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PurposeThis study investigates which expectation formation mechanism governs Eurozone firms regarding their expectations on external finance availability.Design/methodology/approachIn this study, we link consecutive surveys from the Survey on the Access to Finance of Enterprises to bring new evidence on how non-financial corporations shape their expectations on external finance availability.FindingsIn line with the past literature, we demonstrate that the data reject the Rational Expectations hypothesis, and we find evidence in favor of the Adaptive Expectation mechanism.Originality/valueThis is the first study studying firms' expectations of external finance availability, implementing survey data of firms' expectations from the SAFE database on a country level. The formation of firm expectations is vital in directing policymakers in designing appropriate monetary policies, as both the employment and inflation targets of central banks around the world are highly dependent on the firm-level decision process.

In this study, we examine pollution effects on urban housing prices in China, using a fixed effects 2SLS model on a 13-year (2005–2017) panel dataset of 237 prefecture-level cities. We find that urban housing prices are negatively associated with PM2.5 levels, presenting an elasticity of – 0.32 for the entire sample. In large cities with an urban population of ≥ 5 million, the elasticity further increases in absolute value to – 0.34, reflecting greater marginal benefit associated with a unit percentage PM2.5 reduction in a higher pollution band. In addition, PM2.5’s effects on housing markets present temporal variations, and the base elasticity of – 0.29 for earlier periods increases to – 0.33 in the post-2008 period, reflecting increased public awareness of pollution-caused health risk after the Beijing Olympic Games. In the post-2014 period, however, the elasticity declines to – 0.24 with stricter pollution regulations introduced in late 2013 as part of the 12th Five Year Plan. Rational expectations regarding continued air-quality improvement in the future may underlie this trend.

Our experiments investigate the extent to which traders learn from the price, differentiating between situations where orders are submitted before versus after the price has realized. In simultaneous markets with bids that are conditional on the price, traders neglect the information conveyed by the hypothetical value of the price. In sequential markets where the price is known prior to the bid submission, traders react to price to an extent that is roughly consistent with the benchmark theory. The difference’s robustness to a number of variations provides insights about the drivers of this effect. (JEL D44, D82, D84, G12, G14)

We develop a medium-size semi-structural time series model of inflation dynamics that is consistent with the view - often expressed by central banks - that three components are important: a trend anchored by long-run expectations, a Phillips curve and temporary fluctuations in energy prices. We find that a stable long-term inflation trend and a well identified steep Phillips curve are consistent with the data, but they imply potential output declining since the new millennium and energy prices affecting headline inflation not only via the Phillips curve but also via an independent expectational channel. A high-frequency energy price cycle can be related to global factors affecting the commodity market, and often overpowers the Phillips curve thereby explaining the inflation puzzles of the last ten years.

We consider the one-to-one two-sided matching with contracts model in which buyers face financial constraints. In this model there is a stable outcome, but not necessarily a competitive equilibrium as defined in the standard way. We propose a new equilibrium notion, quantity-constrained competitive equilibrium (QCCE) that allows buyers to form rational expectations on the lack of supply when their financial constraints are binding. We show the existence of QCCEs and establish the equivalence among QCCE outcomes, stable outcomes, and core outcomes. We also analyze the existence of QCCEs with uniform prices, the lattice property of QCCEs, and the rural hospital theorem of QCCEs. We finally examine the relation between models with financial constraints and models with price controls.

We study the role of private information in the equity lending market in a rational expectations model with endogenous loan fees. When all investors are privately informed, an increase in information precision reduces the fee by increasing trade aggressiveness and decreasing demand dispersion. However, when some investors are uninformed, the information asymmetry tends to increase the fee, and, thus, the overall effect of an increase in precision is ambiguous. We show that the fee can be incrementally informative given the stock price and that fee opaqueness tends to increase the fee but has an ambiguous effect on the stock price.

This paper revisits the debate on ruling out speculative hyperinflations in monetary models. Although apparently a narrow issue, studying these extreme economies turns out to be quite illuminating in understanding the fundamentals of price level determination. It is also relevant in evaluating the broader claims that advocates of the fiscal theory of the price level have made. In Obstfeld and Rogoff ( 1983 , 1986 ) we show that in pure fiat money models with rational expectations, where the government gives no backing whatsoever to currency, there is in fact no reasonable way to rule out speculative hyperinflations where the value of money goes to zero, even if the money supply itself is exogenous and constant. Such perverse equilibria are ruled out, however, if the government provides even a very small real backing to the currency – a fiscal mechanism, but one that comes into play only as a backstop. Indeed that backing does not have to be certain. Cochrane ( 2011 , 2019 ), however, argues that this result is wrong, and that fractional currency backing is a Maginot line that is insufficient to rule out hyperinflation. We show here why, in fact, his analysis involves a subtle change in model specification that adds a distinct monetary fragility to our model. Our baseline analysis uses a canonical money-in-the-utility-function setup due to Brock ( 1974 , 1975 ), but following Wallace (1981) , we show the same results go through in an overlapping-generations model of money.

This paper extends the exact equivalence result between the allocations realized by self-fulfilling mechanisms and rational expectations equilibrium allocations in Forges and Minelli (1997) to a large finite-agent replica economy where different replicas of the same agent are allowed to receive different private information. The first result states that the allocation realized by any incentive compatible self-fulfilling mechanism is an approximate rational expectations equilibrium allocation. Conversely, the second result states that, given any rational expectations equilibrium satisfying a “uniform continuity” condition on the equilibrium price, one can construct an approximate incentive compatible self-fulfilling mechanism whose equilibrium allocation coincides with the rational expectations equilibrium allocation for all non-monetary commodities.

The paper demonstrates the generic existence of general equilibria in incomplete financial markets with asymmetric information. The economy has two periods and an ex ante uncertainty over the state of nature to be revealed at the second period. Securities pay off in cash or commodities at the second period, conditionally on the state of nature to be revealed. They permit transfers across periods and states, which are typically insufficient to span all state contingent claims to value, whatever the spot price to prevail. Under the standard smooth preference and perfect foresight assumptions, the paper shows that equilibria exist, except for a closed set of measure zero of securities and endowments. This theorem generalizes Duffie and Shafer ’s ( 1985 ) to arbitrary financial and information structures. The equilibrium prices are consistent with any collection of state prices and norm values on spot markets. This refinement permits to extend to asymmetric information Cass’ (1984) theorem that any collection of state prices supports an equilibrium on purely financial markets.

This paper computes semiparametric efficiency bounds for finite-dimensional parameters in discrete choice models with nonparametric regressors in the form of conditional expectations. These can include expectations about exogenous events as well as expectations about the choices of other agents. Thus, the models studied here include incomplete-information games, social-interactions models as well as single-agent discrete choice models with uncertainty as special cases. Our bounds rely on the assumption of rational expectations and on regularity conditions of equilibrium beliefs. The paper focuses on binary-choice models but the derivation of the bounds illustrates how our approach can be extended to multinomial choice cases. Explicit efficiency bound expressions for the models examined here had not been derived before. Furthermore, since we also characterize the efficient influence functions, our results can also potentially be used to construct semiparametrically efficient estimators for these models.

A consumer’s decision to engage in search depends on the beliefs the consumer has about an unknown product characteristic (e.g., price). Because beliefs are rarely observed, researchers typically assume that consumers have rational expectations or update beliefs consistent with Bayesian updating. These assumptions are restrictive and do not enable the researcher or the retailer to price discriminate among consumers on the basis of heterogeneity in beliefs. The authors use Monte Carlo experiments to show how these assumptions affect estimates of search cost. Next, they design an incentive-aligned online study in which participants search over the price of a homogeneous good, and the authors elicit distributions of price beliefs before and after each search. Drawing on data collected from a nationally representative panel, they find substantial heterogeneity in prior price beliefs, such that participants update their beliefs in response to search outcomes but deviate from Bayesian updating in that they underreact to new information. Importantly, the authors show that (1) assuming Bayesian updating does not significantly bias search cost estimates at the aggregate level if the researcher accounts for heterogeneous prior beliefs, (2) eliciting heterogeneity in prior expected prices is much more important than eliciting heterogeneity in prior price uncertainty, and (3) a retailer can increase profits through third-degree price discrimination by recognizing the heterogeneity in prior beliefs.

The Rebuilding Macroeconomic Theory Project, led by David Vines and Samuel Wills (2020), is an important, albeit long overdue, initiative to rethink a failing mainstream macroeconomics. Professors Vines and Wills, who must be congratulated for stepping up to the challenge of trying to make mainstream macroeconomics relevant again, call for a new multiple-equilibrium and diverse (MEADE) paradigm for macroeconomics. Their idea is to start with simple models, ideally two-dimensional sketches, that explain mechanisms that can cause multiple equilibria. These mechanisms should then be incorporated into larger DSGE models in a new, multiple-equilibrium synthesis – to see how the fundamental pieces of the economy fit together, subject to it being ‘properly micro-founded’. This paper argues that the MEADE paradigm is bound to fail, because it maintains the DSGE model as the unifying framework at the center of macroeconomic analysis. The paper reviews 10 fundamental weaknesses inherent in DSGE models which make these models irreparably useless for macroeconomic policy analysis. Mainstream macroeconomics must put DSGE models, once and for all, in the Museum of Implausible Economic Models – and learn important lessons from non-DSGE macroeconomic approaches.

I develop an adaptive learning model to study the welfare effects of Social Security policy uncertainty in an aging economy. Agents combine full knowledge of the political process (which Social Security reforms are possible and when they could occur) with limited knowledge about the structure of the economy. The adaptive learning amplifies cyclical dynamics along the transition path to the new steady state. This magnifies the welfare effects of policy uncertainty, compared to a standard rational expectations model. The ex-ante consumption equivalent variation that equates the expected utility of consumption (with policy uncertainty) to the utility of expected consumption (across the possible policies without uncertainty) ranges between -0.29% and 0.21% of lifetime consumption in the adaptive learning model compared to -0.012% to -0.018% in the standard model. The welfare cost to future generations is also larger in the adaptive learning model compared to the rational model.

This study extends the hybrid version of the baseline New-Keynesian model with heterogeneous agents who may adopt various forecast heuristics. With a focus on consumer expectations, we identify the most appropriate pairs of forecast heuristics that can lead to an equivalent fit to the data compared with the model specification under rational expectations. The competing specifications are estimated using the simulated method of moments. Our empirical results suggest that expectations under bounded rationality in the United States are grounded on consumers’ emotional state, while for the Euro Area they are technical in nature. This observation questions the need for a hybrid model specification under rational expectations.

This study tries to verify the predictive power of the implicit forward rate of the term structure of interest rates in Africa. We used data from Egypt, Ghana, Kenya, Nigeria and the Republic of South Africa. A modified version of the yield term premium and the forward term premium models of Shiller and McCulloch (1990) were used to test the predictive power of the implicit forward rate, rather than the rational expectations hypothesis. We both used FMOLS and DOLS estimators, since they are more consistent than OLS with non-stationary series. The overall results show that the implicit forward rate does not have a significant predictive power in Africa. It therefore appears that operators on African markets should not rely on those predictions.

Recognizing that inflation of the value of output and its costs of production must be equal, we focus on a cost-based macroeconomic structuralist approach in contrast to micro-oriented monetarist analysis. For decades the import and profit shares of cost have risen, while the wage share has declined to around 50% with money wage increases lagging the sum of growth rates of prices and productivity. Conflicting claims to income are the underlying source of inflationary pressure. Inflation affects income (labor’s spending power) and wealth. Monetarist theory around 1900 concentrated on the latter (Bryan and the “Cross of Gold)” leading to the standard Laffer curve. It was replaced by the Friedman-Phelps model which has incorrect dynamics (labor payments do not fall during an expansion – they go up). Samuelson and Solow introduced a version of the Phillips curve that violates macroeconomic accounting. Rational expectations replaced Friedman but was immediately falsified by output drops after the Volcker shock treatment around 1980. There followed a complicated transition from rational expectations to inflation targeting, anchored by economists’ misunderstanding of the physical meaning of ergodicity and ontological blindness. It did not help that the real balance effect is irrelevant because money makes up a small part of wealth. Rather than issuing veiled threats of disaster if its policy advice is not followed, the Fed now announces inflation targets which it cannot meet. Contemporary structuralist theory suggests that conflicting income claims set the inflation rate. Firms can mark up costs but workers have latent bargaining power over the labor share that they can exercise. Import costs and policy repercussions complicate the picture, but a simple vector error correction model and visual analysis suggest that money wages would have to grow one percentage point faster than prices plus productivity for several years if the Fed is to meet a three percent inflation target. The results pose a Biden policy trilemma: (i) the only path toward a more egalitarian size distribution of income is through a rising labor share (money wage growth exceeds price plus productivity growth), (ii) which would provoke faster inflation with feedback to rising interest rates, and (iii) the resulting asset price deflation likely facing political resistance from Wall Street and affluent households.

Purpose This paper aims to analyse the stabilizing macroeconomic effects of economic policies during the COVID-19 crisis in Spain. Design/methodology/approach The contribution of the structural shocks that explain the behaviour of the main macroeconomic aggregates during 2020 are estimated, and the effects of economic policies are simulated using a dynamic stochastic general equilibrium (DSGE) model estimated for the Spanish economy. Findings The results highlight the importance of supply and demand shocks in explaining the COVID-19 crisis. The annual fall in gross domestic product (GDP) moderates at least by 7.6 points in the most intense period of the crisis, thanks to these stabilizing policies. Finally, the potential effects of Next Generation EU in the Spanish economy are estimated. Assuming that Spain may receive from the EU between 1.5 and 2.25 percentage points (pp) of GDP, activity could increase to between 2 and 3 pp in 2024. Originality/value To the best of the authors’ knowledge, the exercises and findings are original. All these results show the usefulness of a DSGE model, such as the estimated rational expectation model for Spain, as a practical tool for the applied economic analysis, the macroeconomic assessment of economic policies and the understanding of the Spanish economy.

The standard search and matching model with rational expectations is well known to be unable to generate amplification in unemployment and vacancies. We document a new feature that cannot be replicated: properties of wage forecasts published by institutions in the near term. A parsimonious model with adaptive learning can provide a solution to both of these problems. Firms choose vacancies by forecasting wages using simple autoregressive models; they have greater incentive to post vacancies at the time of a positive productivity shock because of overoptimism about the discounted value of expected profits.

The article is devoted to modeling the level of long term wages changes expectations of employees, depending on events in their life or in society (channels of wage mobility) which are caused the corresponding expectations. The shadow price of different wage mobility channels is calculated. Shadow price is considered as a cost for the state and society caused by social expectations of the channels profitability. Two approaches to measuring the shadow price are proposed when shadow price recognized: (a) as a societal characteristic that reflects the gap between the expectations associated with the use of certain mobility channels and the basic (minimum) level of social expectations in society or (b) as a characteristic that means the difference between individual wage expectations and the prediction of wages based on the minimum individual life chances on the labor market. We consider channels of wage mobility with internal and external locus of expectations' formation (individual changes vs. changes in the macro environment) and with the source of changes determined by individual activity or the natural course of events (intentional vs. inertial changes). We are also focusing on the wage mobility channels that reflect the social expectations of realizing the "protective" policy by the state. The calculations are based on data of mass survey conducted in May–June 2018 using national representative quota sample.

Higher signal precision helps to predict returns more accurately. But higher signal precision requires higher more costs and longer time. The acquisition of higher precision signals has two opposite effects for investors. First, the higher precision helps with return forecast. Second, the longer processing time is a disadvantage for decision making. We build a rational expected model under the assumption that the longer processing time takes, the higher the signal precision. The results show that higher signal precision is not always better after considering signal processing time. There is an optimal signal waiting time for investors.

This paper provides a look into what Lucas meant by the term ‘analogue systems’ and how he conceived making them useful. It is argued that any model with remarkable predictive success can be regarded as an analogue system, the term is thus neutral in terms of usefulness. To be useful Lucas supposed models to meet further requirements. These prerequisites are introduced in two steps in the paper. First, some properties of ‘useless’ Keynesian macroeconometric models come to the fore as contrasting cases. Second, it is argued that Lucas suggested two assumptions as the keys to usefulness for he conceived them as referring to genuine components of social reality and hence as true propositions. One is money as a causal instrument and the other is the choice-theoretic framework to describe the causal mechanisms underlying large-scale fluctuations. Extensive quotes from Lucas’s unpublished materials underpin the claims.

Rationality is one of the main assumptions in economics, and is represented as the rational expectation in macroeconomics. As such, it is important to note that the effectiveness of economic policy depends on the degree of economic agents’ rationality. According to this point of view, it is only natural to ask how the central bank views economic agents to be either rational or bounded rational. In implementing economic policies, it is possible to assume that the central bank views economic agents to be bounded rational. This is due to the fact that most theoretical arguments state that policy under rationality is not as effective as one under bounded rationality. Based on this argument, this paper employs bounded rational New Keynesian Model proposed by Gabaix to know if rationality matters to the central bank. As a result, as long as the central bank does not follow the full gradualism, it is possible to conclude that the rationality matters to the central bank. However, it is not anymore if the central bank employs full gradualism in monetary policy rule.

In an asymmetric duopoly with quantity competition such that consumers form expectations about network sizes before and after the owners of both firms choose their incentive parameters (fulfilled a...

The presented study addresses the problem of the correlation between the economic interests of market transaction participants and the market expectations of the seller and the buyer. Innovative balance indices of price and quantity are proposed to be used as a tool for solving this problem.Aim. The study aims to show how the balance indices of price and quantity can be used to achieve a parity compromise in market transactions with a fixed purchase and sale budget, which is the optimal result for the seller and the buyer and ensures the stability of mutually beneficial market relations between economic agents.Tasks. To achieve the set aim, the authors analyze the commodity-money balance of interests and its structure from the perspective of the seller and the buyer; substantiate the need to build a balance of market expectations; assess the possibility of using the index method as a synthetic method to resolve (according to Hegel) contradictions between interests and expectations by combining them.Methods. This study uses methods of mathematical analysis, numerical methods of approximate evaluation of functions, index method, method of analogies, provisions of theories of adaptive and rational expectations.Results. The Laspeyres and Paasche indices can be interpreted as changes in the adaptive and rational expectations of economic agents respectively. It is proved that the balance indices of price and quantity are the coordinates of the point of parity compromise, where “pure” and “mixed” market expectations and economic interests of the seller and the buyer converge.Conclusions. It is established that in market transactions with a fixed budget, the balance of economic interests on a compensatory basis is beneficial for the seller and absolutely not beneficial for the buyer. In order for the balance of interests to be beneficial for both participants of the transaction, it must be viewed through the prism of the balance of market expectations. Balance indices of price and quantity serve as a tool that establishes a connection between the balances of market expectations and economic interests.

Purpose This paper aims to investigate the behavior of volatility of Islamic equity indices toward fundamental risk factors. It focuses on the degree and structure of sensitivity to commodity price changes, global risk perception and term premium and whether crises and fragility periods have shaped the degree and structure of this sensitivity. Design/methodology/approach Quantile regression incorporating structural changes and GARCH-class model are used to establish how sensitivities are varying across volatility distribution depending on global events. The data are daily series of return indices, over the period spanning from January 1, 2001 until January 22, 2018. Findings The results show significant sensitivity to fundamental factors. The sensitivity is identified for different regional indices and intensified across quantiles. Speculation has shaped the structure of sensitivity at normal time, but correction holds at time of crisis. The results reveal that even if they share common features, commodities cannot be considered as homogeneous asset class. Indeed, the exact relationship cannot be observed at normal time in presence of speculation and information delay. However, at time of financial fragility and periods of crisis, the sensitivity is assigned with the plausible sign. Practical implications The obtained results present several policy implications as well for academics, portfolio managers and policy-makers. It opens new research paths for academic research, it helps in investment decisions, provides lessons for portfolio diversification, both for price discovery and hedging. The results serve as well to implement effective macroeconomic stabilization policies and even fiscal policies to counteract any inflationary impact of fundamental price changes on investors and Islamic banks. Originality/value This paper contributes to empirical literature by dealing with the sensitivity of Islamic equity indices to commodity prices and term premium along with the effect of investor sentiment. It pays attention to the financial stability of Islamic stock markets by investigating the sensitivity at normal time, during fragility periods and periods of crisis. It considers the financialization process of commodity markets and includes the term premium to control for rational expectations on term structure of interest rates and the VIX (Volatility index) as global risk perception to control for safety and risk aversion.

We propose a novel interpretation and formalization of Kahneman and Tversky's findings in the Linda experiment which implies that subjects are rational in the sense of Muth's hypothesis and provides an approach to specifying rational assessment of uncertainty in macroeconomic models. Behavioral-finance theorists have appealed to Kahneman and Tversky's findings as an empirical foundation for a general approach replacing rational expectations. We show that behavioral models' specifications of participants' irrational forecasts and predictable errors are incompatible with Kahneman and Tversky's findings. Our interpretation of Kahneman and Tversky's findings is supportive of Lucas's compelling critique of inconsistent macroeconomic models.

Significance Prices in asset markets reflect a combination of investor beliefs and their risk preferences. Researchers, as well as policymakers, look to asset market data as a barometer of public beliefs. Such data are informative because investors must be compensated for exposure to macroeconomic shocks, and thus beliefs about future macroeconomic performance are encoded in asset prices. This paper develops a method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We entertain families of potential belief distortions bounded by a statistical measure of divergence. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative., This paper develops a method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We step back from presuming rational expectations and entertain potential belief distortions bounded by a statistical measure of discrepancy. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative. Within our framework, market-implied beliefs may differ from those implied by rational expectations due to behavioral/psychological biases of investors, ambiguity aversion, or omitted permanent components to valuation. Formally, we represent evidence about investor beliefs using a nonlinear expectation function deduced using model-implied moment conditions and bounds on statistical divergence. We illustrate our method with a prototypical example from macrofinance using asset market data to infer belief restrictions for macroeconomic growth rates.

The rational expectations revolution was not only based on the introduction of Muth’s idea of rational expectations to macroeconomics; the introduction of Muth’s hypothesis cannot explain the more drastic change of the mathematical toolbox and concepts, research strategies, vocabulary, and questions since the 1980s. The main claim is that the shift from “Keynesian economics” to “new classical economics” is based on a shift from a control engineering approach to an information engineering methodology. The paper even shows that the “revolution” was more radical. The change of engineering tools has changed macroeconomics more deeply, not only its methodology but also its epistemology and ontology. To show this shift in epistemology and ontology, the history of economics will be interwoven with the history of mathematics which cannot be detangled from the emergence of the digital computer and the influence of this emergence on the changed nature of mathematics: the adoption of a new concept of solution, no longer a number, a formula, or a function, but an algorithm. The result of this new concept of solution was a new approach to the analysis of processes. Information engineering studies the fundamental limits in communication and finds its origins in Shannon’s theory of communication, and incorporates the tools designed by Turing, Shannon, Kalman, and Bellman. The resulting ontology of this kind of engineering is a world populated by machines that communicate with each other by exchanging information. This information does not, however, contain only signals about the system states but also noise that needs to be filtered out. It is not a deterministic world, but one governed by stochastic processes. The decisions these machines take is conditioned on the (noisy) information they have about the current state of the world but at the same time will affect future states. Policy in this world therefore means tracing an optimal trajectory taking all these issues into account.

We study the dynamic optimization of platform pricing in industries with positive direct network externalities. The utility of the network for the consumer is modeled as a function of three components. Platform price and participation rate affect the consumer’s decision to join the platform. The platform operator is assumed to know the consumer’s sensitivities with respect to these components. In addition, the consumer’s utility is a function of other attributes, such as network privacy policies and environmental effects of the service. We assume that the distribution of these unobserved preferences in the potential customer base is known to the platform operator. We show analytically how the unobserved preferences affect the dynamic platform price design. Both static and rational expectations with respect to the platform participation are presented. We simulate an electricity market demand side management service application and show that the platform operator sets low prices in the launch phase. The platform operator can set higher launching prices if it can affect customers’ preferences, expectations or adjustment friction.

This paper is motivated by the fact that the standard deviation of cyclical TFP derived from the standard approach under the stochastic trend is not even close to the real-world data. The main part of the paper devotes to developing a new method to apply geometric Brownian motion to characterize TFP in continuous time and converting it to an estimated process of random walk with drift. As a result, the drift estimate together with the lagged TFP in the random walk process are the stochastic trend of TFP and the stochastic error term in the random walk with drift process is the cyclical component of TFP. I then have two findings: the first one is that the standard deviation of cyclical TFP derived from the new approach is much closer to the real-world data; the second one is that stochastic trend of TFP can be decomposed into three parts: an initial value, a deterministic trend, and a term involved with Weiner process. Moreover, this paper argues that, by recalculating the business cycle statistics based on a rational expectations model, if we remeasure the stochastic trend and cyclical component of TFP using the new approach, then the ability of real business cycle model to mimic real-world economic fluctuations will be significantly improved.