# How does inflation impact the welfare of the economy?

When the government causes inflation through printing money, the individuals who saved their money in the bank are poorer.
Is there a way to determine how different inflation rates impact the welfare of the economy?
I tried answering this question myself using the production function, and, though I was able to come up with some conjectures, I was unable to come to a definite conclusion.

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Keep in mind that they're not poorer if the inflation was anticipated and the interest rate earned at the bank reflects that. (Not true in short term, but generally true in long term.) –  nominally rigid Dec 29 '14 at 2:35

First, there are direct negative effects from inflation, known as the shoe leather cost and menu costs of inflation. These are direct costs which come from price changes: People will carry less cash, need to update their knowledge about prices, firms need to update their prices and wages, and similar. These are usually small, but typically higher given higher inflation rates.

Second, there are direct redistributional effects, which come from the devaluation of money and everything denoted in nominal terms, including most importantly nominal bonds and debt (credits). Usually, we imagine borrowers to be less wealthy than lenders (1). Here (unexpected) inflation will redistribute wealth from the rich to the poor. Under most standard welfare functions, this will be a first-order welfare improvement.

Third, we typically think that poorer people have higher marginal propensity to consume (MPC). Assuming that we are in a situation with inefficiently high savings rates (for example in Keynesian traps), the aforementioned redistribution will improve allocations, but this is typically a second-order effect (but also this will depend on what you believe is true about the Keynesian multipliers).

Wage contracts belong into the second argument, but deserve a special mentioning due to their extensive treatment in the literature.

(1): This is sufficient, but not necessary. In order to get a higher MPC from borrowers than from lenders, it is sufficient that the borrowers are not optimally smoothing consumption over time (for example, because they are up against a borrowing constraint) - we call these types of consumers Hand-to-mouth, because they will typically consume all their disposable income. As long as the distance between the (aggregated) borrowers consumption and what they would like to consume in a frictionless environment is larger than the distance between the (aggregated) lenders' consumption and what they would like to consume in a frictionless environment (2), devaluing debt will increase consumption.

(2): It may sound surprising, but there is a significant mass of wealthy hand-to-mouth consumers. See Kaplan et al, 2014

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I'm with you on the first, but I'm having trouble imagining the model that says poor people are more likely than rich people to be borrowers --- unless you've got some kind of story that says the reason they are poor is that they don't like to save. It's true of course that people who are having a relatively bad year are more likely to be borrowers, but I don't see any reason poor people should have more variance in their incomes than rich people. Can you be more explicit about what you've got in mind? –  Steven Landsburg Dec 28 '14 at 14:28
It doesn't even have to be poor vs. rich in terms of permanent income. Just take into account borrowing constraints, and then think (for an example) about a student accumulating human capital, borrowing up to his borrowing constraint, from the future-himself. –  FooBar Dec 28 '14 at 14:46
I still don't get it. Why would we expect poor people to accumulate more human capital than rich people? I'd have expected exactly the opposite. –  Steven Landsburg Dec 28 '14 at 14:51
In my example there was no poor vs rich in terms of permanent income. There was one young dude, who was temporarily "poor", i.e. little cash on hand and up against his borrowing constraint. –  FooBar Dec 28 '14 at 14:57
@Steven Landsburg, I think that if we take a world where borrowers and savers are the same people (and their marginal welfare is weighted equally by the SWF) but at different parts of their lifecycle, and the borrowers face binding borrowing constraints, then almost by definition a surprise redistribution to them will boost social welfare; the constraints are binding because borrowers have higher MUC today, when borrowing, than in the future. –  nominally rigid Dec 28 '14 at 18:58

In the absence of inflation, the social cost of creating a dollar is essentially zero (at most a few cents worth of paper and ink), but the private cost of holding a dollar is a forgone dollar's worth of consumption. Therefore there must be positive externalities to holding dollars.

Inflation increases the private cost without changing the social cost, so magnifies the externality. Moreover, because there's an externality even when inflation is zero, the additional welfare loss due to the first marginal unit of inflation is already non-zero.

This external cost is the same as the shoe-leather costs that FooBar mentions, but thinking about it as an externality lets you measure it as a triangle and so helps toward quantifying it.

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Completely agreed, but isn't the upshot that the quantitative loss is small for minor departures from the Friedman rule (like those caused by moderate inflation)? If money demand at nominal rate i=0% is 8% of GDP, and the semielasticity of money demand with respect to i is 6 (which seems roughly accurate), then Harberger triangle from having i=4% instead is approximately $(0.08\times 4 \times 0.04^2)/2 = 0.000384$, or 0.04% of GDP. This is probably swamped by gains from taxing foreign or criminal holders of currency. –  nominally rigid Dec 28 '14 at 19:43
nominally rigid: What you say looks right. –  Steven Landsburg Dec 28 '14 at 21:24

As the discussion here suggests, there are many possible costs and benefits to inflation. One source that might be edifying here is the 1996 FOMC discussion that ultimately resulted in the US's 2% inflation target. This discussion focuses on one particular aspect of the inflation tradeoff: namely, the effects of long-term, low levels of inflation. It offers some useful insight into what policymakers view as the most quantitatively important consequences of long-term inflation in a country like the US.

Janet Yellen, who was then a Fed governor and advocated for the 2% target, sums it up on page 43 of the FOMC transcript. She lists one cost from inflation and two benefits:

• The major cost arises from the interaction of inflation with the tax system, which (aside from indexation of brackets) is specified in nominal terms. As a result, inflation implicitly increases the tax rate on capital investment in several ways. For instance, since depreciation is measured for tax purposes at historical rather than current cost, in an inflationary environment depreciation is artificially low and businesses pay taxes on illusory "profits". Similarly, capital gains are measured in nominal rather than real terms, pushing a large tax burden onto sellers even when their real gains are minimal. These tax-interaction effects were emphasized by Martin Feldstein (and some of his students, like Larry Summers), whose recent paper was mentioned by Yellen - who thought he overstated the effects - in 1996.
• The first major benefit Yellen discusses, prophetically enough, was that higher inflation means that one can achieve more negative real interest rates - which might be necessary in recessions - when nominal interest rates are pushed down to their zero lower bound. This is a very important issue today!
• The second major benefit is the possibility that mild inflation makes it easier to overcome downward nominal wage rigidity and achieve needed adjustments; this was famously emphasized by Tobin in his 1971 AEA presidential address and developed more thoroughly by Akerlof, Dickens, Perry (1996), which is also cited in Yellen's discussion.

Given this tradeoff, the committee honed in on a long-term target of 2%.

It is interesting to consider all the issues that were not present in this discussion. The most conspicuous is the usual question of redistribution. This is because, although borrowers benefit and savers lose from unanticipated inflation, fully anticipated inflation should be incorporated into nominal asset returns (except for the tax issues discussed above). Since anticipated rather than unanticipated inflation is the relevant issue for setting a long-term inflation target, this was not such an important question for this debate - though, of course, it still mattered for the transition to any new target.

Another cost of inflation commonly cited by academics is the distortion from departing from the Friedman rule of 0% interest rates: since the central bank can more-or-less costlessly engage in open market operations to buy securities and create more money, a positive interest rate means that individuals hold a less-than-socially-optimal amount of money in their portfolios. This cost was presumably ignored in the discussion because, in a low inflation economy, it is of trivial magnitude - not many people make decisions about how much cash to carry in their wallets based on whether the interest rate is 0% or 4%. Indeed, the cost here may be nonexistent, since a large amount of cash is held either outside the US or in support of illegal activities - and it is optimal for the US government to tax the former and discourage the latter.

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