Since posting this I’ve discovered some relevant sources, so I’ll offer my own answer.
The concept of “allocation” is important in deciding how the footprint of a process, such as food production, should be distributed across many products. (e.g. see the report “Product Carbon Footprinting”). If a farm, for instance, is producing a combination of beef for human consumption, dairy products and meat for pet food, how do you decide how much of the carbon and methane emissions to allocate to each product?
There is no “right” answer to this. Here in the UK we apparently follow PAS 2050, which recommends 3 steps: (1) differentiate between different processes as much as possible, (2) account for co-products using appropriate standard values if possible or (3) divide the footprint on the basis of economic value.
Sources of Pet Food
The US Pet Food Institute has a detailed report on the sources of pet food in the US. The inputs from slaughtering and rendering listed in Table 7 show, for instance, that beef makes up around 11% of the animal products in pet food by weight and 37% by cost. There is also meat from other animals and a large fraction, by weight, is made up of fat and “by-products”. The beef content is priced at $5/kg.
Pet owners may want to skip some of the detail here. Some websites suggest that the rendered remains of dead pets is included, but this appears to be a myth (e.g. snopes) . The UK regulations indicate what is allowed, and the list includes, for instance, meat which is fit for human consumption but of no commercial value (by which I assume they mean “no commercial value in the production of food for human consumption”, because the stuff is clearly being sold to pet food producers).
Prices for the Consumer.
Despite the unappetising ingredients, pet food is not substantially cheaper than much of the meat provided for human consumption. I have not done a detailed check on prices, but a spot check on the product range of a major UK supermarket showed that tinned cat food and beef burgers both cost about £2.50 per kg. The top range meat for humans is, however, much more expensive at around £20 per kg for steak.
What is in a carcass
An article from Drovers.com gives an idea of what can be made from the carcass of a beef cow. In 2011, a carcass in the US sold for about $190 per hundredweight, which works out as $4.20 per kg then, of which about 70% is meat. Since meat makes up virtually all the commercial value, this works out at an average of $6/kg for meat. Adjusting for inflation, that gives about $7/kg at 2020 prices.
About half the meat in a beef carcass is high value meat, and half low value, and the high value cuts retail at around 3 times the price of low value cuts (based on an unscientific survey of supermarket prices). In this breakdown, the value of the non-meat parts of the carcass is not considered worth mentioning.This means that 75% of the value comes from 50% of the meat, or, if we go for cost based allocation of the footprint, the footprint per kg of the low value meat is 50% of the average (half the weight producing a quarter of the value) and the high value meat is 150% of the average.
The US produces about 12.7 millions tonnes of beef carcass per year. Around 400 thousand tonnes (3.1%) of this goes into pet food, of which close to 50% is fat and by-products [Statista]. This is consistent with the Pet Food Institute report cited above, which give 240 thousand tonnes as the weight of beef meat going into pet food.
The Statista results in the previous section show clearly that the amount of meat going into pet foods is a tiny fraction of the amount of meat going into the human food chain. This is at odds with the claim, in “Environmental impacts of food consumption by dogs and cats” by Gregory S. Okin, that pet food in the US is taking up something like 30% of the output from meat production. Okin admits that there is significant uncertainty in his calculation due to the approach based on taking the ratio of human and pet protein intakes which are based on a complex range of assumptions. The much lower figure given by Statista appears to be based on more direct information, though getting full details requires payment of a hefty fee.
It is clear that animal by-products make up a substantial fraction of pet food. This is material which does not contribute significantly to the commercial value of the carcass, and hence, if we take the commercial value approach to allocation, should not be assigned a significant portion of the footprint associated with the production of the carcass.
The actual meat in pet food also contains meat of “no commercial value”, which may have been damaged.
There are three sets of prices discussed above: prices to the consumer, prices paid by the pet food industry to rendering plants and slaughterhouses, and prices received by farmers. These are not directly comparable, and I have not been able to get a set of consistent and complete figures in any one area.
We can get a rough estimate by observing that about 15% of the animal input to pet food is meat from ruminants (11% from cows, 4% from sheep). FAO give 300kg of CO2e per kg of beef protein, or 100kg of CO2e per kg of beef and about half that for sheep. The low value component of this meat that goes for human consumption has an impact which is, based on allocation by price, about half this: 50kg of CO2e per kg for beef and 25 kg CO2e per kg of sheep meat. Since pet food is made up of products which don’t reach the requirements of the low value market, there should be a further reduction based on price based allocation. Unfortunately, this is where my search for reliable numbers failed. Since the answer is surely a number between zero and one, I will guess at 50%.
Chicken and turkey meat has only one third of the carbon footprint of beef, but makes up a larger portion of pet food, at around 44%. Taking into account the percentages above, we get 6.9 kg CO2e per kg of meat based pet food.
Two pets in our household get through about 44kg of meat ingredients in pet food (their diet contains a small amount of vegetable products), which implies an annual 300kg CO2e footprint.