Monday, April 25, 2016

A decade of advances in climate econometrics

I have a new working paper out reviewing various methods, models, and assumptions used in the econometrics literature to quantify the impact of climatic conditions on society.  My colleagues here on G-FEED have all made huge contributions, in terms of methodological innovations, and it was really interesting and satisfying to try and tie them all together.  The process of writing this was much more challenging than I expected, but rereading it makes me feel like we as a community really learned a lot during the last decade of research. Here's the abstract:
Climate Econometrics (forthcoming in the Annual Reviews
Abstract: Identifying the effect of climate on societies is central to understanding historical economic development, designing modern policies that react to climatic events, and managing future global climate change. Here, I review, synthesize, and interpret recent advances in methods used to measure effects of climate on social and economic outcomes. Because weather variation plays a large role in recent progress, I formalize the relationship between climate and weather from an econometric perspective and discuss their use as identifying variation, highlighting tradeoffs between key assumptions in different research designs and deriving conditions when weather variation exactly identifies the effects of climate. I then describe advances in recent years, such as parameterization of climate variables from a social perspective, nonlinear models with spatial and temporal displacement, characterizing uncertainty, measurement of adaptation, cross-study comparison, and use of empirical estimates to project the impact of future climate change. I conclude by discussing remaining methodological challenges.
And here are some highlights:

1. There is a fairly precise tradeoff in assumptions that are implied when using cross-sectional vs. panel data methods. When using cross-sectional techniques, one is making strong assumptions about the comparability of different units (the unit homogeneity assumption). When using panel based within-estimators to understand the effects of climate, this unit homogeneity assumption can be substantially relaxed but we require a new assumption (that I term the marginal treatment comparability assumption) in order to say anything substantive about the climate. This is the assumption that small changes in the distribution of weather events can be used to approximate the effects of small changes in the distribution of expected events (i.e. the climate).  In the paper, I discuss this tradeoff in formal terms and talk through techniques for considering when each assumption might be violated, as well as certain cases where one of the assumptions can be weakened.

2. The marginal treatment comparability assumption can be directly tested by filtering data at different frequencies and re-estimating panel models (this is intuition between the long-differences approach that David and Marshall have worked on). Basically, we can think of all panel data as superpositions of high and low-frequency data and we can see if relationships between climate variables and outcomes over time hold at these different frequencies.  If they do, this suggests that slow (e.g. climatic) and fast (e.g. weather) variations have similar marginal effects on outcomes, implying that marginal treatments are comparable.  Here's a figure where I demonstrate this idea by applying to US maize (since we already know what's going on here).  On the left are time series from an example county, Grand Traverse, when the data is filtered at various frequencies. On the right is the effect of temperature on maize using these different data sets.  The basic relationship recovered with annual data holds at all frequencies, changing substantially only in the true cross-section, which is the equivalent of frequency = 0 (this could be because that something happens in terms of adaptation at time scales longer than 33 yrs, or that the unit-homogeneity assumption fails for the cross-section).

3. I derive a set of conditions when weather can exactly identify the effect of climate (these are sufficient, but not necessary).  I'm pretty sure this is the first time this has been done (and I'm also pretty sure I'll be taking heat for this over the next several months).  If it is true that
  • the outcome of interest (Y) is the result of some maximization, where we think that Y is the maximized value (e.g. profits or GDP),
  • all adaptations to climate can take on continuous values (e.g. I can chose to change how much irrigation to use by continuous quantities),
  • the outcome of interest is differentiable in these adaptations, 
then by the Envelope Theorem the marginal effect of weather variation on Y is identical to the marginal effect of identically structured changes in climate (that "identically structured" idea is made precise in the paper, Mike discussed this general idea earlier). This means that even though "weather is not equal to climate," we still can have that "the effect of weather is equal to the effect of climate" (exactly satisfying the marginal treatment comparability assumption above). If we're careful about how we integrate these marginal effects, then we can use this result to construct estimated effects of non-marginal changes in climate (invoking the Gradient Theorem), which is often what we are after when we are thinking about future climate changes.

Pretty much no paper has ever checked these assumptions before (note that none of these assumptions have anything to do with expectations, the issue most folks focus on when wondering whether weather can be used to measure effects of climate). They are almost certainly not always met, for example they shouldn't necessarily hold for the case of maize and temperature described above (a good reason to think about empirical tests of the MTC assumption, like the one above). But sometimes they are satisfied (by luck?!). For example, in our recent paper on the GDP effects of temperature, these conditions are all probably satisfied (whew!).

I'll dedicate another blog post to going through this result in greater detail, something David suggested (I think because he didn't want to read the paper). But for folks just interested in this idea, here are some slides from a Climate Economics Lunch at Berkeley where I presented it.

4. A lot of the biggest breakthroughs in the field have not been about writing down a different regression or interpreting them in a clever way, but rather by figuring out appropriate ways to measure the climate in socially-meaningful ways.  This is a step in the process that I think is usually underemphasized in papers and seminars, but innovation in this dimension is often the key that opens up whole new areas of inquiry. For example, Wolfram and Mike's work carefully constructing degree days really cracked open the US maize-temperature revolution.  In other cases, thinking carefully about how to measure hurricane exposure, within-season rainfall distributions, or malaria ecology has been key. I also point out in the paper that if we don't construct these measures carefully, based on physical principles, they are unlikely to be useful when making climate change projections or extrapolating results to other countries.  But in cases where this has been done well, we've seen really remarkable convergence of results across samples--something that gives us confidence in making projections.

5. One has to be really careful when estimating nonlinear models. We know how to do this now, and the paper provides step-by-step instructions. But if you don't implement things correctly, you can get all sorts of things. In particular, local and instantaneous nonlinear effects (think: the effect of an hour of heat on a single maize plant) look very different from aggregate effects (think: the effect of seasonal mean national temperature on total maize yields). This can cause results that are actually describing the same thing to appear as if they are different (I think this explains a lot of why Massetti et al think they disagree with Wolfram).

6. Temporal and spatial displacement matters. Again, we've figure out a lot about how to do this in many flexible ways, even with nonlinear models. This matters, especially when thinking about total social costs, because the local and immediate effects of climate are not always the whole story. For example, a hot day generates a lot of excess mortality immediately, but many of those individuals would have died anyway during the following month (see red line below, on left) so an important effect of a hot day is "forward displacement" (in time) of mortality. If we counted all those displaced deaths as if they were totally new, then we would over-estimate the social cost of hot days. The reverse is true for cold days, where excess mortality tends to be delayed several days and doesn't show up immediately (see blue line below). The idea of spatial displacement is pretty much identical, except one thinks about outcomes being displaced in space rather than time--think about ripples in a pond surface moving away after you drop a stone in.  A few papers have thought carefully about this issue (e.g. see green line below on the spatial effects of a hurricane on GDP growth), but this is a bit harder to implement so it hasn't caught on widely in the literature yet, although the implications for computing social cost are very similar.

7. Uncertainty is more complicated than in most econometric problems, but we know some things to consider. For example, accounting for temporal and spatial auto-correlation in residuals is important because we know that most climatic forcing is auto-correlated. Also, accounting for climate model projection uncertainty is really important, since it often dominates statistical uncertainty (Marshall & David has spent a lot of time on this).

8. We know a lot about how to identify and measure adaptation in data, but there is still a lot to figure out.  Most of the approaches in the literature boil down to
  • Indirectly measuring adaptation by using cross-sectional regressions to start with. This approach "captures" the effects of adaptation, but doesn't really let us say anything about adaptation effectiveness or to separate adaptation effects from the direct effects of the weather. Also, as mentioned before, this approach requires strong assumptions about the comparability of different units across space.
  • We can explicitly observe outcomes that we think represent adaptations, such as seeing if hot days lead to more people purchasing AC units. This is nice, because we can see exactly what is going on, but a challenge is that we don't really know if these adaptations are very effective or not, we can just see that they're happening. Also, if the action we are looking at isn't the whole adaptation story, e.g. people buy AC's and pools and go running earlier in the day when it's hot, then we miss out on all the actions we aren't focusing on.
  • We can compare estimated marginal effects of climate across locations that we predict should be adapted differently to see if actual patterns match our intuition. For example, we can see if locations where hurricanes frequently strike are less affected by storms of a fixed intensity, something that might suggest they are well adapted to a hurricane-prone climate. This approach is nice because it let's us see the overall effectiveness of all actions a population might take to adapt. But the downside is we can't really see what's going on under the hood, so if we see effective adaptation we don't know what technologies or actions are being employed.

9. There are now well established approaches for using empirical response functions to attribute historical impacts of climate (as in David and Wolfram's crop trends paper) as well as for projecting future impacts. The two approaches are conceptually identical, although future projections are far more common in the literature, despite the fact that historical attribution exercises often suggest very large (and interesting) impacts of climate, even in the absence of climate change.

10. My short methodological to-do list for enterprising researchers in this field:
  • We need stronger techniques for drilling down and getting at mechanisms. A lot of results in the literature are reduced-form, but efficient policy design often requires that we understand more about what mechanisms link climatic events to social outcomes.
  • Understanding how general-equilibrium effects and spatial reallocations will respond to climate is hard, but it is a dimension of adaptation that is likely to be important. Right now we know very little about these effects and the tools folks are currently using for their analysis is often not up to the task.
  • There  are a lot of events that humans haven't experienced in recent history (or ever), such as rapid sea level changes or ocean acidification, and thus we have essentially no empirical evidence regarding their impact.  Graduate students should dig deep and be innovative to figure out how we can price these impacts using real world data.
  • We need to work harder at figuring out how to integrate empirical findings with theoretical results and the numerical models used to compute the social cost of carbon. Fran Moore and Delavane Diaz did innovative work on this, and our team working on the American Climate Prospectus made some headway, but there is so much more to do and all sorts of conceptual challenges that need to be worked out in order for us to have an empirically-calibrated estimate for the social cost of carbon.

That's all, make sure to check back in 2026!

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