Perfect Foresight Model Research Articles

THE Z-TRANSFORM AND COMPARATIVE DYNAMICS IN DISCRETE-TIME MODELS

This paper develops a general technique for the computation of comparative dynamics in perfect-foresight discrete-time models. The method developed here is both applicable and general; it can be used to analyze the effects of the perturbation of parameters on endogenous variables and the welfare of an economic system derived from more general multisector models. It is neither restricted to the system's dimensions nor restricted by the assumption of distinct eigenvalues in the system.

IMPLICIT EQUILIBRIUM DYNAMICS

We discuss the problem known in economics as backward dynamics occurring in models of perfect foresight, intertemporal equilibrium described mathematically by implicit difference equations. In a previously published paper [Journal of Economic Dynamics and Control 31 (2007), 1633–1671], we showed that by means of certain mathematical methods and results known as inverse limits theory it is possible to establish a correspondence between the backward dynamics of a noninvertible map and the forward dynamics of a related invertible map acting on an appropriately defined space of sequences, each of whose elements corresponds to an intertemporal equilibrium. We also proved the existence of different types of topological attractors for one-dimensional models of overlapping generations. In this paper, we provide an extension of those results, constructing a Lebesgue-like probability measure on spaces of infinite sequences that allows us to distinguish typical from exceptional dynamical behaviors in a measure–theoretical sense, thus proving that all the topological attractors considered in MR07 are also metric attractors. We incidentally also prove that the existence of chaos (in the Devaney–Touhey sense) backward in time implies (and is implied by) chaos forward in time.

The tyranny of rules: fiscal discipline, productive spending, and growth in a perfect foresight model

The performance of alternative fiscal rules is examined in an endogenous growth model. The government spends money on infrastructure, maintenance, and health. Infrastructure affects the production of both commodities and health services. The performance of a balanced budget rule, as well as standard and modified golden rules (including and excluding productive spending) and primary surplus rules are compared numerically. Under a range of plausible parameter configurations, a primary surplus rule that excludes productive spending performs better (in a growth sense, although not necessarily from the perspective of short‐run macro stability) than alternative rules in response to a variety of shocks.

Accounting for the “disconnectedness” of the economy in OLG models: A case for taxing capital income

The paper extends the works by Judd [K.L. Judd, Redistributive Taxation in a Simple Perfect Foresight Model, J. Public Econ. 28 (1985), 59–83.] and Chamley [C. Chamley, Optimal taxation of capital income in general equilibrium with infinite lives, Econometrica, 54 (1986), 607–622.], who establish that in the long run the capital income tax should be zero, by considering a discrete time version of the Blanchard–Buiter–Weil perpetual youth model. We show that an independent source of non-zero taxation arises whenever the economy is “disconnected” and this feature is properly taken into account by the policymaker. More precisely, if the weight attached to each cohort in the social welfare function equals the corresponding actual share in the population, there is a force pushing towards positive taxation of capital income, which acts as a Pigouvian intervention. Moreover, room for this intertemporal correction shrinks as the relative weight of a cohort tends to zero: thus, the optimal tax rate decreases with age and tends to zero for the oldest. We also show that our result depends neither on life-cycle behavior, as pointed out by the previous literature on OLG models, nor on population growth.

Price-level Determinancy, Lower Bounds on the Nominal Interest Rate, and Liquidity Traps

We study standard monetary-policy rules with inflation-rate targets and either interest-rate or money-supply instruments using a flexible-price, perfect-foresight model. We focus mainly on interest-rate rules, but the results for money-supply rules are analogous. A locally-unique target equilibrium always exists. There are also below-target equilibria (BTE) with inflation below target and constant or asymptotically approaching or eventually reaching a below-target value. Liquidity traps are neither necessary nor sufficient for BTE. Such equilibria can also arise if monetary policy keeps the interest rate above a lower bound. We construct monetary-policy rules that preclude BTE. All are non-monotonic and discontinuous in current inflation. Each implies a difference equation in inflation. Some of these difference equations are continuous, but others are not. They are all non-monotonic and non-differentiable at a point. We argue that Japan's difficulties in the 1990s were probably the result of a stabilization problem rather than an indeterminacy problem.

Time-consistent fiscal policy and heterogeneous agents

This paper characterizes the time-consistency properties of the set of Pareto efficient (or second best) fiscal policies, in a two-class, stochastic economy similar to that in [Judd, K.L., 1985, Redistributive taxation in a simple perfect foresight model, Journal of Public Economics 28, 59–83]. The key finding is that the continuation of any Pareto efficient policy is always Pareto efficient. Hence, to require any policy revision to be approved by unanimity safeguards the time consistency of efficient fiscal policy. I also show that any Pareto efficient policy from a timeless perspective can be rendered time consistent by a policymaker whose objective function is given by a utilitarian social welfare function with precise welfare weights. These results link the policymaker's equity considerations with the credibility of efficient fiscal policy.

Backward dynamics in economics. The inverse limit approach

We discuss the problem known in economics as ‘backward dynamics’. In models of perfect foresight, intertemporal equilibrium, rational agents’ decisions at any given moment in time depend on (accurately anticipated) future values of some variables. For certain kinds of structural (e.g., utility) functions, those models determine forward equilibrium sequences only implicitly. Then, the problem arises whether the investigation of backward-moving dynamics can be used to understand the forward dynamics associated with them. We study this problem by means of a mathematical technique known as ‘inverse limits theory (ILT)’ that allows us to establish a correspondence between backward dynamics of a non-invertible map and forward dynamics of a related, invertible map acting on an appropriately defined space of sequences. We apply ILT to certain implicit difference equations occurring in economics, and suggest precise criteria for identifying typical orbits forward in time.

A Time Step Energy Process Model for Germany - Model Structure and Results

The new IKARUS-Model is a time-step dynamical bottom-up linear optimization model where each time interval is optimized by itself using the heritage from all periods before. Contrary to perfect-foresight models, this model does not take into account future changes in each time-step optimization. It therefore shows a more realistic character of prognosis and projection. Aspects like reaction on sudden changes (e.g. of energy prices), flexibility of technical scenarios, lost opportunities etc. can be examined. Interactions with macroeconomic I/O-models or dependencies on elasticities, technological learning etc. are possible. Recent calculations for Germany up to 2030 show that consistent and plausible future energy scenarios can be produced and analyzed.

To Be or Not To Be in Office Again, That is the Question Political Business Cycles with Local Governments

Most opportunistic-type models of political business cycles tend to posit a given objective for incumbents: maximisation of re-election chances. Though taking an opportunistic view too, we suggest a new explanation for a fiscal policy cycle: the incumbent’s concern with her own welfare in cases of victory and defeat. This rationale addresses local policy-making in particular. An equilibrium perfectforesight model is designed which totally dispenses with any form of irrationality (namely, on the part of voters) or the common objective functions (re-election chances). Being well grounded in basic microeconomic theory (welfare maximisation by the individual agent), our model provides another foundation for the emergence of political business cycles at the local level. The empirical plausibility of theoretical predictions is then tested on Portuguese municipal data. The estimation of an error-components econometric framework finds evidence in favour of the proposed explanation during the period 1986 to 1993, and enlightens the role played by several politico-economic determinants of local governments’ investment outlays, such as electoral calendar, re-candidacy decisions, political cohesion and intergovernmental capital transfers.

Price-Level Determinacy, Lower Bounds on the Nominal Interest Rate, and Liquidity Traps

We study standard monetary-policy rules with inflation-rate targets and either interest-rate or money-supply instruments using a flexible-price, perfect-foresight model. We focus mainly on interest-rate rules, but the results for money-supply rules are analogous. A locally-unique target equilibrium always exists. There are also below-target equilibria (BTE) with inflation below target and constant or asymptotically approaching or eventually reaching a below-target value. Liquidity traps are neither necessary nor sufficient for BTE. Such equilibria can also arise if monetary policy keeps the interest rate above a lower bound. We construct monetary-policy rules that preclude BTE. All are non-monotonic and discontinuous in current inflation. Each implies a difference equation in inflation. Some of these difference equations are continuous, but others are not. They are all non-monotonic and non-differentiable at a point. We argue that Japan's difficulties in the 1990s were probably the result of a stabilization problem rather than an indeterminacy problem.

Laplace transform methods for linearizing multidimensional systems

This note develops a Laplace transform method for solving linearizing multidimensional systems raised by multi-sector perfect foresight models, which can be viewed as an extension to Judd's (1982) [Judd, K. 1982. An alternative to steady-state comparisons in perfect foresight models. Economics Letters 10, 55-59.] method for solving two-dimension systems raised by one-sector models.

Price-level Determinacy, Lower Bounds on the Nominal Interest Rate, and Liquidity Traps

We consider monetary-policy rules with inflation-rate targets and interest-rate or money-growth instruments using a flexible-price, perfect-foresight model. There is always a locally-unique target equilibrium. There may also be below-target equilibria (BTE) with inflation always below target and constant, asymptotically approaching or eventually reaching a below-target value, or oscillating. Liquidity traps are neither necessary nor sufficient for BTE which can arise if monetary policy keeps the interest rate above a lower bound. We construct monetary rules that preclude BTE when fiscal policy does not. Plausible fiscal policies preclude BTE for any monetary policy; those policies exclude surpluses and, possibly, balanced budgets.

The parametric path method: an alternative to Fair–Taylor and L–B–J for solving perfect foresight models

The parametric path method applies projection methods to compute the equilibrium time path of economic variables in infinite-horizon dynamic models. We exploit the special structure of equilibrium paths common in such models to construct a low-dimensional set of candidate solutions, and then use efficient integration and equation solution methods to find an approximate solution. Simple illustrative examples show that the parametric path method can find excellent approximations with little computational cost.

Devaluation risk and the business-cycle implications of exchange-rate management

What is the mechanism driving the business cycle associated with stabilization policies anchored on managed exchange rates? Perfect-foresight models used extensively to try to answer this question have been unable to explain key quantitative features of the data. To do so it is necessary to consider devaluation risk in an environment of incomplete insurance markets in which stochastic price and wealth distortions operate. Simulations applied to Mexican data show that these distortions are large and socially costly, and that they rationalize several stylized facts. These findings suggest focusing the debate on exchange-rate regimes on the credibility of policymakers and the stance of fiscal policy.

A perfect foresight model of regional development and skill specialization

This paper proposes a perfect foresight model of a two-region two-sector economy, where localized externalities in the acquisition of skills cause specialization and uneven regional development. The introduction of a new technology either reinforces or reverses this development pattern. Wealth differences are reinforced if, in spite of higher wages, the new technology locates in the advanced region, attracted by skills similar to the needs of the new industry. Otherwise the new technology locates where wages are lower, in which case the lagging region overtakes the leading one. In spite of perfect foresight, history alone determines the outcome in this economy.

A Model of Crises in Emerging Markets

This paper presents a perfect foresight model of speculative attacks on emerging markets. Credit constrained governments are assumed to have two objectives: to accumulate liquid assets in order to self‐insure against shocks to national consumption and to insure poorly regulated domestic financial markets. This policy regime generates endogenous fiscal deficits defined to include the growth of contingent liabilities. The model sets out a sequence of yield differentials consistent with capital inflows followed by anticipated speculative attacks. The model suggests that a common shock generated capital inflows to emerging markets in Asia and Latin America after 1989.

The real dollar-yen exchange rate, asymmetries in trade flows and the current account in a perfect-foresight model for developing East Asia

This paper explores permanent, unanticipated shocks in the yen-dollar exchange rate in a perfect-foresight, infinite-horizon, representative-agent model for an open, semismall economy that produces a single good, imports intermediate inputs and investment goods from Japan and competes with Japan in external markets. Therefore, the model captures some of the features of the developing countries of East Asia. External debt is constrained by a country-risk premium that depends on the level of external debt. The capital stock is maintained and incremented by an endogenous mixture of Japanese and home goods. An appreciation of the dollar against the yen is neutral for external indebtedness and the trade account in the long run, but raises the capital stock, consumption and hence welfare in the long run; the home currency depreciates against the dollar but appreciates against the yen. Whether a cycle of current account surpluses followed by current account deficits or vice versa is generated depends on the initial response of the shadow value of external debt.

Public Sector Wage Cycles and the Co-Movement of the Fiscal Deficit and Inflation in Less-Developed Countries

In this paper I analyze the co-variation of the fiscal deficit and inflation in a simple perfect foresight model that incorporates low- and high-wage cycles of equal depth and duration. When money and consumption are not extremely strong complements and the wage-cycle not extremely short-lived, inflation rises above its pre-stabilization level while the deficit is lower. The results thus argue that public sector wage cycles may underlie the weak empirical correlation of the deficit and inflation.

An Analysis of Historical and Future‐Oriented Information in Accounting‐Based Security Valuation Models*

AbstractThe Ohlson (1995) and Feltham and Ohlson (1995) valuation model provides a rigorous framework for summarizing the information in expected future earnings and book values. However, the model provides little guidance on selecting an empirical proxy for expected future earnings. We examine whether and under what circumstances historical earnings and analyst earnings forecasts offer comparable explanation of security prices. This issue is of particular interest because analyst forecasts are less readily available than historical data. Under appropriate circumstances, historical data may allow wider use of the Feltham‐Ohlson valuation model by researchers and investors. A related issue is the incremental explanatory power of historical earnings and realized future earnings (perfect‐foresight forecasts) for security prices beyond analyst forecasts. If historical earnings are incrementally informative, that would suggest that analyst forecasts do not fully reflect price‐relevant information in past earnings. If future earnings are incrementally informative, that would suggest that security prices reflect investors' implicit earnings forecasts beyond analyst forecasts.We examine these issues using a historical model (based on past earnings), a perfect‐foresight model (based on realized future earnings), and a forecast model (based on Value Line earnings forecasts). All three models provide significant explanatory power for security prices, and each set of earnings data provides incremental explanatory power for prices when used with the other sets of earnings data. We estimate the models separately for firms with moderate and extreme earnings‐to‐price (E/P) ratios, a proxy for earnings permanence. For moderate‐E/P firms, the historical model's explanatory power exceeds that of the perfect foresight model, and is indistinguishable from that of the analyst forecast model. In contrast, for extreme‐E/P firms, the perfect‐foresight model offers greater explanatory power than the historical model, but lower explanatory power than analyst forecasts.Our results suggest that financial analysts' forecasting efforts are best focused on firms whose earnings contain large temporary components (extreme E/P firms). However, in general, both historical data and analyst forecasts are complementary information sources for security valuation.

Stability in models of money and perfect foresight: implications of non-linearity

In this paper we reconsider the rationale for the jump-variable technique, which is a standard component of linear rational expectations models. Using a simple monetary model for illustration, we argue that the traditional justification for jumps in the price level loses much of its force when money demand is non-linear. Instead, with perfect foresight and non-instantaneous price adjustment, the model gives rise to limit cycle behavior with endogenously determined jumps in inflation rates instead of jumps in the price level.