Introduction
Above we noted that the structural form of western welfare states is quite complicated. We would like to have a more enduring result than awareness of complexity, and therefor we adopt the Definition & Reality methodology. As said, a proposition - as a statement on reality - can be regarded as a mathematical theorem about/within a model of stylized facts. When there is a tautology, we attain truth by definition. So we now (a) restate what we consider to be the stylized facts, (b) define our concepts, (c) develop theorems and proofs, (d) link back to conclusions about reality.
The reduced form that is most relevant concerns the (long run) comparative statics of the regimes of full employment (1950-1970; Japan/Sweden) and unemployment (1970-2005).
This kind of comparative statics should not induce us to think that we abolish dynamics, though. Stagflation has both a dynamic (inflation) and a static or stationary (unemployment) aspect. When we skip proper dynamics and discuss regime switches in which unemployment features as an important switch variable, then Phillipscurve processes are included in the switching process, even though they don’t feature explicitly in the reduced form.
To attain the necessary level of generality, we use a reduced form where the economy is mapped into a model with three types of agents. One type is the net receiver; and two types are net tax payers. Since the latter two points give a line, that single line represents the state of the economy. The regime switch depends upon the choice of tax parameters.
Stylized facts
There are regimes of full employment (1950-1970; Japan/Sweden) and unemployment (1970-2005).
In the welfare state, it is more efficient to have full employment. Unemployment causes lower income - not only directly as in old-fashioned capitalism but also, more noteworthy, by the additional benefit burden. Unemployment can have an adverse effect on inflation when it causes a shift of the Phillipscurve.
It turns out that the propositions that are most interesting, from the viewpoint of political economy, do not require continuity, and can be formulated by assuming dichotomous High and Low productivity labour, combined with one class of Benefit recipients. This assumption allows for a reduced form formulation that allows for generality. For expository reasons we can take social subsistence and productivities as purely constant. In the simple mathematical model the dichotomy gives fixed numbers, in actual observation they are subgroup averages which depend upon general equilibrium processes. The benefit level is rather not an average but a threshold, like the surface of the sea at Scheveningen beach. The words Benefit, High, and Low give letters BHL, and this abbreviation may be pronounced - converged upon after many walks - as ‘beachly’.
It is a stylized fact that welfare states are BHL. Checking this requires next definitions.