Government debt causes producer price inflation (PPI) if the economy is at full capacity. If government debt is used to increase capacity utilization rather than operations, this cause is mitigated after a delay during the construction period.

Assuming the economy has excess capacity, as shown by the index of capacity utilization (CU), Kalecki’s price equation is useful to demonstrate that producer price inflation can result from multiple causes, including increased unit labor costs, increased material costs (such as energy), gross profit markup inflation, or a combination of these factors.

Kalecki’s producer price rule is posited:

(1) pₜ = (1 + μₜ) uₜ

where unit prime cost is:

(2) uₜ = wₜ ℓₜ + mₜ

The independent variables include the nominal wage rate (wₜ), employment per unit of output (ℓₜ), and material costs (mₜ). Mu is the gross profit markup.

During Kalecki’s era in the 1930s depression, it was reasonable to consider unit prime cost as the two major components of cost of goods sold (COGS). Today, operating expenses (not included in COGS), such as officers’ compensation, wages and salaries, research and development, and advertising, have become significant. Therefore, the definition of unit prime cost should be updated to include expenses outside of COGS.

To simplify, I keep Kalecki’s historical (now outdated) concept of unit prime cost and continue using uₜ to represent purchases of direct labor and materials. By taking the logarithms and differences of the top equation, a measure of the producer price inflation rate is obtained:

(3) πₜ = Δ ln pₜ = Δ ln uₜ + Δ ln (1 + μₜ)

(4) πₜ = β Δ ln (wₜ ℓₜ) + γ Δ ln mₜ + k Δ ln (1 + μₜ)

where β = wₜ ℓₜ / uₜ and γ = mₜ / uₜ. See Appendix below.

Here are my takeaways:

First, discussing price inflation (or other economic variables) without an explicit policy equation is irresponsible.

Second, assuming excess capacity and operating expenses not included in COGS, producer price inflation can result from three factors:

(i) Increase in unit labor cost (ULC): Δ ln (wₜ ℓₜ).

(ii) Increase in raw materials or energy costs: γ Δ ln mₜ.

(iii) Increase in the gross profit markup: Δ ln (1 + μₜ).

Third, no austerity is necessary to control producer price inflation under excess capacity, because ULC can be reduced (without reducing the nominal wage rate) through increased labor productivity (implying measured job losses). Austerity is a repressive measure to reduce trade unions’ influence and demoralize public employees.

Appendix

The change in unit prime cost satisfies an approximate cost-share decomposition:

Δ ln uₜ ≈ β Δ ln (wₜ ℓₜ) + γ Δ ln mₜ

where β = wₜ ℓₜ / uₜ and γ = mₜ / uₜ. Therefore:

πₜ = β Δ ln (wₜ ℓₜ) + γ Δ ln mₜ + k Δ ln (1 + μₜ)

The contributions of unit labor and materials costs to producer price inflation are weighted by their cost shares rather than simply added.

Converting the logarithms of differences into a regression PPI equation to estimate reaction or policy parameters is not difficult. The policy equation for controlling consumer price inflation (CPI) includes additional parameters, such as the retail profit margin.

References

Kalecki, Michał. Essays in the Theory of Economic Fluctuations. George Allen & Unwin, 1939.

Kalecki, Michał. Theory of Economic Dynamics: An Essay on Cyclical and Long-Run Changes in the Capitalist Economy. George Allen & Unwin, 1954.

Kalecki, Michał. Selected Essays on the Dynamics of the Capitalist Economy, 1933–1970. Cambridge University Press, 1971.