Problems Facing the Government and Wage Setters
Consider first the government’s situation. In period 1, the government chooses the pair of functions
where the equilibrium condition (17) has been taken into account.
Equations (22) and (23) are obtained by taking expectations of equations (16) and (19), based on information available at time 0. Adding
From equations (10) and (11), it follows that
Hence, equation (20) follows from combining equations (A2) and (A3). Equation (24) follows from equations (10) and (1I). By taking expectations of equation (19), it follows that
Equation (21) follows from combining equations (19), (A3), and (A4). Equation (25) is obtained by combining equations (16), (Al), and (A3). Finally, loss function (26) is obtained by using equations (20)—(25).
Assume that B = 0. Then loss function (26) may be written as
It is assumed that
Hence, equations (A6) and (A7) imply that
Using the fact that, at a minimum,
Consider next the case in which
The wage setters’ loss function (27) is obtained from equations (8), (20), and (24). Equation (27) may be written as
The first-order condition for the choice of η is given by
Consider first the case where B = 0. This implies that
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Pablo E. Guidotti is an Economist in the Research Department of the IMF and holds a Ph.D. from the University of Chicago. The topic of this paper emerged from conversations with Guillermo Calvo. The author is grateful to him for useful discussions and to Sophia Aguirre, Allan Drazen, José De Gregorio, Malcolm Knight, Guillermo Mondino, Gian Maria Milesi–Ferretti, Carmen Reinhart, and seminar participants at the International Monetary Fund, the University of Chicago, and Umversidad de San Andres (Argentina) for valuable comments.
Early studies dealing with public debt management policies include Bach and Musgrave (1941), Tobin (1971), Fischer (1975), and Levhari and Liviatan (1976). Recent studies include Lucas and Stokey (1983), Bohn (1988), Persson, Persson, and Svensson (1987), Persson and Tabellini (1990), Alesina and Tabellini(1990), Calvo (1988), Calvo and Guidotti (1990, 1992), Missale and Blanchard (1991), and Cukierman and Meltzer (1989).
1n some cases, as shown by Calvo (1988), nominal debt may even lead to multiple equilibria, and hence to the loss of nominal anchor.
Although the use of debt indexation as a tool to influence governments’ incentives to use the inflation tax has only recently been analyzed formally, it was recognized early by Bach and Musgrave (1941, p. 824), who stated that “by imposing upon the government a contingent liability dependent on its failure to check price inflation, the flotation of stable purchasing power bonds may exert a wholesome pressure upon Congress to adopt aggressive anti–inflationary policies.”
In Calvo (1988), optimal policy calls for 100 percent indexation, since the demand for money is assumed to be interest inelastic and the model is deterministic. In Persson, Persson, and Svensson’s (1987) perfect–foresight model, since the demand for money is interest elastic, the optimal policy calls for issuing nonindexed government assets (see, however, Calvo and Obstfeld (1990)).
The role of unanticipated inflation in smoothing taxes across states of nature as part of optimal monetary policy is developed in Calvo and Guidotti (1989).
It should be noted that, because of the assumption that the government’s targeted level of output coincides with that of the private sector, the inflation bias emphasized by Barro and Gordon (1983) is absent in this paper. The inflation bias emphasized here stems from the fiscal problem stressed by Calvo and Guidotti (1990).
This result provides an interesting insight into the discussion about whether wage indexation weakens the resolve of governments to fight inflation (see Fischer and Summers (1989) and De Gregorio (1991)).
Note that the target level of employment for the government is the same as that for wage setters. Therefore, the time–inconsistency considerations explored by Barro and Gordon (1983) are not present in this analysis. As will become clear in the next section, inflation occurs in this model because of a fiscal problem, as in Calvo and Guidotti (1990), and not because of the government’s attempt to push output above its equilibrium level, as in Barro and Gordon (1983).
In equation (16), it is implicitly assumed that the variation in seigniorage, which results from fluctuations in real money demand (because of output fluctuations), is absorbed through lump–sum taxes. Given that the focus of the paper is on the role of nominal debt in fiscal policy, adding those terms would make the algebra unnecessarily cumbersome. In addition, this assumption helps to maintain closer comparability with the analysis on debt indexation contained in Calvo and Guidotti (1990), where the demand for money is nonstochastic.
Note that actual output deviations also depend on the technological shock, u.
This follows from the assumption that unanticipated inflation is socially costly in this model. If only anticipated inflation were costly, it could be optimal to finance shocks to government expenditure by means of the inflation tax alone (see Calvo and Guidotti (1989)).
In theory, θ could take values outside the (0, 1) range, as discussed in Calvo and Guidotti (1990). When θ > 1, the government swaps nominal debt for indexed assets. Conversely, when θ <0 the government lends in nominal terms against indexed debt. Nothing essential is lost by assuming that θ ∈ (0, 1), since parameters can always he chosen to make optimal θ lie in the unit interval.
Existence of these two possible configurations was established by means of numerical simulations. Note that when schedule W is decreasing, it is less steep than schedule G.
The corresponding analytical derivations can be found in the Appendix.
The effects of comparative statics exercises in the general case were also explored by means of numerical simulations. These suggest that the qualitative response to shocks analyzed in Case II remains robust.
The derivation of equation (32) follows the same methodology set out in the appendix to Calvo and Guidotti (1990),
A stricter condition is assumed for the case of no precommitment in order to make θο > 0, as the Appendix shows.
The proof follows directly from comparing equation (33) to its analog—equation (A7) in the Appendix—in the absence of precommitment.