A recent exchange on X (Tweeter) pointed to a paper that proposes to separate demand from supply-driven inflation by looking at the relation between prices and quantities. According to the paper, if both rise, inflation is treated as demand-driven (as shown below). If prices rise while quantities fall, it is treated as supply-driven (no figure, but easy to visualize, a shock to Ys, the aggregate supply). The problem is that this does not identify the cause of inflation.
Prices can rise because of higher costs (e.g. energy, imported inputs, etc.) while quantities increase for independent reasons (e.g. increase in government transfers to the unemployed). The economy may be recovering, public spending may be growing, credit may be expanding, or firms may be drawing on unused capacity. In that case, prices and quantities rise together, but it does not follow that demand caused the price increase (old post on why prices and quantities can and should be treated as analytically separate here).
The real issue is capacity. Higher demand becomes inflationary when it encounters binding limits on production. But full capacity is not fixed or directly observable. It depends on the technology, on the availability of labor and inventories, on access to imported inputs, and sector-specific bottlenecks. There are many measures of capacity utilization, non perfect, obviously. Most of my discussion of why the inflationary acceleration of the pandemic was not demand driven is based on looking at different measures of that.
A growing economy can therefore have rising prices and rising output for many different reasons. Cost pressures may push prices up while demand supports expanding production. The sign of price and quantity changes cannot tell us which force caused inflation. The procedure classifies observed co-movements. It does not establish the structural source of inflation. To do that, one must examine costs, mark-ups, distributional conflict, supply disruptions, and the actual conditions of production, not simply whether prices and quantities move in the same direction.
