This post is based on some parts (mainly part I.2) of a working paper accessible here. All comments are welcomed.
Jan Tinbergen is mostly remembered today for his macroeconometric models of the late 1930s, the development of a statistical analysis of the relationship of these models, and after the war the study of optimum policies and decision models.
“Macrodynamics” began at the dawn of the 1930s and was marked in particular by Frisch’s propagation-impulsion models. In comparison, Tinbergen’s contributions to macrodynamics had much less impact, although he showed a breadth of ideas that was matched by no other econometrician of the time. We have described in another post the nonlinear model built by Tinbergen in 1936, from the model he presented for the first time in 1934. In this post, we present a 1935 article published in French by Tinbergen, where he used the same model to observe the effects of wage changes.
The basis of the model is a relation between prices, supply and demand according to the following equation:
![\begin{equation*} \label{eq:central_eq} [A + a p(t-2)][P+p(t)] = K+2kp(t-1) \end{equation*}](https://www.economic-instability.com/wp-content/ql-cache/quicklatex.com-d8519fb4da08594eba84525aa2617885_l3.png "Rendered by QuickLaTeX.com")
Supply depends on prices two periods ago, a representation of the long process of production, while the purchasing power, K, depends on revenues from the previous period. The relation can be interpreted in several ways: written as above, purchasing power can buy the real amount of goods produced. If we divide the right hand side by prices (as done in the 1936 article), the idea is basically the same: real purchasing power can buy the quantity of goods supplied. Dividing the purchasing power by supply gives and indication of how prices change, from the (dynamic) mismatch between supply and demand.
Wage changes are introduced both in the supply and the demand side. On the supply side, a change in wages will be accompanied by a rise in prices to maintain profitability (Tinbergen seems to assume that production is constant, which is a bit odd). On the demand side, a change in wages causes a change in income of the same proportions. Thus the final equation after the wage change is complete is:
![\begin{equation*} [A - a \alpha P + a p(t-2)][P+p(t)] = K(1+\alpha)+2k[p(t-1)-\alpha P](1+\alpha) \end{equation*}](https://www.economic-instability.com/wp-content/ql-cache/quicklatex.com-cb6fe49367c80d8c748e61d082aee466_l3.png "Rendered by QuickLaTeX.com")
Tinbergen considers two cases for the period of transition, when the wage change has happened but some process have already begun at the old wage: in the first one, all processes continue at the old wage and price until they are finished, in the second one they are interrupted and restarted at the new wage. Both these cases are represented in the following application, where sensitivity parameters and constant levels (the uppercase letters) can be changed. Tinbergen limited his study to a case where the wage change (a 10% increase or decrease) happened to an endogenous cycle, but all this can of course be changed.
Tinbergen used this model to discuss the effect of a wage increase or decrease at different moment of the cycle. He showed in particular that those changes would have the most “desirable” effect, that his, the most damped effect, when the economy was going through the equilibrium point. As can be seen however, wage increases always have the effect of producing explosive fluctuations! On the other hand, wage decreases stabilize production at the equilibrium point, at least for the values chosen by Tinbergen. It should be noted that while production does not change its equilibrium level, purchasing power and prices decrease to a lower level after a wage decrease.
References:
Link to our WP: