# Accounting for Inflation

Although everyone agrees that inflation is too high, there is much less agreement about the cause. In May, a New York Times poll asked respondents how much they blame the pandemic, supply chain disruptions, corporations, the American Rescue Plan, and the War in Ukraine for high inflation. Most respondents assigned at least a little blame to each. The Biden administration prefers to blame the war in Ukraine. Other Democrats point to corporations for so-called greedflation.

Despite having a mandate from Congress to deliver price stability, the Federal Reserve was not even an option on the New York Times poll. The paper should have consulted their resident Fed watcher. Few economists would rank corporate greed above monetary policy as a potential cause.

Economists typically divide explanations of high inflation into two categories: reduced supply and excessive nominal spending. The New York Times poll focuses primarily on the former, though many economists would say the American Rescue Plan (ARP) boosted nominal spending. Technically, fiscal policy actions like the ARP only boost nominal spending if they are accommodated by monetary policy. The Federal Reserve ultimately controls nominal spending in the United States.

There is no doubt that supply disturbances like the pandemic and the war in Ukraine have pushed prices up. But we can say more than that. With a simple identity and some assumptions about expectations, we can estimate the extent to which today’s inflation is driven by supply disturbances.

### The Identity

Let’s start with an identity. At every point in time, the total amount of money being spent on final goods and services—nominal spending—has to be equal to the nominal value of those goods and services being purchased. More formally, we can write that Nt = PtYt, where Nt is nominal spending at time t, Pt is the price level at time t, Yt is real output at time t, and PtYt is the nominal value of final goods and services produced at time t.

Since we are interested in inflation (i.e., the growth rate of the price level), we need to transform this static identity into a dynamic identity. To do that, we must recognize that the growth rate of a variable that is the product of two factors is approximately equal to the sum of the growth rates of the two factors. Nominal spending (Nt) is the product of two factors (Pt and Yt). Hence, gNt = gPt + gYt, where gNt, gPt, and gYt are the growth rates of nominal spending, the price level, and real output at time t. Subtracting gYt from both sides, we get an identity (gPt = gNt – gYt) that says inflation (gPt) is the difference between nominal spending growth (gNt) and real output growth (gYt) at time t.

This identity holds at each time period t. Therefore, it must also hold for a forecast of some future period. Hence, E(gPt) = E(gNt) – E(gYt), where E(gPt), E(gNt), and E(gYt) are the expected growth rates of the price level, nominal spending, and real output at time t.

Finally, we can combine the actual and forecast identities specified above to express a relationship between actual and expected values. Just subtract E(gPt) from both sides of the equation gPt = gNt – gYt and then substitute E(gNt) – E(gYt) for E(gPt) on the right hand side of the equation: gPt – E(gPt) = (gNt – E(gNt)) – (gYt – E(gYt)). Note that the left hand side refers to the difference between actual and expected inflation, which is precisely what we want to explain.

Before we can consider the extent to which various factors are contributing to inflation, we must first make some assumptions about what would have happened in the absence of the shock we are considering. In other words, we need to specify how much inflation, nominal spending growth, and real output growth were expected just prior to the pandemic.

In what follows, we assume that the price level, nominal spending, and real output would have continued to grow at the same rate that they had grown on average over the prior ten-year period. For consistency, we use the gross domestic product (GDP) implicit price deflator to measure the price level; real GDP to measure real output, and nominal GDP to measure nominal spending. From January 2010 to January 2020, just prior to the pandemic, the price level grew at a continuously compounding annual rate of 1.71 percent. Nominal spending grew 3.93. Real output grew 2.22 percent. Hence, gPt – 1.71 = (gNt – 3.93) – (gYt – 2.22).

### How Much Inflation Can Be Attributed to Supply Constraints?

Suppose supply disturbances were the only thing driving prices up over the course of the pandemic. How high would inflation be? To estimate the relevant counterfactual, we must assume that nominal spending growth is unchanged. Hence gPt – 1.71 = (3.93 – 3.93) – (gYt – 2.22)—or, gPt = 3.93 – gYt.

From January 2020 to July 2022, real GDP grew at a continuously compounding annual rate of 0.99 percent. Hence, if supply constraints were the only thing driving prices up, inflation would have averaged gPt = 3.93 – 0.99 = 2.94 percent over the period.

In fact, inflation averaged 4.46 percent from January 2020 to July 2022—1.52 percentage points more than would have occurred if supply disturbances were the only thing driving prices up. Since real output growth is 2.22 – 0.99 = 1.23 percentage points lower than expected and inflation is 4.46 – 1.71 = 2.75 percentage points higher than expected, we can conclude that supply disturbances account for roughly 1.23/2.75 = 44.73 percent of the excess inflation realized over the course of the pandemic.

### The Relative Share Nominal Disturbances

We can repeat the same exercise to see the extent to which nominal disturbances are driving inflation. This time, we will assume that real output grew as expected—meaning nominal disturbances were the only thing driving prices up. Hence gPt – 1.71 = (gNt – 3.93) – (2.22 – 2.22)—or, gPt = gNt – 2.22.

From January 2020 to July 2022, nominal GDP grew at a continuously compounding annual rate of 5.45 percent. Hence, if nominal disturbances were the only thing driving prices up, inflation would have averaged gPt = 5.45 – 2.22 = 3.23 percent. Since inflation averaged 4.46 percent over the period, we can conclude that nominal disturbances account for roughly (5.45 – 3.93)/(4.46 – 1.71) = 1.52/2.75 = 55.27 percent of the excess inflation realized over the course of the pandemic.

### Conclusion

Supply disturbances are especially salient. We experienced the pandemic. We hear a lot about Russia’s invasion of Ukraine. It is easy to connect those events to reduced production and higher prices. However, a proper accounting of inflation helps us consider the extent to which these supply disturbances actually contributed to inflation.

Most of the excess inflation realized since the onset of the pandemic is not due to supply disturbances. Rather, it is due to a surge in nominal spending. If the Federal Reserve had stabilized nominal spending, inflation would be much lower today. Prices would be higher than was expected prior to the pandemic—but only to the extent necessitated by the reduction in real output and only for as long as output remained below trend. For much of 2021, Fed officials insisted that inflation would be transitory. They have since abandoned that view. The great irony is that inflation would have been transitory if only the Fed had stabilized nominal spending. Prices would have risen above trend to reflect below-trend production and then returned to trend as production recovered. The Fed failed to stabilize nominal spending. Consequently, prices have risen much higher and will remain permanently elevated.