Theory of Economic Policy

Dr. Mahmoud R. Fath-Allah

Economics Department Faculty of Economics and Political Science

Cairo University

Mobile: 01006820651 Email: m.r.fathallah@gmail.com

Graduate Course fall 2015

Contents:

- the basic framework of the theory of economic policy. - Tinbergen-Theil approach:

- Tinbergen’s Fixed Targets Approach - Theil’s flexible target approach

- Rational Expectations and Lucas Critique. - the Policy Game approach

(1) Exogenous variables, which are not explained by the model of the economic system under consideration.

(a) Policy instruments: exogenous variables which are under the control of the policy-maker.

(b) Non-controlled exogenous variables (“data”): exogenous variables which are not controllable by the policy-maker.

(2) Endogenous variables, which are explained by the model of the economic system.

(a) Target variables: endogenous variables which are considered as goals (are evaluated) by the policy-maker.

(b) “Irrelevant” variables: endogenous variables which are not evaluated by the policy-maker and express the side-effects of economic policies.

The above classification makes use of two other basic ingredients of the theory of economic policy which are assumed to be given within this theory: the model of the economic system and the preferences of the policy-maker. On the one hand, the model of the economic system describes the structure and the

functioning of the economy under consideration. It may be a theoretical model or an empirical one, where the latter is usually obtained from econometric estimations; it may be a macroeconomic model for problems relating to stabilization policies, or a microeconomic model to deal with policy problems concerning allocation and distribution. Not only nationwide models may be considered, but also regional or international ones. In any case, the model transforms exogenous to endogenous variables in order to express the influence of the former on the latter. On the other hand, the preferences of the policy-makers may be expressed either by an explicit objective function, which may be interpreted as an individual (for the policy-maker) or collective (“social”) welfare, utility, or cost function, or by an incomplete scale, containing at least a most-preferred value for each target variable (and possibly for some policy instrument variables as well). Following [8, p.21] and [9, p.58], the basic framework of the theory of economic policy can be displayed by the following scheme:

To be more specific, denote by U the set of possible policy instruments, with U∈u , where u may (but need not) be an element of some vector space. The set U expresses institutional, political, physical, and other constraints on the values of the policy instrument variables. The number of elements contained in this set and the set’s dimension are usually specific to the policy problem under consideration; this may not only be a question of factual evidence, but also one of inventing new instruments. Let Z be the set of non-controlled exogenous variables, with Z∈z being a deterministic or a random variable. The economic system can be described by a model ),( zufx = , which may be a reduced-form econometric model, for instance, with X∈x denoting the state of the economy, i.e. everything which results from a combined “action” of the policy instruments and the other exogenous variables on the

economic system. The set of endogenous variables X is constrained by U, Z, and the model (the function f(..)). In particular, when z is a stochastic variable, then x is stochastic, too, and for each u there is a corresponding probability distribution over x. In the latter case, which will be neglected in the following, policy-maker’s preferences have to be defined over probability distributions. Target variables are separately denoted by x1, say. The preferences of the policy-maker can be defined over x1 and u. For instance, if we define

)( 11 uxy ′′= with u1 being those policy instruments which are directly evaluated by the policy-maker, we may have an ordering, i.e. yy ′′′f (meaning that y′ is strictly preferred to y ′′ ), or yy ′′′ ~ (the policy-maker is indifferent between y′ and y ′′ ), or yy ′′′ p ( yy ′′′⇔ f ), for all y′ , Y∈′′y , the set of all possible y. Under some further assumptions this may

non-controlled exogenous variables

irrelevant endogenous variables

economic system (model)

policy instruments target variables preferences of the policy-maker

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS Reinhard Neck

ISSN: 1109-9526 158 Issue 4, Volume 6, April 2009

the basic framework of the theory of economic policy

Source: Neck, Reinhard, 2009

(1)Exogenous variables: not explained by the model of the economic system.

(a) Policy instruments: under the control of the policy-maker. (b) Non-controlled: “data”, not controllable by the policy-maker.

(2) Endogenous variables: explained by the model of the economic system.

(a) Target variables: considered as goals (evaluated) by the policy-maker. (b) “Irrelevant” variables: not evaluated by the policy-maker and express the side-effects of economic policies.

the model of the economic system and the preferences of the policy-maker

the model of the economic system: the structure and the functioning of the economy under consideration

Preferences of the policy- makers: - explicit objective function (welfare, utility) or cost

function: - individual (for the policy-maker). - collective “social”. - incomplete scale, containing at least: most-

preferred value for each target variable (and possibly for some policy instrument variables as well).

The Tinbergen-Theil approachThe classical approach to the theory of economic policy

The Tinbergen-Theil approach “Tinbergen-Theil paradigm”In the early 1950s he addressed in formal terms the issue of the controllability of a fixed set of independent targets by a policymaker facing a parametric context (i.e. facing an economy represented by a system of linear equations) and endowed with given instruments, he was able to state some well-known general conditions for policy existence.

Tinbergen's Fixed Targets Approach

macroeconomic policy-making would consist of the following steps: (i) selecting 'adequate instruments' to achieve the targets; (ii)formulating the connections between targets and instruments; (iii) determining the quantitative values required for the

instruments.

The approach took as given: (a)the structure of the economy; (b)the target variables; (c)the numerical values of the target variables; (d)the nature of the instrument variables.

The Choice of Target Variables:

The usual target variables relate to the level of employment; the rate of change of the price level; the balance of payments; and the rate of economic growth. These, however, can be expressed in different ways and others are possible.

Peston (1982) expresses them as: a) high, stable and increasing level of real income; b) stable or slowly increasing prices; c) balance of payments surplus; d) full employment; e) fair distribution of income among people and regions.

objectives may conflict with each other.

However, there may be other reasons for setting targets. For instance some writers suggests that governments may set targets in order to:

(a) provide information to the private sector about likely government behaviour; (b) influence inflationary expectations; (c) constrain or discipline governments.

government has two targets: income Y* and consumption C* Suppose that the economy can be modelled as the following:

Y = C + I + G C = a + bY I = I

by changing G it is possible to achieve targets for either Y or C but not both simultaneously. To do this a second instrument is needed e.g. a lump-sum tax (T): C = a + b(Y - T) and Y = (a - bT + I + G). 1/(1-b) This allows both T and G to change. We may set the desired changes in Y and C as Y* and C*. Y* = [(-bT + G)/b]. 1/(1-b) (1) C* = b(Y* - T) (2)

Example:

where: I and G exogenous; Y and C endogenous. G :the only instrument.

From (2) we can calculate: C* = bY* - bT T = Y* - (C*/b) This gives us a value for T. We can then substitute it back into (1) to give us the required change in G.

In this model we can go on to develop an income tax case with three instruments: G, v (the marginal tax rate), and u (the tax exemption level): Y = C + I + G T = u + vY C = a + b (Y-T) = a + b (Y - u - vY) = a - bu + b(1-v) Y I = I and Y = (a - bu + I + G)/[1 -b(1-v)]

With three instruments and two targets there will be a degree of freedom in the system: one could either change u to achieve the desired level of C and then change G to achieve the desired level of Y; or change v and then G.

a policymaker (Government) can reach any given (fixed) set of independent target values by an appropriate vector of instruments if and only if the number of independent instruments is equal to, or greater than, the number of targets.

how to deal with systems in which the number of instruments is less than that of targets?

“non-Tinbergen” systems.

Tinbergen’s fixed target approach

Golden Rule (Tinbergen Theorem):

Henri Theil provided a solution for many of the issues that had been left unsolved in the Tinbergen theory.

- policymaker should minimize a loss (or maximize a utility) function defined on the relevant target variables, subject to constraints describing the responses of the economy.

- overcame Tinbergen’s rigid distinction between targets and instruments, by allowing the latter to be relevant in their own right (for example, where policymakers have preferences over how the instruments should be used; or have strong views over whether their use should be restricted to certain “acceptable” values) and introducing them directly into the objective function.

- develop a theory of economic policy in a multi-period dynamic setting.

- introduced uncertainty into the model of the economy and the policy process with an appeal to the principle of certainty equivalence.

- improvements and advances in the theory as to the existence, uniqueness and design of economic policies.

- development of modern methods of control theory.

Theil’s flexible target approach- solved a non-Tinbergen system.

governments are trying to solve a stochastic optimisation problem by maximising an objective function subject to constraints implied by the structure of the economy -given by the transformation curve

Theil’s flexible target approach (Optimisation approach)

assume the existence of a social welfare function (SWF) which expresses society's (or the government's) view of the relative importance of the different objectives and the trade-offs that the government is prepared to accept.

The problems associated with these approaches are: (a) It is difficult to specify the preference functions of policy makers; (b) The approach assumes that deviations above or below a target are equally bad; (c) Such an approach may lead to undue caution in terms of what is feasible (there is too much stress on constraints); (d) Policy makers don't behave in this way.

effectiveness of specific policy instruments (Not concerned by Tinbergen-Theil) an issue that has been raised more prominently in the subsequent economics literature with reference to specific policy problems; particularly in monetary policy, in fiscal policy, and in other applications.

(Barro, 1974). A proposition of policy neutrality or policy “invariance” was thus stated with regard to the two most widely used macroeconomic policy instruments.

rational expectations (REs)1960s

ineffectiveness of monetary policyMilton Friedman, 1968fiscal policy was considered ineffective as an instrument for managing income levels

policy neutrality or policy “invariance”

(Barro, 1974)

effectiveness: An instrument is effective with respect to a target variable if changes in the instrument determine changes in the equilibrium value of that target; otherwise it is ineffective.

exogenous policy neutrality: Economic policy is neutral with respect to a target variable, if all the instruments are ineffective with respect to that target variable.

Definitions:

endogenous policy neutrality: Economic policy is neutral with respect to a target variable yi , if its equilibrium value is not affected by any change in policymaker’s preferences.

Controllability: A system is controllable if the Government can determine the values of the target variables for any possible vector of desired targets by choosing an appropriate policy (i.e. vector of instruments).

Controllability and sub (partial) controllability: if the matrix C is square and full rank, the system is controllable. This is also the case of a rectangular matrix C with more columns (instruments) than row (targets) and a rank equal to the number of rows. By contrast, if C is a rectangular matrix with more rows than columns, the system is not controllable and a flexible target approach should be used.

Theory of Rational Expectations

Theory of Rational Expectations

● Expectations will be identical to optimal forecasts using all available information

expectation of the variable that is being forecast

= optimal forecast using all available information

e of

e

of

X X

X

X

=

=

Implications

● If there is a change in the way a variable moves, the way in which expectations of the variable are formed will change as well

● The forecast errors of expectations will, on average, be zero and cannot be predicted ahead of time

Econometric Policy Critique

● Econometric models are used to forecast and to evaluate policy

● Lucas critique, based on rational expectations, argues that policy evaluation should not be made with these models – The way in which expectations are formed (the

relationship of expectations to past information) changes when the behavior of forecasted variables changes

– The public’s expectations about a policy will influence the response to that policy

New Classical Macroeconomic Model

●All wages and prices are completely flexible with respect to expected change in the price level

●Workers try to keep their real wages from falling when they expect the price level to rise

●Anticipated policy has no effect on aggregate output and unemployment

●Unanticipated policy does have an effect ●Policy ineffectiveness proposition

Short-run response to an expansionary policy (a New classical Model)

Unanticipated anticipated

Less expansionary than expected

Short-run response to an expansionary policy (a New classical Model)

Short-run response to an expansionary policy (a New Keynesian Model)

Unanticipated anticipated

Implications for Policymakers

● Policymakers must understand public’s expectations to know outcome of the policy.

● There may be beneficial effects from activist stabilization policy

● Design policy rules so prices will remain stable

Designing the policy is NOT easy because the effect of anticipated and unanticipated policy is very different

• Stabilization policy usually falls under the category of anticipated policy

• Therefore, it is generally correctly anticipated through rational expectations

• Systematic policies are useless • Because of rational expectations, only “erroneous” (completely

unanticipated) changes in the money supply influence the level of economic activity

1. More aware of importance of expectations and credibility

2. Lucas critique has caused most economists to doubt use of conventional econometric models for policy evaluation

3. Since effect of policy depends on expectations, economists less activist

4. Policy effectiveness proposition not widely accepted, most economists take intermediate position that activist policy could be beneficial but is tough to design

Impact of Rational Expectations Revolution

● Expectations formation will change when the behavior of forecasted variables changes

● Effect of a policy depends critically on the public’s expectations about that policy

● Empirical evidence on policy ineffectiveness proposition is mixed

● Credibility is essential to the success of anti-inflation policies

● Less fine-tuning and more stability

Impact of the Rational Expectations Revolution

Tinbergen-type decision model is inconsistent with the assumption of REs

private sector behaviour to be invariant to the policy vector itself

when the private sector has REs of future developments

the policymaker will lose control of the economic system,

existence of an equilibrium X

The policy game approach

Strategic interactions between the private sector and the policymaker then ensure that the REs of both are satisfied.

The policy game approach

Barro and Gordon (1983)

policy decision within a strategic context

modeling the behaviour of players by considering separate but not independent optimisation problems.

a strategic game in which the leader moves first and then the follower move sequentially.

Stackelberg equilibrium conditions:- The leader must know ex ante that the follower observes its action.- The follower must have no means of committing to a future non-Stackelberg follower

action and the leader must know this. - if the 'follower' could commit to a Stackelberg leader action and the 'leader' knew this,

the leader's best response would be to play a Stackelberg follower action.

Stackelberg leadership model

- Private sector is leader and trades off real wages and employment when setting the nominal wage rate.

- long run monetary neutrality as a result of the private sector expectations of discretionary monetary policy

- the private sector forms REs and fully crowds out monetary effects on real output.

A superior solution, for the public sector, would be to commit to a certain rule.

Stackelberg game between central bank and private sector

- having induced favorable private sector expectations, the policymaker would always be tempted to cheat and renege on his commitment,

- being aware of this possibility, the private sector would (in self-defense) anticipate worse results; results that can be avoided only if the temptation to cheat is balanced by a fear that the policymaker might lose his reputation and no longer be able to act effectively if this game of interactions with the private sector is repeated.

Two fundamental propositions that characterize the new theory of economic policy:

Proposition 1 (ineffectiveness): If one (and only one) player satisfies the golden rule, all the other players’ policies are ineffective.Proposition 2 (existence): Existence of the game equilibrium requires that two or more players do not satisfy the golden rule (unless they share the same target values).

Thank you