Fiscal policy under commitment and discretion

Transcription

1 Fiscal policy under commitment and discretion

2 Tasks and topics Model-building task: construct a simple one period model in which it is possible to readily solve for fiscal policy equilibrium Under commitment, defined as a situation in which the government chooses tax and expenditure policies i before the private sector chooses its activities Under discretion, defined as a situation in which the government chooses its policies after the private sector chooses its activities 2

3 Tasks and topics (cont d) Additional desired feature: set up model so that there are no state variables, to make for a tractable dynamic setting in which the effects of reputation and/or credibility can be studied, each of may introduce a state variable. Additional desired feature: stay close to representative agent model, but allow for a limited amount of heterogeneity so that the closely l related issues of alternative ti social welfare functions and political economy can be studied. 3

4 Tasks and topics (cont d) Question: Are various measures of fiscal policy (level of tax rate, level of public expenditure) higher or lower under discretion than under commitment? Question: Since apparently arbitrary fiscal policies may introduce complementarity and thus lead to multiple equilibria, do optimal policies i also? How is discretion different from commitment in this regard? 4

5 Structure of Model Private actors: continuum of households, similar except for a fixed cost of participating in market (taxable) activity, with their only decision being whether to enter the market. These households value consumption produced at home or in the market and a public good. Government: choose an output tax rate to finance public good provision, using a social welfare function as its objective. 5

6 Household s s decision Household has a fixed cost ξ of entering market activity. Home production: Its endowment of 1 unit of time produces 1 unit of output Market: Its endowment of 1 unit of time produces a*(1-τ) units of after-tax output with a>1. 6

7 Optimal entry into the market Individual enters market if after-taxtax income isn t smaller than entry and opportunity costs, i.e., a*(1-τ) (1τ) >1+ ξ (we assume enter if indifferent, but could assume reverse and it would make no difference since marginal guys are infinitesimal). 7

8 Supply of market participants Suppose that there is a distribution of market participants that have different entry cost, with the distribution function being F(x): that is, fraction μ= F( x ) of agents have adjustment costs of ξ<x Then the supply curve of market participants is μ= F[a*(1-τ)-1], since this gives fraction of agents with lower costs than critical entry level. 8

9 Figure 1: supply of market participants i (to be added d in class) 9

10 Reminder list for figure High enough taxes drive out market participation: maximum tax rate makes zero entry cost individuals indifferent in terms of participation. Productivity level and maximum participation (which occurs at a zero tax rate) τ μ ξ a 1 = ( ) < 1 and = 1 if ( a 1 ) 0 a 10

11 Implications for government tax revenue Government revenue in this economy is very simple: g=τ*a* a*μ where the preceding analysis indicates that μ=μ(τ) is The economy has a Laffer curve for all probability distributions since g(0)=0 and g(1)=0. The Laffer curve is single peaked for many probability distributions (concave cdfs). 11

12 Figure 2: The Laffer curve (to be added d in class) 12

13 Household welfare Households derive welfare from consumption c and public goods g according to a utility function u(c,g), which we sometimes specialize to c+b(g) with b(g) increasing and strictly concave. Given the market participation decision, they have an indirect utility function v(ξ,g,τ)=max [u(1,g), u(a*(1-τ) - ξ, g)]. 13

14 Government objective Choose the tax rate and the associated level of public goods so as to maximize social welfare V = vc ((), ξ g, τ ) d Φ () ξ subject to the government budget constraint and a measure of participation p 14

15 Two types of government (with the particular utility function) Chavez: Maximize the welfare of the poorest: V=1+b(g). That is, maximize government services. Bush: Maximize the average guy s welfare [1 μ] + [(1 τ ) a μ m] + b( g) where m is the truncated mean of entry costs (those paid by actual entrants) 15

16 Commitment and discretion: sequence of events Commitment Discretion Subperiod 1 Tax (τ) Subperiod 2 Entry (μ) Entry (μ) Subperiod 3 Tax (τ) 16

17 General aspects of government choice Under commitment, the government maximizes taking into account the (future) private sector supply response to taxes, formally μ(τ) Under discretion, the government maximizes i taking into account the (predetermined) supply, formally μ 17

18 Policy under commitment: Chavez Maximizing the amount of public goods involves choosing a tax rate that yields the top of the Laffer curve. There is only one such tax policy. Formally, maximizing public good production b(g)=b[τ*a*μ(τ)] )] requires that some agents are induced to undertake production so as to generate tax revenue. 18

19 Policy under discretion: Chavez Under discretion, maximizing the quantity of goods involves complete confiscation of market production (τ=1). The government does not worry about the fact that previous beliefs (expectations) about its tax policy might have affected the level of response μ(ετ): it appropriately treats these beliefs as predetermined. 19

20 Equilibrium under discretion: Chavez Equilibrium (rational expectations, Bayesian Nash) requires that beliefs be correct. No equilibrium can have positive participation, since μ=0 when Eτ=1 1 and τ=1 when μ>0 20

21 Equilibrium under discretion: Chavez An equilibrium with the properties suggested by τ=1 and μ=0 can be established if there is a fraction ε of guys that will participate in the market no matter what. Then τ=1 and μ=ε is an equilibrium for any abitrarily small ε. 21

22 Equilibrium under discretion: Chavez Discretionary equilibria have taxes that are too high, relative to the commitment case for the same objective Under commitment, t Chavez does not wind up on the wrong side of the Laffer curve, but under discretion, he does. 22

23 Policy under commitment: Bush Bush chooses the tax rate to maximize (1 μ( τ )) + ((1 τ ) a μτ ( ) m( τ)) + b [ τ a μτ ( )] He cares about the fact that a higher tax rate depresses (average) private consumption, as well as increasing public services. 23

24 Policy under commitment: Bush Not possible to explicitly determine optimal tax rate without some further assumptions on b and F. Latent in the following FOC and BC: 0 = a μ + bg ( g) [ a μ + a τ μ τ ] g = a τ μ We ll get a bound on this tax rate later. 24

25 Policy under discretion: Bush Aside: some conservatives in US strongly dislike Bush s fiscal policy, which they view as opportunistic (departing from conservative rules of thumb) A discretionary Bush treats μ as predetermined d just like a discretionary Chavez did. 25

26 Discretionary policy: Bush Latent in the following FOC and BC: 0 = a μ + b ( g) [ a μ] = a* μ*[ 1 + b ( g)] g = a τ μ g Simple rule: marginal benefit from new public goods should be exactly equal to the value of the consumption lost by the private sector. Let s assume that this occurs at g lower than the top of the Laffer curve. g 26

27 Equilibrium under discretion: Bush Since g = τ *a* μ, the tax rule is τ = g / (a*μ) OR a policy reaction function τ (μ) We already have a private sector reaction function μ(τ) Formally, a discretionary equilibrium is a pair μ e,τ e such that: μ e =μ(τ e ) and τ e =τ(μ e ). One approach is to use the reaction functions to find one or more fixed points 27

28 The Laffer curve approach (to be added d in class) 28

29 Analysis of the two discretionary i equilibria i One is higher than the other One is on the wrong side of the Laffer curve and the other is not. One is better for Bush and for all private agents than is the other But how does the better one compare to the commitment outcome? 29

30 Analysis (cont d) Reorganize the FOC under commitment a b g g g 1 a a Optimal public expenditure is lower under commitment because the decision-maker takes into account that a higher tax rate will lower the tax base. The tax rate under commitment is therefore lower than that under discretion. 30

31 Summary Discretion leads to a tax rates higher than the commitment value for a wide range of types of policymakers (Chavez, Bush) Discretion can also lead to multiple, welfare-ranked ranked equilibria because under discretion, policy reacts to the state of the economy, which is based on prior beliefs about policy. [Other examples: monetary policy, flood control] 31

32 Question from readings Fischer: Is it desirable for a benevolent policymaker to dissemble when in a discretionary setting? (Fischer is a former MIT professor, senior IMF economist, and is now head of the central bank of Israel) 32