Tuesday , September 28 2021
Home / J. W. Mason: SLACK WIRE / Alternative Visions of Inflation

Alternative Visions of Inflation

Summary:
Like many people, I’ve been thinking a bit about inflation lately. One source of confusion, it seems to me, is that underlying concept has shifted in a rather fundamental way, but the full implications of this shift haven’t been taken on board. I was talking with my Roosevelt colleague Lauren Melodia about inflation and alternative policies to manage it, which is a topic I hope Roosevelt will be engaging in more in the later part of this year. In the course of our conversation, it occurred to me that there’s a basic source of confusion about inflation.  Many of our ideas about inflation originated in the context of a fixed quantity money. The original meaning of the term “inflation” was an increase in the stock of money, not a general increase in the price level. Over there you’ve got a

Topics:
JW Mason considers the following as important: , , , , , , , ,

This could be interesting, too:

Marc Chandler writes What’s Next?

Jeffrey P. Snider writes Finally The Taper Tantrum, Or What’s Wrong With August?

James Picerno writes US Growth For Q3 Estimate Continues To Ease

James Picerno writes Macro Briefing: 24 September 2021

Like many people, I’ve been thinking a bit about inflation lately. One source of confusion, it seems to me, is that underlying concept has shifted in a rather fundamental way, but the full implications of this shift haven’t been taken on board.

I was talking with my Roosevelt colleague Lauren Melodia about inflation and alternative policies to manage it, which is a topic I hope Roosevelt will be engaging in more in the later part of this year. In the course of our conversation, it occurred to me that there’s a basic source of confusion about inflation. 

Many of our ideas about inflation originated in the context of a fixed quantity money. The original meaning of the term “inflation” was an increase in the stock of money, not a general increase in the price level. Over there you’ve got a quantity of stuff; over here you’ve got a quantity of money. When the stock of money grows rapidly and outpaces the growth of stuff, that’s inflation.

 In recent decades, even mainstream economists have largely abandoned the idea of the money stock as a meaningful economic quantity, and especially the idea that there is a straightforward relationship between money and inflation.

Here is what a typical mainstream macroeconomics textbook — Olivier Blanchard’s, in this case; but most are similar — says about inflation today. (You can just read the lines in italics.) 

Alternative Visions of Inflation

There are three stories about inflation here: one based on expected inflation, one based on markup pricing, and one based on unemployment. We can think of these as corresponding to three kinds of inflation in the real world — inertial, supply-drive, and demand-driven. What there is not, is any mention of money. Money comes into the story only in the way that it did for Keynes: as an influence on the interest rate. 

To be fair, the book does eventually bring up the idea of a direct link between the money supply and inflation, but only to explain why it is obsolete and irrelevant for the modern world:

Until the 1980s, the strategy was to choose a target rate of money growth and to allow for deviations from that target rate as a function of activity. The rationale was simple. A low target rate of money growth implied a low average rate of inflation. … 

That strategy did not work well.

First, the relation between money growth and inflation turned out to be far from tight, even in the medium run. … Second, the relation between the money supply and the interest rate in the short run also turned out also to be unreliable. …

Throughout the 1970s and 1980s, frequent and large shifts in money demand created serious problems for central banks. … Starting in the early 1990s, a dramatic rethinking of monetary policy took place based on targeting inflation rather than money growth, and the use of an interest rate rule.

Obviously, I don’t endorse everything in the textbook.1 (The idea of a tight link between unemployment and inflation is not looking much better than the idea of a tight link between inflation and the money supply.) I bring it up here just to establish that the absence of a link between money growth and inflation is not radical or heterodox, but literally the textbook view.

One way of thinking about the first Blanchard passage above is that the three stories about inflation correspond to three stories about price setting. Prices may be set based on expectations of where prices will be, or prices may be set based on market power (the markup), or prices may be set based on costs of production. 

This seems to me to be the beginning of wisdom with respect to inflation: Inflation is just an increase in prices, so for every theory of price setting there’s a corresponding theory of inflation. There is wide variation in how prices get set across periods, countries and markets, so there must be a corresponding variety of inflations. 

Besides the three mentioned by Blanchard, there’s one other story that inflation is perhaps even more widespread. We could call this too much spending chasing too little production. 

The too-much-spending view of inflation corresponds to a ceiling on output, rather than a floor on unemployment, as the inflationary barrier. As the NAIRU has given way to potential output as the operational form of supply constraints on macroeconomic policy, this understanding of inflation has arguably become the dominant one, even if without formalization in textbooks. It overlaps with the unemployment story in making current demand conditions a key driver of inflation, even if the transmission mechanism is different. 

Superfically “too much spending relative to production” sounds a lot like “too money relative to goods.” (As to a lesser extent does “too much wage growth relative to productivity growth.”) But while these formulations sound similar, they have quite different implications. Intuitions formed by the old quantity-of-money view don’t work for the new stories.

The older understanding of inflation, which runs more or less unchanged from David Hume through Irving Fisher to Milton Friedman and contemporary monetarists, goes like this. There’s a stock of goods, which people can exchange for their mutual benefit. For whatever reasons, goods don’t exchange directly for other goods, but only for money. Money in turn is only used for purchasing goods. When someone receives money in exchange for a good, they turn around and spend it on some good themselves — not instantly, but after some delay determined by the practical requirements of exchange. (Imagine you’ve collected your earnings from your market stall today, and can take them to spend at a different market tomorrow.) The total amount of money, meanwhile, is fixed exogenously — the quantity of gold in circulation, or equivalently the amount of fiat tokens created by the government via its central bank.

Under these assumptions, we can write the familiar equation

MV = PY

If Y, the level of output, is determined by resources, technology and other “real” factors, and V is a function of the technical process of exchange — how long must pass between the receipt of money and it spending — then we’re left with a direct relationship between the change in M and the change in P. “Inflation is always and everywhere a monetary phenomenon.”2

I think something like this underlies most folk wisdom about inflation. And as is often the case, the folk wisdom has outlived whatever basis in reality it may once have had.3

Below, I want to sketch out some ways in which the implications of the excessive-spending-relative-to-production vision of inflation are importantly different from those of the excessive-money-relative-to-goods vision. But first, a couple of caveats.

First, the idea of a given or exogenous quantity of money isn’t wrong a priori, as a matter of logic; it’s an approximation that happens not to fit the economy in which we live. Exactly what range of historical settings it does fit is a tricky question, which I would love to see someone try to answer. But I think it’s safe to say that many important historical inflations, both under metallic and fiat regimes, fit comfortably enough in a monetarist framework. 

Second, the fact that the monetarist understanding of inflation is wrong (at least for contemporary advanced economies) doesn’t mean that the modern mainstream view is right. There is no reason to think there is one general theory of inflation, any more than there is one general etiology of a fever. Lots of conditions can produce the same symptom. In general, inflation is a persistent, widespread rise in prices, so for any theory of price-setting there’s a corresponding theory of inflation. And the expectations-based propagation mechanism of inertial inflation — where prices are raised in the expectation that prices will rise — is compatible with many different initial inflationary impulses. 

That said — here are some important cleavages between the two visions.

1. Money vs spending. More money is just more money, but more spending is always more spending on something in particular. This is probably the most fundamental difference. When we think of inflation in terms of money chasing a given quantity of goods, there is no connection between a change in the quantity of money and a change in individual spending decisions. But when we think of it in terms of spending, that’s no longer true — a decision to spend more is a decision to spend more on some specific thing. People try to carry over intuitions from the former case to the latter, but it doesn’t work. In the modern version, you can’t tell a story about inflation rising that doesn’t say who is trying to buy more of what; and you can’t tell a story about controlling inflation without saying whose spending will be reduced. Spending, unlike money, is not a simple scalar.

The same goes for the wages-markup story of the textbook. In the model, there is a single wage and a single production process. But in reality, a fall in unemployment or any other process that “raises the wage” is raising the wages of somebody in particular.

2. Money vs prices. There is one stock of money, but there are many prices, and many price indices. Which means there are many ways to measure inflation. As I mentioned above, inflation was originally conceived of as definitionally an increase in the quantity of money. Closely related to this is the idea of a decrease in the purchasing power of money, a definition which is still sometimes used. But a decrease in the value of money is not the same as an increase in the prices of goods and services, since money is used for things other than purchasing goods and services.  (Merijn Knibbe is very good on this.4) Even more problematically, there are many different goods and services, whose prices don’t move in unison. 

This wasn’t such a big deal for the old concept of inflation, since one could say that all else equal, a one percent increase in the stock of money would imply an additional point of inflation, without worrying too much about which specific prices that showed up in. But in the new concept, there’s no stock of money, only the price changes themselves. So picking the right index is very important. The problem is, there are many possible price indexes, and they don’t all move in unison. It’s no secret that inflation as measured by the CPI averages about half a point higher than that measured by the PCE. But why stop there? Those are just two of the infinitely many possible baskets of goods one could construct price indexes for. Every individual household, every business, every unit of government has their own price index and corresponding inflation rate. If you’ve bought a used car recently, your personal inflation rate is substantially higher than that of people who haven’t. We can average these individual rates together in various ways, but that doesn’t change the fact that there is no true inflation rate out there, only the many different price changes of different commodities.

3. Inflation and relative prices. In the old conception, money is like water in a pool. Regardless of where you pour it in, you get the same rise in the overall level of the pool.

Inflation conceived of in terms of spending doesn’t have that property. First, for the reason above — more spending is always more spending on something. If, let’s say for sake of argument, over-generous stimulus payments are to blame for rising inflation, then the inflation must show up in the particular goods and services that those payments are being used to purchase — which will not be a cross-section of output in general. Second, in the new concept, we are comparing desired spending not to a fixed stock of commodities, but to the productive capacity of the economy. So it matters how elastic output is — how easily production of different goods can be increased in response to stronger demand. Prices of goods in inelastic supply — rental housing, let’s say — will rise more in response to stronger demand, while prices of goods supplied elastically — online services, say — will rise less. It follows that inflation, as a concrete phenomenon, will involve not an across-the-board increase in prices, but a characteristic shift in relative prices.

This is a different point than the familiar one that motivates the use of “core” inflation — that some prices (traditionally, food and energy) are more volatile or noisy, and thus less informative about sustained trends. It’s that  when spending increases, some goods systematically rise in price faster than others.

This recent paper by Stock and Watson, for example, suggests that housing, consumer durables and food have historically seen prices vary strongly with the degree of macroeconomic slack, while prices for gasoline, health care, financial services, clothing and motor vehicles do not, or even move the opposite way. They suggest that the lack of a cyclical component in health care and finance reflect the distinct ways that prices are set (or imputed) in those sectors, while the lack of a cyclical component in gas, clothing and autos reflects the fact that these are heavily traded goods whose prices are set internationally. This interpretation seems plausible enough, but if you believe these numbers they have a broader implication: We should not think of cyclical inflation as an across the board increase in prices, but rather as an increase in the price of a fairly small set of market-priced, inelastically supplied goods relative to others.

4. Inflation and wages. As I discussed earlier in the post, the main story about inflation in today’s textbooks is the Phillips curve relationship where low unemployment leads to accelerating inflation. Here it’s particularly clear that today’s orthodoxy has abandoned the quantity-of-money view without giving up the policy conclusions that followed from it.

In the old monetarist view, there was no particular reason that lower unemployment or faster wage growth should be associated with higher inflation. Wages were just one relative price among others. A scarcity of labor would lead to higher real wages, while an exogenous increase in wages would lead to lower employment. But absent a change in the money supply, neither should have any effect on the overall price level. 

It’s worth noting here that altho Milton Friedman’s “natural rate of unemployment” is often conflated with the modern NAIRU, the causal logic is completely different. In Friedman’s story, high inflation caused low unemployment, not the reverse. In the modern story, causality runs from lower unemployment to faster wage growth to higher inflation. In the modern story, prices are set as a markup over marginal costs. If the markup is constant, and all wages are part of marginal cost, and all marginal costs are wages, then a change in wages will just be passed through one to one to inflation.

We can ignore the stable markup assumption for now — not because it is necessarily reasonable, but because it’s not obvious in which direction it’s wrong. But if we relax the other assumptions, and allow for non-wage costs of production and fixed wage costs, that unambiguously implies that wage changes are passed through less than one for one to prices. If production inputs include anything other than current labor, then low unemployment should lead to a mix of faster inflation and faster real wage growth. And why on earth should we expect anything else? Why shouldn’t the 101 logic of “reduced supply of X leads to a higher relative price of X” be uniquely inapplicable to labor?5

There’s an obvious political-ideological reason why textbooks should teach that low unemployment can’t actually make workers better off. But I think it gets a critical boost in plausibility — a papering-over of the extreme assumptions it rests on — from intuitions held over from the old monetarist view. If inflation really was just about faster money growth, then the claim that it leaves real incomes unchanged could work as a reasonable first approximation. Whereas in the markup-pricing story it really doesn’t. 

5. Inflation and the central bank.  In the quantity-of-money vision, it’s obvious why inflation is the special responsibility of the central bank. In the textbooks, managing the supply of money is often given as the first defining feature of a central bank. Clearly, if inflation is a function of the quantity of money, then primary responsibility for controlling it needs to be in the hands of whoever is in charge of the money supply, whether directly, or indirectly via bank lending. 

But here again, it seems, to me, the policy conclusion is being asked to bear weight even after the logical scaffolding supporting it has been removed. 

Even if we concede for the sake of argument that the central bank has a special relationship with the quantity of money, it’s still just one of many influences on the level of spending. Indeed, when we think about all the spending decisions made across the economy, “at one interest rate will I borrow the funds for it” is going to be a central consideration in only a few of them. Whether our vision of inflation is too much spending relative to the productive capacity of the economy, or wages increasing faster than productivity, many factors are going to play a role beyond interest rates or central bank actions more broadly. 

One might believe that compared with other macro variables, the policy interest rate has a uniquely strong and reliable link to the level of spending and/or wage growth; but almost no one, I think, does believe this. The distinct responsibility of the central bank for inflation gets justified not on economic grounds but political-institutional ones: the central bank can act more quickly than the legislature, it is free of undue political influence, and so on. These claims may or may not be true, but they have nothing in particular to do with inflation. One could justify authority over almost any area of macroeconomic policy on similar grounds.

Conversely, once we fully take on board the idea that the central bank’s control over inflation runs through to the volume of credit creation to the level of spending (and then perhaps via unemployment to wage growth), there is no basis for the distinction between monetary policy proper and other central bank actions. All kinds of regulation and lender-of-last-resort operations equally change the volume and direction of credit creation, and so influenced aggregate spending just as monetary policy in the narrow sense does.

6. The costs of inflation. If inflation is a specifically monetary phenomenon, the costs of inflation presumably involve the use of money. The convenience of quoting relative prices in money becomes a problem when the value of money is changing.

An obvious example is the fixed denominations of currency — monetarists used to talk with about “shoe leather costs” — the costs of needing to go more frequently to the bank (as one then did) to restock on cash. A more consequential example is public incomes or payments fixed in money terms. As recently as the 1990s, one could find FOMC members talking about bracket creep and eroded Social Security payments as possible costs of higher inflation — albeit with some embarrassment, since the schedules of both were already indexed by then. More broadly, in an economy organized around money payments, changes in what a given flow of money can buy will create problems. Here’s one way to think about these problems:

Social coordination requires a mix of certainty and flexibility. It requires economic units to make all kinds of decisions in anticipation of the choices of other units — we are working together; my plans won’t work out if you can change yours too freely. But at the same time, you need to have enough space to adapt to new developments — as with train cars, there needs to be some slack in the coupling between economic unit for things to run smoothly. One dimension of this slack is the treatment of some extended period as if it were a single instant.

This is such a basic, practical requirements of contracting and management that we hardly think about it. For example, budgets — most organizations budget for periods no shorter than a quarter, which means that as far as internal controls and reporting are concerned, anything that happens within that quarter happens at the same time.6Similarly, invoices normally require payment in 30 or 60 days, thus treating shorter durations as instantaneous. Contracts of all kinds are signed for extended periods on fixed money terms. All these arrangements assume that the changes in prices over a few months or a year are small enough that they can be safely ignored.can be modified when inflation is high enough to make the fiction untenable that 30, 60 or 90 days is an instant. Social coordination strongly benefits from the convention that shorter durations can be ignored for most periods, which means people behave in practice as if they expect inflation over such shorter periods to be zero.

Axel Leijonhufvud’s mid-70s piece on inflation is one of the most compelling accounts of this kinds of cost of inflation — the breakdown of social coordination — that I have seen. For him, the stability of money prices is the sine qua non of decentralized coordination through markets. 

In largely nonmonetary economies, important economic rights and obligations will be inseparable from particularized relationships of social status and political allegiance and will be in some measure permanent, inalienable and irrevocable. … In monetary exchange systems, in contrast, the value to the owner of an asset derives from rights, privileges, powers and immunities against society generally rather than from the obligation of some particular person. …

Neoclassical theories rest on a set of abstractions that separate “economic” transactions from the totality of social and political interactions in the system. For a very large set of problems, this separation “works”… But it assumes that the events that we make the subject of … the neoclassical model of the “economic system” do not affect the “social-political system” so as … to invalidate the institutional ceteris paribus clauses of that model. …

 Double-digit inflation may label a class of events for which this assumption is a bad one. … It may be that … before the “near-neutral” adjustments can all be smoothly achieved, society unlearns to use money confidently and reacts by restrictions on “the circles people shall serve, the prices they shall charge, and the goods they can buy.”

One important point here is that inflation has a much greater impact than in conventional theory because of the price-stability assumption incorporated into any contract that is denominated in money terms and not settled instantly — which is to say, pretty much any contract. So whatever expectations of inflation people actually hold, the whole legal-economic system is constructed in a way that makes it behave as if inflation expectations were biased toward zero:

The price stability fiction — a dollar is a dollar is a dollar — is as ingrained in our laws as if it were a constitutional principle. Indeed, it may be that no real constitutional principle permeates the Law as completely as does this manifest fiction.

The market-prices-or-feudalism tone of this seems more than a little overheated from today’s perspective, and when Arjun and I asked him about this piece a few years ago, he seemed a bit embarrassed by it. But I still think there is something to it. Market coordination, market rationality, the organization of productive activity through money payments and commitments, really does require the fiction of a fixed relationship between quantities of money and real things. There is some level of inflation at which this is no longer tenable.

So I have no problem with the conventional view that really high inflations — triple digits and above — can cause far-reaching breakdowns in social coordination. But this is not relevant to the question of inflation of 1 or 2 or 5 or probably even 10 percent. 

In this sense, I think the mainstream paradoxically both understates and overstates the real costs of inflation. They exaggerate the importances of small differences in inflation. But at the same time, because they completely naturalize the organization of life through markets, they are unable to talk about the possibility that it could break down.

But again, this kind of breakdown of market coordination is not relevant for the sorts of inflation seen in the United States or other rich countries in modern times. 

It’s easier to talk about the costs (and benefits) of inflation when we see it as a change in relative prices, and redistribution of income and wealth. If inflation is typically a change in relative prices, then the costs are experienced by those whose incomes rise more slowly than their payments. Keynes emphasized this point in an early article on “Social Consequences of a Change in the Value of Money.”7

A change in the value of money, that is to say in the level of prices, is important to Society only in so far as its incidence is unequal. Such changes have produced in the past, and are producing now, the vastest social consequences, because, as we all know, when the value of money changes, it does not change equally for all persons or for all purposes. … 

Keynes sees the losers from inflation as passive wealth owners, while the winners are active businesses and farmers; workers may gain or lose depending on the degree to which they are organized. For this reason, he sees moderate inflation as being preferable to moderate deflation, though both as evils to be avoided — until well after World War II, the goal of price stability meant what it said.

Let’s return for a minute to the question of wages. As far as I can tell, the experience in modern inflations is that wage changes typically lag behind prices. If you plot nominal wage growth against inflation, you’ll see a clear positive relationship, but with a slope well below 1. This might seem to contradict what I said under point 4. But my point there was that insofar as inflation is driven by increased worker bargaining power, it should be associated with faster real wage growth. In fact, the textbook is wrong not just on logic but on facts. In principle, a wage-driven inflation would see a rise in real wage. But most real inflations are not wage-driven.

In practice, the political costs of inflation are probably mostly due to a relatively small number of highly salient prices. 

7. Inflation and production. The old monetarist view had a fixed quantity of money confronting a fixed quantity of goods, with the price level ending up at whatever equated them. As I mentioned above, the fixed-quantity-of-money part of this has been largely abandoned by modern mainstream as well as heterodox economists. But what about the other side? Why doesn’t more spending call forth more production?

The contemporary mainstream has, it seems to me, a couple ways of answering the question. One is the approach of a textbook like Blanchard’s. There, higher spending does lead to to higher employment and output and lower unemployment. But unless unemployment is at a single unique level — the NAIRU — inflation will rise or fall without limit. It’s exceedingly hard to find anything that looks like a NAIRU in the data, as critics have been pointing out for a long time. Even Blanchard himself rejects it when he’s writing for central bankers rather than undergraduates. 

There’s a deeper conceptual problem as well. In this story, there is a tradeoff between unemployment and inflation. Unemployment below the NAIRU does mean higher real output and income. The cost of this higher output is an inflation rate that rises steadily from year to year. But even if we believed this, we might ask, how much inflation acceleration is too much? Can we rule out that a permanently higher level of output might be worth a slowly accelerating inflation rate?

Think about it: In the old days, the idea that the price level could increase without limit was considered crazy. After World War II, the British government imposed immense costs on the country not just to stabilize inflation, but to bring the price level back to its prewar level. In the modern view, this was crazy — the level of prices is completely irrelevant. The first derivative of prices — the inflation rate — is also inconsequential, as long as it is stable and predictable. But the second derivative — the change in the rate of inflation — is apparently so consequential that it must be kept at exactly zero at all costs. It’s hard to find a good answer, or indeed any answer, for why this should be so.

The more practical mainstream answer is to say, rather than that there is a tradeoff between unemployment and inflation with one unambiguously best choice, but that there is no tradeoff. In this story, there is a unique level of potential output (not a feature of the textbook model) at which the relationship between demand, unemployment and inflation changes. Below potential, more spending calls forth more production and employment; above potential, more spending only calls forth higher inflation. This looks better as a description of real economies, particular given that the recent experience of long periods of elevated unemployment that have not, contrary to the NAIRU prediction, resulted in ever-accelerating deflation. But it begs the question of why should be such a sharp line.

The alternative view would be that investment, technological change, and other determinants of “potential output” also respond to demand. Supply constraints, in this view, are better thought of in terms of the speed with which supply can respond to demand, rather than an absolute ceiling on output.

Well, this post has gotten too long, and has been sitting in the virtual drawer for quite a while as I keep adding to it. So I am going to break off here. But it seems to me that this is where the most interesting conversations around inflation are going right now — the idea that supply constraints are not absolute but respond to demand with varying lags — that inflation should be seen as often a temporary cost of adjustment to a new higher level of capacity. And the corollary, that anti-inflation policy should aim at identifying supply constraints as much as, or more than, restraining demand. 

  1. Though I don’t reject everything either. I often use Blanchard in my macro classes, not as an example of mainstream thinking to criticize — I think this is bad pedagogy — but because it gives a good introduction to a lot of genuinely useful concepts.
  2. For the purpose of this post, I’m ignoring the severe problems with the monetarist story even in a world with an exogenously fixed money stock.
  3. The problem is first, the quantity of “money” is not well defined in a modern economy, and second, whatever definition of money one adopts, one will find that both that both the demand and supply for it are quite unstable and, more importantly, themselves dependent on the macroeconomic outcomes changes in the money supply are supposed to explain. The Blanchard textbook emphasizes the demand side of this (because he is committed to the IS-LM model which treats money as exogenous) but the flexibility in the supply of money is even more important. At one point there were great battles on this field, with then-dominant monetarists opposed by Keynesians who fought under the banner of “endogenous money”; but this is one debate the heterodox side has decisively won. See this Bank of England explainer for the current consensus view.
  4. I try not to link to paywalled articles, but there doesn’t seem to be a free version of this online. But you can reach it through sci-hub.
  5. Of course there are plenty of good reasons why simple 101 logic doesn’t apply to labor, or many other things. But they don’t get us any closer to the textbook story.
  6. Back when I worked for New York City government, I sometimes had to deal with the “fifth quarter” of the year — a budget period that existed to handle items that were associated with one year but for whatever reason had to be recorded after the normal reporting period had closed. I have no idea how general this is, but it was a fascinating reminder of the difference between calendar time and accounting time.
  7. Keynes at this point defined inflation in the conventional way, as “an expansion in the supply of money to spend relatively to the supply of things to purchase.” But his assessment of its costs and benefits was not at all conventional. So I suppose if I am arguing for a tight link between the underlying concept of and practical understanding of inflation, this would have to count as a counterexample.
About JW Mason
JW Mason
Assistant professor of economics at John Jay College - CUNY, and fellow at the Roosevelt Institute. RT = Read This

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.