The Corona crisis triggered very expansionary monetary and fiscal policies in industrialised countries to stabilise the economy. Central banks lowered interest rates to zero, granted extensive credit lines and bought government bonds in significant volumes. This allowed for enormous fiscal policy support programmes while keeping debt servicing costs low.
What initially sounds like a win-win situation, however, has a catch. For the large fiscal programmes go hand in hand with high budget deficits. The national debt in relation to the gross domestic product rose to the highest level since the Second World War, and in the USA even beyond. 
An often-suspected correlation is that the historically high budget deficits lead to a noticeable increase in inflation rates. But is this really the case?
Of course, in a world characterised by uncertainty, no "safe predictions" are possible about how things will turn out this time. What we can do, however, is to make a historical classification. This is exactly what Michael Bordo and Mickey Levy did in their paper "Do Enlarged Fiscal Deficits Cause Inflation", which they published in December 2020.  In it, they look at the relationship between expansionary fiscal policy and inflation over more than two centuries. They conclude that deficits can have an inflationary effect if they are financed by monetary expansion.
The historical analysis shows that the relationship between deficits and inflation depended on whether peacetime or wartime prevailed. This is because in the 18th century inflation became an important component of war financing. Thus, early central banks such as the Bank of England were established explicitly to support government military objectives. And in the world wars of the 20th century, central banks set short- and long-term interest rates, which is again discussed today as a tool (controlling the yield curve) to support financing.
In peacetime, by contrast, fiscal policy has long been controversial and more associated with emerging economies whose financial systems are poorly developed. But there were also developed countries where high fiscal deficits were accompanied by unfunded expansion. In these cases, central banks were usually dominated by fiscal policy, which is a problematic constellation.
According to the study, there are two main factors that can cause this:
political pressure: In the 1920s, the dysfunctional government in France could not agree on how to finance its spending. In the end, the Banque de France activated its printing press. Conversely, in the USA of the 1960s, the Fed was pressured to avoid tight monetary policy.
theoretical belief: In the 1970s, Keynesian views and the belief in a trade-off according to the Phillips curve (correlation between the unemployment rate and the price level) dominated the policy debate in the US and the UK. The focus was on inflation being generated by higher costs rather than expansionary monetary policy.
Once inflation rates rise significantly, it can be difficult or painful to maintain control. This was demonstrated by the Great Inflation of the 1970s, which was only ended by extraordinarily tight monetary policy. Two decades of Great Moderation followed, during which moderate inflation with a stable economy prevailed. Central banks became independent, pursued inflation targeting strategies and gained credibility. It seemed very unlikely that they could move to tolerate - or even "wish" for - higher inflation rates.
Higher inflation possible
The fact that deficits do not always lead to inflation was shown, for example, after the great financial crisis of 2008/09. Expansionary monetary and fiscal policies prevailed, as a result of which inflation remained subdued. The situation has been similar in Japan since the great crash of the early 1990s, where even the long zero interest rate policy did not bring about a sustained rise in inflation despite high budget deficits.
However, it could be dangerous to rely on there being no inflation effect this time either. In the wake of Corona, both central banks and fiscal policy have once again moved to very expansionary measures. In the process, as once in history, fiscal-policy dominance could loom, as a result of which inflation rates could pick up significantly again.
The scenario from the historical framing: a high deficit in a peacetime combined with loose monetary policy that increase the risk for a persistent excess demand fuelled by monetary growth. In this context, the Fed's new policy of allowing some room for inflation could loosen the important anchor of inflation expectations in the markets.
History does not repeat itself, but it does rhyme. There are lessons from the past that should be kept in mind. In principle, economic policies that promote growth are to be welcomed. However, one should be cautious about permanently financing budget deficits through monetary policy. Therefore, independent central banks, the avoidance of fiscal dominance by policymakers and a good anchoring of inflation expectations in the markets are particularly important. The more these factors are undermined, the higher the inflation risks. Some tendencies in this direction can already be observed.