A genuine “real wage protection” mechanism
Is indexation conducive to real wage protection? The analysis presented here was put for-ward by Lance Taylor in Structuralist Macroeconomics, Chapter 6, which relies on Bacha & Lopes (1983).
λ Suppose nominal wages are fully indexed to past inflation. If inflation increases by p in the year t, p is added to the nominal wage w: wt+1 = wt (1+p). Backward indexation means if inflation is p in 2021, then in the beginning of 2022 p is added to w.
λ However, inflation is a continuous time phenomenon, not a discrete variable. The on-going inflation has better be represented by a logarithmic function: inf=(dp/dt)/p. Ok but wages aren’t instantly adjusted. Wages aren’t continuous; inflation is.
λ Wages are adjusted ex post at various intervals, yearly or twice a year. We denote the time that elapses until adjustment is made by k: wt+k/w =epk.
t
Then, 100% indexation yields wt+k/pt+k=w .
*
λ The real wage is represented by w*. The target real
wage wreal is supposed to be constant. Dynamically, the average real wage reads as w = w/k = (w*/k) ɔk0 e-inft dt = (w*/inf. k)[1-e-inf. k]. If the inf.k product is called z, as z goes to zero w approaches wreal.
λ This means the average real wage converges to the target real wage as z goes to zero. But when does z converge to zero? This happens only when either the logarithmic (on-going) inflation nears zero or the inflation adjustment interval shrinks to zero. In the last instance we obtain an instantaneous, say, daily, inflation adjustment. A complete protection against inflation is possible if and only if wages are continuously adjusted.
λ In fact, if we look at the Istanbul Chamber of Commerce’s Istanbul living cost index for those who work in industry, the index has been up by 16% per annum over the last two decades. Has there been a parallel increase in nominal wages? No. λ Even if they were at the same rate after a year has passed, what happens to a real wage index over two decades of c. 16% annual increase? What happens now that food inflation stands at 70.3%? Remember, real wages erode more as inflation soars if adjustment isn’t continuous. λ Indexation accommodates inflation and lowering it will be difficult if there is indexation. Correct, but indexation – or wage adjustments at frequent intervals – is the only way to protect the real wage.