class: center, middle, inverse, title-slide # Lecture 14 ## Climate // Identification, Ricardian, Two Way FEs, Integrated Assessment ### Ivan Rudik ### AEM 6510 --- exclude: true ```r if (!require("pacman")) install.packages("pacman") ``` ``` ## Loading required package: pacman ``` ```r pacman::p_load( tidyverse, xaringanExtra, rlang, patchwork, nycflights13 ) options(htmltools.dir.version = FALSE) knitr::opts_hooks$set(fig.callout = function(options) { if (options$fig.callout) { options$echo <- FALSE } knitr::opts_chunk$set(echo = TRUE, fig.align="center") options }) ``` ``` ## Warning: 'xaringanExtra::style_panelset' is deprecated. ## Use 'style_panelset_tabs' instead. ## See help("Deprecated") ``` ``` ## Warning in style_panelset_tabs(...): The arguments to `syle_panelset()` changed ## in xaringanExtra 0.1.0. Please refer to the documentation to update your slides. ``` --- # Roadmap - Climate science for economists - Estimating the effects of climate change - Ricardian model - Weather / two way fixed effects approach - Integrated assessment - Dynamic Integrate Climate-Economy (DICE) model --- # Intro to climate science (Hsiang and Kopp, 2018) A key notion for climate change is *energy balance* -- Sunlight enters our atmosphere from space -- If the earth is to maintain a stable average temperature, the incoming energy from sunlight must be matched by an outgoing flow of energy -- 30% of the incoming energy is reflected away by the surface or clouds, the remaining 70% is absorbed by the earth's surface and atmosphere and is balanced by emitting back infrared radiation (heat) -- If we didn't have greenhouse gases in the atmosphere the global mean surface temperature would be about `\(-18^\circ C\)`! --- # Intro to climate science (Hsiang and Kopp, 2018) Greenhouse gases (GHGs) distort energy balance because they are transparent to incoming visible and ultraviolet light (big piece of the sun's spectrum), but they absorb infrared light which hinders the emission of energy back into space from the surface and lower atmosphere -- GHGs absorb infrared and then re-emit it in all directions, so some of the energy is returned to earth, and by conservation of energy, the earth and lower atmosphere warm up -- This increases the amount of out-going radiation and equilibrium is reached when it equalizes the trapping effect of GHGs --- # Feedbacks If the earth was just a plain sphere, doubling `\(CO_2\)` concentrations would lead to `\(1.2^\circ\)`C of warming -- But, additional warming also triggers .hi-red[feedbacks] in the climate system that alters how much warming we get from `\(CO_2\)` -- Feedbacks include things like: -- - A warmer atmosphere being able to hold more water vapor (humidity): water vapor is the most powerful absorber of outgoing infrared energy -- - Melting white sea ice being replaced dark blue ocean: the earth has become less reflective --- # Radiative forcing GHGs alter the radiative properties of the atmosphere, this influence is measured by .hi-red[radiative forcing]: how much human GHGs distort the average flow of radiation into the atmosphere relative to pre-industrial levels -- The change in `\(CO_2\)` concentrations from pre-industrial to now (about 278 ppm of `\(CO_2\)` to 410 ppm) exerts a radiative forcing of about `\(2.1 W/m^2\)` -- Changes in radiative forcing do not immediately translate into changes in temperature at the surface -- The ocean is cold and can absorb a lot of heat, it takes centuries to warm and slows down the overall warming of the surface of the planet --- # Historical climate <div style= "float:right;position: relative;"> <img src="figures/14-paleoclimate.png" width="575px" /> </div> The spike in `\(CO_2\)` is large, we can see seasonal variation in `\(CO_2\)` in the shorter panel caused by changes in the strength of ocean and land carbon sinks --- # Historical climate <div style= "float:right;position: relative;"> <img src="figures/14-paleoclimate.png" width="575px" /> </div> Until recently, the earth was slowly cooling because of slow variations in earth's orbit -- Now we are warming rapidly -- Sea level is responding only very slowly because water and ice can absorb a lot of heat --- # Climate models Climate models are mathematical representations of the physical climate system -- They range from very simple (1 equation!) to super complex earth system models that have very fine temporal and spatial resolution -- The simplest climate models are .hi-blue[energy balance models]: they just budget the energy in different parts of the earth and atmosphere -- These can be simulated in less than a second on a laptop for thousands of years -- Pen and paper versions of these models existed in the late 1800s --- # Climate models .hi-blue[General circulation models] popped up in the 1960s using fluid dynamics These capture the 3D structure of the earth and the dynamic evolution of the atmosphere -- Recent versions of these models are called .hi-blue[earth system models] which have elaborate representations of the ocean, sea ice, land surface, atmospheric chemistry, vegetation dynamics, and other things -- These are computationally very expensive: it can take several hours on a super computer to simulate one year of climate --- # Detection and attribution <div style= "float:right;position: relative;"> <img src="figures/14-detection.png" width="575px" /> </div> A central goal of climate science has been to detect and attribute changes to the climate -- Detection is where we need to determine if there has been a change in climate, attribution is figuring out what caused it --- # Detection and attribution <div style= "float:right;position: relative;"> <img src="figures/14-detection.png" width="575px" /> </div> When trying to determine human causes, we need to simulate counterfactual climates without human influence -- The intergovernmental panel on climate change (IPCC) has reported the current consensus on these points since 1990 --- # Attribution to humans <div style= "float:right;position: relative;"> <img src="figures/14-model_vs_obs.png" width="575px" /> </div> In counterfactual climates without human activity (blue on LHS), global average temperature has barely changed -- In the actual observations (black), we've seen a significant increase -- Model runs including human activity (red) closely match the observed data -- We are projected to have about triple the current warming by end of century if we follow a moderate emissions scenario (RCP 4.5) --- # Spatial heterogeneity in climate change <div style= "float:right;position: relative;"> <img src="figures/14-projected_temp.png" width="575px" /> </div> With an average increase in temperature of `\(1^\circ\)`C, there is substantial heterogeneity across the globe -- The arctic is predicted to warm substantially more than the rest of the planet, while the southern hemisphere is projected to have much less warming --- # Spatial heterogeneity in climate change <div style= "float:right;position: relative;"> <img src="figures/14-projected_temp.png" width="575px" /> </div> Warming also results in substantial differences in the change in rainfall -- The arctic, equator, and areas around the middle east and Indian ocean will see huge increases in rain -- South America and western Europe will see decreases in rainfall --- # Changes in temperature <div style= "float:right;position: relative;"> <img src="figures/14-us_rcp85.png" width="575px" /> </div> Climate change will be sort of like changing our current climate to that of another state or country -- If we follow a business as usual emissions path (RCP 8.5), New York at the end of the century will have similar summer temperature to recent summer temperatures in North Carolina or Kansas --- # Changes in temperature <div style= "float:right;position: relative;"> <img src="figures/14-us_rcp85.png" width="575px" /> </div> On average, temperatures in the USA will be more likely South Africa or Mexico! --- # Changes in flooding <div style= "float:right;position: relative;"> <img src="figures/14-flooding.png" width="575px" /> </div> Climate change will cause sea-level rise and increase hurricane intensity -- This increases the size and frequency of flooding events in coastal regions --- # Other changes Climate change will affect a lot of outcomes that are important for economics - .hi-blue[Precipitation:] changes in the mean or variance of precipitation has significant implications for agriculture -- - .hi-blue[Humidity:] humidity is important for human health, high humidity makes it difficult to cool yourself through sweating -- - .hi-blue[Cyclones/hurricanes:] climate change is expected to increase the strength and frequency of high intensity hurricanes but decrease the frequency of lower intensity hurricanes --- # Other changes Climate change will affect a lot of outcomes that are important for economics - .hi-blue[Ocean acidification:] the ocean absorbs a large chunk of the `\(CO_2\)` we emit, it turns into carbonic acid in water and will alter marine ecosystems in negative ways -- - .hi-blue[Ecosystems:] Animals and plants will need to migrate to adapt to climate change, slow moving organisms (e.g. Redwoods) will not be able to track the climate zones they live in -- - .hi-blue[Tipping elements:] There are multiple stable states of climate and climate change can lead to a rapid switch from one to another (e.g. permanent ice sheet melt, rainforest dieback, AMOC collapse) --- # What is climate? What is the definition of climate? -- A formal definition is that it is the .hi-blue[distribution] of possible weather at a particular place and time -- At each point in space `\(i\)`, and each time `\(t\)`, there is a vector of random variables `\(\mathbf{v}_{it}\)` that characterizes the conditions of the atmosphere and ocean `$$\mathbf{v}_{it} = \left[temperature_{it}, precipitation_{it}, humidity_{it}, \dots\right]$$` --- # What is climate? For some interval in time `\(\tau = [\underline{t}, \bar{t})\)` (e.g. a day, month, year, etc) there is a joint probability distribution `\(\psi(\mathbf{C}_{i\tau})\)` which characterizes the possible realizations of `\(\mathbf{v}_{it}\)` -- `\(\mathbf{C}_{i\tau}\)` is a vector is parameters that define the distributions (e.g. mean, variance, kurtosis, etc) -- `\(\mathbf{C}_{i\tau}\)` .hi-red[thus defines the climate] since it tells us what are the possible realized states (weather) --- # What is climate? For each time interval `\(\tau\)` there's also an .hi-blue[empirical distribution] `\(\psi(\mathbf{c}_{i\tau})\)` which characterizes the distribution of `\(\mathbf{v}_{it}\)` that actually occurred -- The empirical distribution is just the distribution of .hi-red[actual weather] -- `\(\mathbf{C}_{i\tau}\)` and `\(\mathbf{c}_{i\tau}\)` are .hi-red[not] the same: `\(\mathbf{C}_{i\tau}\)` characterizes the expected distribution of weather, while `\(\mathbf{c}_{i\tau}\)` characterizes the actual distribution of weather -- e.g. `\(\mathbf{C}_{i\tau}\)` is the expected minimum temperature in December, `\(\mathbf{c}_{i\tau}\)` is the actual minimum temperature --- # Climate versus weather The key takeaway: .hi[climate is not weather nor the realized distribution of weather] -- The actual weather is drawn from `\(\psi(\mathbf{C}_{i\tau})\)`, but `\(\mathbf{C}_{i\tau}\)` is never actually observed -- All we actually observe is `\(\mathbf{c}_{i\tau}\)` which includes things like -- - Observed/sample mean or variance of temperature in January -- - Observed/sample total rainfall in January -- - Maximum observed wind gust in a 24 hour period --- # Climate versus weather `\(\mathbf{C}_{i\tau}\)` includes things like -- - *Population/actual* mean or variance of temperature in January -- - *Population/actual* total rainfall in January -- - Theoretical maximum wind gust in a 24 hour period --- # Example difference <!-- --> --- # Example difference <!-- --> --- # Example difference <!-- --> --- # Example difference <!-- --> --- # Estimating the effect of climate change Climate can affect social outcomes in two ways: 1. .hi-red[Direct effect:] The climate during `\(\tau\)` affects the actual weather realizations `\(\mathbf{c}\)` which affects the economy -- 2. .hi-blue[Belief effect:] Beliefs `\(\mathbf{b}\)` about `\(\mathbf{C}\)` can affect decisions and economic outcomes regardless of what `\(\mathbf{c}\)` actually happens -- We can write that an outcome `\(Y\)` is a function of climate through these two channels $$ Y(\mathbf{C}) = Y[\mathbf{c(C),b(C)}] $$ --- # Estimating the effect of climate change The marginal effect of climate on `\(Y\)` is given by the vector of derivatives `\begin{align} \frac{dY(\mathbf{C})}{d\mathbf{C}} = \sum_{k=1}^K \frac{\partial Y(\mathbf{C})}{\partial \mathbf{c}_k} \cdot \frac{d\mathbf{c}_k}{d\mathbf{C}} + \sum_{n=1}^N\frac{\partial Y(\mathbf{C})}{\partial \mathbf{b}_n} \frac{d\mathbf{b}_n}{d\mathbf{C}} \end{align}` -- The first sum is the .hi-red[direct effect], the second sum is the .hi-blue[belief effect] -- The belief effect and interactions between belief and direct effects are commonly called .hi[adaptations], e.g. crop switching, or buying an air conditioner --- # Estimating the effect of climate change: ideal In an ideal scenario how would we estimate the effects of climate change? -- Basically run an experiment: -- 1. Have two identical copies of earth -- 2. Pump a lot of `\(CO_2\)` into the atmosphere of one of the earths, hold the other climate constant -- 3. Compare outcomes across the two earths as a function of whatever `\(\mathbf{c}\)` parameters are of interest (e.g. average temperature, heating degree days, etc) --- # Estimating the effect of climate change: ideal This experiment will give us an accurate, unbiased estimate of the *effect* of climate change net of adaptations since people in the climate changed earth presumably took up adaptive actions to deal with it -- What doesn't it tell us? -- 1. The gross effect of climate change -- 2. The .hi-red[cost] of adaptation (unless we have data on adaptive actions) --- # Estimating the effect of climate change: cross-section We don't have an alternative earth so we need to make due with just one -- The simplest way to try to recover an estimate of the effect of climate change is to use a .hi-blue[cross-sectional regression] -- Main idea: compare areas with different climates, look at how outcomes of interest differ -- What is the association between climate and outcomes at a given point in time? -- Mendelsohn, Nordhaus, Shaw (1994) do this for agriculture --- # Mendelsohn, Nordhaus, Shaw (1994) <div style= "float:right;position: relative;"> <img src="figures/14-value_of_farmland.png" width="575px" /> </div> Main idea: Compare *farmland values* in areas with different climates, conditional on other relevant variables -- Why farmland values instead of profits or production? -- What do farmland values tell us? --- # Mendelsohn, Nordhaus, Shaw (1994) The value of land is the .hi-blue[present value of the expected stream of profits] that can be obtained from that land -- That means farmland values internalize expected adaptive behavior like crop switching, input substitution, irrigation, etc -- Why focus on agriculture? -- 1. Agriculture is expected to be very climate sensitive -- 2. Lots of good data --- # Mendelsohn, Nordhaus, Shaw (1994): Data Ag data: 1982 Census of Agriculture Climate data: 30 year average temperature and precipitation (normal) from 1951-1980 Socio-economic data Soil data --- # Mendelsohn, Nordhaus, Shaw (1994): Estimation $$ \text{farmland value}_i = \alpha + \textbf{climate vars}_i' \cdot \mathbf{\beta} + \textbf{controls}_i' \cdot \mathbf{\gamma} + \varepsilon_i $$ -- We are interested in `\(\mathbf{\beta}\)` which tells us the .hi-blue[average marginal effect of changes in climate variables] -- Key assumption for `\(\beta\)` to be estimated correctly: -- `$$\mathbb{E}\left[\textbf{climate vars}_i \,\,\, \varepsilon_i|\textbf{controls}_i \right] = 0$$` -- Climate must be uncorrelated with omitted variables conditional on controls --- # Mendelsohn, Nordhaus, Shaw (1994) <center> <img src="figures/14-ricardian_table_1.png" width="500px" /> </center> Data are weighted either by cropland or crop-revenue Results are pretty sensitive to this choice: cropland weights --- # Mendelsohn, Nordhaus, Shaw (1994) <center> <img src="figures/14-ricardian_figure_1.png" width="575px" /> </center> The value of current climate for farmland across the US --- # Mendelsohn, Nordhaus, Shaw (1994) <center> <img src="figures/14-ricardian_figure_2.png" width="575px" /> </center> The value of `\(5^\circ\)`C of warming and 8% increase in precipitation under farmland weighting --- # Mendelsohn, Nordhaus, Shaw (1994) <div style= "float:right;position: relative;"> <img src="figures/14-ricardian_figure_3.png" width="575px" /> </div> The value of `\(5^\circ\)`C of warming and 8% increase in precipitation under crop-revenue weighting This shows a very different story because crop-revenue weights put more emphasis on irrigated land and products which will likely do better under a warmer, more humid climate --- # Mendelsohn, Nordhaus, Shaw (1994) <center> <img src="figures/14-ricardian_table_2.png" width="700px" /> </center> Results are pretty different depending on weighting .hi-red[Overall takeaway:] climate change could be moderately bad (4-6% losses), or mildly positive --- # Cross-section issues Should we believe these results? Why or why not? -- Remember the .hi-red[key assumption:] climate is uncorrelated with omitted variables conditional on controls -- This is very unlikely to hold in the cross-section -- What else varies across space similarly to temperature? -- Ozone, wealth, other productive uses of land besides agriculture, lots of things --- # Ortiz-Bobea (2019) <div style= "float:right;position: relative;"> <img src="figures/14-ariel_1.png" width="705px" /> </div> -- Since 1900, correlations between farmland values and soil quality and measures of climate are decreasing -- Indicates that there are other major factors influencing farmland values -- What could be driving this? --- # Ortiz-Bobea (2019) <div style= "float:right;position: relative;"> <img src="figures/14-ariel_2.png" width="600px" /> </div> Big increases in farmland value in weird places (Ozark and Appalachin Mountains, Vermont, upper Minnesota) -- Strong correlation between changes in farmland values and changes in housing values -- This points to demand for land for non-farm purposes (vacation homes!) as a primary driver of farmland values --- # Ortiz-Bobea (2019) So demand for non-farm purposes appears to affect farmland value -- Why is this a problem for estimating the effects of climate change? -- People's demand for housing is a function of climate Demand for housing is in `\(\varepsilon_i\)` since it affects farmland values `\(\rightarrow\)` .hi-red[our key assumption is violated] --- # The problem with cross-sectional approaches The big issue with cross-sectional approaches is that there are A LOT of variables we don't have data for -- These will be inside `\(\varepsilon_i\)` and many of them may be correlated with climate, so we need to control for them -- It is diffcult to control for lots and lots of variables in the cross-section --- # The problem with cross-sectional approaches Example: effect of climate on global mortality -- Very hot and very cold temperatures are both bad for mortality, what's the overall effect of climate change? -- Problems: - Climate is spatially correlated with economic development: countries in cooler climates are generally richer, have more safety net policies, etc -- - This will overstate the effect of climate change on mortality: countries in cooler climates are healthier because they're rich, not just because of the climate --- # The problem with cross-sectional approaches Example: effect of climate on global mortality -- Problems: Very hot and very cold temperatures are both bad for mortality, what's the overall effect of climate change? 2. Will not account for adaptation: mortality doesn't capture expected future outcomes like farmland values do, people will migrate, buy air conditioning, etc -- - This will overstate the effect of climate change: we are ignoring the possibility of adaptation --- # Panel approaches to estimation How can we find a way to handle all these possible omitted variables? -- Use .hi[panel data]: data where you have a time series for each person, country, etc over time -- Why does this help? -- Panel data approaches allow you to better control for large sets of variables for which you might not have data -- How? Let's find out --- # Panel approaches to estimation Suppose that the true relationship for climate change on farmland value is `$$\text{farmland value}_{it} = \textbf{time invariant vars}_i\cdot\alpha + \\ \textbf{climate vars}_{it}' \cdot \mathbf{\beta} + \textbf{controls}_{it}' \cdot \mathbf{\gamma} + \varepsilon_{it}$$` It is the same as before but now we have observations for each county `\(i\)` and year `\(t\)` -- We also broke out the .hi-red[entire] set of variables that are specific to each county `\(i\)`, but *do not vary over time*: `\(\text{time invariant vars}_i\)` --- # Panel approaches to estimation What we can do is estimate this using an approach called .hi-blue[fixed effects] This demeans all the data within each `\(i\)`, let bars indicate means within `\(i\)` `$$\text{farmland value}_{it} - \overline{\text{farmland value}}_{it} = \\ (\textbf{time invariant vars}_i' - \overline{\textbf{time invariant vars}_i}')\cdot\alpha + \\ (\textbf{climate vars}_{it}' - \overline{\textbf{climate vars}_{it}}') \cdot \mathbf{\beta} + \\ (\textbf{controls}_{it}' - \overline{\textbf{controls}_{it}}') \cdot \mathbf{\gamma} + \varepsilon_{it}$$` Remember: `\(\text{time invariant vars}_i\)` does not vary over time --- # Panel approaches to estimation This means that when we average within `\(i\)`, we have that `$$\overline{\textbf{time invariant vars}_i} = \textbf{time invariant vars}_i$$` It falls out of the estimating equation! -- This is why this approach is called .hi-blue[fixed effects:] anything 'fixed' (i.e. time-invariant) within `\(i\)` is controlled for by demeaning within `\(i\)` --- # Panel approaches to estimation `$$\text{farmland value}_{it} - \overline{\text{farmland value}}_{it} = \\ (\textbf{climate vars}_{it}' - \overline{\textbf{climate vars}_{it}}') \cdot \mathbf{\beta} + (\textbf{controls}_{it}' - \overline{\textbf{controls}_{it}}') \cdot \mathbf{\gamma} + \varepsilon_{it}$$` What does this mean? -- .hi-red[All] variables that are time-invariant within a county over time are implicitly controlled for when we demean the data! This means we do not need to explicitly control for time-invariant things like soil quality, elevation, average sunlight, etc for which we might not have data --- # Panel approaches to estimation We re-write the equation by including county fixed effects `\(\mathbf{\alpha_i}\)` `$$\text{farmland value}_{it} = \mathbf{\alpha_i} + \textbf{climate vars}_{it}' \cdot \mathbf{\beta} + \textbf{controls}_{it}' \cdot \mathbf{\gamma} + \varepsilon_{it}$$` where `\(\alpha_i\)` is a dummy variable equal to 1 for county `\(i\)` and 0 otherwise -- Since `\(\alpha_i\)` is always the same for county `\(i\)` no matter which year `\(t\)`, it effectively controls for all things in county `\(i\)` that are not changing over time, `\(\textbf{time invariant vars}_i'\)`, just like demeaning the data --- # Panel approaches to estimation Notice that there's nothing special about doing this with respect to `\(i\)` -- We could easily do this with respect to `\(t\)` for variables that are changing over time but are the same across all counties so there is no `\(i\)` index `$$\text{farmland value}_{it} = \textbf{common vars}_t' \cdot\alpha + \\ \textbf{climate vars}_{it}' \cdot \mathbf{\beta} + \textbf{controls}_{it}' \cdot \mathbf{\gamma} + \varepsilon_{it}$$` -- Take the average of the all the variables within a given year `\(t\)` (across all counties), and then demean the variables --- # Panel approaches to estimation `$$\text{farmland value}_{it} - \overline{\text{farmland value}}_{it} = \\ (\textbf{common vars}_t' - \overline{\textbf{common vars}_t}')\cdot\alpha + \\ (\textbf{climate vars}_{it}' - \overline{\textbf{climate vars}_{it}}') \cdot \mathbf{\beta} + \\ (\textbf{controls}_{it}' - \overline{\textbf{controls}_{it}}') \cdot \mathbf{\gamma} + \varepsilon_{it}$$` where now the bar indicates the average within each year `\(t\)` -- Similar to before, `\(\textbf{common vars}_t' = \widehat{\textbf{common vars}_t}\)` since these variables are not changing within a given `\(t\)` --- # Panel approaches to estimation This gives us: `$$\text{farmland value}_{it} - \overline{\text{farmland value}}_{it} = \\ (\textbf{climate vars}_{it}' - \overline{\textbf{climate vars}_{it}}') \cdot \mathbf{\beta} + (\textbf{controls}_{it}' - \overline{\textbf{controls}_{it}}') \cdot \mathbf{\gamma} + \varepsilon_{it}$$` This is the same idea as when we demeaned within each county `\(i\)` so its equivalent to each year having its own intercept: `$$\text{farmland value}_{it} = \mathbf{\eta_t} + \textbf{climate vars}_{it}' \cdot \mathbf{\beta} + \textbf{controls}_{it}' \cdot \mathbf{\gamma} + \varepsilon_{it}$$` where `\(\mathbf{\eta_t}\)` is called a year fixed effect --- # Panel approaches to estimation What does this mean? -- .hi-red[All] variables that are invariant across all counties within a year are implicitly controlled for when we demean the data -- What does this control for? -- Recessions, the current president, nationwide ag policy, etc --- # Two way demeaning: fixed effects Key thing: we can have fixed effects for `\(i\)` and `\(t\)` at the same time to simultaneously control for: 1. Variables that are constant within a county over time 2. Variables that are constant across counties within a given year `$$\text{farm outcome}_{it} = \mathbf{\alpha_i} + \mathbf{\eta_t} + \textbf{climate vars}_{it}' \cdot \mathbf{\beta} + \textbf{controls}_{it}' \cdot \mathbf{\gamma} + \varepsilon_{it}$$` -- This implicitly controls for A LOT of variables -- What's left 'omitted' that can cause us problems with estimating the effects of climate change? --- # Two way demeaning: fixed effects What's left 'omitted' that can cause us problems with estimating the effects of climate change? -- Only variables that are changing both within a county .hi-red[AND] over time -- This is the norm for panel regressions in applied economics (although you can't do this with farmland values) --- # Two way demeaning: fixed effects Note that you can't have a fixed effect with respect to `\(i\)` **and** `\(t\)` here -- e.g. `\(\omega_{it}\)`, a county-by-year fixed effect -- A county-by-year fixed effect controls for all things that are time-invariant within a county-year (e.g. things not changing in Tompkins County in 2019) -- Our data only vary at the county-year level -- A county-by-year fixed effect would control for everything on which we have data: we can't actually estimate anything --- # Alternative explanation for FE in climate economics What's the "gold standard" for estimating causal effects? -- Randomized control trials -- Suppose we have a group of 100 people and want to know the effect of a drug on hypertension We randomly assign 50 people to get treatment (e.g. drugs), and the other 50 people are controls (e.g. no drugs) --- # Alternative explanation for FE in climate economics Since we randomly assigned treatment, both groups should be identical .hi-blue[on average] -- The difference we see between the two groups in average hypertension outcomes after the drug treatment can be attributed to the drug -- .hi[Randomization] is key for estimating the effect of different kinds of treatments --- # Alternative explanation for FE in climate economics Is climate random from our (the economist's) perspective? -- No! -- People move to specific climates because of tastes -- Farmers select crops that are suitable to grow in their current climate -- Tourist economies are selected to be in specific climates --- # Alternative explanation for FE in climate economics Is weather random from our (the economist's) perspective? -- Sort of: Randomness comes from weather being a random variable drawn from `\(\psi(C_{it})\)` -- `\(i\)`: We know Ithaca's generally cold in January and warm in July -- But in Ithaca in January, *there's some randomness in how cold it is, given the climate `\(C_{it}\)`* --- # Alternative explanation for FE in climate economics `\(t\)`: We know the climate is generally getting warmer across the earth -- But in any given year, *there's some randomness in global temperature, given the climate `\(C_{it}\)`* --- # As good as random weather If we demean the data to control for time-invariant climate features of a county `\(i\)`, and trends in climate `\(t\)` what are we estimating the effect of? -- Deviations in weather from average weather -- We might think these are as good as random -- When farmers decide to plant in spring, they can't predict deviations from average weather during the growing season -- They appear to be effectively random --- # Weather vs climate If weather is random, then we can estimate the .hi-blue[marginal effect of weather] `\(c_{it}\)` -- Does this help us understand the marginal effect of climate `\(C_{it}\)`? -- A reasonable assumption is that the effect of weather provides an upper bound on the effect of climate change -- Why? --- # Weather vs climate Climate change is a long-run phenomenon: in the long-run we can adapt -- Farmers can switch crops, people can migrate, households can install air conditioning -- These actions aren't possible on a day to day basis -- Estimating the effect of weather is useful then, it tells us how bad climate change might be --- # Deschenes and Greenstone This 'random weather' approach was used by Deschenes and Greenstone (2007) to estimate the effect of weather on **farm profits** `$$\text{farm profits}_{it} = \mathbf{\alpha_i} + \mathbf{\eta_t} + \textbf{climate vars}_{it}' \cdot \mathbf{\beta} + \textbf{controls}_{it}' \cdot \mathbf{\gamma} + \varepsilon_{it}$$` -- Why profits? -- Because farmland values shouldn't change in response to random annual weather shocks (since they're random and transient, not permanent changes) --- # Deschenes and Greenstone: cross-section DG shows why the cross-sectional approach doesn't cut it, the estimated effects are very sensitive to controls, sample <center> <img src="figures/14-dg_1.png" width="700px" /> </center> --- # Deschenes and Greenstone: panel DG use .hi-blue[degree days] to capture climate: the sum of daily average temperature during the growing season <center> <img src="figures/14-dg_2.png" width="600px" /> </center> Main takeaway: little effect of climate change! --- # Deschenes and Greenstone: panel <div style= "float:right;position: relative;"> <img src="figures/14-dg_3.png" width="575px" /> </div> This is super surprising right? -- It should be -- In the short run, we'd think very hot weather would be bad for crops -- We'd expect farmers have little ability to adapt to (randomly) hot weather during the growing season --- # Deschenes and Greenstone: panel <div style= "float:right;position: relative;"> <img src="figures/14-dg_3.png" width="575px" /> </div> In the long run, it would be less surprising to find little effect since farmers can change crops or add irrigation if its persistently hot -- Turns out this result is because of a massive data error and too liberal use of fixed effects -- .hi-blue[Moral of the story:] data cleaning is the most important part of research, be extremely careful --- # Identifying climate from weather Are there cases where the effect of a change in weather tells us the effect of a change in climate? -- Recall, climate affects outcomes through two channels: -- 1. .hi-red[Direct effect:] The climate during `\(\tau\)` affects the actual weather realizations `\(\mathbf{c}\)` which affects the economy 2. .hi-blue[Belief effect:] Beliefs `\(\mathbf{b}\)` about `\(\mathbf{C}\)` can affect decisions and economic outcomes regardless of what `\(\mathbf{c}\)` actually happens --- # Identifying climate from weather If there are situations where belief effects are approximately zero, then marginal effect of weather `\(=\)` marginal effect of climate -- Suppose we're considering a farmer who's maximizing profit: -- `$$\pi_t(x_t; C_t) = \max_{x_t} \mathbb{E}_t \left\{ p^o_t [\alpha(C_{t}) \, x_t(C_t)] - p^i_t x_t(C_t)^2/2 \right\}$$` where `\(\pi_t(x_t; C_t)\)` is maximized expected profit, `\(x_t(C_t)\)` is how many acre are planted as a function of the expected climate, `\(p^o_t\)` is the output price, `\(p^i_t\)` is the input price, and `\(\alpha(C_{t})\)` is how climate affects output --- # Identifying climate from weather Suppose we're considering a farmer who's maximizing profit: `$$\pi_t(x_t; C_t) = \max_{x_t} \mathbb{E}_t \left\{ p^o_t [\alpha(C_{t}) \, x_t(C_t)] - p^i_t x_t(C_t)^2/2 \right\}$$` -- Let `\(x^*_t(C_t)\)` be the optimal choice of `\(x_t\)` given some climate `\(C_t\)` (i.e. the solution to the maximization problem) -- We can re-write the problem as: `$$\pi_t(x^*_t; C_t) = \mathbb{E}_t \left\{ p^o_t [\alpha(C_{t}) \, x_t^*(C_t)] - p^i_t x_t^*(C_t)^2/2 \right\}$$` -- Now differentiate with respect to `\(C_t\)` --- # Identifying climate from weather Differentiate with respect to `\(C_t\)`: `$$\frac{d \pi_t}{d C_t} = \mathbb{E}_t \left\{p^o_t \left[\frac{d\alpha(C_{t})}{d C_t} \, x_t^*(C_t) + \alpha(C_{t}) \frac{d x_t^*(C_t)}{d C_t}\right] - p^i_t x_t^*(C_t) \frac{d x_t^*(C_t)}{d C_t} \right\}$$` -- Collect terms into direct effects and belief effects: -- `$$\frac{d \pi_t}{d C_t} = \mathbb{E}_t \left\{p^o_t \frac{d\alpha(C_{t})}{d C_t} \, x_t^*(C_t) + \left[ p^o_t \alpha(C_{t}) - p^i_t x_t^*(C_t) \right] \frac{d x_t^*(C_t)}{d C_t} \right\}$$` -- The first term is the .hi-red[direct effect] while the second is the .hi-blue[belief effect] --- # Identifying climate from weather What does the firm's profit-max FOCs tell us about the direct effect? -- From the firm's profit maximization problem, `$$\left[ p^o_t \alpha(C_{t}) - p^i_t x_t^*(C_t) \right] = \frac{d\pi(x_t)}{dx} = 0 \text{ at } x^*_t$$` -- This gives us that `\begin{align} \frac{d \pi_t}{d C_t} =& \mathbb{E}_t \left\{p^o_t \frac{d\alpha(C_{t})}{d C_t} \, x_t^*(C_t) + \left[ p^o_t \alpha(C_{t}) - p^i_t x_t^*(C_t) \right] \frac{d x_t^*(C_t)}{d C_t} \right\} \notag\\ =&\mathbb{E}_t \left\{p^o_t \frac{d\alpha(C_{t})}{d C_t} \, x_t^*(C_t) \right\} \notag \end{align}` --- # Identifying climate from weather `\begin{align} \frac{d \pi_t}{d C_t} = \mathbb{E}_t \left\{p^o_t \frac{d\alpha(C_{t})}{d C_t} \, x_t^*(C_t) \right\} \notag \end{align}` All that's left is the .hi-red[direct effect!] -- This is an application of the **Envelope Theorem** -- Envelope Theorem: > The marginal effect of a parameter (climate) on an optimized objective (profit) is only composed of its direct effect and not secondary effects through changes in choice variables (belief effect) --- # Envelope theorem Why is the envelope theorem useful? -- The direct effect of climate is .hi[just the effect of weather] -- For outcomes that are optimized objectives, the marginal effect of weather is equivalent to the marginal effect of climate! -- This helps us better pin down the effects of climate change on a subset of interesting outcomes on which we may have data: -- 1. Firm profits 2. Ag land values (discounted stream of profits) 4. Income --- # Deryugina and Hsiang <div style= "float:right;position: relative;"> <img src="figures/14-dh_1.png" width="575px" /> </div> If we have the marginal effect of climate change, we can integrate across climates to get the .hi-blue[total effect of climate change] -- The left hand side shows the variation that allows us to estimate the marginal effect of climate change .grey[Gray:] The actual climate (average weather distribution) .red[Red:] Weather as drawn from the distribution of climate .blue[Difference:] Deviations from average --- # Deryugina and Hsiang <div style= "float:right;position: relative;"> <img src="figures/14-dh_1.png" width="575px" /> </div> The right side shows us how we can estimate the effect of non-marginal changes in climate: we integrate (sum) over marginal changes in climate -- If we want to know what happens to St. Paul with Orlando's climate we just add up all the marginal effects for climates along the way (red) --- # Integrated assessment Integrated assessment is the combination of both economic and climate models The most famous integrated assessment model (IAM) is Bill Nordhaus' Dynamic Integrated Climate Economy (DICE) model <center> <img src="figures/14-iam_1.png" width="900px" /> </center> --- # Integrated assessment Why do we need integrated assessment models? -- So we can compute the .hi-blue[social cost of carbon (SCC):] the present value of the marginal damage caused by an extra ton of `\(CO_2\)` along a given economic trajectory --- # Integrated assessment We compute the SCC at time `\(t\)` in a three step procedure: 1. Take a baseline economy (trajectories of emissions, consumption, temperature, etc) 2. Take this baseline and then increase `\(CO_2\)` emissions at some time `\(t\)` by 1 ton 3. Compute the SCC at time `\(t\)` as the difference in present value of the sum of damage after time `\(t\)` between 1. and 2. --- # Integrated assessment The baseline economy can be anything you want, business as usual, an optimal economy, whatever -- The social cost of carbon is defined for any particular future trajectory -- .hi-red[Key:] the social cost of carbon along the optimal trajectory will also be the socially optimal carbon tax --- # Integrated assessment The social cost of carbon depends on what we believe the economy and climate will be doing in the future -- Consider two possible futures: high economic growth and low economic growth -- The lower economic growth world is poorer `\(\rightarrow\)` we should save more for the future -- One way we can save for the future is by *avoiding the accumulation `\(CO_2\)`* -- If we think of the environment as an asset we are saving for the future by preserving/saving environmental quality --- # Integrated assessment: economic module We have iso-elastic utility: `\(U(c_t) = c_t^{1-\eta}/(1-\eta)\)` -- We store wealth as capital `\(K_t\)` and it can accumulate over time through investment, it also depreciates over time: `\(K_{t+1} = (1-\delta)K_t + I_t\)` -- We produce output `\(Y_t\)` using a Cobb-Douglas production function: `\(Y_t = A_t K_t^\alpha L_t^{1-\alpha}\)` where `\(A_t\)` measures productivity and `\(L_t\)` is labor -- The production process generates industrial emissions `\(E_t\)` as a by-product which go into the atmospheric `\(CO_2\)` stock `\(M^a_t\)` --- # Integrated assessment: climate module There are also exogenous non-industrial emissions `\(B_t\)` (e.g. land-use change) that enter the atmospheric `\(CO_2\)` stock `\(M^a_t\)` Net emissions are `\(e_t = (1-\alpha_t)E_t + B_t\)` where `\(\alpha_t \in [0,1]\)` is the percent of industrial emissions abated --- # Integrated assessment: climate module There are three different `\(CO_2\)` stocks: atmosphere `\(M^a_t\)`, upper ocean `\(M^u_t\)`, and lower ocean `\(M^l_t\)` `\(CO_2\)` can move according to the following linear system: $$ `\begin{bmatrix} M^{a}_{t+1} \\ M^{u}_{t+1} \\ M^{l}_{t+1} \end{bmatrix}` = `\begin{bmatrix} \phi_{11} & \phi_{21} & 0 \\ \phi_{12} & \phi_{22} & \phi_{32} \\ 0 & \phi_{23} & \phi_{33} \end{bmatrix}` `\begin{bmatrix} M^{a}_{t} \\ M^{u}_{t} \\ M^{l}_{t} \end{bmatrix}` + `\begin{bmatrix} e_t \\ 0 \\ 0 \end{bmatrix}` $$ `\(CO_2\)` in the atmosphere can be exchanged with the upper ocean The opper ocean can exchange with the atmosphere and lower ocean The lower ocean can exchange only with the upper ocean Emissions only directly enter the atmosphere --- # Integrated assessment: climate module Atmospheric `\(CO_2\)` traps heat and increases radiative forcing which is a function of the `\(CO_2\)` stock and other exogenous forcers `\(EF_t\)` `$$F_{t}(M_{t}^{a}) = f_{2x} \, log_2(M_{t}^{atm}/M_{pre}) + EF_{t}$$` --- # Integrated assessment: climate module Temperature at the surface of the earth `\(T^s_t\)` and in the lower ocean `\(T^o_t\)` is: `\begin{align} T^s_{t+1} &= T^s_t + C_1 \left[F_{t+1}(M^{a}_{t+1}) - \frac{f_{2x}}{s}T^s_t + C_3 \left(T^o_t - T^s_t \right) \right] \notag\\ T^o_{t+1} &= C_4 \, T^s_t + (1-C_4)\,T^o_t \end{align}` Surface temperature is a function of itself (first and third term), radiative forcing (second term), and heat transfer with the ocean (last term) Ocean temperature is a convex combination of itself and surface temperature where `\(C_4\)` determines how quickly the lower ocean warms --- # Integrated assessment: climate-economy linkage Surface temperature causes damages to production of output so that output net of damages is: `$$Y^n_t = \frac{Y_t}{1 + d_1 \, T_t^2}$$` -- Net output can be used for consumption, investment, and abatement `$$Y^n_t = c_t + I_t + Y^n_t G_t(\alpha_t)$$` where `\(G_t(\alpha_t)\)` is the fraction of output spent on abatement --- # Integrated assessment: web version Plug and play version of the DICE model: [http://webdice.rdcep.org/](http://webdice.rdcep.org/) Under the parameters tab you can simulate outcomes that optimize policy, choose a particular kind of carbon tax, or enforce a climate treaty You can also change parameters (e.g. growth, sensitivity of climate to emissions, etc)