"Trickle Down", "Magic Dirt", memes and deep parameters

"Trickle Down Theory" is a meme used (mostly by non-economists) to ridicule certain economic policies and the theories on which those policies are supposedly based. My first year students sometimes ask me to explain it to them, not understanding that it's a meme and not a theory.

"Magic Dirt Theory" is a similar meme, of more recent (and "deplorable") origin (a quick search tells me it's from Vox Day/Supreme Dark Lord). But ideas, including memes, should be evaluated on their merits. Here is a critique of that meme, from a nationalist/conservative perspective.

You have probably heard of "Trickle Down Theory". But only 16% of the (probably unrepresentative) 127 people who answered my Twitter poll (thanks!) had heard of "Magic Dirt Theory". And the percentage was smaller for economists than for non-economists. This is a smaller percentage than I thought it would be, but not trivially small. I don't know whether in the long run it is memes that are powerful for good or evil.

Standard economic theory has a reasonably good defence against the implied critique in the Trickle Down Theory meme. "Will the benefits in fact trickle down from rich to poor (or trickle up from poor to rich)?" is the sort of question we can answer, at least in principle. "It depends" is normally the right answer, and we can say what it depends on, in particular the specific policy change being considered. This caricature of economic theory doesn't really work, if you have any knowledge of economics.

I am less confident that standard economic theory has a reasonably good defence against the implied critique in the Magic Dirt Theory meme. The caricature sometimes seems to fit. Translated into economese, the critique is about productivity parameters that are implicitly assumed to be policy-invariant, without much thought about what precisely those parameters represent, and whether they would in fact be invariant to the sorts of policy changes the model is used to evaluate. It's a Lucas Critique. Magic Dirt is the cross-sectional version of time-series phlogiston productivity shocks (pdf).

If I read 'It is places, not individuals, that are productive' the Magic Dirt Theory meme springs to my mind. (Memes are effective). What is that special property of different places that creates those productivity differentials? Can we assume it remains fixed, if individuals move around?

Here's my version of the meme:

Start with a very simple model. Land and labour produce corn. Constant returns to scale technology (if you double both labour and land inputs you double corn output). Diminishing Marginal Product of Labour (the extra output per extra worker falls as you add more and more labour to a fixed amount of land). All land is identical. All labour is identical. Same technology everywhere. Perfect competition, so the real wage in any country equals the MPL in that country. Countries with a higher land/labour ratio will have higher MPL and wages, lower rents, and higher GDP per worker. Workers who migrate from countries with a low land/labour ratio will see their wages rise, and world output of corn will rise too (because their MPL will be higher in their new country than in their old country). Open borders (and no costs of migration) will equalise wages everywhere and maximise world output. Malthus and Ricardo would have understood this model.

Now change one assumption. The fertility of the land differs across countries. But the economists who study the world economy do not know this. All the economists know is that, for some unexplained reason, wages and productivity of labour and land are higher in some countries than in others. So they model the world economy with each country having its own country-specific production function.

Those economists have a "Magic Dirt Theory" of the world economy. Some countries have an unexplained Absolute Advantage over other countries, and the economists treat that absolute advantage as a structural ("deep") parameter that is invariant to the open borders policy experiment.

Fortunately for the economists, the "dirt" really is "magic" in this case. Because I assumed it is. So their model of the world economy works perfectly well, even if they don't know why it works. Open borders will maximise world output and equalise wages just like in the simpler model. The only difference is that land rents and land/labour ratios will be different across countries (more fertile land will have higher rents and probably more workers per acre).

The danger comes if the economists use a magic dirt theory where the dirt is not in fact magic, and the parameters that are assumed to be policy-invariant are not in fact policy-invariant. Like if it is cross-country variance of some sort of social institutions that creates productivity differentials. Unlike magic dirt, those social institutions may or may not change when migration policy changes. Do institutions remain attached to the place, like the fertility of the soil, even if all the people move? It depends. But I'm not confident that economists have any special ability to say what it depends on.

We can at least recognise the problem.

Comments

[andrewknorr]

This may be the most careful and indirect statement of crime-thought that I've read yet.

[Frances Woolley]

Good post - or clear and thought-provoking anyways!

Is the alternative to magic dirt theory then magic seed theory? (I know (or rather hope) you don't really believe that. For decades you have been arguing that rules and institutions matter, and I think that's what you're getting at here. But you can see how the anti-dirt argument can easily turn into a pro-seed argument).

[Nick Rowe]

andrew: there's more than one direction we can go with the Magic Dirt meme. I think this is the most sensible direction. Countries aren't just areas of land; they are clubs of people sharing a set of social institutions, which matter.

[Nick Rowe]

Frances: thanks! Yep, this is just another way for me to recycle my old rules and institutions hobby-horse.

[James Hudson]

“[S]ocial institutions may or may not change when migration policy changes.” And social institutions may or may not change when migration policy stays the same. Now in fact social institutions will almost certainly change, in any case. The relevant questions are: how good (for productivity) are the social institutions that would follow upon the adoption of this or that immigration policy (including the retention of the old policy)? I doubt that we can have much confidence in any precise answers to these questions.

[Nick Rowe]

James: yep. I think that's the big unknown. And it seems to me that the sensible policy, if you currently have a pretty good country, is to proceed slowly and not make any big sudden changes. Like driving in fog. Small c conservatism.

[Ken Houghton]

"Standard economic theory has a reasonably good defence against the implied critique in the Trickle Down Theory meme. "Will the benefits in fact trickle down from rich to poor (or trickle up from poor to rich)?" is the sort of question we can answer, at least in principle. "It depends" is normally the right answer, and we can say what it depends on, in particular the specific policy change being considered. This caricature of economic theory doesn't really work, if you have any knowledge of economics."

However, if you have a knowledge of history, you will quickly ask for examples of the Trickle Down Theory working in practice, with the general result this side of the Great Lakes being a bunch of hand-waving about how the Kennedy Administration managed to screw up everything except economic policy (and a paucity of supporting data for that argument).

[Nick Rowe]

Ken: when I hear the "trickle down" metaphor, the economic model that comes to mind is a hydraulic keynesian circular flow model, where income effects and the multiplier are the mechanism. And provided the rich/poor buy some goods produced by the poor/rich (and don't live in separate autarkic economies), income will indeed trickle both down and up in that model. But if Aggregate Demand deficiency is not the underlying problem. we would have to think about cuts in tax rates having substitution effects that work on the supply side, and we would need to think in terms of a general equilibrium model with lots more elasticities to figure out whether benefits would trickle up and down from whoever gets the tax cut.

[James Hudson]

". . . proceed slowly and not make any big sudden changes." But what strikes us as a "change" in a situation will depend on which properties are in focus. For example, if this year the population of the country is P, there will be a change unless next year the population is P. On the other hand, if this year the absolute rate of change of the population is +Q people per year, there will be a change unless next year the population is P + Q (and the following year P + 2Q, etc.). If we focus on both size of population and absolute rate of change, we will have to reconcile ourselves to (what strikes us as) "change"--change in at least one of these properties. (And then, on the third hand, if this year the population is growing at n%, there will be a change unless next year the population is P * (100 + n)/100 (and the following year [P * (100 + n)/100] * [(100 + n)/100]. Etc.)

Conservatism is incoherent without some underlying assumption about the relative importance of properties. The idea must be to avoid big changes in the more important properties, with correspondingly less worry about changes in the less important ones. But since we probably do not agree about the relative importance of different social properties, conservatism will not take us very far.

[Handle]

@Nick Rowe: "Magic Dirt" was Steve Sailer's clever quip - in a devastating but perfectly common-sensical critique - summarizing the ludicrous implied explanatory thesis of Raj Chetty's flawed analysis of inter-generational social mobility based on reported income.

Frances Woolley said, "Is the alternative to magic dirt theory then magic seed theory? (I know (or rather hope) you don't really believe that."

The equally preposterous alternative to "magic seed theory" is "anti-magic seed theory", which I know (or rather hope) you don't really believe either, because it's obviously false.

Anti-magic-seed theory would be the claim that all seeds are really the same, or even if different, that seed characteristics are irrelevant to outcomes and all results are completely independent of seed quality (try telling that to any farmer and not getting laughed in your face.)

Indeed, it is anti-magic-seed theory precisely which, if assumed, requires ridiculous Magic Dirt theory as the only possible remaining explanation, and which is precisely how Chetty arrived at his silly conclusion so patently erroneous that even amateur bloggers can explain obvious invalidating methodological shortcomings in a few plain paragraphs, and why the entire Chetty phenomenon is a scandalous embarrassment and testament to the sorry state of media coverage of the profession.

Any farmer will tell you that everything matters - the land, the weather, the seeds, the techniques, etc. - and so everything is a little "magic" in the sense of contributing to the explanation for the variety of outcomes. But if one denies the little magic of any important factors, as with anti-magic-seed theory, then one ends up only with predictably unrealistic and inevitably inaccurate models, absolutely dependent on truly crazy fantasies like "Magic Dirt".

[Nick Rowe]

Handle: Steve Sailer used it, but did not invent the meme, AFAICT from a quick search.

Suppose that there are big workers and small workers, and a big worker can do the same work as two small workers, and so gets twice the wage. That doesn't make any difference to the benefits of open borders in the model in my post. (It would make a difference if there were redistributive taxation, but even then it would replace foreign aid.) It's the social institutions that matter for policy.

[Nick Rowe]

Or suppose some workers have strong arms, so have a comparative advantage at scything, and other workers have long arms, so have a comparative advantage at stooking, that strengthens the case for open borders, so you get the right mix of workers as well as the right land/labour mix.
It's rules and institutions.

[C Trombley]

I don't understand your point. Let me try to be concrete. You claim that Historical Materialism (Magic Dirt Theory) has deep problems with respect to policy invariance. Let post-policy land fecundity be indexed by \Theta.

Historical Materialism would describe the world of King David like this: "It is the High Bronze Age. The world is powered by the flow of tin coming out of mines in Persian dominated Afghanistan and copper in Egypt dominate Cyprus. Egypt and Persia dominate because they have the agricultural fecundity to create the armies to dominate these lands. At the center of ancient river valleys there is the city of Jerusalem. David conquered Jerusalem in order to control those valleys.". You seem to be saying that the main problem is that Jebusite loyalists *could have* sewn their own fields with salt and starved to death to spite David if they wanted it enough. The value of Jerusalem is not policy invariant. The Jebusites could set land fecundity \Theta = 0. Historical materialists don't get that policy is indexed by \Theta \in [0,1], not \Theta \in (0,1). Do I understand you correctly?

But who cares, since such policies are never enacted? David conquered the Jebusites and became a mighty king in Jerusalem. Is not your fractious southern neighbor's main advantage over yourself her massive, massive farmland (and massive, massive coal mines)? Historical Materialist claim: the government of Canada's policies will never make Canada more fertile than America (in value terms). The historically materialist claim is obviously positively successful. If I understand you right, you say there's something philosophically wrong with this claim (despite its positive success) because Canada could nuke the United States. To the historical materialist, this means that you just have a bizarre definition of institutions. There's something philosophically wrong with your claim that "Canada could nuke the United States" because it is positively a failure. If the post-policy land fecundity index is always near but less than 1, the behavior near zero is metaphysics in its worst sense.

I'm not David Lewis, so I can't be held as an expert on modal metaphysics of what Canada or the Jebusites "could" do. But I'd naively judge this one in the historical materialist's favor.

[Nick Rowe]

CT: I don't understand you. But I suspect you don't understand me. You lost me at this point: "You claim that Historical Materialism (Magic Dirt Theory).."

[C Trombley]

That's just a joke and not a very good one.

Let me put it this way. Do a) peasants do constrained optimization given institutions or b) princes do constrained optimization given agricultural productivity? It seems to me b) is what you call Magic Dirt Theory. Princes think agricultural productivity is just a parameter that a country has to deal with. And, contrariwise, a) is your critique, "Obviously agricultural productivity is not policy invariant and not immigration policy invariant in particular. It's conceivable that if Bonnie Prince Charlie brings in Chinese peasants out from under Jiaqing Taishang, then agricultural output will go down in both countries.".

But a) and b) are dual to each other. "Magic Dirt Theory" and your preferred institutional theory are inherently the same theory.

Maybe "Magic Dirt Theory" vs your theory is about the comparative statics of the deeper general equilibrium theory? "If Bonnie Prince Charlie brings in Chinese peasants very slowly, agricultural productivity will decline by exactly the rate that cancels out the extra man hours." vs "If Bonnie Prince Charlie brings in Chinese peasants very slowly, agricultural output will climb by exactly (initial agricultural productivity)*(man hours)."

[Majromax]

I'm a little bit confused by the summary here, and the link to the conservative critique of 'Magic Dirt Theory' appears to be blocked by my workplace firewall at the moment. Does this theory refer to the idea that different regions/nations have persistent differences in the level of productivity, or instead does it refer to the idea that these regions have persistent differences in the growth rates of productivity?

If it's the former, then I'm not sure that the theory is too harmful as at least a short-term modeling assumption. If the causes of the level-difference are not easy to discern, then proposed policy prescriptions are only accidentally going to affect them. In the meantime, nation-specific fixed effects might help bolster against false confidence, as in "if only this developing nation narrowly respected the property rights of multinational companies, it will experience an economic boom -- never mind its problem of corrupt and criminal domestic administration."

If it's the latter, then it's a bigger issue because growth-rate differences can, over a long enough horizon, become arbitrarily large level differences.

I'm of course more familiar with the 'Trickle-Down' characterization, and I see the same sort of ambiguous-effects there. If the idea is that a less-progressive system leads to an increase in the output level, there can still be plenty of debate about whether the winners outweigh the losers. Instead, however, I more commonly see arguments about long-term growth rates bandied about, which ultimately assume that the rising tide keeps on going.

Perhaps the core of the problem is that macroeconomics has yet to come up with a reasonable, intuitive, and mechanistic explanation for TFP growth. In recent years I've seen lots of blogosphere discussion and analysis of "if TFP growth / the real rate has fallen from 2.5%/yr to 1%/yr or less, then[...]," but discussion of what economic or social (or 'magic soil') policies cause such a drop is at best brainstorming. If we had a more complete formalism, then we'd at least be able to check the strongest claims of trickle-down or magic soil theories.

[rsj]

Do a) peasants do constrained optimization given institutions or b) princes do constrained optimization given agricultural productivity? It seems to me b) is what you call Magic Dirt Theory.

No, I would say both a) and b) are "magic dirt". The opposite view is that the agricultural productivity and institutions are what peasants bring with them -- they spring from the population, rather than from the soil or geography.

Now maybe we believe that ultimately, over many generations, the soil and geography determine everything. For example, I've heard some just so stories that cold areas are more productive because they force people to cooperate more as well as to fight harder to survive. Maybe. Or that protestant nations are more productive because of some theological differences. Possibly.

But whatever the explanation for why some nations are more tolerant of corruption, or less supportive of liberal values, or women's rights, etc, if you bring in a million people from such a nation, you will find that the individuals are not blank slates that start immediately optimizing against a different set of institutions, rather they carry those values and traditions with them. If you bring in a large population of muslims from the middle east into London, sure you get some muslim arab bankers, but you also get some acid attacks and female genital mutilation as well. People are not changed by the dirt, they set up their own institutions and pressure existing institutions to conform to their wishes.

In undergrad I had a hispanic friend who was also a math major, but he often confided to me that he felt pressured to get a job and get married. He just turned 20, and a part of him always thought he wasn't a real man if he was just going to school when all his friends already had jobs. School is for boys, but men work. Eventually, it got to him, and he dropped out of college and got a job as a mover, and got married. I was shocked -- if that happened to me, I would be afraid to face my friends, as I would clearly be considered a failure. He was afraid to face his friends by still not working. Culture matters. Ethnicity matters. We are not blank slates, and we carry ethnicity with us. Even on the same piece of dirt, there are many different identities and values all competing to shape our institutions.

[Spencer Hall]

Don’t deal "magic", only dish "dirt". To presuppose that: "If the Fed can cause a 500 basis point change in interest rates, it is absurd to wonder if monetary policy is important", when said modeling is magic, is disingenuous, and not dirt.

RoC's in money flows, volume X's velocity = RoC's in P*T (where N-gDp is a subset). But we are not done. The distributed lag effect of money flows, both the proxy for real-output, and the proxy for inflation, have been mathematical constants for > 100 years.

Ergo, then you will know, in advance, whether *real* (& nominal) rates will increase and vice versa.

[Basil Marte]

Not an agricultural, but industrial era model of "magic dirt" is possible. I call it the Kapi Valley.

If there is some initial noise in distribution of productivity (i.e. the Kapi Valley is lucky), it will be the first to build turnpikes, because it is the first to afford them. But this improved transportation infrastructure means that "normal" businesses (and people) will prefer to locate there, rather than somewhere else. This gives an above-average density of businesses, which makes the area the place where building a canal gives the best returns, so the area will get canals before others. This improved infra draws businesses, so the Valley gets a rail network before others, drawing businesses, rinse and repeat.

The same model applies not just to different Kondratiev waves within the same field (transportation), but to different fields. An above-average density of enterprise (due to improved transportation infra) *also* makes the Kapi Valley the best place for erecting a telecomm network (telegraph), banks, power networks (hydraulic, electric). The large concentrated population draws (a) university/-ies. These then all feed back into improving returns for "normal" businesses.

In a single sentence, there exist complementary fields where investing capital in one (locally) improves the returns to capital in the other(s), and vice versa. This can create spots of "magic dirt" where productivity stays above average for several Kondratiev waves. In fact, it's quite possible that an Industrial Era example gives a higher return to capital than capital-starved Bulungi in the same era, so capital actually moves to the higher capital/labor region when seeking returns. This is possible even if population *doesn't* move.

Naturally, the above model relies on technological change. If we freeze tech but let the economy run, returns to capital will gradually fall in the high-tech, high-productivity location as capital continues to be accumulated. Eventually returns to capital in the low-tech region will exceed the decreasing returns offered by the high-tech one, so capital will be invested there. If it is otherwise similar (as we assumed), it will reach the same level of development.

[Jonathan]

Probably most economists are on board with institutions being the main driver of international income differences over longer time horizons. But a reasonable question is to what degree these institutions are embedded in people rather than in the governing structures in a particular country.

For example, maybe the reason that the US is more productive than country X is because we have democracy, rule of law, a good regulatory structure, low taxes, responsible federal reserve, etc. Then people can come over from country X and more or less just benefit from these better institutions. In this case there's good economic and moral reason to promote immigration and take down barriers that prevent it.

Alternatively, maybe the differences are about certain social, economic, and political norms and cultural beliefs (e.g. high-trust vs. low-trust societies). Then when people immigrate, they bring their old norms and cultural beliefs with them. If enough people immigrate from country X, and especially if they are concentrated in certain geographic areas, then the economic, social, and political norms of the US (and especially the region with a high number of X immigrants) could start to shift.

Of course, there are even worse possibilities. For example, maybe it only takes a small number of defectors to break a good institutional equilibrium. Or maybe there are large advantages to having everyone share a similar culture. One practical and obvious example is language: I'm sure there are huge economic benefits to having everyone in a country fluent in a mutually intelligible language so they can all communicate. But there are more subtle things, like cultural norms and unspoken assumptions about how people behave or how they communicate. If you live in a country with sufficiently diverse norms, you might lose the benefits of having norms at all (you could never be confident that a stranger shared your norms).

Of course these are all potentially testable.

[rsj]

There is also the inconsistency between the two pillars of faith: "diversity is our strength" and "magic dirt", or exogenous institutions. If people are blank slate optimizers against exogenous institutions, then there is no benefit to diversity. All of the pro-diversity arguments assume that changing the mix of people will change the functioning of the institutions and always in a universally better way. Unless it's european people, who only make things worse.

In other words, take a group of people living in a nation with poor institutions, and they are helpless to improve those institutions and are not responsible for their existence -- evil western imperialists or aliens must have created those institutions and imposed them on the locals who are now powerless to reform their societies. At the same time, take a small sample of that population and put it in a nation with better institutions, and suddenly in the new nation in which they are a minority, the immigrants will improve the institutions of their adopted nations.

I think the only intellectually honest position here is that one side has no national sentiments or loyalty to improve the particular nation in which they live. The whole concept of commitment to a place or ethnic group is offensive to them, and to the degree that any national institutions are weakened by importing large numbers of people with different values, then this is a feature rather than a bug. They can live in their favorite urban bubble, or a gated community, or an environment with restrictive zoning, and enjoy lower cost service workers, much as the elite do in the nations the immigrants are fleeing from.

[Nick Rowe]

Jonathan: "Probably most economists are on board with institutions being the main driver of international income differences over longer time horizons. But a reasonable question is to what degree these institutions are embedded in people rather than in the governing structures in a particular country."

Yep. And I think the only sensible answer is: a bit of both, and it depends (on the sorts of things you talk about).

[Fang__z]

"And it seems to me that the sensible policy, if you currently have a pretty good country, is to proceed slowly and not make any big sudden changes."

Hang on though. Maybe your 'magic dirt' is the rate of change of your policy changes. Your country is effective and productive because people expect government to be flexible, to try different things, so that short term issues will swiftly be solved. Maybe that's the aspect of your country that means effective people stick around.

In terms of immigration, it might be the case that the benefit of open immigration policy is not just the quality of the people coming in, but that the policy in itself improves the productivity of people in that location. Highly educated and productive people want that sort of policy, they want to live in tolerant neighbourhoods that people want to immigrate into.