Thursday, October 10, 2019

Wage growth in NY and PA

Without meaning to start an argument, I concurred with Steve Roth and @Promethus_Fire that a minimum wage study by the NY Fed might not have taken into account factors that may have confounded the study in contradiction to J. W. Mason's assertions without evidence that a) border discontinuity automatically controls for them (it does not), and b) economic data is continuous across the NY-PA border (it is not, and I provide several examples that by inspection should give us pause in making that assumption).

Even otherwise arbitrary political boundaries that you might think were transparent to the people living there create weird effects. One example I remember vividly on my many drives between UT Austin and the suburbs of Houston (where I grew up) on US 290 while I was a student was the border between Washington county and Waller county whereupon crossing the Brazos river the road suddenly became terrible. There's no particular reason for this in terms of demographics or geography, but the political boundary meant some completely different funding formula or crony capitalist network at the county level. Something similar happens at the NY-PA border:

On the NY side we have shoulder markings and shoulders that vanish right when you cross the border into PA. It's a tiny difference, but it means more materials and hundreds more labor hours of public spending on the NY side of what is basically the same road. And it's not like people travel into PA never to be heard from again — on this stretch of road traffic is likely balanced in either direction and most certainly isn't discontinuous at this specific point.

Anyway, that was the point I was trying to make. Other things like level of education also vary across this border as well as the PA side being much more likely to have an old-fashioned male breadwinner model of household income. My most recent piece of evidence was that the rate of foreign born residents was higher on the NY side (which looks like New England) than the PA side (which looks like West Virginia).

But then J. W. Mason expressed incredulity at my claim that the wage growth data was relatively smooth. This led me down a rabbit hole where I put together a dynamic information equilibrium model (DIEM) of wage growth on both sides of the border based on the NY Fed data. This data was restricted to leisure and hospitality sectors, but it turns out to be interesting nonetheless. Here's the NY Fed's graphic:

Now I put together the wage growth model at the national level about two years ago. And one of the reasons I went down this rabbit hole was that the Atlanta Fed just released data for September in their wage growth tracker today and I had just compared that data with the forecast:

Pretty good! And it's definitely better than any other forecast of wage growth in the US that's available. If we use this model to describe the NY and PA data, we get a pretty good fit:

There's a single non-equilibrium shock that slows growth that comes right at the beginning of 2012 — coincidentally right when the ARRA deficit spending dries up. There are no other effects and the rest of the path — including all the data through the NY minimum wage increases — is a single smooth growth equilibrium.

How smooth? The smooth model fits the data to within about 2%. It's quantitative evidence J. W. Mason's incredulity was completely unfounded. If we look at these residuals (that are less than 2%), there is a noticeable correlated deviation right during the NY minimum wage increases:

However, this correlated deviation is mirrored in the PA data which means that PA and NY saw the same deviation from smooth growth. There's no meaningful difference between the two that's correlated with the NY minimum wage increases: both saw the same correlated deviation, but more importantly both saw basically wages grow as expected with the deviation from trend growth being less than about 2%. If you forecast in 2010 that average wages would be 10 dollars per hour in 2016, they'd be 10 dollars ± 20 cents.

It's important to emphasize the part about the lack of differences correlated with the minimum wage hikes — over the entire period, wage growth is not just higher but it increases faster on the NY side. But that's a difference between the NY and PA sides of the border that's persistent through the period 2010-2019.

Does this mean minimum wages are bad? No! In fact, since wages are largely a good proxy for economic output, it means that this shows minimum wages likely have no effect on economic growth. Unlike the naysayers who say minimum wage hikes slow growth or cause unemployment, this aggregate data shows they have no real effect.

Wait, no effect? How can that be good?

Because it's no effect at the aggregate level. At the individual level, earning more money for an hour of minimum wage work is a great benefit since one earns the money faster while allocating a given amount of one's limited time to work. If you don't see any aggregate effects, it basically means minimum wage workers effectively have more free time since they're ostensibly producing the same output for the same total compensation (which they arrive at faster because of the higher wage) — otherwise, there'd be aggregate effects!

If your car gets a boost and now travels 100 mph instead of 70 mph, but you still get from Seattle to Portland in three hours, you must have had spent more time stopped at a rest stop or eating at a restaurant — increased leisure time.

Of course, this is assuming the data is measured properly and these conclusions are correct about no aggregate effects — some studies see net gains from minimum wage increases (i.e. we get from Seattle to Portland in two and a half hours).

Wednesday, October 9, 2019

Calling a recession too early (and incorrectly)

A little over a year ago, I said that the JOLTS Job Openings Rate (JOR) data was indicating a possible recession in the 2019-2020 time frame based on the dynamic information equilibrium model (DIEM). It appears that even if there is a recession in 2020, this "forecast" will not have been accurate. This post is a "post mortem" for that failed forecast looking at various factors that I think provides some interesting insights.

Data revisions

As noted in the forecast itself, there was always the possibility of data revisions — especially in the March data release around the Fed March meeting. The March 2019 revision was actually massive, and affected every single data point in the JOLTS time series ... in particular JOR. It made the previous dip around the time the forecast was made largely vanish.

Leading indicators?

The original reason to look to JOLTS data as a leading indicator was based on the fact that the JOLTS measures seemed to precede the unemployment rate in terms of the non-equilibrium shock locations. In 2008, the hires rate (HIR) seemed to lead with JOR closely following. Closer analysis shows that HIR falls early in part due to construction in the housing bust (which also affected JOR). Now I speculated at the time that the ordering probably changed depending on the details of the recession. In the more recent data, it looks like the quits rate (QUR) might be the actual leader. This would make more sense in terms of a demand driven and uncertainty-based recession where people cut back on spending or future investments (or having children) and so seeing a rough patch ahead might be less inclined to quit a job.

Second order effects!

Recently I noticed a correlation in the fluctuations around the dynamic equilibrium for JOR and the S&P 500. A rising market seems to causes a rise in JOR about a year later. When the forecast was made in 2018, the market rise of 2017 had yet to manifest itself in the JOR data. The "mini-boom" of 2014 along with the precipitous drop of 2016 made it look more like a negative shock was underway.

I should note that these fluctuations are on the order of 10% relative to the original model (i.e. less than a percentage point in estimating the rate), so represent a 10% effect on top of the dynamic equilibrium.

Mis-estimating the dynamic equilibrium

These various factors combined into a bad estimate of the JOR dynamic equilibrium that was much larger (i.e. higher rate) than it appears today. The rate was estimated to be about 25% higher (10.7% versus 8.7%), which meant a persistent fall in JOR relative to the forecast:

I should also note that the entropy minimization procedure (described here as well as in my talk at UW econ) has a much better result (i.e. well-defined minimum) with the additional data:

This did not affect the other JOLTS measures as strongly — and in fact the HIR data has shown little evidence of a "recession", especially since I discovered the longer HIR data series a couple months after the original forecast. The quits data has only recently been showing the beginnings of a deviation from the original 2017 forecast:

While all this is bad for my 2018 recession prediction, it actually means the dynamic equilibrium model was really good at forecasting the data over the past two years.

Saturday, September 14, 2019

Odds and ends from the first half of September

I been really busy these past few weeks, so haven't made many updates to the blog — mostly posting half-thoughts and forecast tracking on twitter. One thing I did post about was a fluctuation in the JOLTS data around the dynamic equilibrium appeared correlated with the S&P 500. I updated it today to emphasize that this is a 2nd order effect — on the order of a few percent deviation from a dynamic equilibrium. I did try out a scheduled tweet that came out just before the unemployment data was released at 8am ET on Friday 6 September 2019 (click to enlarge):

The DIEM forecast got the data exactly right. I also noted in the thread that the DIEM forecast outperforms linear extrapolation — even if you try to choose the domain of data you extrapolate from (the different lines in the second graph show all the different starting points for the extrapolation):

This means that the DIEM is conveying real information about the system.

CPI data came out this week and the DIEM continues to do well there too (continuously compounded and year over year inflation):

One thing to note is that the DIEM model is extremely close to a fit to the pre-forecast and post-forecast data (black dashed) and the non-linearity in the DIEM model (red) actually improves the relative performance:

This means that for a function that is this smooth over time, no other model could be anything more than a marginal improvement. The only possibility of doing better is if the fluctuations around the DIEM path are not noise — and in fact the "cyclic" fluctuations around the DIEM path might be related to the fluctuations around the JOLTS log-linear path:

If you squint, the inflation fluctuations might be in sync with the JOLTS fluctuations:

However, this is fairly uncertain — it's not a robust conclusion at this point.


In addition to looking at macro time series, I also took a look at some demographic data about childhood mortality using a new data set. We can see the effect of sanitation in the UK, as well as a potential effect of the more general legalization of abortion:

The data for Japan doesn't go back as far, but shows data consistent with a similar "sanitation transition" (when extrapolated) as well as the effect of WWII:

The US data doesn't go back far enough to make any conclusions (and the shocks are somewhat ambiguous):

Thursday, September 12, 2019

Market-correlated fluctuations in employment data

Something I noticed in the JOLTS data was that if you subtracted out a "dynamic equilibrium" (log-linear path) [1], the residual data was almost sinusoidal (click to enlarge):

I wouldn't expect this sinusoidal fluctuation with a constant frequency to continue simply because there aren't a lot of true waves in economics — the sine wave is more of a curiosity [ETA: the period is about 3.5 years].

But then I noticed that this pattern matched the same residual S&P 500 fairly well, but with a lag of about a year (meaning the S&P predicts the fluctuation):

In fact, all of the other JOLTS data series appear to show this correlation as well (separations = TSR, hires = HIR, quits = QUR):

Even the unemployment rate shows the same fluctuation — but with a lead of about 16 months:

That is to say this would indicate the fluctuations in the unemployment rate predict the S&P 500. As the unemployment data goes back farther, I can look at whether the correlation holds up over time. Eyeballing the data, it actually looks more correlated at zero lag/lead. The run-up in the market before the 1987 crash (might be interesting viewed in the context of the post-80s recession step response), the dip in the mid-90s, and the dip in the 2002-2003 time period line up with fluctuations of the unemployment rate data away from a local log-linear fit. It's also just much noisier in general. 

In any case, I will look more closely at this as well as "help wanted" index data from Barnichon (2010) (see e.g. here).


Update 14 September 2019

One thing I would like to point out is that this fluctuation is on the order of a few percent on top of the dynamic equilibrium path —  a second order effect.



[1] Take the data series JTSJOR (job openings on FRED) take the log and fit a line y = a t + b to the log data and subtract log JTSJOR − (a t + b) ≡ Δlog JTSJOR.

Monday, September 2, 2019

Under-employment case studies: US and Australia

Happy labor day (in the US)!

John Quiggin was surprised at the steady increase in Australian under-employment [1] — I was, too. In the US, most of these labor metrics all follow the unemployment rate ... it's as if there's a prototype labor market time series and all the other metrics are just minor log-linear transformations. And that's true for US under-employment (employed part time for economic reasons) as well:

There was either a change in the way the data was recorded, or a major policy success in January 1994 (I'll look into it more, and would be grateful for anyone who might have any suggestions). In any case, it's not continuously rising, but rising in recessions and falling in their aftermath like most other labor market metrics in the US.

The article Quiggin discusses also talks about youth unemployment (ages 15-24), which in the US shows exactly the expected behavior — following the US unemployment rate:

The youth employment rate also shows the same basic structure:

As a side note, the previously observed dip in the youth employment rate appears to have faded (link shows both employment and unemployment).

The one major difference in behavior is in the fraction of long term unemployed ("long term" is 27 weeks or longer), which in the US seems to have undergone a change since the 1990s:

The basic structure is again similar to the US unemployment rate, but each subsequent recession since the 90s has increased the fraction of long term unemployed without a commensurate drop in the recovery. This results in an increasing fraction of long term unemployed over time relative to the unemployment rate.

Australia on the other hand has just seen a relatively steady increase (about 2.5% per 25 years, or 0.1% per year) in under-employment since the late 70s with only a big surge in the (last) Australian recession in the 90s. Note: no major surge occurs with the 80s recession in Australia ... only a tiny blip. This is primarily driven by people aged 15-24 [2].

At this rate, 10% of the population will be under-employed in 15 years — whereas the US will, in the absence of a recession, get down below 2%.



[1] The nut "graph" in the article on Australia (click to enlarge):

[2] Here's the breakdown by age showing it's driven by youth under-employment (click to enlarge):

Saturday, August 31, 2019

Personal consumption expenditures and other data

The various components of Personal Consumption Expenditure (PCE) data came out today (here it is on FRED). One thing that the data revisions have done is made the hypothesized shock at the end of 2017/beginning of 2018 due to the TCJA in the dynamic information equilibrium model (DIEM) narrower (i.e. shorter duration) — but integrated it is about the same, it's just a bit higher for a shorter period. Here are the graphs of the level and rate (click to enlarge):

PCE tracks GDP fairly closely (in fact, they're almost informationally equivalent), so this gives us a hint as to how Q3 GDP will come out. However, both are lagging indicators of recessions, so this doesn't shed any light on US economic weakness either way.

The rate of change of the price level of PCE excluding food and energy, aka core PCE inflation, also has been consistent with the DIEM forecast since I started tracking it over two years ago:

*  *  *

There's been a lot of new about bond yields and fluctuations in the stock market these past couple weeks, however the story remains for the most part the same. Here's the 10-year rate forecast from four years ago that's still doing well — the rate dove down close to the lower edge of the expected fluctuations but is still consistent with the information equilibrium (IE) forecast:

BCEI is the Blue Chip Economic Indicators forecast (in red) of the same vintage. It's done ... poorly.

The other interest rate I've been tracking is Moody's AAA rate, for which the daily observation is now at the lower edge of the fluctuations in the monthly average band:

That gray vertical band is the estimate from here of the recession onset relative to yield curve inversion (using the median of multiple spreads, which turns out to be remarkably close to the principal component [1]). I've added monthly averages to the figure (in orange) because the various indicators were computed using monthly averages, not the daily data (red) which is just for tracking purposes:

The daily data has entered the range of the lowest spread observed before a recession for the past three recessions, so the monthly average will probably be close. The recession onset once hitting this lowest point was between one and five quarters since the 90s in the US. Note that this is not a rigorous analysis, just a comparison of against the prior three recessions for context.

Speaking of comparisons against prior recessions that aren't rigorous but rather just context, here's the S&P 500 forecast from two and a half years ago overlaid with a counterfactual shock comparable to the 2000 recession shock:

The post-forecast data is in black. As we can see, the data is falling consistently below the center prediction, but is still within the error band (the errors tend to be correlated in the short run, but longer run are closer to normally distributed).

As a side note, I've often encountered detractors that say the error bands on these forecasts are quite  large. However, despite their considerable size, they represent separation between predictable trend and unpredictable human behavior. The probability that someone is selling you snake oil (or insider information) rapidly approaches 100% as the error bands tighten from roughly this size. There's only so much that is knowable about a complex adaptive system.



[1] Here's the average (blue), median (yellow) and principal component (green) [click to enlarge]:

Wednesday, August 28, 2019

Milton Friedman's Thermostat, redux

Ext. Dagobah — Swamp

Jason: It seems monetary policy and inflation are completely uncorrelated. It seems reasonable to believe monetary policy doesn't actually affect inflation.

[Milton Friedman appears as a force ghost dressed as a Jedi from behind a some foliage.]

Milton: I see you haven't heard my thermostat argument! Imagine a car ...

Jason: Actually, I have but ...

Milton: [Undaunted] ... driving on a hilly road trying to keep the same speed. If the driver was really good, the speed on the speedometer would be constant and you'd see the gas pedal go down and up in perfect correlation with the hills. But what you wouldn't see is speed changing — it'd be uncorrelated with the hills and the gas pedal.

Jason: Wait, is this a speedometer or a thermostat?

Milton: Quiet, you! I'm not finished ... Now if the driver wasn't very good, you might think you could tease out the relationship by looking at the gas pedal and the hills. But no! All you'd see in the gas pedal data when compared to the hills are the driver's random errors. No information about the relationship between the gas pedal and speed is available.

Jason: Ok, but how did we figure out looking at the gas pedal was important?

Milton: This isn't about whether we know about the gas pedal. We could be ignorant of the gas pedal — the point is that the model could exist!

Jason: So assume a complex model relationship between gas and speed when there appears to be no correlation?

Milton: Yes!

Jason: Sounds kind of like the opposite of Occam's razor to me. I think I'll stick with Occam.

Milton: Wait, I mean no! Anyone can see monetary policy affects inflation.

Jason: How?

Milton: Look at hyperinflation!

Jason: Ok, but can we extrapolate from 100% inflation down to 2% inflation? That's equivalent to extrapolating processes that happen on a time scale of a year to a time scale of 50 years ...

Milton: Gah! Physicists!

Jason: In fact, data seems to show a definite change in behavior around 10% inflation, which is remarkably close to the time scale between recessions ... [trails off, staring up at the sky]

Milton: Look, you. We have lots of evidence that monetary policy affects inflation.

Jason: Awesome! Why didn't you just show me that evidence instead of basically telling me that Occam's razor isn't always right? I mean, Occam's razor is a heuristic, not a theorem ... of course it's not always right. So are the models built using this evidence pretty good at forecasting, then?

Milton: Well, not exactly ...

Jason: Hmm. Can I see your evidence monetary policy affects inflation?

Milton: Here you go! All the evidence that monetary policy affects inflation!

Jason: Thanks, wow! Why didn't you just show me this in the first place?

Milton: I wanted to teach you about the thermostat!

Jason: But the reason we don't go with Occam's razor in this case is that we have all this evidence you just showed me ... it has nothing to do with thermostats or speedometers ... that's just question begging ... assuming we already have all this evidence ...

Milton: You're welcome!

[The force ghost suddenly vanishes.]

But here's what really happened ...

Jason: Hmm. Can I see your evidence monetary policy affects inflation?

Milton: You see, you won't be able to tease it out of the data. Imagine the Fed is a thermostat keeping a constant temperature ... the turning on and off of the heater is going to be completely uncorrelated with the temperature inside the house.

Jason: That's the same argument as the speedometer. Are you just trying to get out of showing me evidence because you don't have any?

Milton: You see, what I said is true ... from a certain point of view.

Jason: Certain point of view!??

Milton: Bye!

[The force ghost suddenly vanishes.]

Monday, August 26, 2019

A Solow Paradox for the Industrial Revolution

I've been toying with the idea of applying the Workers' History methodology to the Industrial Revolution and the rise of "capitalism" for my next book. The recent 1619 project articles in the New York Times magazine set off a weird firestorm on the internet involving this very subject.

The underlying debate here appears to be a moral/ethical one — are capitalism and the industrial revolution (IR) the offspring of slavery (and therefore "tainted" morally), or did they help bring about slavery's demise (as a technocratic "white savior")? Was the wealth of the US (and/or the UK) built on slavery or was growth and industrialization in the Southern US hindered by it?

I'm not going to be the person who answers this moral question, but one thing that I do think I can contribute to is analysis of the time series data. If we can get the events in the time series straight, then it helps focus the discussion of moral questions.

In fact, I already have looked at this a bit, inspired by Dietrich Vollrath's great blog post on the question of when "sustained growth" started [0]. Recent analysis of the data seems to point to an earlier starting point around 1650:
"... the onset of sustained growth in annual earnings much earlier than the actual Industrial Revolution. Both the GDP per capita and the annual earnings series being to accelerate around 1650."
Emphasis in the original. When I looked at the UK annual income data index with the dynamic information equilibrium model [1], I came up with similar results — possibly even earlier due to an overlapping negative shock to income growth in the late 1500s. This earlier shock may be purely a nominal one due to the so-called price revolution.

Important observations in this framework are that:

  1. The growth shock to UK income matches up with the slave trade
  2. The IR comes along as surge in income growth fades (i.e. no income growth from the IR)
  3. It's not a permanent shock to sustained growth, but rather part of a series with the second shock coming in the 1830-40s possibly associated with the railroad boom in the UK

As an aside, I noted parallels between the IR the Solow paradox/IT revolution — both occurring as a growth shock fades (slavery, women entering the workforce), and neither showing up in macro growth metrics. This discussion brought up some additional questions about the causality — did the IR cause the decline in the slave trade? But the data on the number of African slaves trafficked shows the fading of the growth shock had already begun before the IR:

This graph shows that if we just look at data before 1780, we still see the same saturation (purple dashed curve). It also shows that abolition comes as a genuine surprise in this data at this resolution (25 years) — only appearing in the last data point.

A plausible interpretation of events here is that exploitation of slaves began to see diminishing returns so that investment was directed elsewhere (i.e. seeking "alpha") — in particular the rail boom (that took over transportation from the canal system). The products of the industrial revolution — specifically rail — were a plausible target [2]. Whether abolition forced this shift in attention or instead just came after slavery was no longer as lucrative (and rail became lucrative) is not definitively adjudicated in the data, but the latter proposition has slightly stronger evidence.

This doesn't really say whether slavery caused (e.g. funded) the IR, but it does say that the IR did not cause the decline in slavery — slavery might have just been limited by its own logistics. The Haitian revolution (1791-1804) might be seen in this light as evidence of the limits of controlling slaves. In the aftermath, white Southerners in the US moved toward tighter controls which may have impacted exploitative growth in slavery. It's also possible practical limits on the number of slave ships traversing the middle passage intervened. Whatever the reason, slavery's expansion slowed because of factors that would have been already apparent in the first half of the 18th century.

The other question is whether "investment" in exploiting slaves delay industrialization of the US South (or even more broadly in the British Empire). This counterfactual analysis is possibly unanswerable as it involves knowing what redirecting investment to other areas (like industrialization) would have accomplished. However, there's something that came up when I began reading about this aspect — a myth about Eli Whitney's cotton gin.

I was reading this Bloomberg article by Karl Smith summarizing one case that instead of being a source of growth, slavery held back growth in the US compared to a (dubious) counterfactuals. In it, Smith says that:
"In 1795, the year after the invention of the cotton gin, the U.S. produced 8 million pounds of cotton. Widespread adoption of the gin raised that to 40 million pounds by 1801."
The implication here is that the cotton gin had an impact on cotton production. However, the only apparent change in cotton production in the US is a surge that begins sometime before 1790, with the gin coming right in the middle of that surge in 1795:

I made the cheeky suggestion/hypothesis that the legal framework established by the adoption of the US Constitution was a more likely cause of that jump in cotton production. But it's also plausible that the end of the US Revolutionary War resulted in some "catch-up" growth along with opening up new markets besides Britain — remember that aim of the revolution? In any case, the data shows precious little else happened between 1790 and 1860 except for that 10 year growth spurt at the beginning. The war of 1812 is almost indistinguishable from a statistical fluctuation.

Likely because of my claim, Sri Thiruvadanthai sicced Pseudoerasmus on me who agreed with my point about the cotton gin but then said my interpretation of the time series was "silly and preposterous" [3] before sending me a time series that not only didn't support Pseudoerasmus' claims about it (there is no "surge" in British demand evident in the data) but in fact confirmed my claims that if anything happened, it happened before 1790. Pseudoerasmus' time series came without a source, but covered cotton imports to Britain from 1778 to 1819. As you can see there are very few features in the data besides a surge around the end of the US revolutionary war and a fluctuation around the war of 1812.

There's actually a bit of below trend imports right in the middle of the US production surge!

My claim that nothing happened after about 1790 holds up even if you look at that data with a pure logistic description (per discussion with Michael aka @profplum99 on Twitter):

You might ask what level of confidence we should have in using these simplistic models to describe the data. The truth is that there's so little data (~ 70 points for US production, ~ 41 points for UK imports), it cannot support a complex model. In fact, a heuristic estimate (1 parameter per 20 data points) says that anything beyond 2-3 parameters is probably over-fitting leaving us with log-linear models. With circumstantial evidence (independent measures of the timing of the wars), we can probably add a couple more.

Of course, Pseudoerasmus takes it a bit further (here, here) ...
England imported 7 million lbs of cotton in 1780 but 56 mn lbs in 1800. There was this thing called the Industrial Revolution going on, Jason might have heard of it. At the same time, there was a surge in cotton output not only in the USA, but also in the West Indies & Brazil. 
The USA just prior to the Louisiana Purchase in 1803. the southern states but especially Georgia opened up new (within-state) frontier lands, one major reason being to plant cotton to meet suddenly booming British demand. 
It's pretty simple: the extra 50 million pounds of cotton (esp long-lint cotton) England imported by 1800 (relative to 1780) could not be all met from traditional sources. Also states like Georgia only acquired its hinterland after 1776.
As we can see, these claims from Pseudoerasmus are not supported by the data. There was a surge around the US Revolutionary war and a statistically significant drop around the War of 1812. There is no signal from the industrial revolution, and growth proceeds at roughly a constant rate from 1800 to 1860 (US production data) or 1790 to 1820 (British import data). Any causal factor happens before 1790. It is possible these claims might be supported by evidence besides this data — however, that would mean his claims still had no impact on the recorded time series and historical estimates.

To a great degree, it seems there's a "Solow paradox" around the Industrial Revolution — it shows up everywhere except the macroeconomic statistics [3]. The primary effect is that the IR appears to have provided the technological substrate for the railroad boom in the UK that ended in the Panic of 1847. The IR might have had an effect on manufacturing and industrial processes, but many of those got their start in gun manufacture (which incidentally, was a "medium of exchange" for the slave market). Plus, any growth beyond the 1840s is more likely dwarfed by sanitation improvements and the resulting population growth. 

Where are the macro effects of the industrial revolution?



Also in Karl Smith's article, he makes a claim about growth in cotton production that is basically false — while the saturation level might have been higher (likely due to cotton being grown in more areas of the US without having to compete with slave labor), the growth rate was only 8.5% after the Civil War while being 9.0% before it:



[0] It also points to Malthus possibly being wrong even in the time he was speaking — or at least his mechanism had a smaller impact than is commonly assumed.

[1] Paper here. The model itself is a maximum entropy approach to complex systems where exponential growth is an equilibrium with sparse non-equilibrium "shocks" away from it. In a sense, we are making minimal assumptions about the underlying processes given the guiding assumption that growth rates are well-defined observables. If growth rates aren't well-defined observables, then pretty much any question about economic growth is actually moot.

[2] As a second parallel between the post-WWII period and the IR, we have a rail boom and bust coming after the growth surge of the 1700s fades while in the US we have a dot-com and a housing boom (and respective busts) after the growth surge of the 60s and 70s fades.

[3] It seems to show up in the micro statistics — in the productivity of individual laborers given industrial equipment to run. But it's a fallacy of composition to assume these micro impacts aggregate to a macro effect.