Conversions from expenditure to quantities consumed requires prices. Conversion from expenditure on nutrition requires an additional conversion of food quantities to calories or other macronutrients. This second step is critical for estimates of nutritional availability. The problem is more complicated than it may first appear—expenditures may not align to the prices used in conversion to quantities, and the quantity conversion to calories requires a number of assumptions. The authors of the preceding comment have carefully analyzed both of the conversions performed in my earlier work (Logan Reference Logan2006, Reference Logan2009). They should be commended for deriving estimates of calorie availability for the British sample of the 1888CEX and for a thorough discussion of the sampling of the British households in the data. Their work embodies the best principles of scientific replication.

For the first conversion, from prices to quantities, the authors find that the prices I used in the Aldrich Report are consistent with the other available prices that could be used to derive quantities (see Gazeley, Newell, and Bezabith Reference Gazeley, Newell and Bezabith2015, Table 2). Despite the restrictive nature of the Aldrich Report prices, they are fairly consistent with other contemporaneous prices. We agree, then, on the physical amount of food present in late nineteenth-century British diets.

We disagree on the nutritional value of those quantities. In my original work (Logan Reference Logan2006, Reference Logan2009) I was not concerned with calorie levels since the focus was on demand—that is, the relationship between calories per capita and expenditure or income. The conversion needed to be systematic so as not to introduce a spurious relationship between expenditure and calories per head. This is could happen unintentionally if one assumed that food items that form a larger share of food quantity for wealthy/poor households were significantly higher/lower than their true relative nutritional content. I therefore considered the prices in the food groupings (as defined by the prices used in the conversion) and used generic descriptions of the relevant food item to be consistent.

The food groupings in the 1888CEX are sometimes overly broad and the quantities converted to are therefore defined by the prices used in the conversion. My procedure for food groupings did not use the totality of food products for a given category, but a generic value of single products that would be most applicable for historical purposes. For example, for fish I used the nutritional value of the fish used in fish prices to construct food quantities (fish prices included cod, oysters, and salmon for the British sample and also mackerel for the American sample), and I explicitly excluded all specialized products on the market today.

One must be careful to note that the nutritional content of food derived from contemporary calorie conversions could overstate nutritional content when applied to the past. Contemporary conversions reflect current food quality, fortification, and processing. I explicitly considered the implications of bias in calorie levels influencing the demand results and saw that such concerns were not warranted. This included removing the poorest third of households in each survey, a detailed consideration of measurement error, comparative analysis of the calorie and food group shares as a function of income, instrumental variables estimates that produced biased downward estimates of the demand elasticity, accounting for home production of calories, and non-parametric analysis (Logan Reference Logan2006, Reference Logan2009).

The authors take a different approach to calorie conversion, and it drives the results they find. Instead of using the generic food item that corresponds to the prices used in the conversion of expenditures to quantities, they exploit the full range of food items available in modern conversions (Nutribase 2001). This gives a mean for each broad food category and a distribution (which they define as variation within each category), and they take these values to the quantities to produce new estimates of calorie availability. From their results (Gazeley, Newell, and Bezabith Reference Gazeley, Newell and Bezabith2015, Tables 4 and 5), it appears that my conversion is much more conservative than theirs, and also that their revised estimates are more consistent with the other analysis on similar diets (Gazeley and Horrell Reference Gazeley and Horrell2013).

Does this mean that they are correct? Only if the use of the mean of calories in a contemporary food grouping is the appropriate conversion for historical diets. On this point we disagree. The use of mean calories by food grouping in a contemporary nutritional accounting book is inappropriate for several reasons. First, the food groupings contain products which would have been unavailable in the nineteenth century. For example, the authors note that there are 350 types of bread—they do not mention that more than 200 of those types are commercial bread products which should not be used in calorie estimation (and many of which are not available in Great Britain to this day). Imagine multiplying historical hours worked by contemporary marginal products of labor—the results would be quite high but would not reflect historical productivity but rather modern technology. The same applies to food.

Second, treating each food in the grouping equally (each type of bread, for example) implicitly assumes that it was consumed by historical households. This is certainly not true. Such a procedure applies no weight to account for the fact that foods most likely to be consumed within such a category should have a larger impact on the calorie conversions. Treating each food within a grouping equally makes an additional assumption about consumption which is not tenable. I seriously doubt that French Meadow Yeast-Free Organic Sourdough bread was consumed by families in 1888, and yet the authors make just that assumption by including the value in the bread calorie conversion.

A closer look at Tables 3 and 4 bears this out. For example, the mean and “low” estimates for eggs are similar, as they are for pork, coffee, and tea. There is wide divergence, however, for “other meat,” potatoes, fish, bread, poultry, cheese, and even rice (in percentage terms). The reasons for this are obvious—bread today is not the bread of the past, and the changes in animal science drive variation in meat nutritional content (see Olmstead and Rhode Reference Olmstead and Rhode2008). The mean bread equals the “high” estimate for bread, for example, which suggest that bread in the modern conversion table is quite calorie rich.

The largest movements of calories per 100g (Table 3) are seen for staple food items, and nearly all of those movements show the mean to be closer to the “high” estimate than the “low” estimate. This suggests a skewed distribution of nutritional food groups – exactly what we would expect if the distribution in contemporary calorie conversions is weighted towards modern, calorie-rich foods. Take potatoes as an example. As a staple of the diet, increasing potato calories by more than twenty percent (when moving from the low to mean) should result in a substantial revision of calorie levels. This leaves aside the MCance/Widdowson estimates, which are sometimes far above the Nutribase (2001) calculated values but are also modern nutritional conversions. The question that remains to be answered is whether the potatoes (or beef or rice, etc.) consumed in 1888 were near the mean in nutritional content as recorded in contemporary calorie conversions or a lower value. The authors have produced little from the narrative record to support such an assumption.

The use of contemporary food nutritional counts creates problems that I believe are only exacerbated by the use of the full contemporary distribution of nutritional content. By taking the mean of the distribution for food groupings, which is skewed to larger calorie values, the authors are implicitly assuming that workers in the late nineteenth century has access to foods that they did not, and, in turn, substantially better nutrition. Only by excluding those food items that could not have been consumed in the past can one make a reasonable conversion. My approach was to use the generic category, which has its own problems as it may be a conservative estimate. Using the entire distribution from today's plentiful bounty introduces an assumption of dietary equivalence from past to present that is more problematic.

What the authors have produced is a stylized check of the conversion in Logan (Reference Logan2006). Assuming that these historical households had modern diet availability (with its increased calorie content) do the calorie levels line up with other availability estimates? The answer is yes, but given the problems with the conversion I just noted, this raises more questions than answers. Which calorie conversions we use will determine the calorie levels we estimate. When performing calorie conversions one must take great care to consider the actual quality of the food being consumed at the time.

Furthermore, revisions to calorie levels do nothing to change the interpretation derived from, say, the budget share devoted to food or the nutritional shares of the diet as a function of expenditure (detailed in Logan Reference Logan2006 and Reference Logan2009). In and of itself, that points to the limitations of using estimated calorie levels to draw conclusions about historical diets. The conflicting evidence is why I used the alternative measure of diet demand as opposed to availability (Logan Reference Logan2006, Reference Logan2009). Demand for calories rests of basic economic principles and they are by definition unit-free estimates of demand responsiveness. As such, the conclusions we draw from those comparisons depend on rational preferences, utility maximization, and the belief that preferences for nutrition will be revealed by expenditures on food. This moves us away from arguments based on physiology, nutritional science, calorie conversions, and the difficulty of estimating the exact nutritional content of historical diets. Even then, comparisons must be done with care as estimated calorie levels, budget shares, and even elasticities are just that—estimates which make a host of implicit assumptions that should be checked carefully against a variety of sources.