21 Jul 2016

Open Borders and NGDP Targeting: A Numerical Example

Bryan Caplan, David Beckworth, Economics, Scott Sumner 55 Comments

In my last post, in which I argued that Open Borders plus NGDP (or even total labor compensation) targeting would lead to disaster, I fired off some quick numbers that (although technically not wrong) made it look as if I were missing the basic logic of Sumner’s framework. Thus, David Beckworth in the comments said:

The point of a NGDP target (or some variant of it) is to stabilize the nominal income (or nominal wage) growth and allow output prices to fluctuate inversely to supply shocks. In your scenario, there would be benign deflation of roughly 10% along side the stable stable nominal wage growth of 5%. Real wages growth of 15% would still emerge.

Your scenario is basically a large positive supply shock. Whether such a shock comes from a surge in labor or a surge in technology, the Fed would keep nominal wage growth stable–which NGDP is a rough approximation–but would be indifferent to the price level. This has ALWAYS been the implication of NGDP targeting. It allows benign deflation to emerge when there are rapid gains to the supply side of the economy.

So no, Caplan’s plan and Scott’s plan do not conflict with each other. They actually complement each other.

Again, my numbers in the last post were not clear, but in the above excerpt David is not seeing the problem. So I’ll be clearer in this version:

Originally the country has 1 million workers who each make $100,000 per year. So total labor compensation in nominal terms is $100 billion.

The central bank targets 5% growth in total nominal labor compensation. So next year, workers are going to be paid $105 billion total in wages/salaries.

Suppose that at the same time, productivity jumps 15%. In other words, the workers are producing 15% more in real goods and services. Is this a problem?

Nope. As David’s comment above said, it just means the prices of goods and services falls 10%. (Give or take, we always round in these exercises even though the math isn’t exactly right with growth rates.) So the typical worker made $100,000 in year 1 with CPI at 100, and in year 2 makes $105,000 with CPI at 90.

* * *

But now we’re going to start over, and introduce a different change. We’re back to the original scenario, where there are 1 million workers who each make $100,000 per year. The central bank is still targeting 5% growth in total labor compensation, meaning next year workers will collectively be paid $105 billion.

But in the meantime, the government throws open the borders and lets in another 150,000 workers, who are identical in productivity to the original batch. Assume there are no changes in productivity because of the addition, so that total real output goes up by 15%. Is this a problem?

Yes, it is, if you think “sticky wages” and “sticky debt contracts” are a problem. There is now $105 billion in total labor compensation to be spread among 1,150,000 workers, meaning each worker gets paid $91,304. It’s true that consumer prices will drop, which (if we had perfectly flexible prices) would just compensate, keeping real wages constant. (After all, per capita the workers are producing, and hence consuming, the same amount as before the influx of immigrants.)

But the whole point of NGDP targeting is that we don’t have perfectly flexible wages and debt contracts. The worker who signed a 30-year mortgage is going to be hurt by his nominal paycheck going from $100,000 down to $91,304, even if food prices are lower.

Moreover, if for various reasons nominal wages can’t fall to $91,304, but instead are stuck at $100,000 (or close to it), then the only way to enforce the central bank’s cap on total labor compensation growth is to reduce employment. After the immigrants come in and boost the labor force to 1,150,000, if wages stay fixed at $100,000 and total labor compensation is capped at $105 billion, then only 1,050,000 workers can keep their jobs. Another 100,000 will be involuntarily unemployed. If the immigrants are identical to the original population, then we would expect a bunch of the original workers to be “thrown out of work by the immigrants.”

In this outcome, Steve Sailer would be running victory laps, and poor Bryan Caplan would have to say, “It’s not my fault! Blame Sumner!”

P.S. I’m writing this post pretty late so it’s possible I made an arithmetic mistake. If you guys catch anything I’ll fix it in the morning.

55 Responses to “Open Borders and NGDP Targeting: A Numerical Example”

  1. Major.Freedom says:

    And here is where the “pragmatism” will arise, and after years of saying target NGDP like a laser, it’ll be “when the facts change, do you change your mind, sir?” and the nominal wage growth rate will be bumped up to 15%, so that an influx of 150,000 workers will mean wages do not have to fall. Oh just make it 20% so that wages grow.

    Then when people blame immigration for high inflation, it won’t be their fault! Blame the immigration office.

  2. DZ says:

    So every source of changing labor conditions would need special consideration? Like shifts from part to full time or changes in labor participation.

    Also, couldn’t a targeting policy be counter-productive from a trade standpoint. If consumers shifted more purchases than normal overseas (higher imports) in a given year, and as a result the Fed eased, it would only serve to make domestic goods/services even less competitive…assuming I guess that domestic prices are impacted more than global prices.

    • Andrew_FL says:

      Trade is not a competition.

      • DZ says:

        Ok, but can easing have a greater impact on domestic prices than foreign prices? If so, is it not conceivable that price movements for domestic firms, as a result of easing to counteract the fall in GDP after purchases shift to foreign firms, are in the opposite direction from what they otherwise would be?

  3. RPLong says:

    And, not to beat my hobby horse completely dead, this is a great example of how one needs to target inflation in order to target NGDP. NGDP isn’t “better than” inflation targeting, it is literally the same thing. Call it “inflation targeting in a fancy hat.”

    • Andrew_FL says:

      How do you figure?

      • RPLong says:

        NGDP = RGDP + inflation

        inflation = NGDP – RGDP

        We have the same three unknowns, no matter which one we attempt to target. NGDPLT is typically justified on grounds that we don’t need to know what part of a GDP level change is “real,” we just need to know that it happened (or that NGDP futures markets expect it to happen) and modify the money supply accordingly.

        This statement is literally exactly the same thing as saying that we don’t need to know what part of a price level change (or an expected one as measured by existing futures markets) is a change in output, we just need to modify the money supply accordingly.

        • Andrew_FL says:

          Ah I see the problem. You think RGDP is an actual thing that’s measured first, and then converted into NGDP by multiplying it by some index of prices.

          RGDP does not exist, it’s a fiction. NGDP is just a sum of a subset of expenditures. It’s an actual thing that exists.

          • RPLong says:

            “You think RGDP is an actual thing that’s measured first, and then converted into NGDP by multiplying it by some index of prices.”

            Nope. All RGDP means is “output.” We get a sense of that output by measuring both NGDP and inflation.

            Similarly, we get a sense of inflation by comparing NGDP to other measures of output, such as labor force participation and commodity supplies.

            No matter how you shake it, you can’t define-away every other economic thing by absorbing it into NGDP. I know that’s what Scott Sumner wants you to do, but you’re a smart guy and somewhere deep inside of you, you know that the economy must be more complex than that.

            • Andrew_FL says:

              I do know that. The point isn’t targeting “the entire economy.” The point is targeting a crude measure of the effective money stream.

              The reason Sumner says targeting NGDP is “Monetary Policy” is that it’s how he measures *money*. He doesn’t call it “Total Economy Policy”

              • RPLong says:

                Either he’s trying to address business cycles with monetary policy, or he’s not. If NGDPLT isn’t a policy aimed at the whole macroeconomy, then why implement NGDPLT?

              • Andrew_FL says:

                He’s specifically trying to separate the kind of business cycles he thinks something can and should be done about from the kind that cannot.

              • RPLong says:

                I think you might be missing my point…

          • RPLong says:

            Also, I know that my comment history on this blog makes it really, really difficult not to assume that I’m just a yahoo who doesn’t know much of anything, but I’m asking you to please give me the benefit of the doubt as you discuss things with me.

            FWIW, my comment under the previous post said this:

            “When I present these arguments to NGDPLT fans, the response is always the same: Step One, assume I just don’t get the basic architecture of it; Step Two, re-hash Sumner’s arguments against the Taylor Rule, as though that is what I am arguing for; Step Three, insist that it’s possible to create an NGDP futures market; Step Four, call me an idiot.”

            If we can avoid that pattern, we’ll prove me wrong in at least one important way – and I’d like to be proven wrong in that way! 🙂

            • Andrew_FL says:

              You’re a smart guy, but you opened with an accounting identity and then misinterpreted it.

              • RPLong says:

                Actually, I didn’t, but you’d have to assume I did in order for your critique of my post to pass muster.


                My humble request: Relax that assumption, re-read my post, and then respond under a new assumption, i.e. that I haven’t misinterpreted anything.

              • Andrew_FL says:

                Our interpretations disagree. So now you’re just saying “No, I’m right.” so instead of engaging that, I will explain my interpretation of the accounting identity and you can tell me where you disagree.

                the growth rate of “real gdp” is the difference between the growth rate of final domestically produced new goods and services expenditures and the growth rate of *some index of prices*.

                Your argument is that NGDP targeting “really is inflation targeting”. But it differs in a substantial way from inflation targeting.

                Note that, there are as many “RGDP”s as there are price indices.

                ngdp = cpgdp + cpi
                ngdp = pcegdp +pcei
                ngdp = gdpdefgdp + gdpdef

                Note that only the last is the “canonical” “real” GDP growth rate.

                Notice that in all cases, however, the inflation rate and the “real growth rate” are equal to the growth rate of final domestically produced new goods and services expenditures. The *exact same* measure of NGDP.

                So, to start with, targeting NGDP is indifferent to how we define the “price level”.

                Next, note that NGDP targeting is indifferent to the actual *rate* on a quarter to quarter basis.

                Now imagine these two different policies in action:

                The inflation rate targeting central bank wants a two percent inflation rate, whether “RGDP” is 3% or -3% or anything in between or any other number at all. So if the inflation rate as measured by their preferred index starts to go above 2% they will try to tighten policy until it goes back down to 2%.

                The NGDP targeting central bank, on the other hand, doesn’t care if inflation as measured by any given index increases or decreases. It keeps the same growth rate target for NGDP regardless. If gpddefgdp drops to -15% from 3% the NGDP targeting central bank is now “targeting” a higher gdp deflator inflation rate of 20% instead of 2%.

              • RPLong says:

                Andrew, now I’m certain you’ve missed my point.

                If NGDP starts to fall below target, the central bank must expand the money supply by whatever it takes to get NGDP back on trend, that’s the Sumnerian view.

                There is still RGDP being produced and inflation happening, regardless of whether the central bank decides to openly acknowledge that fact. Just because they’ve made them endogenous to the NGDP growth rate function doesn’t mean they’re no longer an implicit part of the target.

                If you decided to get in shape by “using a VO-2-max target,” your training would still impact body composition, muscle growth, specific oxygen, metabolism, etc. Those things don’t go away just because you choose VO-2-max as your benchmark.

                Of course, the more scientific way to train your body is to look at all those things, and feed them into your overall physiological picture, which informs your training regimen. People would think you’re pretty dumb if the only metric you used to train your body was VO2-max.

                But for some reason, when we do monetary policy, notions change. Why do you think that is?

              • Andrew_FL says:

                RPLong-RGDP does not exist. Until you get the notion that it exists out of your head, you will not make any progress understanding the logic of NGDP targeting.

              • Bob Murphy says:

                Andrew_FL but in fairness, NGDP doesn’t exist other. It is certainly not “the total volume of expenditures,” even though Market Monetarists often speak like that.

              • Andrew_FL says:

                Bob-There are expenditures on domestically produced new final goods and you can add them together into a total, theoretically, yes?

              • RPLong says:

                Andrew, if your best defense of NGDPLT is that it onlyl makes sense under the assumption that real output doesn’t exist, then the notion is thoroughly hollow.

        • Yancey Ward says:

          I have tried in vain to make that point repeatedly. I gave up.

          It appears that the belief is that RGDP will do what it does as long as NGDP is steady. When you ask why RGDP can’t do that with NGDP steady at -5, -1, 0, 1, 2, 5, 20, 50, 100%, you hear crickets.

          • RPLong says:



          • Andrew_FL says:

            The usual answer to your question is “sticky wages” and “money illusion”.

            Since I don’t think that is a problem as long as you have the right long term expectations, the answer to your question is, actually, RGDP can do that with those different rates, in the long run, as long as that is what people are used to.

            But ¯\_(ツ)_/¯ indeed.

  4. Silas Barta says:

    Okay, but isn’t that why Sumner had added the afterthought “Or target nominal wage growth *per capita*”?

    • tesc says:

      yes, and him and Larry White have done it since long time ago.

      And we have Paleo-Austrians to helps us remember.

    • Andrew_FL says:

      Right Bob has said Sumner is nuanced from the beginning. But his point is, when Sumner advocates and sells policy to actual policy makers, the nuance disappears. He has to give them something they can understand: set up an NGDP futures market, target 5%.

      • Silas Barta says:

        But then Bob’s core point is still correct — if the same model can justify both “5% NGDP growth” and “5% nominal per capita W growth”, then that’s a really confused model. What *actual* dynamic are you taking advantage of, to produce what *actual* good thing?

        Why does GM do “the right thing” both when they predict 5% NGDP growth, and when they predict 5% nominal per capita wage growth?

  5. Scott says:

    I have not followed this whole thing, but I just wanted to point out that it is totally ridiculous to think you could add 15% to the population with no loss of productivity. That is absolutely insane. I get that I’m supposed to ignore that & this is an argument about math and definitions…but still. It’s so bad I can’t even make myself think through the problem.

    Ignoring even great gobs of nuance, you’d need about 15% more land and capital, too. Does any intelligent person really approximate the economy as purely the product of labor?!?

    Oh wait…

    • Tel says:

      Capital is the product of labour in the past, so the answer is “yes” on that score.

      Natural resources are not the product of labour, however the value of natural resources is the product of labour. Consider for example that in 5000 BC the Sumerian civilization used crude oil and tar to paint their mud houses (keeps the water off) and they had easy access to tar pits right at the surface. The value of this commodity was very low because it was easy to get and anyway you don’t need a whole lot to paint a house. Some thousands of years later and we have a huge industry that drills the same oil out of the ground, processes it, refines it into gasoline, plastics, lubricants, synthetic rubber and also much better quality house paints… all of that industry is the product of human labour which is where the economic value of crude oil really comes from.

      For a long time mining operations that dug up uranium would throw it away as useless (traditionally called “pitchblende” it was considered completely useless). These days uranium is the basis of another whole industry… all from human labour.

      Now I agree, that part of the capital in a society is not just physical machinery, but also social conventions (they don’t come from thin air) and knowledge (often hard won) and a general methodology. Those things cannot quickly be boosted just be pumping a society with immigrants. Social conventions need to be learned, knowledge transfer is slow and difficult, and new knowledge might take many years. All of it comes from human labour, but not all human labour is arbitrarily interchangeable.

      • Scott says:

        Yeah, OK, but we’re talking the span of a single year here. Forget language & customs, unless each of these guys comes in with a house, a factory, and a stretch of highway strapped to his back…

        • Tel says:

          Agree, there’s a time factor involved.

      • Andrew_FL says:

        Gotta be honest, didn’t take you for a Marxist, Tel.

        • Tel says:

          If you think that’s Marxist, then tell me one thing that has economic value that does not gain value by human labour.

          • Bob Murphy says:

            Tel tell us one thing that has economic value that does not gain value by natural resources. So are they the source of all value (or whatever phrase you used regarding labor)?

            • Tel says:

              Sure I can do that.

              A gold nugget that sits out in the bush is a natural resource. But no one picked it up, no one even knows it is there… economic value = 0.

            • Tel says:

              Actually, I have a better example which is Neodymium.

              The pre-cursor mineral “Didymium” was discovered in 1841, but it took until 1885 until it was discovered that Didymium could be split down into praseodymium and Neodymium (the history is on Wikipedia and other places). At that time, plenty of the raw minerals were available for this element, but the extraction effort was considerable and there were only a handful of uses for it (such as a glass additive) with extremely low production rates.

              At the time, adding more of these mineral ores would have produced absolutely no economic value, because plenty were already available, and no one had either a pressing purpose or a workable process for producing Neodymium in any great quantity.

              However in 1982 it was discovered that you could make powerful magnets from Neodymium, also in the meantime better extraction processes had been discovered (take note: all of this requires human effort). These powerful magnets found their way into electric motors, computer hard drives, wind turbines, and a bunch of other applications. Suddenly rare earth ores were hot property. So for more than 100 years people knew about this element but there was no significant economic demand for the material and suddenly, because of human discovery, the price of Neodymium went nuts and the material had an economic value.

              So there’s a clear case where you had a 100 year window and during that time could have piled up Neodymium-bearing ores in the streets and people would have seen it as a nuisance… but suddenly the exact same ores have economic value, thanks to human effort discovering applications for this stuff.

          • RPLong says:

            Wild berries. The value added by human labor pertains solely to the transportation costs.

            This example pertains to many of the examples you gave. Refined oil is not the same thing as crude; they are different products that have different values. This is the whole “higher order” and “lower order” goods discussion from Human Action.

            • Tel says:

              Add on the human labour of searching and finding the berries, which is considerable.

              Refined oil is not the same thing as crude

              These days you can’t just pick up crude from the ground, it requires a largish operation to search for it, and drill for it. That’s not just human labour in the drilling itself, but also human labour in all those bits of equipment you need to do the drilling, and human labour in the study and research to know how to do this. And transport on top of that, and building the pipelines and pumps that you can do the transport, and making steel to build the pipeline, and digging the iron and coal to make the steel, and building the blast furnace that you need in order to combine the iron and the coal…

              Even one single barrel of crude requires a very large amount of human labour when you consider all the things required to get that barrel. The human component is much larger than the natural resource component.

              • RPLong says:

                Tel, you’re conflating the word “labor” with a large number of things that are not generally called “labor.” What you’re saying is true, but you’re using a highly unorthodox language. I think that’s the main disagreement here.

    • Silas Barta says:

      Wait, what? It’s entirely plausible that higher populations have higher per capita productivity — that allows for specializations and synergies.

      • scott says:

        put it this way — a present day American has, what, several hundred times the productivity of an indigenous-type population individual?

        Yeah, you can get ‘synergies’ from higher population & divided labor. And you could maybe conceive of incorporating ~1-2% population increase into existing capital structure with minimal loss of productivity.

        You’re not gonna get hundreds of times output with 15% increase of population without the addition of significant physical capital & additional resources. You’re just not. Especially not instantaneously. That is positively insane. LTV-type arguments take a (very) long term perspective.

        • RPLong says:

          “a present day American has, what, several hundred times the productivity of an indigenous-type population individual?”

          — Controlling for capital, and technology, our advantage is not anywhere near “hundreds.” You are welcome to cite some empirical evidence in favor of your claim.

          “And you could maybe conceive of incorporating ~1-2% population increase into existing capital structure with minimal loss of productivity.”

          But then there’s this:
          “We estimate that a 10% increase in the fraction of the population ages 60+ decreases GDP per capita by 5.7%. We find that this reduction in economic growth caused by population aging is primarily due to a decrease in growth in the supply of labor.”

          “You’re not gonna get hundreds of times output with 15% increase of population without the addition of significant physical capital & additional resources.”

          I might have missed this, but… who made the claim of “hundreds?” I’m not seeing it.

          • scott says:

            Controlling for capital, and technology, our advantage is not anywhere near “hundreds.”

            The whole point is *not* controlling for capital and technology. People don’t cross borders with houses and factories and highways strapped to their backs. Yeah, I’m just using simple classical economics, but its a valid point — and far less of an approximation than if i just say output is proportional to labor.

            Studies show that when you control for everything, nothing matters… Surprise!

            Empirical evidence — USA PCGDP – ~$55K
            Congo PCGDP – ~$700.

            From wikipedia.

            And I would assume that Congo already has at least a substantial amount of capital… and land…

            who made the claim of “hundreds?” I’m not seeing it.

            I guesstimated it. I assumed it would be non-controversial… but then I also assumed it would be non-controversial to say you can’t increase one factor of production, keep the others constant, and expect the gain of output to be proportional to the one factor’s increase. Or that people with no tools and no land aren’t very productive.

            Holy cow.

  6. scott says:

    I propose a new theory of economics — call it the Land Theory of Value.

    In my theory, ultimately all economic value can be ascribed to land, for very abstract and arm-wavey reasons. The core of this abstract theory derives from the notion that when you give labor more land, you get more labor. Because Rabbits. You know biology, right? Therefore :

    labor + land = more labor. Plus capital. And stuff. Call it the Rabbit Theory of Labor.

    Consequently, if you increase land by some factor X, you eventually increase output by factor X.

    My policy prescription is therefore that the US should buy Canada. This would effectively double the GDP of the US, and therefore the US could easily pay the Canadians out of the increase of output. The rest is pure profit.

    How can any intelligent person argue with my policy prescription?

    • Andrew_FL says:

      Scott-You might enjoy this post by Nick Rowe.

      • Scott says:

        Ha, ha!

        Oh well, back to the drawing board… (Thx!)

    • Tel says:

      So your theory is that a square mile of land on Manhattan Island sells for the same price as a square mile of land at Maralinga? Or you believe a farm in South Korea is worth the same as the same sized farm in North Korea?

      Well, good luck with that theory, I hope your land investments are successful.

      As for what I actually said though (thanks for Straw-Manning me, I really love that), I did not propose any “theory of value” nor did I declare that natural resources have zero value. What I said was most value comes from human labour, by far.

      Nick Rowe claims (not seriously) that labour comes out of land because humans come out of land. He doesn’t know that. Life originated in the ocean after all… but besides that, only after minimal intelligence developed did a concept of individual subjective economic value even exist (land cannot have a subjective opinion on anything) only once life had evolved to the point where trade is possible did we have a concept of economic value in the sense of exchange.

  7. scott says:

    No, Tel, I got you the firat time & agree with you. some sort of LTV is a reasonable approximation of things in certain circumstances & for certain purposes & that just goes to show that it does capture some very significant truth of things (like what you were talking about).

    the point was just that it is also outrageous in other circumstances, like when there is not nearly enough time for things to evolve. the land theory of value also has some truth to it, but obviously not to the ends I was putting it. i was more ribbing RPLong & Silas. you obviously git the point.

    • scott says:

      also (&OT) —

      Along the lines of Nick Rowes post, I have often thought in my mind about all goods being capital goods, because if I do not get my pizza & my hi-speed internet connection out of it, I’m darn sure not showing up for work tomorrow…

    • Tel says:

      To repeat myself, I never proposed any theory of value, neither LTV nor any other.

      What I said was that most of the economic gains that we see come from labour and only a little bit comes from land, and this includes pretty much all the capital improvements you can name, be they physical structures like roads and factories or intellectual achievement such as skills, and technology. And yes I agree that when importing workers you have a host of factors which take time to adjust (learning job skills, assimilation to local culture, creating new jobs, more housing, more physical infrastructure, etc). All of these can be solved by human effort (presuming the incentive exists to make it work, and presuming organisational issues don’t obstruct). It would be fair to point out that any major economic shift will fall into the same category… it takes time and human effort to make the adjustments. This could be caused by whatever outside shock you care to name.

      There seems to be a current of thinking around here based on the logic: Marx thought labour had value, we don’t like Marx, therefore labour has no value. This is brain-dead.

      • Scott says:

        OK. Fair point, but this still sounds like some basic LTV idea to me (which I don’t really have a problem with as long as it’s understood to be just a generalization/approximation that is sometimes (but not always) a useful way of framing a situation). To each his own.

        FWIW if I recall (please don’t ask me to remember where I saw it — I haven’t actually read Wealth of Nations. I think maybe Gary North talked about it one time) I believe Adam Smith’s basic idea of things was also LTV. If one time Marx said the sky was blue, there are people who would argue that obviously it couldn’t be.

        • Andrew_FL says:

          Yeah Marx just borrowed the LTV from classical political economy. But it’s not wrong because he said it, it’s wrong because it’s wrong.

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