Signal Extraction Problem Research Articles

Aggregate Output Stability: Divergent Perspectives

The main objective of this article was to describe two asymmetric perspectives of the aggregate imbalance approach. Starting from the contrast of the Rational Expectations and Keynesian approaches, we analyze the characterization that the general reserve makes of the causes of inflation and the implications that it has on economic policy decisions. From the rational expectations approach, companies and workers form a kind of coherent group that jointly experiences fluctuations in the prices of their products and faces in unison the problem of signal extraction. On the other hand, the Keynesian approach to effective demand explains price fluctuations in principle as an expression of insufficient demand that generates involuntary unemployment. It was identified that the increase in margins during 2021 sought to pass on to consumers and end users of the goods and services of oligopolistic structures the increase in marginal costs induced by the fall in effective demand; resulting in an effect of price increases on the supply side or cost inflation.

Research on the Depth Image Reconstruction Algorithm Using the Two-Dimensional Kaniadakis Entropy Threshold.

The photon-counting light laser detection and ranging (LiDAR), especially the Geiger mode avalanche photon diode (Gm-APD) LiDAR, can obtain three-dimensional images of the scene, with the characteristics of single-photon sensitivity, but the background noise limits the imaging quality of the laser radar. In order to solve this problem, a depth image estimation method based on a two-dimensional (2D) Kaniadakis entropy thresholding method is proposed which transforms a weak signal extraction problem into a denoising problem for point cloud data. The characteristics of signal peak aggregation in the data and the spatio-temporal correlation features between target image elements in the point cloud-intensity data are exploited. Through adequate simulations and outdoor target-imaging experiments under different signal-to-background ratios (SBRs), the effectiveness of the method under low signal-to-background ratio conditions is demonstrated. When the SBR is 0.025, the proposed method reaches a target recovery rate of 91.7%, which is better than the existing typical methods, such as the Peak-picking method, Cross-Correlation method, and the sparse Poisson intensity reconstruction algorithm (SPIRAL), which achieve a target recovery rate of 15.7%, 7.0%, and 18.4%, respectively. Additionally, comparing with the SPIRAL, the reconstruction recovery ratio is improved by 73.3%. The proposed method greatly improves the integrity of the target under high-background-noise environments and finally provides a basis for feature extraction and target recognition.

A model of greedflation

I present a model where desired markups increase with the volatility of the general price level. Confronted with a change in the price of a good, consumers solve a signal extraction problem to infer the good’s relative price. Yet general price volatility obscures price signals, and consumers attribute part of any price change to variation in the price level. This confers firms with greater market power, which in turn raises the aggregate profit share and magnifies inflationary shocks. These predictions are in line with recent empirical evidence.

A theory-based method to evaluate the impact of central bank inflation forecasts on private inflation expectations

We propose a theory-based method to assess the impact of central banks’ inflation forecasts on private inflation expectations. We use regressions derived from a leader-follower model with noisy information and public signals. The leader is the Central Bank (CB), which solves a signal extraction problem to estimate the rational expectation of inflation. Private agents then act by solving an analogous problem to estimate this same value by using their own information and the forecasts disclosed by the CB. The method allows for estimating the structural parameters that characterize noisy information models, which are hard to estimate using purely econometric tools. It also sheds light on the issue of the alleged CB’s superiority in predicting inflation behavior.

Zombification and Central Bank Risk Taking: The LOLR as a Signal Extraction Problem

Zombification and Central Bank Risk Taking: The LOLR as a Signal Extraction Problem

Indeterminacy and imperfect information

We study equilibrium determination in an environment where two types of agents have different information sets: Fully informed agents observe histories of all exogenous and endogenous variables. Less informed agents observe only a strict subset of the full information set and need to solve a dynamic signal extraction problem to gather information about the variables they do not directly observe. Both types of agents know the structure of the model and form expectations rationally. In this environment, we identify a new channel that generates equilibrium indeterminacy: Optimal information processing of the less informed agent introduces stable dynamics into the equation system that lead to self-fulling expectations. For parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium is indeterminate. We illustrate our framework with monetary policy models where an imperfectly informed central bank follows an interest rate rule.

Research on the Weak Signal Extraction Method with Adaptive Stochastic Resonance Based on the Time Grid Sensor for PMSM

Because the output signal of the time grid sensor is so weak and is easily affected by the disturbing noise, it is difficult to extract the induction signal containing the position information, when the time grid sensor is used to detect the rotor position of the permanent magnet synchronous motor (PMSM). In this paper, an adaptive monostable stochastic resonance method is proposed to realize the weak signal detection of the time grid sensor. The tunnel magnetoresistance effect sensor (TMR) is adopted to detect the change of the rotor magnetic field of the motor in this method, and the detection model of the time grid sensor about PMSM is constructed. The monostable stochastic resonance theory is applied to extract the induction signal of the time grid sensor. As to the problem of the tuning the parameters of the monostable stochastic resonance system, the genetic algorithm is adopted to optimize the parameters of the monostable stochastic resonance system. The experimental results show that the monostable stochastic resonance method based on the genetic algorithm can effectively detect the weak induction signal of the time grid sensor about PMSM. This method solves the problem of the weak signal extraction of the time grid sensor for PMSM, and the detection accuracy is also improved.

The cyclicality of entry and exit: The role of imperfect information

In the U.S. manufacturing sector, the entry margin is strongly procyclical, whereas the exit margin is acyclical. This study attempts to explain the entry-exit margin asymmetry. It introduces imperfect information in an industry equilibrium model and finds that potential entrants cannot disentangle aggregate productivity from their own productivity, inducing a signal extraction problem. With imperfect information on the aggregate productivity, potential entrants underestimate variations in equilibrium factor prices and overestimate variations in the value of entering. This amplified entry margin, combined with a reasonable amount of general equilibrium forces, mute cyclical variations in the exit margin. With the proposed mechanism, the model economy generates 28% of the observed variations in the entrants’ productivity. Notably, several testable implications of the model economy are consistent with the properties of the U.S. data.

Anchored Inflation Expectations and the Slope of the Phillips Curve

We estimate a New Keynesian Phillips curve that allows for changes in the degree of anchoring of agents' subjective inflation forecasts. The estimated slope coefficient in U.S. data is stable over the period 1960 to 2019. Out-of-sample forecasts with the model resolve both the "missing disinflation puzzle" during the Great Recession and the "missing inflation puzzle" during the subsequent recovery. Using a simple New Keynesian model, we show that if agents solve a signal extraction problem to disentangle transitory versus permanent shocks to inflation, then an increase in the policy rule coefficient on inflation serves to endogenously anchor agents' inflation forecasts. Improved anchoring reduces the correlation between changes in inflation and the output gap, making the backward-looking Phillips curve appear flatter. But at the same time, improved anchoring increases the correlation between the level of inflation and the output gap, leading to a resurrection of the "original" Phillips curve. Both model predictions are consistent with U.S. data since the late 1990s.

Dispersed information and the non-neutrality of money: fifty years after Lucas, 1972

ABSTRACT This paper highlights the renewed interest in Lucas’s explanation of the non-neutrality of money put forward in his 1972 article – explanation based on information dispersion and signal extraction problems – by an increasing part of the literature investigating the transmission mechanism of monetary policy shocks. We review the main contributions to this renewal, and illustrate the relationship between this work and Lucas’s own model. We also show that some of the assumptions made by this line of research have been questioned by subsequent developments on the same track, thereby challenging its ability to produce large amounts of monetary non-neutrality and calling for further research.

Rational Expectations Models with Higher-Order Beliefs

This paper develops a general method of solving rational expectations models with higher order beliefs. Higher order beliefs are crucial in an environment with dispersed information and strategic complementarity, and the equilibrium policy depends on infinite higher order beliefs. It is generally believed that solving this type of equilibrium policy requires an infinite number of state variables (Townsend, 1983). This paper proves that the equilibrium policy rule can always be represented by a finite number of state variables if the signals observed by agents follow an ARMA process, in which case we obtain a general solution formula. We also prove that when the signals contain endogenous variables, a finite-state-variable representation of the equilibrium may not exist. For this case, we develop a tractable algorithm that can approximate the solution arbitrarily well. The key innovation in our method is to use the factorization identity and Wiener filter to solve signal extraction problems conditional on infinite observables. This method can be used in a wide range of applications. We demonstrate its strong practicability by solving several classical models featuring higher order beliefs, and also a full-blown business cycle model that is driven by confidence shocks.

Tail Risk and Expectations

We study changes in expectations by incorporating tail risk in a Bayesian learning framework with information frictions. Using a signal extraction problem, we find that economic agents behave differently in the face of tail risk. First, under tail risk, uncertainty shocks lead to a decrease in expectations, which implies more pessimistic forecasts. In comparison, in the absence of tail risks, uncertainty shocks do not influence expectations. Second, we show that individuals overreact under tail risk, that is, individuals are excessively optimistic and pessimistic as compared to a Bayesian learning framework without tail risk. Third, the magnitude of overreaction under tail risk depends on the level of uncertainty in the economy. To validate these theoretical findings, we use quantile regressions to estimate the GDP growth distribution and its measure of tail risk. By comparing the state of the economy in tail risk and non-tail risk episodes, we find that uncertainty shocks lead to a larger fall in sentiments when the economy exhibits tail risk. In addition, using an event study approach, we show that there is more overreaction under tail risk episodes. Also, consistent with the theoretical findings, overreaction is larger in periods of higher uncertainty. Our findings seek to shed light on factors driving overreaction in expectations, and to highlight the importance of uncertainty shocks in propagating macroeconomic stability.

Signal extraction: experimental evidence

We report on an experiment examining whether individuals can solve a simple signal extraction problem of the type found in models with imperfect information. In one treatment, subjects must form point predictions based on observing both public and private signals, while in another they receive the same information but must decide on the weight to attach to each signal, which then determines their point prediction. We find that, at the aggregate level, signal extraction provides a good characterization of subjects’ behavior in both treatments, but at the individual level, there is considerable heterogeneity in subjects’ ability to perform signal extraction.

The Effects of Permanent and Transitory Shocks under Imperfect Information

We study an economic environment affected by shocks that may be either permanent or transitory in nature. Contrary to the standard perfect information setup, we assume that households cannot distinguish between the two types of shocks. We describe how to solve the model under this imperfect information assumption in the context of the one-sector neoclassical model. We show that the solution involves a recasting of the driving process in terms of estimates of the exogenous states and forecast errors made by households rather than the states themselves. Given observations on the driving process, the signal extraction problem used to obtain these estimates and forecast errors may be solved independently of the calculation determining the stability of the model's dynamics. Moreover, standard linear rational expectations toolkits still apply. Given that information available to households is imperfect, the paper highlights the possibility of real economic responses to errors made in reading the economic environment rather than to actual changes in fundamentals.

The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions

Numerous contexts in macroeconomics, finance, and quality control require real-time estimation of trends, turning points, and anomalies. The real-time signal extraction problem is formulated as a multivariate linear prediction problem, the optimal solution is presented in terms of a known model, and multivariate direct filter analysis is proposed to address the more typical situation where the process’ model is unknown. It is shown how general constraints – such as level and time shift constraints – can be imposed on a concurrent filter in order to guarantee that real-time estimates have requisite properties. The methodology is applied to petroleum and construction data.

Uncertainty and Voting on the Bank of England’s Monetary Policy Committee

Differences of opinion are a natural and vital part of monetary policy making by committee. With the appropriate stance for monetary policy both unobservable and uncertain, individual policymakers need to synthesise a wide range of information, including the views of other committee members. Using a novel measure of views that we construct from text analysis of the Bank of England Monetary Policy Committee’s minutes and speeches, we show that both individual economic assessments and broader committee views are important in explaining individual voting. But in periods of high uncertainty both become more volatile and carry less weight in votes, consistent with the predictions of a simple voting model embedding a signal extraction problem. There is no increase in the dispersion of economic assessments in periods of uncertainty, nor in the mean dissent rate. Thus we show that interpreting the voting record as a reflection of policy uncertainty is unreliable, and highlight the value of individual committee members’ communications — such as speeches — for conveying differences in view.

Indeterminacy and Imperfect information

We study equilibrium determination in an environment where two kinds of agents have different information sets: The fully informed agents know the structure of the model and observe histories of all exogenous and endogenous variables. The less informed agents observe only a strict subset of the full information set. All types of agents form expectations rationally, but agents with limited information need to solve a dynamic signal extraction problem to gather information about the variables they do not observe. In this environment, we identify a new channel that leads to equilibrium indeterminacy: Optimal information processing of the less informed agent introduces stable dynamics into the equation system that lead to self-fulling expectations. For parameter values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium is indeterminate. We illustrate our framework with a monetary policy problem where an imperfectly informed central bank follows an interest rate rule.

Dissecting interbank risk using basis swap spreads

AbstractThis paper analyses interbank risk using the information content of basis swap (BS) spreads, floating‐to‐floating interest rate swaps whose payments are associated with euro deposit rates for alternative tenors. To identify the impact of shocks affecting interbank risk, we propose an empirical model that decomposes BS quotes into their expected and unexpected components. These unobservable constituents of BS spreads are estimated by solving a signal extraction problem using a particle filter. We find that expected components covariate with aggregate liquidity and risk aversion while systemic risk arises as the main driver behind unexpected fluctuations. Our empirical findings suggest that macroprudential analysis emerges as a key device to ease asset pricing in a new multi‐curve scenario.

Indeterminacy and Imperfect Information

We study equilibrium determination in an environment where two kinds of agents have different information sets: The fully informed agents know the structure of the model and observe histories of all exogenous and endogenous variables. The less in-formed agents observe only a strict subset of the full information set. All types of agents form expectations rationally, but agents with limited information need to solve a dynamic signal extraction problem to gather information about the variables they do not observe. We show that for parameters values that imply a unique equilibrium under full information, the limited information rational expectations equilibrium can be indeterminate. In a simple application of our framework to a monetary policy problem we show that limited information on part of the central bank implies indeterminate outcomes even when the Taylor Principle holds.

Brunner and Leijonhufvud: friends or foes?

Karl Brunner and Axel Leijonhufvud constantly pointed out the prominence of imperfect information in macroeconomic analysis. This paper argues that, despite strong oppositions related to their rival schools of thought, this emphasis on informational problems led them to adopt similar views on many theoretical and methodological issues. These issues encompass the perception of the economic agent in society, the theory of price inflexibility and unemployment, the role of relative prices, the importance of signal-extraction problems and the position within the Marshall-Walras divide.