# Relation between budget deficit and inflation?

In Iran we have had a high inflation rate for several decades (usually above 20 percent). Some of the top economists of the country say that it is mainly because the government spending is considerably more than its revenues. If I'm not mistaken, this is called "budget deficit" and leads to debt of the government. On the other hand, Paul Krugman believes that debt is good for the economy and people should love debt. As a layman, I'm confused here. When does debt result in harmful levels of inflation?

• The question in the title and the question in the body of the text are different. Which one interests you? Commented Aug 12, 2021 at 19:35
• @Giskard, I hope that now you find them in more harmony. Commented Aug 13, 2021 at 3:19

## 2 Answers

Relation between budget deficit and inflation?

There is no direct relationship between budget deficits and inflation, however, inflation is one of the ways government can choose to finance government deficit, and consequently highly indebted nations often choose to do so for various reasons, but it is not a necessity.

Government budget constraint is by definition (in its static form) given as:

$$G−T=\theta + \beta$$

where $$G$$ is government spending, $$T$$ is the net tax revenue after transfers and interest payments, $$\theta$$ is government financing by high powered money and $$\beta$$ is government financing by bonds (see for example Blinder & Solow, 1973; Christ, 1968; Tobin & Buiter 1976).

All these variables $$G$$, $$T$$, $$\theta$$ and $$\beta$$ are choice variables of the government singe government can choose its spending, taxes, high powered money supply or bond issuance. However, what choices government makes here will have different effect on inflation.

Now price level (positive change of which is by definition inflation), is given by a money market equilibrium that in common modern models is given by (see Romer Advanced Macroeconomics for more detail):

$$M/P = L(i,Y) \implies P= \frac{M}{L(Y,i)}$$

where, $$M$$ is money stock, which is function of the high powered money $$M(\theta)$$, $$L$$ is money demand which is function increasing in the real output $$Y$$ and decreasing in interest rates $$i$$.

Consequently, when government decides to fund budget deficit $$G-T>0$$ with high powered money $$\theta$$, this will increase $$M$$ and ceteris paribus it will increase $$P$$ as well which will lead to inflation. In addition, highly indebted government typically wants central bank to keep interest rates low (to make maintenance of its debt easier), which will again contribute to the inflation since low $$i$$ decreases $$L$$ and fall in $$L$$ again increases $$P$$. Consequently, it can be historically observed that many government that were highly indebted eventually choose to (at least partially) monetize their debt by combination of issuance of high powered money and keeping low interest rate (see discussion of that in Rogoff and Reinhart: This Time is Different*).

However, that is not the only thing that government can do. Governments can try to outgrow their debts by keeping deficits lower than the growth of the economy and finance these deficits purely by bond issuance to the public without putting pressure on interest rates via central bank (or buying the bonds itself using high powered money). In such case there is no reason why government deficit should lead to inflation.

Consequently, there is no necessary link between government deficits and inflation. It is all up the government to decide how to finance its deficits, there are always non-inflationary options. Although, most economists do not consider mild inflation (2-4%) a problem but a good thing (see this excellent answer of FooBar for more info on that).

When is debt harmful?

This is different question. Debts are generally considered harmful if they are used to finance unproductive activity or do not pass cost-benefit analysis (i.e. activity for which net present value is less than zero).

For example, borrowing \$1.000.000 at 10% interest is completely fine if government discovered some new oil field and the \$1.000.000 is used to set up an oil rig that will generate \$200.000 cashflows each year for next 30 years, as the net present value of the project is positive (that is the project pays for the debt, interest rate, and still leaves us with positive net value). In addition, to just monetary cashflows it is also reasonable to factor in welfare benefits that the government project has for people (see discussion of that in Carnot et al Economic Forecasting and Policy), however then things get more complex as in such case there might be some issues with debt sustainability (but this is issue too broad for a single SE answer so I won't go into greater depth on that here). However, if the government decides to spend that \$1.000.000, borrowed at 10% for a new private palace for president, which will have no positive cashflows for government or no welfare benefit for society, then that debt will be harmful.

This being said, note that the above are only very rough outlines of discussion when debt is and is not harmful, that question in itself is too broad to explore fully in SE format as it all depends on the context.

* Note this book was criticized for their analysis of effect of debt on growth, where they made some serious mistakes making that portion of their analysis discredited so you should not pay much attention to that part, but their historical analysis of how governments dealt with high debt levels is still valid.

• Thanks for your answer. By "indebted nation" you mean a nation being in debt to other nations, or it also includes a government being in debt to a fraction of its own people? Commented Aug 13, 2021 at 9:54
• @apadana I just mean nation being in debt without any distinction of who owns the debt.
– 1muflon1
Commented Aug 13, 2021 at 10:01
• If a government finances its deficit by increasing the monetary base $\theta$, is it considered to be some sort of debt? or the meaning of the term "debt" doesn't include that? By the way, your answer was very helpful. Thanks again. Commented Aug 13, 2021 at 10:39
• @apadana no, increasing $\theta$ is not debt per se although one of the ways how government can increase $\theta$ is to ask its central bank to create new money and purchase its debt. This way government effectively purchases its debt from itself with new money. The reason why governments do this is that it makes easier to destroy that new money later (by repaying the debt to itself) and because it pushes pressure on lowering interest rate on government debt, meaning government can borrow more cheaply from other actors than itself.
– 1muflon1
Commented Aug 13, 2021 at 10:44
• Consolidate balance sheets of the fiat government and central bank into one unit that I call the Sovereign finance sector. Sovereign can cover the budget deficit three ways: (1) print and spend currency to increase M1 money supply; (2) write checks via central bank, cleared by bank sector, to increase reserve balances in base money and bank deposits in M1 money supply; (3) issue Treasury securities and/or interest-bearing central bank accounts to drain base money and M1 money at the same rate as the deficit spending would tend to increase base money and M1 money. Commented Aug 13, 2021 at 13:30

This article argues that growth in the money supply is caused by the government printing money:

https://en.radiofarda.com/a/iran-s-money-supply-skyrockets-parallel-to-inflation/30671910.html

However the credit system can increase the money supply via expansion of bank credit and/or increase the velocity of money via expansion of non-bank credit offered by non-bank creditors.

This article describes the political and structural problems Central Bank of Iran faces with efforts to target rampant inflation:

https://www.rethinkingiran.com/iranundersanctions/mazarei

In a simplified model of rampant inflation if there is no shock to aggregate production (for example a natural or social disaster destroys factories or other means of economic production) then inflation is caused by too much aggregate demand (purchasing power) which enables prices of inputs to production and outputs to rise rampantly. Then the economic community can debate the sole and/or joint causes of too much aggregate demand. Again in the simplified model the government deficit, expansion of bank credit and other sources of credit in the credit/debt markets, and/or so-called increase in the velocity of money are joint causes of greater aggregate demand. In modern economies if the government is running a high deficit and there is rampant inflation the central bank can "kill" the inflation only by forcing the bank sector to ration future credit deals to the non-bank sector or it can jawbone the government to reduce the deficit. There is no deterministic model for how the government budget deficit drives inflation because the credit system and so-called velocity of money are independent drivers of inflation.

Some argue that unions bargain for higher wages and this causes inflation but then such rising wages are either paid via increasing the velocity of money which is hard to accomplish or via increasing the credit provided via financial deals that producers use to pay wages and sell output at rampantly rising prices. So blaming high inflation on something other than the government budget being too big and the credit system expanding too fast is a spurious model.