welfare and consumer and producer surplus. Utilitarianism again provides a very clear ethical system here.
Connecting Production to Welfare
The Basic Accounting Identity
We talked about the Ramsey model and how growth essentially comes from accumulating capital. We are going to tell the same basic story. The amount we produce, Y_T, can be either saved or consumed. So Y_T equals C_T plus I_T, where C_T is consumption and I_T is investment (savings). That harkens back to the basic accounting identity we have seen, with the only difference being that we are now generating Y_T with a bunch of different types of capital.
Why Consumption Matters
The reason we care about C_T is that consuming is what generates welfare in one time step. What we really want to care about for sustainability is how much of that welfare we are going to be able to produce going forward. That is where V_T, the net present value, comes in.
V_T is the net present value of all future consumption.
You might be wondering why there is a T subscript on this. It is because you can assess this at any step. If you ask yourself today how much welfare you are going to get over the rest of your life, you could calculate that. But tomorrow, there would be a different calculation. So we can assess at any given time period how much future well-being there is.
The Mathematical Definition of Sustainability
With this framework in place, sustainability is simply that this V_T is non-declining—everywhere greater than zero in terms of its change. In derivative terms, sustainability means the change in V_T with respect to T is greater than or equal to zero. We are not going to do full derivations, but it is a useful way of keeping track of variables. All this boils down to the idea that future well-being is not declining.
The appealing aspect is that we now have a complete framework. We know that value comes from welfare, welfare comes from production, and we can tie it all together.
The Mathematical Framework
The Net Present Value Expression
Let us give a mathematical expression of V_T. It is going to be the sum over all future time steps up to the infinite horizon. The reason we keep track of S and T is that at time T, we care about the value from that point forward. We express that by summing over all those different future time periods a discounted utility function of how much happiness we get from consumption. The discount rate, just like we talked about last class, lowers the value of utility received further in the future.
The Capital Accumulation Equation
We also know specifically that C_T depends on productivity in the economy, which comes from plugging all of our capital types into the production function. And the capital in the next period would be our savings—how much we produced minus how much we consumed, minus the depreciated value of the remaining capital stock.
It took a while and there are a lot of moving parts, but now we have everything to very specifically and mathematically define what sustainability means: the derivative of this over time is everywhere positive.
Application of This Framework
In a PhD class, students would solve these equations using Hamiltonian or Jacobian optimization approaches. But what is important here is being able to, given something like this mathematical expression, make a statement about what it is saying.
Illustrating Sustainability with Elephant Diagrams
The Unsustainable Path
Let us depart from the math and return to it in words and visual figures. If sustainability is defined as non-declining human well-being, we can think about two different trajectories: an unsustainable one and a sustainable one.
In the unsustainable scenario, the C_T—the consumption portion—is quite large. Because C_T and savings have to equal however much was produced, large consumption means very small savings. This is a bad choice in time period T. The society gets a bunch of consumption—great—but what happens as a result?
Their capital stocks, starting from the initial level, fell quite a bit. All of their capital stocks fell because they are not replacing them at a rate sufficient to deal with depreciation. In this case, they degraded nature significantly and did not use the value created to increase produced capital. Which means in the next time period, production has a smaller amount of capital plugged into it, so less is produced—less to split between consumption and savings.
This society also does not try to correct their mistake in the subsequent period, again putting almost everything into consumption. Capital stocks continue to fall, production falls with them, and welfare declines over time. In other words, they were too greedy—they had a sugar rush early, and the consequence is that later they do not have as much to consume even if they wanted to.
The Sustainable Path
Conversely, in the sustainable world: we normalize so that both paths start with the same capital at time step one and the same production level. The big difference is that consumption is much narrower and the savings portion is much larger.
Consider two hypothetical individuals—Sustainable Joe and Unsustainable Fred. Fred is looking pretty good early on. He is having a great time, spending freely. But Joe says: just wait.
What Joe did was invest, which shows up as an increase in capital stocks. Produced capital goes up, and so do the others. It is worth noting that in the sustainable case here, total capital has gone up even though natural capital fell a little bit—there was some loss of nature but more than offset by increasing produced capital. So in the next period, this person can produce a larger Y_T.
Fred is still a little bit ahead and is still mocking his more frugal friend. But if this continues, the underinvestment strategy means the greedy consumer will eventually get outpaced. The frugal person—still saving a lot and not spending everything—now has absolutely more production to work with. Even with their frugality, they are now consuming more than Fred in absolute terms.
You can see that this is sustainable: the Y_T never goes down, which means C_T and welfare never go down. That is what sustainability is—there was enough savings such that they could keep their welfare from declining.
The Departure from GDP
This framework represents a departure from GDP, and it speaks to an important point: even if you hated the environment, you still would not want to use GDP as a metric. If you just measured GDP in the first time period, the unsustainable path would look best. But that is not a good metric because GDP then falls. And this argument holds even if you do not have natural capital in the picture—it is just especially impactful when you do.
Substitutability Between Capital Types
One really important thing to note is that there is substitutability between capital types. In both of our diagram examples, there was a reduction in natural capital. Even in the sustainable case, there is less nature over time. Natural capital is going down, and whether the path is sustainable simply comes down to whether we can compensate for the loss of natural capital with a now larger stock of produced capital.
This leads us to one important divergence in the definition of sustainability: strong sustainability versus weak sustainability. You might be thinking—is this not an environmental course? Why are we okay with the stock of natural capital going down? Can we really substitute? That is a fair question that deserves exploration.
Weak Sustainability vs. Strong Sustainability
Understanding the Distinction
Using interactive applications, we can see different consumption parameters. The most important one is the consumption rate—essentially, what percentage of Y are we going to use as consumption. A value close to 1 means consuming almost everything; a much lower value means consuming very little. The second parameter is depreciation.
With high levels of depreciation, no amount of savings can offset it. It is like there is a war going on and everything is being destroyed; in that case, the optimal savings rate ironically falls to zero—just live it up while it lasts.
But with lower levels of depreciation, we can see that there are different levels of consumption where inclusive wealth—this dV_T/dT—is going up over time. Strong sustainability is characterized by inclusive wealth consistently rising while maintaining all capital stocks. A weaker form of sustainability still has inclusive wealth rising overall. And unsustainable is anything where we are consuming away our well-being and drawing down our inheritance.
Weak Sustainability Defined
Weak sustainability means that dV_T/dT is greater than zero. Writing it with a bit more detail, inclusive wealth—which is a function of produced capital, human capital, and natural capital—is everywhere increasing over time. This just says the total inclusive wealth is always increasing.
Strong Sustainability Defined
Strong sustainability is much more restrictive—it requires that the change in the natural capital stock specifically is not declining. You can see why one is called strong and one weak. Strong sustainability says you cannot call yourself sustainable if your natural capital stock is decreasing. That aligns with a standard definition of environmentalism: preserve nature, make sure it never gets worse.
It is a lofty goal. But the rest of this course has been building towards the argument that if we want to stay in the planetary donut, we need to think not just about the ecological ceiling—which is related to strong sustainability—but about how that ceiling relates to the other things we care about in the social foundation.
A Developing Country Scenario
Consider a scenario where we start off in a very pristine state with greatly increased natural capital relative to the others. This might represent a developing country: less produced capital, less human capital, but an intact natural resource base. That is not far from geopolitical reality today—there is intense competition among wealthy nations to lock down resources in lower-income countries, because high-income countries have already depleted much of their own natural capital and are now looking at countries with high natural capital and low produced and human capital and wanting their lithium and other minerals.
When we have this higher natural capital world, in order for inclusive wealth to rise above the starting point, we are dramatically trading off—natural capital is falling quickly while other capital stocks increase. This is the fundamental challenge of the planetary donut: there is indeed a trade-off. Producing enough of the things we want in this basic growth formula does come at a cost.
In this example, the derivative of inclusive wealth with respect to T is clearly going up—so it is weakly sustainable. But what we can rule out is strong sustainability, because the natural capital stock is indeed declining.
If you believe that strong sustainability is the right policy standard, you would say this is bad.
To be strongly sustainable, you need to be at least weakly sustainable, but you also need a much higher level of inclusive wealth, because the only way to achieve it without degrading natural capital is to be much more productive. The strong sustainability scenario is one where all capital stocks are everywhere going up.
The Flow Visualization
Using the flow view, we can see the same basic idea represented by the width of arrows. If consumption is at a higher level, there is a lot of utility and welfare coming out, but the savings arrow is relatively thin. Conversely, if we save a lot, we are not throwing as big a party early on—but the party can continue and the capital stocks grow. When we consume everything, the capital stock shrinks and utility falls over time. But if we save enough, we can get onto the sustainable path, and if we save a lot, we can even achieve strong sustainability.
The Power of the Inclusive Wealth Framework
This framework is valuable because it is really hard to debate. Whenever you get into debates of values—preferences for one thing over another—you cannot make a compelling argument that one is objectively better. But in economic theory, if you are willing to accept that minimum set of assumptions—preferences, transitivity, the things covered in early microeconomics—everything else from there holds mathematically. The argument is unambiguous.
Of course, that does not mean the assumptions will always hold. You can always push back by questioning whether an assumption is reasonable in a specific context. But if the assumptions hold, there is no ambiguity here—and that makes this a really powerful tool.
It is a good definition of sustainability precisely because it lets us have a metric that is not ambiguous. That turns out to be really important.
Why Inclusive Wealth Is a Superior Metric
Inclusive wealth is argued to be one of the better, if not the best, metrics for potentially replacing GDP for several reasons.
First, it measures the stock of wealth, not the flow. Second, it is forward-looking—GDP is just the current year, and many other indicators are also just the current year, capturing how happy we are right now. Inclusive wealth is forward-looking, so actions that degrade your future well-being actually show up as costs. Third, it has an unambiguous definition of sustainability—at least if you accept the underlying preference framework, the answer to “is this sustainable?” is a clear yes or no. That is really different from something like the SDGs, which is a dashboard approach. If you have 169 indicators and some are going up and some are going down, it is hard to make a definitive statement about sustainability without making judgment calls about which indicators you care about more. Finally, inclusive wealth is grounded in economic theory—it is not an ad hoc correction to GDP, but an improved version of that standard logic.
Empirical Evidence on Inclusive Wealth
Looking at empirical studies, the story sketched out in our conceptual exercises is very clearly evident: natural capital per capita is declining, while human capital and produced capital are increasing.
Graphically, we see natural capital falling, produced capital rising sharply, and human capital following a positive trend. This means two things. First, GDP keeps going up pretty reliably, and people look at that and say things are going great. But the story is more nuanced if you look at it from an inclusive wealth perspective. The world is just barely holding even, and there is nothing to guarantee that natural capital will not fall enough that inclusive wealth itself starts declining.
The more specific story is that human capital has been the star. We have greatly increased human capital in developing countries, and improvements in education and access to health services are what have been driving the increases in inclusive wealth globally.
Breaking it down by specific countries, growth rates in inclusive capital vary a lot—not everywhere is increasing, so that global picture is a bit rosier than reality. And natural capital does appear to be declining as a share of total wealth. That is a problem.
Conclusion
Inclusive wealth will be used as the metric to assess sustainability going forward. When we start running sustainability policies or looking at specific challenges, we always want to ask not what does this do to GDP, or what does it do to the sustainable development goals, but what does it do to inclusive wealth. This framework provides the analytical foundation for the remainder of the course’s exploration of natural resource management, climate change, and ecosystem services.