Critique of 'Lotka's wheel and the long arm of history': Best available historical data shows major differences pre-1970, raising new questions

CC1: 'Comment on egusphere-2025-699', Andrew Jarvis, 25 Feb 2025 reply

Critique of ’Lotka’s wheel and the long arm of history’: Best available historical data shows major differences pre-1970, raising new questions.

This submission sets out some analysis of, and initial thinking around, the findings in Garrett et al., (2022). Although it touches on many different issues, its main focus appears to be on the robustness of the way Garrett et al., integrated GWP data to produce their estimates of all history time integrated GWP, and how you interpret the subsequent ratio of this to annual global primary energy use, 1970 - 2019. Like the author, I admire and have been influenced by a lot of Garrett’s thinking. However, also like the author I would question some of his analysis and handling of observations, especially given the interpretation often has such profound and far-reaching implications for society. I have never been happy with summing up such uncertain GWP data over such long time horizons, especially given the subsequent analysis is so sensitive to the substantial compound errors. This applies to the authors analysis too. Also, although we can point to some very long timescale phenomena in society (language, belief systems, practices etc.) the arguments constructed to support the use of the time integral of GWP (which has perfect memory!) have always waived away the first order effects of decay on the productive structures being described and the timescales this imposes. Attempting to reintroduce these decay effects through inflation always felt like a contradiction of the time integral GWP analysis. Hanley attempts to detail some of these arguments, supporting his points with a fresh analysis of what he believes are better data. Our problem is that the paper is so poorly constructed and written that it is hard to believe he has taken more care than Garrett et al., did. It is certainly very hard to access his arguments, or really understand what the scientific objectives are beyond a somewhat loose review of Garrett et al. This is a pity, because I do think a careful independent exploration of the Garrett time integral GWP analysis/framework is justified given it has been in circulation since 2011.

I would want to encourage the author to refocus their writing having first decided what the precisely they believe needs communicating and with some regard for the writing norms of the journal. I would also encourage them to see if compound errors/uncertainties could be brought into the analysis so the reader can start to gain some appreciation of what is and isn’t significant when we are looking at lines on graphs going up and down, or not.

A.Jarvis – 25/02/2025

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Citation: https://doi.org/10.5194/egusphere-2025-699-CC1

AC1: 'Reply on CC1 - This Lotka's wheel critique is carefully focused.', Brian Hanley, 27 Feb 2025 reply

This initial cut at a review by Jarvis mirrors discussion with the editors prior to submission. The editors also expressed an interest in a deep review of Garrett's work. That is a different article. This article should help move Garrett's economics work along. Good, empirical data, and clear critique should help him strengthen what he's developed. Perhaps something can be worked on together at some point. Clearly, the field thirsts for a good article like Jarvis pines for.
However, this article is laser-focused on two problems with the Lotka's wheel paper. The abstract is crystal clear on what those are. The introduction provides background, and cites the specific pages laying out Garrett's thermodynamic argument for those interested. I could be accused, perhaps, of beating the first problem mentioned in the abstract to death, but I believe it is warranted. Obviously, the authors and the reviewers of the original article did not do this work that I present. I find it surprising that a serious reader could miss these points. Yes, I discuss the larger context, but that is because one cannot understand these parts without them.
I am glad the author shares my interest in seeing the decay function promised in Lotka's wheel provided. I agree, and express this in section 5 (line 295). But this paper is focused on certain serious problems specific to Lotka's wheel that need addressing. This decay function is not a primary focus.
May I request that remarks be: within scope and reference specifics in the paper to ask a question, or claim an error was made? There are line numbers, section numbers, figure numbers and panel letters for this, so that we tie our discussion to my submission.
Care was taken in making this critique like a proof. This is why, for instance, the Energy Based Cobb-Douglas equation from Keen was brought in, to formally show the presence of energy in GDP. Yes, we "know it's there", but at present Keen's equation is the best developed as to how it works for GDP. This care to make it like a proof is also why math steps are shown that bridge the gaps in Lotka's wheel's presentation. This was not a trivial amount of work, and it is not a "loose review" of Garrett's work. As the article title states, it is a critique of one specific paper of Tim Garrett's. The abstract clarifies it is on two points. The discussion and concluding remarks are intended to be encouraging to Tim Garrett (and others) for exploration of a new way of looking at this. To help him, I found the best data available, cite my sources, explain interpolations carefully so anyone can repeat them, and point the reader at who is working on the problem of extending energy consumption and GDP estimation into history, and even extending into deep human time of 10-300 kya. If someone has better data I would like to know.

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Citation: https://doi.org/10.5194/egusphere-2025-699-AC1
RC2:
'Reply on CC1', Timothy Garrett, 06 Mar 2025 reply

I would like to comment on a couple criticisms raised by Andrew Jarvis.
1. "I have never been happy with summing up such uncertain GWP data over such long time horizons, especially given the subsequent analysis is so sensitive to the substantial compound errors."
It is true that the analysis presented in Garrett et al. (2022), hereafter GGK22, is sensitive to uncertainties in prior reconstructions. As a rule, it may be expected that the uncertainties increase the farther back in time one goes, and this has a cumulative effect. However, the impact on the analysis is less than might be imagined because, as described in GGK22, economic production is also progressively smaller the further back in history one goes, in fact much smaller because so much of the acceleration of humanity has happened fairly recently, presumably lit afire by the consumption of oil. Because it is much smaller, even though it covers a long timespan, it is not in sum the bulk contributor to current economic wealth. In fact, as stated in the abstract, over two thirds of the increase in global energy demands and historically cumulative inflation-adjusted economic production has happened since 1970. I think this makes some intuitive sense. Certainly to me it seems that our current state is determined to a primary degree by what has been established over the last half century or so. Nonetheless, this rather remarkable statement about societal acceleration does have some sensitivity to certain assumptions about the distant past made in the reconstruction. But again, as referenced in the Methods Section (Garrett et al. 2020 in PLoS ONE), rather liberal adjustments to the reconstructions have only a small impact on the calculated value of w = W/E, and do not affect the primary conclusion that w is effectively a constant parameter.
2. "Also, although we can point to some very long timescale phenomena in society (language, belief systems, practices etc.) the arguments constructed to support the use of the time integral of GWP (which has perfect memory!) have always waived away the first order effects of decay on the productive structures being described and the timescales this imposes. Attempting to reintroduce these decay effects through inflation always felt like a contradiction of the time integral GWP analysis."
There is no presumption of perfect memory in the summation. That would be obviously fallacious, especially for an article fundamentally tied to the 2nd Law of Thermodynamics for open systems. There is a downward adjustment on nominal economic production related to economic inflation, a devaluation of what has previously been produced, and one that is hypothesized to be linked to things falling apart. The conclusions of GGK22 state "Historically, hyperinflation has been associated with periods of societal contraction (Zhang et al., 2007), suggesting some link between current economic inflation and the fraying of previously built societal networks (Garrett, 2012). The Garrett, 2012 article in ESD goes into some detail on the link between economic inflation and material decay of the previously constructed, so I refer the reader to that article. One notable outcome of the analysis is that, averaged over some time period, inflation is simply the inverse of Energy Returned on Invested (EROI). That is if the inflation rate is 4%/year, then the EROI for that year is 25.

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Citation: https://doi.org/10.5194/egusphere-2025-699-RC2
- AC2: 'Reply on RC2', Brian Hanley, 07 Mar 2025 reply
  
  Tim, I will reply to all of this, point by point. But I cannot imagine how I could be more kind or respectful to what you have tried to do. I made a point of that in the introduction, and in the concluding remarks. How can you say that I make "personal asides"? What on earth are you referring to?
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2025-699-AC2
AC5: 'Reply on CC1 - Some basic analysis of Garrett 2011. See uploaded PDF for complete figures and discussion.', Brian Hanley, 03 Apr 2025 reply

Garrett 2011 Summary equations rendered for economist use - See pdf for version with TOC and figures.

Garrett, T.J. Are there basic physical constraints on future anthropogenic emissions of carbon dioxide?. Climatic Change 104, 437–455 (2011). https://doi.org/10.1007/s10584-009-9717-9
Key conceptual issue: λ is an aggregate Λ(t) [J/$] ≡ ∑ λ_i(t) [J/$]
The thermodynamic model in appendix A, is borrowed from growth of a snowflake or droplet. This atmospheric science model is then used for the human child growing up metaphor (Pg 440 after eq 3) Garrett 2011. In both cases, the model works well enough, as both snowflakes and human children grow in more or less equivalent units by a mechanism that can be considered singular. However, an economy is like a global ecology, with many different organisms interacting. Adding manufacturing and supply chains, etcetera, within the ecology makes for more complexity.

This simple model appears to have led to a conceptual issue, because snowflakes and droplets have one unchanging mechanism. This conceptual issue includes the incorrect belief that if λ is not a constant then the thermodynamic model is false. (section 4, pg 443) Let us not throw the baby out with the bathwater, because of this conceptual problem.
The λ constant has dimensions of [J/$] (Joules per dollar). So λ is how energy is used to convert resources into utility economy products which are each evaluated using currency for GDP. A bit of thought makes clear that this is industrial production, and it must be an aggregation function. This step of conversion of materials into products incorporates a huge population of different industrial processes with widely varying efficiency of conversion. This population of industrial processes change yearly, and even day by day as do the products produced. Entirely new products having value appear, and old products disappear. So λ should represent a large aggregation of outputs varying in t. This aggregate of functions will have new functions introduced and old ones removed. This necessarily means that λ cannot be a constant. It also means that any derivatives are complex. Any such summation is an estimate.

For clarity, let us represent λ with a capital Λ:

Λ(t)[J/$] ≡ ∑ λ_i(t)[J/$] where λ_i is one of the 359 million plus businesses in the world, and each λ_i is represented by some unique production function.
Energy & production equations

These are shown with their dimensions in brackets. J = Joules, $ = US dollars,

ΔG ≡ E_G(t) [J] This is the Gibbs free energy yield from consumption of some fuel source. (Eq. 1)

a ≡ E_a(t) [J] = α · E_G(t) This is base energy, for instance electrical power, or torque from an ICE engine. (Eq. 2)

w [J] ≡ E_x(t) [J] = ε · E_a(t) = ε · α · E_G(t) This is the net exergy that goes into products

α ≡ E_a(t)[J]/E_G(t)[J] = α(t) where 0 ≤ α(t) ≤ 1

ε ≡ Ex(t)[J]/Ea(t)[J] = ε(t)   where 0 ≤ ε(t) ≤ 1
P(t) ≡ Y(t) = Ea(t)[J]/Λ(t)[J/$]     This is one year of GDP .
Constants that really aren’t constant

ε and α are dimensionless, treated as constants. However, both are aggregates, and what makes up each efficiency factor is different. Still, these values are between zero and one.
Alpha α – α(t) The efficiency of engines, and mixtures of them

α describes the efficiency of engines used to harness energy for human use, which can vary based on maintenance, type of generation equipment and fuel source. This efficiency is shown in figures A and B, below. Note that the efficiencies shown are maximums for top of the line, properly tuned engines. In the real world, each engine of the same type is a bit different, equipment ages, and the mix of power sources can vary a great deal during the course of a day, to say nothing of a year or from year to year. Thus, in the real world, α should be a function varying in t.
α ≡ E_a(t)/E_G(t) = α(t)
Can α be treated as a constant? It is probably defensible for 5-10 year periods, maybe longer.
Epsilon ε – ε(t) the exergy used to manufacture products, and variable mixtures of them

ε is a different aggregate that to my knowledge is not tracked. ε gives the fraction of E_a(t) that ends up being used to make products and is not wasted (mostly as heat). This means that ε should be different for each λ_i and over the aggregation of Λ(t) probably display a broad range. Because the Λ(t) mix of industrial processes and products varies during the course of any given year and from year to year, I think it is required to say that ε is a function in t.
ε ≡ E_x(t)/E_a(t) = ε(t)
That said, I think ε can be ignored because there is no data to work with. Thus, I would normally set ε = 1, and use α, or E_a(t).

In the real world, E_a(t) is the majority of what is available as energy data. Electricity generation is easy to obtain. E_G(t) data would come from consumption of fossil fuel primarily, with some contribution from nuclear. E_a(t) easy, and E_G(t) mostly is a theoretical issue not normally used in economics, except that it is desirable to have the highest possible efficiency conversion of E_G(t) to E_a(t).
Eta η – and natural logarithms of energy functions

Garrett 2011 makes use of log functions and their derivatives, apparently with the assumption that these growth equations are logarithmic. However, I do not think this assumption being always true is warranted, although in economics, endless exponential growth equations are postulated and used. Additionally, η is a function that varies in t, per the definition given by Garrett.
d ln(a)/dt = d ln(ΔG)/dt = η this is from the end of figure 1 caption.
The above equation means the natural logs of two different energy equations have the same slope always at any time t. This could happen if and only if, the equations are the same equation, but modified by adding or subtracting a constant. This would mean a ≡ F1(t) and ΔG ≡ F2(t).

The addition of a constant to t will shift the curve left or right. [ F1(t+C) = F2(t+C) ] The addition of a constant to the equation will shift the curve up or down. [ F1(t) + C = F2(t) + C. ] In these cases, the first derivative does not change from the constant. In the first, the constant C is added outside of the function, as t can be any value. In the second, the C added to the equation disappears in the derivative.



However, here we see that the relation E_a(t)= α · E_G(t) is a proportion. In this case (treating α as a constant) α becomes part of the derivative in a nice way. We confirm by inspection of slopes (figure C) that the first derivative of two curves (red and blue) is not identical when it is a proportion.
Therefore, d ln(E_a(t))/dt ≠ d ln(E_G(t))/dt = η

From this we know that there are two or three rates, not one, and they are related by α. I will assign the derivative of ln(EG(t)) the value η and use subscripts for the others.
d ln(E_x(t))/dt = η_x and d ln(E_a(t))/dt = η_a and d ln(E_G(t))/dt = η

Therefore:

η ≡ d ln(E_G(t))/dt = η(t)



The system of equations

Putting this together, the basic system of equations is:
E_a(t) [J] / Λ(t) [J/$] = Y(t) [$]

E_a(t) [J] / Y(t) [$] = Λ(t) [J/$]

Y(t) [$] · Λ(t) [J/$] = E_a(t) [J]



C(t) [$] ≡ ∑ Y(t) [$]
Thus, it appears it should be possible to create a reasonable Λ(t) dataset, and fit functions to that dataset.

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Citation: https://doi.org/10.5194/egusphere-2025-699-AC5

RC1: 'Comment on egusphere-2025-699', Timothy Garrett, 04 Mar 2025 reply

AC3: 'Comment on egusphere-2025-699 Reply to Garrett', Brian Hanley, 14 Mar 2025 reply

RC3: 'Comment on egusphere-2025-699', Blair Fix, 24 Mar 2025 reply

Critique of "Lotka’s wheel and the long arm of history"

Blair Fix comments

Hanley's paper represents a welcome addition to the heterodox literature on how economic growth relates to energy use. I'm glad he's delved into Garrett's growth model. I think the paper deserves to be published, with some clarifying revisions.

# The big picture

Perhaps a good place to start is to comment on the herculean task of measuring global 'economic production'. The task is immense for modern times, let alone the distant past.

The chief problem is to realize that economist don't measure economic 'production' in any meaningful sense. What they measure is the flow of money, which can be tracked either from the expenditure side or the income side. From this flow of money, economists claim to infer the 'quantity of production'. But this inference depends crucially on a huge list of assumptions, and rests on the fraught task of collapsing price change (which varies between commodities and regions) down to a singular measure of inflation.

The problem is not that this inference can't be done. The problem is that there are no convincing reasons why any *specific* way of doing the calculation is the 'correct way'. As such, a reasonable conclusion is that there is tremendous ambiguity in the measurement of GDP, even for a single country, let alone the world.

I've written about this issue in detail here: https://link.springer.com/article/10.1007/s41247-018-0051-6

Preprint here: https://osf.io/3smra/

I mention this problem mostly to set expectations when testing the Garrett model. My expectation is that the W/E ratio should depend hugely on the dataset used, and the assumptions that go into that particular dataset. And I would argue that there are no compelling reasons to think that a particular GDP dataset is 'better' than others.

I'm also skeptical that the concept of 'global inflation' is meaningful, since it too rests on the many assumptions required to compare price change across commodities and countries. I'm even more skeptical that the concept of 'global inflation' is meaningful as we go into the deep past, where the vast majority of human activity was not monetized. What does it mean to speak of 'inflation' when there are no prices?

To summarize, my impression is that Garrett's thesis vastly oversteps what macro-economic data is actually capable of telling us. It seems to me that Hanley reaches a similar conclusion.

# Comments on format

1. Charts. In general, I'd like to see the charts better labeled. That should include labeling time series inside the charts, or providing legends. I think it would also be helpful for each panel to have a title. Also, can the charts have color? If so, it would greatly aid interpretation to have the various series differentiated by color.

2. Methods. My preference would be to move details about the reconstruction and replication dataset to an appendix, where the necessary details won't interrupt the flow of the paper. Also, it would be helpful to discuss the methods that go into the OWD dataset, since its GDP estimates depend on Maddison's work, which means the 'replication' dataset is not entirely independent of Garrett's original data.

3. Paper order. From the introduction, the reader is given the impression that the main aim of the paper is test the constancy of of W/E. However, the results and discussion of this test are buried amidst other tests/discussion. I think the test of constant W/E should have it's own section that precedes any other tests of the Garrett model (for example, regarding claims about inflation)

# Other datasets of interest

In his book 'The Measure of Civilization', Ian Morris estimates human energy consumption dating back to 15,000 BCE. See Table 3.1 and Table 3.4. Per capita energy use estimates are provided for the 'West' and for the 'East'. With population data for these regions, one can estimate global energy consumption far into the past.

I think it would be useful to include Morris' data in the analysis.

# Regarding Garrett's critique

Garrett raises a good point that the Hanley paper doesn't really justify the choice of data/methods that went into the replication dataset. This should be addressed.

Also, Garrett argues the GDP data should be based on Market Exchange Rate (so combining different currencies using the monetary exchange rate) rather than purchasing power parity (PPP). I'm not sure why this is justified.

At any rate, it appears that the OWD data used by Hanley is based on PPP. Also, it's my understanding that the Maddison data for historical GDP is calculated using PPP. (See the detailed discussion here: https://ourworldindata.org/grapher/gdp-per-capita-maddison-project-database). So it would seem like if Garrett is recommends MER GDP for recent data, that amounts to switching methods mid-way.

At any rate, I don't think that Garrett's criticism warrants rejecting the Hanley paper. If anything, I'm in favor of an open exchange via published responses.

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Citation: https://doi.org/10.5194/egusphere-2025-699-RC3

RC4: 'Reply on RC3', Blair Fix, 25 Mar 2025 reply

I should clarify that when I say the GDP data should be 'justified', I mostly mean that the methods underlying it should be described in more detail.

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Citation: https://doi.org/10.5194/egusphere-2025-699-RC4
AC4: 'Reply on RC3 - Responding to Blair Fix. Short version. Yes, to pretty much all of these suggestions.', Brian Hanley, 25 Mar 2025 reply

# The big picture
Great reference. I will beef up the introduction with material on the difficulty of assessing GDP, and how PPP is required for deep time datasets.
I think that the audacious attempt Garrett engaged to try to understand the relationship between energy consumed to operate economies, the production of that economy, and the valuation of money by what it can buy, is unique and valuable.
There are, indeed, major issues to wrestle with that will always be there. What the components of capital (K) are, and how to assess capital’s monetary and real economy value is at least as difficult as those of GDP. What GDP means, and how to assess it in monetary terms in the deep past is a question. Monetized systems have existed in hunter-gatherer societies. The Papua-New Guinea feather belts, shell money in Asia, Australia and North America, the giant stone wheel money of the Yap Islands all were used in hunter-gatherer societies. Accounts for commodities exchanged as money have clay records going back to ancient Mesopotamia. Assyrian records of "corporation" stamps to operate a business date to 1800 BC. Those certainly included people that lived by hunting, fishing, and foraging.
I agree that whether the concept of global inflation is meaningful is matter to wrestle with. I lean toward believing that inflation probably is globally meaningful because interest and inflation are integral to the operation of financial systems. Each monetary system, taken alone, usually displays inflation as a characteristic, although the CPI on which inflation is based is crucial for measuring this. Not all systems necessarily displayed this though---the old Jewish temple-lending system punctuated by jubilee forgiveness of debt may not have. The existence of the concept of debt implies that there is accounting that treats money as an abstract apart from any physical currency representation of the money. Financial systems become unhealthy when deflation rules, because the greater the deflation rate the greater the disincentive to invest or spend. Inflation can be thought of as the near universal de facto implementation of the demurrage currency of Germany that inspired the Worgle experiment in Austria. The difference is that demurrage cost for holding uninvested currency is fixed and predictable, but inflation is variable and uncertain.
# Comments on format
1. Charts. Yes to everything. I specifically removed color to comply with colorblindness accessibility standards. But I can put it back and continue to comply.
2. Methods. Either an Appendix, or a supplement works for me. OWID has publications I can try to summarize.
3. Paper order. Ok. I will work on that. I ordered it from the abstract, and I can see how the flow could be better.
# Other datasets of interest
Ian Morris - Thanks very much for that cite. Book is ordered. Did not know about him.
# Regarding Garrett's critique
I will beef up my discussion of Market Exchange Rate vs purchasing power parity (PPP). You can justify PPP into the past and deep past based on a CPI basket of commodities for living. Market Exchange Rate (MER) has no meaning before a currency existed.

.So it would seem like if Garrett is recommending MER GDP for recent data, that amounts to switching methods mid-way.
Yes, exactly. It's switching methods for the last 10%. Even so, for the modern era, this has a pretty minor effect.

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Citation: https://doi.org/10.5194/egusphere-2025-699-AC4

RC5: 'How to add dimensioned quantities: Comment on egusphere-2025-699', Timothy Garrett, 29 Mar 2025 reply

AC6: 'Reply on RC5 - Response to Garrett', Brian Hanley, 05 Apr 2025 reply

I appreciate that Garrett appears accepting of consensus on most matters of the critique. It is my hope it should be clear that I do not consider this critique to mean that the method of applying thermodynamic modeling to economics is unusable. And yet, I get the sense that we are stuck in a bit of a pothole here. The reason that I (Hanley) performed the work of this critique was to better understand Garrett's work, find any issues, and by doing so strengthen the work. I also hope to make it more accessible to others. It would be quite surprising if everything was perfect considering how far afield from economics atmospheric physics is. One could perhaps make the case that the economics field is even further from atmospheric physics.
Here, Garrett reiterates claims that his work has been misrepresented. He concentrates primarily on the Market Exchange Rate (MER) vs Purchasing Power Parity (PPP) issue, implicitly suggesting that this may refute the critique points relative to replicated GDP and W datasets, and is a highly significant error. Garrett uses an energy metaphor, "A rate defined in units of energy per time cannot mix e.g. exajoules per year with millions of barrels of oil equivalent per month." This metaphor is a bit exaggerated, as it would suggest that Hanley had done something as foolish as adding dollars, Yuan, Yen, Florins, Guilders, Denari, etcetera, between time periods without conversions. I did not make any such error(s). I took a dataset created by others who are accepted experts in the field of economics in deep time. The Maddisson dataset is a major part of their life's work. I used PPP because those experts in that field used PPP, and because I understand that PPP is the correct choice.

Thus, the point is now made twice regarding MER vs PPP. However, this point shows a misunderstanding of concept by Garrett, as is explained in my previous response. MER is meaningless in the not so distant past, to say nothing of millennia. How does one determine a rate of exchange between US dollars and Denari which ceased to be used 1000 years ago? It is done using the methods PPP uses. In any case, this MER matter is moot because I demonstrate the illustrated problem without reference to my replicate GWP data using Maddison Project data.

Perhaps Garrett missed that section because of the format, in which I place his text at the top of each section in Times New Roman, and my replies in Serif Sans? If not, and consensus is being avoided because of concerns over MER vs PPP, the fact that the MER vs PPP matter is moot should mean we come to consensus that way. We should achieve consensus because the issue presented in my critique remains clearly visible without any reference to the replication dataset that I created. This is seen under the "Figure 1-C with addition of Y_LW/E_Rep" heading. This renders the rest of the discussion moot relative the the primary matter displayed.
The MER vs PPP issue is discussed starting on page 7 of Hanley's "Response to Tim Garrett" posted above. The section title is "Market Exchange Rate (MER) versus Purchasing Power Parity (PPP)". The Table of Contents displays the headings, that in themselves tell the story, reproduced below.
Market Exchange Rate (MER) versus Purchasing Power Parity (PPP) .......................... 7
Take Y_Rep off the table and the replication of results problem persists ................... 7

Figure 1-C with addition of Y_LW/E_Rep .......................................................................... 7

Minor points addressing the MER vs PPP concerns. ....................................................... 8

Inflation is accounted for in OWID dataset .................................................................... 8

data between 1960 and 1990, using NYGDPMKTPCDWLD is accounted properly ... 8

PPP vs MER background ................................................................................................... 8

44% difference between the GGK22 and Hanley datasets ........................................... 9

Equation 5 difficult to understand. ................................................................................... 10

Adjustment from PPP to MER dollars ............................................................................... 10

PPP to MER is a red herring ............................................................................................. 10

Background on CPI ........................................................................................................... 11
Hanley's methods of interpolation are slightly different. I think those interpolation methods are mildly better, albeit with the caveat that any such interpolation has error margins. In any case, those interpolation methods do not have significant bearing on the issues discussed.

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Citation: https://doi.org/10.5194/egusphere-2025-699-AC6

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Critique of 'Lotka's wheel and the long arm of history': Best available historical data shows major differences pre-1970, raising new questions

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