Remark: An example of ‘meaningful’ are subgroup subperiod averages.
Remark: Stability can sometimes be found by normalizing, e.g. take subperiod H(t) as the subperiod numeraire.
Remark: A person’s benefit is often related to the former period working wage. However, anything can be clustered into a social subsistence average. People ‘between jobs’ could be taken to be basically in the employed cluster, people with serious unemployment could be in the other cluster. Don’t object that this makes the matter tautological - since that is exactly what we try to do. (We try to find the definitions that make our understanding tautological.)
Remark: A nonrevolutionary welfare state still allows for politics and economic change.
Lemma I: A welfare state is BHL iff there is stability over the regimes for the variables B, H, L and the associated numbers of agents.
Proof: Self evident. Q.E.D.
Remark: The relevant notion is that the change from unemployment towards full employment (or vice versa) does not destroy the productive base of the economy. Instead of taking this notion explicitly, we have taken a stronger property of nonrevolutionarity, that allows, if bhl-ness applies too, to take (approximate) constancy of the variables.
Remark: At first glance these definitions seem self-defeating for the effort to apply the mathematical method to employment regime switches. When 35 million, nowadays unemployed in the OECD, are supposed to find a job, then apparently the policy maker is supposed to be able to judge on the ‘stabilities’ involved. That seems an impossibly strong assumption. We may however remind about the regime switch from 1950-1970 to 1970-2005. In addition, as modellers we discuss equilibrium states of various paths. Also, it is possible to give the variables an incremental interpretation, e.g. take 34 of the 35 (million) as permanently on benefit, and only look at 1 million on the margin (giving “local-BHL-ness”).
Lemma II: For a welfare state, the (apparent) existence of people with a productivity L’< B, does not block the application of BHL-ness.
Proof: Consider the pathological case of people with productivity L’< B, i.e. so low that (in whatever regime) their net market income is lower than B. Take the dentists, who in a regulated market cannot start a practice, and who are very bad at farming in a flowerpot (which could be done with a Cobb-Douglas production function). These people can be treated as: