Long-Run Implications of Social Security Taxation for Growth and Fertility.

• Author: Zhang Jie
• Position: Statistical Data Included

Jie Zhang [*]

This paper compares long-run implications for growth and fertility of four types of taxation for social security with positive bequests. A tax rise under lump-sum taxation enhances growth but lowers fertility, while other types of taxation do so under additional restrictions. A tax rise under consumption taxation is less likely to stimulate growth and to reduce fertility than under payroll taxation. A rise in an interest income tax raises fertility, reduces both savings and human capital investment, and hence is harmful for growth. The case with zero bequests is also discussed.

1. Introduction

   All developed countries and most developing countries have social security programs for their retired population. These programs are widely divergent in formulation in terms of how to collect social security contributions and how to allocate social security benefits (U.S. Department of Health and Human Services 1992). On the spending side, social security programs are distinguished by whether they are funded or unfunded and by whether benefits are linked to individuals' own contributions. On the taxation side, social security programs differ in the sources of their revenues. In some countries (e.g., France and the United States), social security benefits come (almost) exclusively from taxes on labor earnings. In some countries (e.g., Australia), the benefits depend only on governments' general revenue from levying direct or indirect taxes. In many countries (e.g., Canada, Germany, Italy, and the United Kingdom), the benefits come from both payroll and general tax revenues.

   In the literature on social security, however, lump-sum contributions are widely assumed (Barro 1974; Becker and Barro 1988; Nishimura and Zhang 1992) even if they are rare in practice. The emphases of the existing work have been laid on how to spend on social security programs. In particular, the impact of a pay-as-you-go program (i.e., an unfunded plan) on savings has been the focus of the debate. (In practice, unfunded social security is much more popular than funded social security.) Feldstein (1974), for example, argued that unfunded social security depresses savings and hence has a negative impact on growth. Barro (1974) showed that in a dynastic family model incorporating operative intergenerational transfers, social security is neutral. When fertility is endogenous, Becker and Barro (1988) found that increasing social security benefits reduces fertility and raises capital intensity because more transfers from the working generation to the coexisting retired generation cause a rise in bequests per chi ld and hence a rise in the cost of raising a child. Using an endogenous growth model, Zhang (1995) found that unfunded social security benefits promote growth by reducing fertility and increasing human capital investment if parents value their children's welfare sufficiently.

   This paper considers long-run implications for growth and fertility of different types of taxation for social security: a lump-sum tax, a consumption tax, a payroll tax, and an interest income tax. In doing so, we assume operative bequests as in Barro (1974) and Becker and Barro (1988). The main results are the following. A tax rise under lump-sum taxation enhances growth but lowers fertility, while other types of taxation do so under additional restrictions. A tax rise under consumption taxation is less likely to stimulate growth and to reduce fertility than under payroll taxation. A rise in an interest income tax raises fertility, reduces both savings and human capital investment, and hence is harmful for growth. I also discuss results with exogenously fixed fertility or with zero bequests, which are substantially different from those with endogenous fertility and positive bequests except for the case with the interest income tax.

   The remainder of the paper is organized as follows. The next section introduces the model. Section 3 examines and compares the effects of using a lump-sum tax, a consumption tax, or a payroll tax to finance social security by assuming positive bequests. Section 4 discusses the results first with interest income taxation for social security and then with zero bequests. The last section provides some concluding remarks.

2. The Model

   This model has an infinite number of overlapping generations of three-period-lived agents. Let subscript t denote a period in time and superscript t the generation born in period t - 1. Let [L.sub.t] be the number of middle-aged agents living in period t. Each parent has 1 + [n.sub.t]] (identical) children at the beginning of middle age. Agents learn when young, live in retirement in old age, and are each endowed in middle age with one unit of time that can be supplied to the labor market or spent on rearing children. Let v denote the units of time needed to rear a child (0 [less than] v [less than] 1).

   The utility of a middle-aged agent, [V.sub.t], depends separately on own middle-age consumption, [[c.sup.t].sub.t]; own old-age consumption, [[c.sup.t].sub.t+1]; the number of children, 1 + [n.sub.t]; and the utility of each child, [V.sub.t+1]:

   [V.sub.t] = ln [[c.sup.t].sub.t] + [beta] ln [[c.sup.t].sub.t+1] + p ln (l+[n.sub.t]) + [alpha][V.sub.t+1], 0 [less than] [alpha] [less than] 1, 0 [less than] [beta] [less than] 1, 0[less than] [rho] [less than] 1.

   Here, [beta] is the discount factor on utility from old-age consumption, [rho] the taste for the number of children, and [alpha] the taste for the welfare of each child.

   The production function for goods has the form

   [Y.sub.t] = D[[K.sup.0].sub.t],[([L.sub.t][l.sub.t][h.sub.t]).sup.1-[theta]], D [greater than] 0, 0 [less than] [theta] [less than] 1,

   where [K.sub.t] is (aggregate) physical capital, [l.sub.t], the input of labor per middle-aged agent, and [h.sub.t] a middle-aged agent's human capital.

   The human capital of a child, [h.sub.t+1], depends positively on the investment of goods per child, [q.sub.t], and the human capital of his parent, [h.sub.t]:

   [h.sub.t+1] = A[[q.sup.[delta]].sub.t][[h.sup.l-[delta]].sub.t], A [greater than] 0, 0 [less than] [delta] [less than] 1.

   In period t, each middle-aged agent spends v(1 + [n.sub.t]) units of time rearing children, works for the remaining 1 - v(1 + [n.sub.t]) units of time, and earns [1 - v(1 + [n.sub.t])][W.sub.t]. This agent receives a bequest, [b.sub.t], from his parent at the beginning of period t and leaves a bequest, [b.sub.t+1], to each child at the beginning of period t + 1, where bequests have no direct contribution to physical capital accumulation. [1] The middle-aged agent spends the earning and inheritance on own middle-age consumption, [[c.sup.t].sub.t], life-cycle savings, [s.sub.t][1 - v(1 + [n.sub.t])][w.sub.t]; bequests to children, [b.sub.t+1](1 + [n.sub.t]); and investments in children, [q.sub.t](1 + [n.sub.t]). To finance social security benefits, [B.sub.t+1] per retiree, there is a lump-sum tax at the amount [T.sub.t] per worker, a payroll tax at rate [[tau].sub.1], and a consumption tax at rate [[tau].sub.c]. (The case with an interest income tax has no closed-form solution and will be discussed in section 4.) Then, an individual's budget constraints are

   (1 + [[tau].sub.c])[[c.sup.t].sub.t] = [b.sub.t] + [1 - v(1 + [n.sub.t])][w.sub.t](1 - [s.sub.t] - [[tau].sub.t]) - [T.sub.t] - [q.sub.t](1 + [n.sub.t]), (1)

   (1 + [[tau].sub.c])[[c.sup.t].sub.t+1] = (1 + [r.sub.t+1])[s.sub.t][1 - v(1 + [n.sub.t])][w.sub.t] + [B.sub.t+1] - [b.sub.t+1](1 + [n.sub.t]), (2)

   where w and r denote the wage rate and interest rate, respectively. The government budget constraint is given by

   [B.sub.t] = (1 + [n.sub.t-1]){[T.sub.t] + [[tau].sub.1][w.sub.t][1 - v(1 + [n.sub.t])] + [[tau].sub.c][[c.sup.t].sub.t]} + [[tau].sub.c][[c.sup.t-1].sub.t], (3)

   where a bar over a variable refers to its average.

   Firms maximize profits on perfectly competitive markets. Let [e.sub.t] [equivalent] [K.sub.t]/([L.sub.t][l.sub.t][h.sub.t]) be the physical capital-effective labor ratio where h is average human capital and l the average labor demand per worker. For simplicity, I assume that physical capital lasts for one period in the production of goods. The first-order conditions of firms maximizing profits are

   [w.sub.t] = (1 - [theta])D[[e.sup.[theta]].sub.t][h.sub.t], (4)

   1 + [r.sub.t] = [theta]D[(l/[e.sub.t]).sup.1-[theta]]. (5)

   Equation 4 implies that a middle-aged agent's wage rate depends positively on his own human capital. Labor and capital markets clear when

   [l.sub.t] = 1 - v(1 + [n.sub.t]), (6)

   [K.sub.t] = [L.sub.t-1][s.sub.t-1][1 - v(1 + [n.sub.t-1])][w.sub.t-1]. (7)

   Constant returns to scale and perfect competition imply a zero profit. By Walras's law, the goods market clears as well. Since...