Will a food carbon tax lead to more animals being slaughtered? A quantitative model
Does a food carbon tax increase animal deaths and/or the total time of suffering of cows, pigs, chickens, and fish? Theoretically, this is possible, as a carbon tax could lead consumers to substitute, for example, beef with chicken. However, this is not per se the case, as animal products are not perfect substitutes.
I’m presenting the results of my master’s thesis in Environmental Economics, which I re-worked and published on SSRN as a pre-print. My thesis develops a model of animal product substitution after a carbon tax, slaughter tax, and a meat tax. When I calibrate[1] this model for the U.S., there is a decrease in animal deaths and duration of suffering following a carbon tax. This suggests that a carbon tax can reduce animal suffering.
Key points
Some animal products are carbon-intensive, like beef, but causes relatively few animal deaths or total time of suffering because the animals are large. Other animal products, like chicken, causes relatively many animal deaths or total time of suffering because the animals are small, but cause relatively low greenhouse gas emissions.
A carbon tax will make some animal products, like beef, much more expensive. As a result, people may buy more chicken. This would increase animal suffering, assuming that farm animals suffer. However, this is not per se the case. It is also possible that the direct negative effect of a carbon tax on chicken consumption is stronger than the indirect (positive) substitution effect from carbon-intensive products to chicken.
I developed a non-linear market model to predict the consumption of different animal products after a tax, based on own-price and cross-price elasticities.
When calibrated for the United States, this model predicts a decrease in the consumption of all animal products considered (beef, chicken, pork, and farmed fish). Therefore, the modelled carbon tax is actually good for animal welfare, assuming that animals live net-negative lives.
A slaughter tax (a tax per slaughtered animal) would be more tax-efficient if the death of an animal is valued at ~10% or more of the Social Cost of Carbon (SCC), assuming that all animal deaths are valued equally. (The SCC is approximately $185, so the threshold is about $18.5.)
Anticipating tax effects is difficult, and this approach has its limitations. The takeaway from this post should not be “carbon taxation is great for animal welfare”, but rather to not instantly dismiss a carbon tax as bad for animal welfare.
This forum post provides a basic overview of the model and the most important results. Please see the full paper for the full methodology, all results, and the references.
The Small Animal Replacement Problem
Animal products are generally bad for the climate, but some animal products much more than others. Beef is by far the animal product with the highest carbon emissions, while chicken and farmed fish have lower emissions. If consumers swap out beef for chicken because of climate reasons, this could lead to the Small Animal Replacement Problem. Chicken and farmed fish are much smaller than cows, so it is necessary to kill more animals for the same amount of food. Therefore, substituting eating larger carbon-intensive animals with smaller, climate-friendly animals increases animal suffering on the extensive margin. (Assuming that all farmed animals live equally net-negative lives.)
For this reason, animal welfare advocates have been concerned about food carbon taxes, as it could incentivize substituting beef with chicken or other small animals. This concern has been voiced by users of the EA forum. It has also been researched by Animal Ask (2022) and Bruers (2024), who both found that a carbon tax could increase animal suffering, albeit with some methodological limitations.
However, food carbon taxes do not lead to a Small Animal Replacement Problem per se. There are two mechanisms at work here:
First, a food carbon tax increases the price of chicken meat, albeit by much less than the increase in the price of beef. This creates an incentive to buy less chicken meat.
Second, a food carbon tax creates a substitution effect from carbon-intensive and heavily-taxed animal products (like beef) to less-taxed animal products (like chicken). Because animal products are not perfect substitutes, a decrease in consumption of one product does not lead to an equivalent increase in the consumption of another animal product.
If the first effect is larger than the second, a carbon tax would actually decrease the consumption of larger and smaller animals and the policy will reduce animal suffering rather than increase it. This post presents the quantitative model that considers both of these effects.
The model
Input data and market model
To know whether a carbon tax will increase or decrease the number of slaughtered animals and the duration of their suffering, we can make a quantitative model based on the following data:
The carbon intensity of animal products (CO2-eq. emissions/kg).
The sensitivity of the demand and supply of animal products w.r.t. their own prices. (In economic terms: the own-price elasticities of demand and supply.)
How substitutable different animal products are. (In economic terms: the cross-price elasticity of demand.)
The pre-tax prices and quantities sold of each animal product.
The model assumes that the supply and demand functions of all animal products exhibit constant elasticities of demand and supply. The benefit of this approach is that the demand curve is convex, i.e. demand will be more than zero for all prices. This makes the approach more realistic than e.g. linear demand, where even moderate taxation levels predict a negative beef consumption, which is not possible.
Model equation
(You can skip this section and still understand the post.)
The left side of the equation describes the quantity demand of animal product , and the right side the quantity supplied of animal product . These must be equal in the post-tax market equilibrium. The quantity demanded depends on a scaling parameter , the price of the product itself (), the own-price elasticity of demand , and the prices of all substitute products with cross-price elasticities . Quantity supplied depends on a similar scaling parameter , the price that producers receive (which is the consumer price minus the tax on the product, and the own-price elasticity of supply .
I solved the non-linear system of equations numerically using the Newton-Raphson method in R. You can find all equations in the full text (Chapter 2) and the code on GitHub.
Measuring animal welfare impacts
I used the number of direct deaths, total deaths, direct duration of suffering, and total duration of suffering per kg of animal product from Faunalytics. These indicators are useful proxies for animal suffering, but do not measure animal suffering directly. For example, the lives of some species may be worse than others, and one might attach a higher moral value to some species than others.
Direct lives per kg. The number of animals slaughtered to produce 1 kg of food. This includes the loss proportion between primary production and retail.
Total lives per kg. Identical to direct lives per kg, but also includes pre-production mortality, male chicks and calves being killed, and feed fish deaths.
Direct days of suffering per kg. The days an animal is alive to produce 1 kg of food. It is a product of the direct lives per kg and the average lifespan of the relevant species.
Total days of suffering per kg. Identical to direct days of suffering per kg, but also includes the duration of suffering of animals dying pre-production, male chicks and calves killed after birth, and feed fish. Feed fish are generally wild-caught and therefore assumed to suffer for one day.
Results
Carbon taxes
At multiple levels of carbon taxation, the calibrated model predicts a decrease in the consumption of small animals like chicken and farmed fish. This means that the carbon tax reduces animal suffering, measured as the number of animals killed and the total time they spend suffering.
Table: Simulated effects of a $25 USD tax per tonne of CO2-eq. GHG emissions per capita per year. (NB: F. fish means farmed fish. Tax revenue is the gross effect of this policy only, excluding changes in other tax revenues.)
Beef | Chicken | Pork | F. fish | Total | ||
Economic effects | Tax (USD/kg) | $2.11 | $0.25 | $0.31 | $0.34 | |
Δ Consumer price (USD/kg) | $0.94 | $0.11 | $0.22 | $0.32 | ||
(12.8%) | (2.3%) | (2.5%) | (1.7%) | |||
Δ Producer price (USD/kg) | -$1.17 | -$0.14 | -$0.09 | -$0.02 | ||
(-15.8%) | (-3.1%) | (-1.0%) | (-0.1%) | |||
Δ Consumption (kg) | -2.505 | -0.214 | -0.139 | -0.005 | -2.863 | |
(-9.9%) | (-0.7%) | (-0.6%) | (-0.1%) | (-3.4%) | ||
Tax revenue (USD) | $48.12 | $7.56 | $6.75 | $1.77 | $64.21 | |
Climate effect | Δ Emissions (kg CO2-eq.) | -211.582 | -2.110 | -1.716 | -0.062 | -215.470 |
(-7.7%) | ||||||
Animal welfare effects | Δ Direct deaths | -0.013 | -0.199 | -0.003 | -0.003 | -0.217 |
(-0.7%) | ||||||
Δ Total deaths | -0.014 | -0.229 | -0.116 | -0.027 | -0.387 | |
(-0.5%) | ||||||
Δ Direct time of suffering (days) | -14.504 | -9.732 | -0.485 | -0.894 | -25.615 | |
(-1.0%) | ||||||
Δ Total time of | -14.892 | -9.907 | -0.621 | -0.982 | -26.403 | |
(-0.9%) |
Unsurprisingly, a carbon tax of $25/kg CO2-eq. mainly reduces beef consumption, which is the most polluting animal product. The reduction in greenhouse gas emissions (-7.7%) is for 98% attributable to less beef consumption.
The animal welfare effect of the policy is small. There are reductions in all indicators for animal suffering on the extensive margin, but none of those effects have a magnitude larger than −1.0%.
The qualitative results are similar for carbon taxes of $10 and $50 USD/tonne CO2-eq. When—as robustness checks—the substitutability between animal products is doubled or the own-price elasticity of demand is lowered to estimates from a different paper, the policy causes a small increase in the ‘total deaths’ indicator of 0.39% and 0.7%, respectively.
Slaughter taxes
I also calibrated the same model for a slaughter tax, where consumer pay a tax per slaughtered animal rather than per kilogram of greenhouse gas emissions associated with an animal product. Because chickens and farmed fish are much smaller than cows and pigs, a slaughter tax causes the price of chicken and fish to increase more than the price of beef and pork.
Because animal products differ more on the animal welfare impacts than the climate impacts, a slaughter tax of $2.50 per slaughtered animal does increase the consumption of beef and pork, but not enough to increase total greenhouse gas emissions over all animal products.
Is a carbon tax or a slaughter tax better?
In the calibrated model, neither a carbon tax nor a slaughter tax causes the external cost that is not taxed to increase. In other words: when only considering climate change and animal suffering, neither policy will have net-negative effects. However, depending on how one values tackling climate change to reducing animal suffering, one policy may be better than the other.
I compare food carbon taxes and slaughter taxes at equal tax revenues to find the ‘threshold’ of a Social Cost of Animal Use (SCAU) at which a slaughter tax becomes a better policy than a carbon tax. When the death of an animal is valued at 10% of the Social Cost of Carbon (SCC) or more, a slaughter tax is more effective at reducing external costs than a carbon tax, per dollar of tax revenue collected. In practice, that means that a slaughter tax is better than a carbon tax when the “social cost” of a killed animal is $17.48 or higher.
Because the system of equations that describes the market dynamics is non-linear, the threshold value depends on how high the taxes are. At higher tax revenues (>100 USD/person/year), a slaughter tax becomes an even more attractive option.
Can’t we just put a simple tax on meat and fish instead?
Yes, we can. Unsurprisingly, this reduces the greenhouse gas emissions and the animal suffering indicators of animal products by approximately equal relative amounts.
Doing this sort of “second-best” policies will cause sleepless nights for economists because it’s less efficient, but it’s probably a lot easier to implement.
Limitations
“All models are wrong, but some are useful.”—Often attributed to George Box
I assumed that there is no abatement in the supply chains. A carbon tax incentivizes producers to produce animal products in a more climate-friendly way. This could increase animal suffering on the intensive margin (e.g. intensification), and reduce the tax on the product. If, for example, beef producers switch to more environmentally-friendly practices, the tax on beef becomes lower and substitution effects decrease.
I assumed a functional form for the supply and demand functions. The functional form may be different, especially for the supply function. The supply function may be downward-sloping if there are increasing returns to scale. This could affect the qualitative conclusions from the model.
I weighed the time of suffering and the deaths of all animals equally. One may want to weigh these differently, based on (for example), welfare ranges or suffering-adjusted days. Since the main model predicted a decrease in the consumption of all animal products, this will not affect the qualitative results of the model.
This is a prediction model. Prediction models predict, but do not measure. Markets sometimes behave unpredictable.
It would be interesting to explore what the implications would be of including other animal products, like eggs and milk. My hunch is that this does not change the qualitative results, since eggs and milk are not good substitutes for meat products. But I am happy to update my views on this.
Full thesis
You can read the full pre-print on SSRN. The document explains the methodology in more detail and provides results tables for alternative calibrations.
You can replicate the results or run simulations yourself with the R code available on GitHub.
- ^
Calibration is a modelling term for picking numbers for the parameters of a model to make it match the real world.
This is a class act in reasoning transparency. I love how easy it is to skim and drill down into things for more detail. Same goes for the pre-print and replication code.
Nits:
I was confused what calibration meant since I think of this exercise as simulation. To me, calibration is taking some observed data and reverse engineering the elasticity. But this is starting with the elasticity values—taken from the Bouyssou et al. (2024) meta-analysis—and seeing how that goes forward in a pretend-tax situation.
I would have loved to hear about how trustworthy you found the Bouyssou et al. (2024) study, since it’s providing the elasticity values for your main analysis. That meta-analysis is really cool and probably the best we have. But it also feels like a bucket of numbers that doesn’t think too critically about its inputs. And cross-price elasticity feels like a tricky thing to estimate, something Rethink Priorities wrote about here.
But it’s still really cool. I like how simple this is conceptually and that (given some assumptions) carbon tax can be net-positive for all animals.
Thank you for the kind words and the useful feedback!
My understanding is that calibration is picking numbers for parameters in a otherwise pre-defined model to make it match the real world, and what you’re describing I think of as estimation rather than calibration. I’ll add a footnote to make my use of the word a little clearer!
You’re right on the validity of the Bouyssou et al. (2024) paper. There are quite some differences in the measured elasticity estimates in the literature, unfortunately. I’m more worried about the own-price elasticity of supply, though, as the literature is much more scarce and old.
Great post, Soem! I strongly upvoted it.
Your estimate for the relative reduction in animal-years is 11.7 % (= 0.009/0.077) of your estimate for the relative reduction in CO2eq. I estimate the harms caused to farmed animals by a random person in 2022 were 217 times as large as the harms they caused to humans because of their greenhouse gas (GHG) emissions. This suggests the benefits of your modelled carbon tax to farmed animals would be 25.4 (= 0.117*217) times as large as the benefits to humans.
Poorer welfare standards tend to have a lower carbon footprint, and you estimated a reduction of only 0.9 % in animal-years, which is quite small in light of the above and all other uncertainties. So, since I think the effects on farmed animals dominate, I think it is unclear to me whether a carbon tax would be beneficial or harmful overall. In contrast, I would say taxing the negative effects on farmed animals based on the time they spend in pain, as assessed by the Welfare Footprint Project (WFP), is robustly beneficial.
You’re right to point out the trade-off between low-carbon production and high welfare standards! Theoretically, it should be possible to adapt the model to weigh the animal welfare impacts on the extensive margin (=number of animals) by the intensity of the suffering of different animals, and to make intensity of suffering in turn a function of the carbon tax. That makes the whole model a bit more wonky but I think it’s important work that needs to be done.
I agree! I think it will be quite difficult to implement this, though. Will policymakers like to implement a tax based on ‘suffering units’ with quite some uncertainty? I wonder if we can find a decent proxy that is easier for taxation.
I think it is worth trying. Higher welfare animals tend to grow slower and reach smaller slaughter weights, so taxing animal-years and animals slaughtered will tend to desincentivise welfare reforms, and, if there is a carbon tax, doubly so because they tendentially imply greater GHG emissions.
I agree the suffering of farmed animals is more uncertain than GHG emissions, but I think it may well be less uncertain than the suffering of humans caused by GHG emissions, which I would say is a more relevant comparison. Bressler 2021 estimates “the 2020 MCC [mortality cost of carbon] is 2.26 × 10⁻⁴ [low to high estimate −1.71×10⁻⁴ to 6.78 × 10⁻⁴] excess deaths per metric ton of 2020 emissions”. So there is significant uncertainty with respect to whether GHG increase or decrease human mortality. For comparison, below are the time hens and broilers spend in pain as estimated by WFP. I think the bars are supposed to be the 95 % confidence intervals, although I did not find information about this in the page.
The uncertainty respecting the suffering of animals is much larger than suggested by the above due to uncertainty in welfare ranges and pain intensities. Yet, one can at least be pretty sure eating animals causes them pain, and this happens very soon after consumption. In contrast, Bressler 2021 estimates roughly no impacts until 2055.
I still think you have a point because people may overestimate the uncertainty of the impacts on animals, and underestimate that of the impacts on humans. In addition, people may care about other types of uncertainty beyond uncertainty about the direction of the effect, which is the one I think is lower for animal suffering.
Executive summary: A quantitative model shows that a carbon tax on food would likely decrease both greenhouse gas emissions and animal suffering in the US, contrary to concerns that it might increase animal deaths by encouraging substitution of beef with chicken.
Key points:
While beef has high carbon emissions but fewer animal deaths per kg, and chicken has lower emissions but more deaths per kg, model shows direct price effects outweigh substitution effects
When calibrated for US markets, a $25/ton CO2 tax reduces both emissions (-7.7%) and animal deaths (-0.7%), mainly through decreased beef consumption
A slaughter tax becomes more efficient than a carbon tax if the social cost of an animal death is valued at >10% of the Social Cost of Carbon (~$18.50 per death)
Key uncertainty: Model assumes no supply chain adaptations that could increase intensive farming
Simple meat/fish tax could be easier to implement though less economically efficient than targeted carbon/slaughter taxes
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