Perfect Foresight Model Research Articles

Heterogeneous expectations and equilibria selection in an evolutionary overlapping generations model

The way agents form their expectations, and which equilibria are consequently selected, are issues that come over macroeconomic growth models that study the transition between states characterized by different levels of capital. Existing theoretical works in this area have been mostly dominated by perfect foresight models although alternative expectations schemes have been proposed in the last decades. In the present paper we propose an OLG model with capital accumulation assuming that agents employ simple yet heterogeneous rules to forecast the future course of the interest rate and the real wage. The forecasting rules are selected according to an evolutionary mechanism that, on the basis of a fitness measure, evaluates the performance of the heuristics agents are currently adopting. We analytically show that, in the heterogeneous setting we consider, multiple equilibria are possible, but the evolutionary heuristic switching allows for a decrease in the number of possible steady states, drives their selection, and reduces the actual possibility that the economy might be locked into a poverty trap.

Impact of imperfect foresight on the optimal DER deployment, remuneration and policy

This paper proposes a decision-making framework to optimize electricity tariffs and remuneration policy for renewable energy sources operating in transmission- and distribution-level (T&D) marketplaces. We develop perfect and imperfect foresight models with a multi-level structure to investigate the effects of the inability of actors to correctly predict future remuneration on the efficiency of the decisions made by policymakers. The important advantage of the proposed models is that while they are capturing conflicting interests and different information availability of stakeholders involved, they also account for techno-economic constraints on operations of generation, transmission and distribution assets. The presented models can accommodate net metering, value stack, and distribution locational marginal price (DLMP)-based remuneration policies, which allows for their numerical comparison in terms of the effect on the optimal roll-out of distributed energy resources (DERs). The case study carried out for the NYISO and Manhattan T&D networks reveals that inaccurate foresight on the DER remuneration diminishes the social welfare under all DER remuneration policies, with the maximum loss of 1.6% across all considered scenarios.

Financial Risk Management and Transmission Mechanism of Monetary Policy: An Empirical Evidence from Pakistan

Monetary policy plays a vital role in achieving development for any country. This study attempts to analyze the impact of the monetary transmission mechanism on unhedged interest rate exposure in the case of Pakistan. The study used time series data from 1980 to 2020 and applied the ARDL model to check the short-run and long run association between all the variables. First, URE (Unhedged interest rate exposure) was calculated and then estimated the factors affecting it. The study also used the perfect foresight model for addressing household behavior. The outcomes indicated that all exchange rates, interest rates, and money supply positively impact unhedged interest rate exposure, and they are significant both in the short and long-run. The interest rate substantially affects unhedged rate exposure more than the money supply. Development expenditures and money supply are negatively associated with income inequality; unhedged interest rate exposure is positively associated with income inequality.

Parallel Extended Path Method for Solving Perfect Foresight Models

We parallelize the extended path method for solving rational expectations models, and apply it to compute perfect foresight competitive equilibrium for the global economy with multiple goods, regions, industries, and households. At each iteration, first intertemporal variables are updated, then equations for intra-temporal variables are solved in parallel. We compare serial, and parallel, versions of the extended path method in high-performance computing environments based on scenarios with long time horizons that include future populations, economic growth, energy use, and carbon dioxide emissions. Relative to the serial version, the speedup factor for the parallel extended path method grows almost linearly up to about 30 times with 18 cores, and computing times reduced from over 10 h for the serial version down to about 20 min for the parallel version.

A general method for comparative dynamics in continuous‐time models

AbstractThis paper develops a general and applicable method for the computation of comparative dynamics in continuous‐time perfect foresight models. The key technique in our method is the Jordan decomposition of the Jacobian matrix. This enables us to derive analytical solutions when dealing with high‐dimensional systems with repeated eigenvalues. In an application, we compute comparative dynamics of an unanticipated expansionary monetary policy in scenarios with and without repeated eigenvalues. We find that the short‐run effects on the social welfare are opposite in the two scenarios, while the long‐run effects are similar.

On probability of default and its relation to observed default frequency and a common factor

This paper considers a definition of through-the-cycle (TTC) as independent from an economic state that can result in a time-varying TTC probability of default (PD). A top-down approach is proposed to transform hybrid PDs into TTC PDs through the use of a point-in-time-ness (PITness) parameter as an additional parameter to the Vasicek model, which expresses the dependency of a hybrid PD on a common factor. The proposed framework aims to explain fluctuations in observed default frequency (ODF) and modeled default frequency time series. A novel approach is considered that defines ODF as analogous to an aggregated PIT PD stemming from a perfect foresight model, which is not available to the modeler but can be assumed backward in time for calibration purposes. An elaborate segmentation framework is considered to understand differences in both the Vasicek correlation and the PITness parameter for a portfolio of obligors; this can be applied to both retail and nonretail portfolios.

Equity Pricing: Perfect Foresight versus Rational Expectations

This study demonstrates that when the length of the excess earnings period is not known with certainty, all rational expectations pricing models result in some degree of overpricing when compared ex post facto to perfect foresight models. This study examines the time paths of price under existing valuation models such as Baek et al. [1] and Ohlson and Jeuttner-Nauroth [2] under the following stylized facts: we assume that we are dealing with an all-equity firm with opportunity cost of equity of r, and with a proprietary technology which enables it to achieve a marginal return on equity of R > r for approximately N periods, after which a Schumpeterian event Sis predicted to occurs and the marginal return on equity is expected to revert to the opportunity cost of equity r. Our study demonstrates a deviation of the predicted rational expectations price from the perfect foresight price and demonstrates that such deviation may become extreme near the end of the excess earnings period, resulting in a catastrophic price adjustment when that period comes to an end.

The effects of the near-zero interest rate policy in a regime-switching dynamic stochastic general equilibrium model

Standard Dynamic Stochastic General Equilibrium (DSGE) models cannot explain the near-zero interest rate policy (near-ZIRP) by the Federal Reserve. I study two methods of modeling the near-ZIRP in DSGE models: the perfect foresight model and the Markov regime-switching model developed in this paper. The near-ZIRP has a significant expansionary effect, and the regime-switching model generates a more realistic predicted path of macro variables than the perfect foresight model. Furthermore, the government purchases multiplier in the near-ZIRP regime is smaller than what the literature finds at the zero lower bound (ZLB), and the contractionary effects of higher productivity found by the recent literature at the ZLB are not present in the regime-switching model.

The influence of uncertainty in the development of a CO2 infrastructure network

This study aimed to analyze whether, and how, uncertainty influences the layout and costs of a CO2 transportation network. The case without uncertainty is modelled with a perfect foresight (PF) model and with uncertainty with the real option approach (ROA). In this study, uncertainties in the CO2 price, tariff received per tonne of CO2 transported, the willingness, probability and moment that sources join the CO2 transportation network are incorporated in the analysis. The results show that uncertainty leads to higher required CO2 prices before investments in carbon dioxide capture and storage (CCS) are made. With a volatility of 47% in the CO2 price, the required CO2 price almost triples in comparison with the net present value approach. Hence, under uncertainty less sources are retrofitted with CCS and less CO2 is captured and stored over time. For instance, for the analyzed case study 31 Mt and 137 Mt CO2 is projected to be captured in the base scenario of ROA and PF model, respectively, in the period 2015–2050. If the volatility of the CO2 price is reduced with 50%, 96 Mt is projected to be captured in the ROA, which is still about one third less than in the PF model.Furthermore, the results show that uncertainty leads to less development of trunklines. All this leads to an increase in the transport and storage costs. For instance, for our case study, the average CO2 transport and storage costs in 2050 increase from 2.8 €/t to 13 €/t in the base scenario of the ROA compared to the PF model. If the volatility is reduced with 50%, the transport and storage costs decrease to 7.5 €/t in the ROA, which is still 2.5 times as much as in the PF model.Our findings indicate that the implementation of CCS can best be stimulated by reducing the volatility of the CO2 price, reducing capture costs and facilitating cooperation between nearby sources.

A NOTE ON DETERMINING VIABLE ECONOMIC STATES IN A DYNAMIC MODEL OF TAXATION

Viability theory is the study of dynamical systems that asks what set of initial conditions will generate evolutions that obey the laws of motion of a system and some state constraints, for the length of the evolution. We apply viability theory to Judd's dynamic tax model [The welfare cost of factor taxation in a perfect-foresight model, Journal of Political Economy 95(4), 675–709 (1987)] to identify which economic states today are sustainable under only slightly constrained tax-rate adjustments in the future, when the dynamic budget constraint and the consumers' transversality condition at infinity are satisfied. We call the set of such states the economic viability kernel. In broad terms, knowledge of the viability kernel can tell the planner what economic objectives are achievable and assist in the choice of suitable controls to realize them. We observe that high consumption levels can only be sustained when capital is abundant and, unsurprisingly, that a very high consumption economy lies outside such kernels, at least for annual tax-adjustment levels limited by 20 percentage points. Furthermore, we notice that by and large the sizes of the kernel slices do not diminish as the tax rate rises; hence high-taxation economies are not necessarily more prone to explode, or implode, than their low-taxation counterparts. In fact, higher tax rates are necessary to keep many consumption choices viable, especially when capital approaches the constraint-set boundaries.

Assessing the Effects of the Zero-Interest-Rate Policy Through the Lens of a Regime-Switching DSGE Model

Standard dynamic stochastic general equilibrium (DSGE) models assume a Taylor rule and forecast an increase in interest rates immediately after the 2007-2009 economic recession given the predicted output and inflation, contradictory to the extended period of near-zero interest rate policy (ZIRP) conducted by the Federal Reserve. In this paper, I study two methods of modeling the ZIRP in DSGE models: the perfect foresight rational expectations model and the Markov regime-switching model, which I develop in this paper. In this regime-switching model, I assume that, in one regime, the policy follows a Taylor rule, while, in the other regime, it involves a zero interest rate. I also construct the optimal filter to estimate this regime-switching DSGE model with Bayesian methods. I fit those modified DSGE models to the U.S. data from the third quarter of 1987 to the third quarter of 2010, and then, starting from the fourth quarter of 2010, I simulate the U.S. economy forward with and without the ZIRP intervention. I compare the predicted paths of the macro variables, and I find that the ZIRP intervention has a significant effect. The estimated regime-switching model I develop implies a substantial stimulative effect (on average a 0.12% increase in output growth rate and a 0.9% increase in inflation accumulatively over 20 quarters if ZIRP is kept for 6 quarters). The actual path from the fourth quarter of 2010 onward is closer to the predicted path derived from the regime-switching model than that generated by the perfect foresight model. The perfect foresight model generates an explosive and spurious rise in inflation. Therefore, the regime-switching model I propose is more appropriate to assess the effectiveness of the ZIRP, which is effective in stimulating the economy.

The Effect of Uncertainty on Optimal Control Models in the Neighbourhood of a Steady State.

For both discrete and continuous time this paper derives the Taylor approximation to the effect of uncertainty (in the simple sense of risk, not Knightian uncertainty) on expected utility and optimal behaviour in stochastic control models when the uncertainty is small enough that one can focus on only the first term that involves uncertainty. There is a close and illuminating relationship between the discrete-time and continuous-time results. The analysis makes it possible to spell out a tight connection between the behaviour of a dynamic stochastic general equilibrium model and the corresponding perfect foresight model. However, the quantitative analytics of the stochastic model local to a certainty model calls for a more thorough investigation of the nearby certainty model than is typically undertaken.

Optimal capital-income taxation in a model with credit frictions

AbstractThe optimality of the long-run capital-income tax rate is revisited in a simple neoclassical growth model with credit frictions. Firms pay their factors of production in advance, which requires borrowing at the beginning of the period. Borrowing, in turn, is constrained by the value of collateral that they own at the beginning of the period, leading to inefficiently low amounts of capital and labor. In this environment, the optimal capital-income tax in the steady state is non zero. Specifically, the quantitative analyses show that the capital-income tax is negative and, therefore, the distortions stemming from the credit friction are offset by subsidizing capital. However, when the government cannot distinguish between capital-income and profits, the capital-income tax is positive as the government levies the same tax rate on both sources of income. These results stand in contrast to the celebrated result of zero capital-income taxation of Judd (Judd, K. 1985. “Redistributive Taxation in a Simple Perfect Foresight Model.”

Operating Strategies for a GB Integrated Gas and Electricity Network Considering the Uncertainty in Wind Power Forecasts

In many power systems, in particular in Great Britain (GB), significant wind generation is anticipated and gas-fired generation will continue to play an important role. Gas-fired generating units act as a link between the gas and electricity networks. The variability of wind power is, therefore, transferred to the gas network by influencing the gas demand for electricity generation. Operation of a GB integrated gas and electricity network considering the uncertainty in wind power forecast was investigated using three operational planning methods: deterministic, two-stage stochastic programming, and multistage stochastic programming. These methods were benchmarked against a perfect foresight model which has no uncertainty associated with the wind power forecast. In all the methods, thermal generators were controlled through an integrated unit commitment and economic dispatch algorithm that used mixed integer programming. The nonlinear characteristics of the gas network, including the gas flow along pipes and the operation of compressors, were taken into account and the resultant nonlinear problem was solved using successive linear programming. The operational strategies determined by the stochastic programming methods showed reductions of the operational costs compared to the solution of the deterministic method by almost 1%. Also, using the stochastic programming methods to schedule the thermal units was shown to make a better use of pumped storage plants to mitigate the variability and uncertainty of the net demand.

Assessing the Effects of the Zero-Interest-Rate Policy Through the Lens of a Regime-Switching DSGE Model

Standard dynamic stochastic general equilibrium (DSGE) models assume a Taylor rule and forecast an increase in interest rates immediately after the 2007-2009 economic recession given the predicted output and inflation, contradictory to the extended period of near-zero interest rate policy (ZIRP) conducted by the Federal Reserve. In this paper, I study two methods of modeling the ZIRP in DSGE models: the perfect foresight rational expectations model and the Markov regime-switching model, which I develop in this paper. In this regime-switching model, I assume that, in one regime, the policy follows a Taylor rule, while, in the other regime, it involves a zero interest rate. I also construct the optimal filter to estimate this regime-switching DSGE model with Bayesian methods. I fit those modified DSGE models to the U.S. data from the third quarter of 1987 to the third quarter of 2010, and then, starting from the fourth quarter of 2010, I simulate the U.S. economy forward with and without the ZIRP intervention. I compare the predicted paths of the macro variables, and I find that the ZIRP intervention has a significant effect. The estimated regime-switching model I develop implies a substantial stimulative effect (on average a 0.12% increase in output growth rate and a 0.9% increase in inflation accumulatively over 20 quarters if ZIRP is kept for 6 quarters). The actual path from the fourth quarter of 2010 onward is closer to the predicted path derived from the regime-switching model than that generated by the perfect foresight model. The perfect foresight model generates an explosive and spurious rise in inflation. Therefore, the regime-switching model I propose is more appropriate to assess the effectiveness of the ZIRP, which is effective in stimulating the economy.

Oil Exporters’ Dilemma: How Much to Save and How Much to Invest

Summary Policymakers in oil-exporting countries confront the question of how to allocate oil revenues among consumption, saving, and investment in the face of high income volatility. We study this allocation problem in a precautionary saving and investment model under uncertainty. Consistent with data in the 2000s, precautionary saving is sizable and the marginal propensity to consume out of permanent shocks is below one, in stark contrast to the predictions of the perfect foresight model. The optimal investment rate is high if productivity in the tradable sector is high enough.

THE ROLE OF TWO INTEREST RATES IN THE INTERTEMPORAL CURRENT ACCOUNT MODEL

We analyze the role of the lending-deposit interest rate spread in the dynamics of the current account in developing countries. For that purpose, we extend the standard perfect-foresight intertemporal model of the current account for the existence of the interest rate spread and simulate the convergence path of developing economies. This model helps explain why in many cases it is optimal for a fast-growing, low-income country to run a balanced current account.

Oil Exporters’ Dilemma: How Much to Save and How Much to Invest

Policymakers in oil-exporting countries confront the question of how to allocate oil revenues among consumption, saving, and investment in the face of high income volatility. We study this allocation problem in a precautionary saving and investment model under uncertainty. Consistent with data in the 2000s, precautionary saving is sizable and the marginal propensity to consume out of permanent shocks is below one, in stark contrast to the predictions of the perfect foresight model. The optimal investment rate is high if productivity in the tradable sector is high enough.

Continuous-Time Methods for Integrated Assessment Models

Continuous time is a superior representation of both the economic and climate systems that Integrated Assessment Models (IAM) aim to study. Moreover, continuous-time representations are simple to express. Continuous-time models are usually solved by discretizing time, but the quality of a solution is significantly affected by the details of the discretization. The numerical analysis literature offers many reliable methods, and should be used because alternatives derived from intuition may be significantly inferior. We take the well-known DICE model as an example. DICE uses 10-year time steps. We first identify the underlying continuous-time model of DICE. Second, we present mathematical and computational methods for transforming continuous-time deterministic perfect foresight models into systems of finite difference equations. While some transformations create finite difference systems that look like a discrete-time dynamical system, the only proper way to view the finite difference system is as an approximation of the continuous-time problem. DICE is an example where the usage of finite difference methods from numerical analysis produces far superior approximations than do simple discrete-time systems.

Oil Exporters' Dilemma: How Much to Save and How Much to Invest

Policymakers in oil-exporting countries confront the question of how to allocate oil revenues among consumption, saving, and investment in the face of high income volatility. We study this allocation problem in a precautionary saving and investment model under uncertainty. Consistent with data in the 2000s, precautionary saving is sizable and the marginal propensity to consume out of permanent shocks is below one, in stark contrast to the predictions of the perfect foresight model. The optimal investment rate is high if productivity in the tradable sector is high enough.