2  Razin et al’s theoretical model

Razin et al construct a median voter model with overlapping generations. This section sketches out features of the model that are relevant to the extension and reanalysis described below. There are two generations: young workers and old dependants. The young are assumed to outnumber the old. The only tax is a labour tax, which is proportional to labour income.[1] The budget is balanced in every period, and the entire tax revenue is spent on benefit payments. Everyone, young or old, receives the same payment. People care only about their own income.

Young people face the decision of whether or not to acquire an education. Workers with an education have higher productivity and earn a higher wage than workers without an education. However, acquiring an education takes time, and has an opportunity cost in forgone wages. Young workers vary in their innate ability. The greater a person’s innate ability, the more quickly the person can complete an education, and the lower the education’s opportunity cost. All those whose ability is greater than a certain level acquire an education, while none of those whose ability is lower than this level acquire an education. The location of the cut-off point depends on taxes, wages, the pecuniary cost of education, and the extent to which education improves productivity. The lifetime incomes of the educated vary, depending on their innate ability and hence the time spent in the workforce. The lifetime incomes of the uneducated are identical.

As with standard median voter models, taxes and benefits are at their equilibrium level when the income that the median voter would gain through an increase in benefits exactly equals the income that he or she would loose through the corresponding increases in taxes. No other combination of taxes and benefits is politically sustainable. Suppose, for instance, that the median voter would gain more from a small increase in benefits than he or she would loose through the corresponding increase in taxes. The median voter would join a pro-benefits coalition, which would then have a majority, and the new regime of benefits and taxes could be voted in.

Old people pay no taxes, and are therefore always in favour of raising taxes and benefits. Young people are divided into pro-benefit and anti-benefit groups. Young people who do not acquire an education are either all pro-benefit or all anti-benefit, since they all receive the same income. Young people who do acquire an education are, in general, divided into pro-benefit and anti-benefit groups. The greater the educated young person’s ability, and hence the higher their income, the more anti-benefit they are. The fact that young people can be ranked from most anti-benefit to most pro-benefit according to their innate ability keeps the analysis of coalition formation relatively simple. The identity of the median voter, and hence the equilibrium level of taxes and benefits, depends ultimately on the ratio of old to young, and on the distribution of innate ability among the young.

An increase in the ratio of old to young has opposing effects on the level of taxes and benefits. All the extra old people favour increasing tax and benefit levels. The rise in the number of dependants per taxpayer means, however, that a smaller proportion of any taxes paid are returned to taxpayers in the form of benefits; Razin et al describe this as an increase in ‘fiscal leakage’. Increased taxes also lower pre-tax incomes by discouraging some young people from undertaking productivity-enhancing education. The first effect makes it more likely that the median voter will favour higher taxes and benefits, while the second and third effects makes it less likely. The balance between these effects, and hence the new level of taxes and benefits, depends on the ratio of old to young, and on the distribution of innate ability among the young.