Refining linear rational expectations models and equilibria

This paper develops the case for forward convergence as a model refinement scheme for linear rational expectations models and an associated no-bubble condition as a solution selection criterion. We relate these two concepts to determinacy and characterize the complete set of economically relevant rational expectations solutions to the linear rational expectations models under determinacy and indeterminacy. Our results show (1) why a determinate solution is economically cogent in most, but not all, cases, and (2) that those models that are not forward-convergent have no economically relevant solutions.     

Money demand, the Cagan model, testing rational expectations vs adaptive expectations: The case of Turkey

This paper estimates the Cagan type demand for money function for Turkish economy during the period 1986:1–1995:3 and tests whether Cagan's specification fits the Turkish data using an econometric technique assuming that forecasting errors are stationary. This paper also tests the hypothesis that monetary policy was implemented in aiming to maximize the inflation tax revenue. Finally, the Cagan model is estimated with the additional assumption of rational expectations for Turkey for the considered period. First version received: March 1998/final version received: October 1998     

Beauty contest,bounded rationality,and sentiment pricing dynamics

We present a dynamic asset pricing model that incorporates investor sentiment, bounded rationality and higher-order expectations to study how these factors affect asset pricing equilibrium. In the model, we utilize a two-period trading market and investors make decisions based on the heterogeneous expectations principle and the “sparsity-based bounded rational” sentiment. We find that bounded rationality results in mispricing and reduces it in next period. Investor sentiment produces more significant effects than private signals, optimistic investor sentiment increases hedging demand, thus causing prices to soar. Higher-order investors are more rational and attentive to the strategies of other participants rather than private signals. This model also derives the dampening effect of higher-order expectations to price volatility and the heterogeneity expectation depicts inconsistent investor behavior in financial markets. In the model, investors' expectations about future price is distorted by their sentiment and bounded rationality, so they obtain a biased mean from the signal extraction.     

When does the cost channel pose a challenge to inflation targeting central banks?

In a sticky-price model where firms finance their production inputs, there is both a lower and an upper bound on the central bank's inflation response necessary to rule out the possibility of self-fulfilling inflation expectations. This paper shows that real wage rigidities decrease this upper bound, but coefficients in the range of those on the Taylor rule place the economy well within the determinacy region. However, when there is time-variation in the share of firms who finance their inputs (i.e. Markov-switching) then inflation targeting interest rate rules frequently result in indeterminacy, even if the central bank also targets output. Adding a nominal growth target to the policy rule can often alleviate this indeterminacy and therefore anchor inflation expectations.     

Model reference adaptive expectations in Markov-switching economies

This paper offers a theory of model reference adaptive beliefs as a selection device in Markov-switching economies under equilibrium indeterminacy. Consistent with the classical rational choice paradigm, our theory requires that endogenous expectations be replaced with a general-measurable function of the observable states of the model, to be determined optimally. This forecasting function is derived as the regime-independent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight state motion (the reference model). We show that model reference adaptive expectations always generate a rational expectations equilibrium, irrespective of the presence of nonlinearities and/or imperfect information. Under equilibrium indeterminacy, this forecasting mechanism enforces the unique mean-square stable solution producing nearly perfect-foresight dynamics.     

Wealth in utility,the Taylor principle and determinacy

Wealth in the utility function leads to the discounting to consumer’s Euler equation, enlarging determinacy regions and making it easier for the monetary authority to ensure equilibrium determinacy. We show that a passive policy rule which adjusts nominal interest rate by less than one-for-one in response to the inflation rate is able to rule out equilibrium indeterminacy, if properly specified, due to the presence of the demand channel of the Taylor principle and equilibrium determinacy. Furthermore, the extent to which monetary policy rule can be passive in order to avoid indeterminacy depends critically on the degree of preference over wealth as well as the underlying structures and parameters of the model.     

Business cycle amplification with heterogeneous expectations

This paper studies the implications for business cycle dynamics of heterogeneous expectations in a stochastic growth model. The assumption of homogeneous, rational expectations is replaced with a heterogeneous expectations model where a fraction of agents hold rational expectations and the remaining fraction adopt parsimonious forecasting models that are, in equilibrium, optimal within a restricted class. Our approach nests the literature on rational expectations in business cycle models with a recent approach based on adaptive learning. We demonstrate that (i.) heterogeneous expectations can lead to substantial improvement in the internal propagation of equilibrium business cycle models and (ii.) the internal propagation depends on the degree of heterogeneity. A calibrated model with heterogeneity provides a closer fit to business cycle data than its representative agent, rational expectations counterpart.     

Real Indeterminacy in Monetary Models with Nominal Interest Rate Distortions

This paper demonstrates that in a standard flexible-price monetary model there exists real indeterminacy whenever the nominal interest rate moves too closely with either current or forecasted inflation. However, an aggressive response to lagged inflation will ensure determinacy. These conclusions are robust to a wide range of calibrations, and a monetary environment that allows for endogenous velocity. The results are affected by the inclusion of investment spending in the transactions constraint. Journal of Economic Literature Classification Numbers: E4, E5.     

Term structure and forward guidance as instruments of monetary policy

This paper studies a simple monetary model with a Ricardian fiscal policy in which equilibria are indeterminate if monetary policy consists solely of a rule for fixing the short-term interest rate. We introduce explicitly into the model the agents’ expectations of inflation which create the indeterminacy and show that there are two types of policies—a term structure rule or a forward guidance rule for the short rate—which lead to determinacy. The first consists in fixing the interest rates on a family of bonds of different maturities as function of realized inflation; the second consists in fixing the short-term interest rate and the expected values of the short-term interest rate for a sequence of periods into the future as a function of realized inflation. If the monetary authority chooses an inflation process that satisfies conditions derived in the paper and applies one of these rules, it anchors agents’ expectations to this process, in the sense that it is the unique inflation process compatible with equilibrium when the interest rates or expected future values of the short rate are those specified by the term structure or forward guidance rule.     

WHEN DOES DETERMINACY IMPLY EXPECTATIONAL STABILITY?

Since the introduction of rational expectations, there have been issues with multiple equilibria and equilibrium selection. We study the connections between determinacy of rational expectations equilibrium and learnability of that equilibrium in a general class of purely forward‐looking models. Our framework is sufficiently flexible to encompass lags in agents' information and either finite horizon or infinite horizon approaches to learning. We are able to isolate conditions under which determinacy does and does not imply learnability and also conditions under which long‐horizon forecasts make a clear difference for learnability. Finally, we apply our result to a relatively general New Keynesian model.     

Asset prices,nominal rigidities,and monetary policy

Should monetary policy respond to asset prices? This paper analyzes this question from the vantage point of equilibrium determinacy. A central bank responding to asset prices is indirectly responding to firm profits. In a model with sticky prices, increases in inflation tend to lower firm profits so that a central bank responding to share prices implicitly weakens its overall response to inflation. This is the novel source of equilibrium indeterminacy highlighted in the paper.     

Wicksellian Rules and the Taylor Principle: Some Practical Implications*

In this paper, we derive and compare the determinacy regions of price-level targeting rules (Wicksellian rules) and Taylor rules in a standard New Keynesian model. We conclude that Wicksellian rules do not require the Taylor principle to hold in order to induce determinacy. Our results have two implications. First, in a univariate setting, the estimation of simple Taylor rules when the true rule is Wicksellian can lead to the erroneous conclusion that the equilibrium is indeterminate. Second, indeterminacy is ruled out when using system-based methods, but it can be concluded that the central bank is less averse to inflation movements than it actually is.     

A Characterization of the Dynamical System in a Two-sector Overlapping-generations Model: The Case of Unbounded Growth

This paper characterizes perfect-foresight equilibria in a two-sector overlapping-generations economy for the case of unbounded growth. The analysis demonstrates that gross substitutability in consumption is not sufficient to ensure the determinacy of equilibrium. Unlike Boldrin and Rustichini (1994), indeterminacy of equilibria can arise within the framework of an overlapping-generations model with convex technology. The finite time horizon of agents is the source of such indeterminacy.
JEL Classification Number: 041.     

Fiscal Rules,Interest Payments on Debt,and the Irrelevance of the Taylor Principle

We show that in New Keynesian models with non‐neutral government debt, the Taylor principle ceases to be relevant for equilibrium determinacy if the government follows a fiscal rule of levying taxes in proportion to its interest payments on existing debt. This is in contrast with previous studies, which typically have assumed that taxes respond to the level of debt, and have found either a confirmation or reversal of the Taylor principle depending on the feedback from debt to taxes. We find, instead, that the equilibrium effect of the interest rate on debt is crucial for determinacy. If, as in our model, taxes are raised in response to debt interest payments, the range of indeterminacy monotonically decreases with the fiscal feedback parameter. When interest payments are completely tax‐financed, indeterminacy is ruled out without any restrictions on monetary policy.     

The demand for money during a period of inflationary expectations. Some FIML based estimates for Greece

This paper estimates and tests a model of the demand for money function, which uses the public's expectations of future inflation as a proxy of the opportunity cost of holding money. The hallmark of the paper is that expectations are rational inMuth sense. The cross-equation rational expectations restrictions are derived and then tested, using quarterly Greek data of the high inflation period 1973I to 1981 IV. The paper concludes that the evidence is consistent with the rational expectations assumption and supports the adopted specification of the money demand function.     

The Liverpool macroeconomic model of the United Kingdom

The paper describes the Liverpool Model, a rational expectations model of the UK economy used for forecasting since March 1980. The model is of the ‘new classical’ type, in that all markets clear; in the labour market, there is a union sector with one-year nominal wage contracts but the non-union sector clears excess demands. Equilibrium (or ‘natural rate’) values of output, employment, real wages, etc are endogenously determined. In- and out-of-sample errors, a full set of simulations, and a complete listing are included. The interim experience of the model as a test bed for rational expectations methods is ‘far from discouraging’.     

Useful Government Spending and Macroeconomic (In)stability under Balanced-Budget Rules

It has been shown that an otherwise standard one‐sector real business cycle model may exhibit indeterminacy and sunspots under a balanced‐budget rule that consists of fixed and “wasteful” government spending and proportional income taxation. However, the economy always displays saddle‐path stability and equilibrium uniqueness if the government finances endogenous public expenditures with a constant income tax rate. In this paper, we allow for productive or utility‐generating government purchases in either of these specifications. It turns out that the previous indeterminacy results remain unchanged by the inclusion of useful government spending. By contrast, the earlier determinacy results are overturned when public expenditures generate sufficiently strong production or consumption externalities. Our analysis thus illustrates that a balanced‐budget policy recommendation which limits the government's ability to change tax rates does not necessarily stabilize the economy against belief‐driven business cycle fluctuations.     

Global and local determinacy in a one-step forward looking New Keynesian model

In this paper we consider a New Keynesian model for optimal monetary policy in a staggered fashion. We provide the relations of a non linear model of general economic equilibrium, implementing a suitable Taylor-type interest rate rule. We characterize the conditions that guarantee local determinacy and explore conditions under which local bifurcations of the target equilibrium may occur. Afterwards, we argue how local determinacy might be associated with global indeterminacy, providing some numerical examples.     

Indeterminate forecast accuracy under indeterminacy

This paper studies whether the observed time variation in the forecast accuracy of macro-econometric models can be reconciled with the monetary policy stance that induces (in)determinacy in stylized DSGE models. Using a small-scale New Keynesian monetary framework as laboratory and structural parameters calibrated to the estimates obtained on U.S. data from different macroeconomics regimes, we exploit reduced-form econometric models – such as Vector Autoregressions – to assess their regime-specific forecastability. We show that conducting (pseudo) out-of-sample forecast comparisons in the presence of indeterminacy is a non-trivial exercise, even when sunspot shocks play no role in generating the data. Overall, our simulation experiment suggests that equilibrium indeterminacy need not lead to superior (absolute or relative) forecast accuracy. This finding challenges the view that the deteriorating performance of forecast models over the Great Moderation relative to the Great Inflation was entirely due to changes in the U.S. monetary policy.     

Macroeconomic expectations and time varying heterogeneity:evidence from individual survey data

ABSTRACT

The goal of this paper is to investigate forecast heterogeneity and time variability in the formation of expectations using disaggregated monthly survey data on macroeconomic indicators provided by Bloomberg from June 1998 to August 2017. We show that our panel of forecasters are not rational and are moderately heterogeneous and thus confirm that previously well-established results on asset prices hold for macroeconomic indicators. We propose a flexible hybrid forecast model defined at any time as a combination of the extrapolative, regressive, adaptive and interactive heuristics. Controlling for endogenous structural breaks, we find that experts adjust their forecast behaviour at any time with some inertia in extrapolative and adaptive profiles. Changes in the formation of expectations are triggered mostly by financial shocks, and uncertainty is dealt with by using complex processes in which the fundamentalist component overweighs chartist activity. Forecasters whose models combine different relevant rules and display high temporal flexibility provide the most accurate forecasts. Authorities can then stabilize the domestic markets by encouraging fundamentalists’ forecasts through increased transparency policy.