Statistical Field Theory and Neural Structures Dynamics I, II, III & IV
Pierre Gosselin, Aïleen Lotz
Statistical Field Theory and Neural Structures Dynamics I: Action Functionals, Background States and External Perturbations
Abstract: This series of papers models the dynamics of a large set of interacting neurons within the framework of statistical field theory. The system is described using a two-field model. The first field represents the neuronal activity, while the second field accounts for the interconnections between cells. This model is derived by translating a probabilistic model involving a large number of interacting cells into a field formalism. The current paper focuses on deriving the background fields of the system, which describe the potential equilibria in terms of interconnected groups. Dynamically, we explore the perturbation of these background fields, leading to processes such as activation, association, and reactivation of groups of cells.
Statistical Field Theory and Neural Structures Dynamics II: Signals Propagation, Interferences, Bound States
Abstract: We continue our study of a field formalism for large sets of interacting neurons, together with their connectivity functions. Expanding upon the foundation laid in ([9]), we formulate an effective formalism for the connectivity field in the presence of external sources. We proceed to deduce the propagation of external signals within the system. This enables us to investigate the activation and association of groups of bound cells.
Statistical Field Theory and Neural Structures Dynamics III: Effective Action for Connectivities, Interactions and Emerging Collective States
Abstract: This paper elaborates on the effective field theory for the connectivity field previously introduced in ([7]). We demonstrate that dynamic interactions among connectivities induce modi cations in the background state. These modifications can be understood as the emergence of interacting collective states above the background state. The emergence of such states is contingent on both interactions and the shape of the static or quasi-static background, which acts as a conditioning factor for potential emerging states.
Statistical Field Theory and Neural Structures Dynamics IV: Field-Theoretic Formalism for Interacting Collective States
Abstract: Building upon the findings presented in the first three papers of this series, we formulate an effective field theory for interacting collective states. These states consist of a large number of interconnected neurons and are distinguished by their intrinsic activity. The field theory encompasses an infinite set of fields, each of which characterizes the dynamics of a specific type of collective state. Interaction terms within the theory drive transitions between various collective states, allowing us to describe processes such as activation, association, and deactivation of these states.
I, II, III & IV Keywords: Neural activity, Field theoretic formulation, Transitions, Emerging states, Collective states, connectivity functions.
Statistical Field Theory and Networks of Spiking Neurons
Pierre Gosselin, Aïleen Lotz, Marc Wambst
Abstract: This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems in interaction [45][46]. Our model keeps track of individual interacting neurons dynamics but also preserves some of the features and goals of neural field dynamics, such as indexing a large number of neurons by a space variable. Thus, this paper bridges the scale of individual interacting neurons and the macro-scale modelling of neural field theory.
The Expected Interest Rate Path: Alignment of Expectations vs. Creative Opacity
Pierre Gosselin, Aïleen Lotz, Charles Wyplosz
Abstract: We examine the effects of the release by a central bank of its expected future interest rate in a simple two-period model with heterogeneous information between the central bank and the private sector. The model is designed to rule out common-knowledge and time-inconsistency effects. Transparency—when the central bank publishes its interest rate path—fully aligns central bank and private-sector expectations about the future inflation rate. The private sector fully trusts the central bank to eliminate future inflation and sets the long-term interest rate accordingly, leaving only the unavoidable central bank forecast error as a source of inflation volatility. Under opacity—when the central bank does not publish its interest rate forecast—current-period inflation differs from its target not just because of the unavoidable central bank expectation error but also because central bank and privatesector expectations about future inflation and interest rates are no longer aligned. Opacity may be creative and raise welfare if the private sector’s interpretation of the current interest rate leads it to form a view of expected inflation and to set the long-term rate in a way that systematically offsets the effect of the central bank forecast error on inflation volatility. Conditions that favor the case for transparency are a high degree of precision of central bank information relative to private-sector information, a high precision of early information, and a high elasticity of current to expected inflation.
Interest Rate Signals and Central Bank Transparency
Pierre Gosselin, Aïleen Lotz, Charles Wyplosz
Abstract: The present paper extends the literature on central bank transparency that relies on information heterogeneity among private agents in four directions. First, it adds the interest rate to the list of signals that the central bank can reveal. Second, it allows for more than one economic fundamental. Third, it extends the range of uncertainties that matter. So far the literature has focused on uncertainty about the economic fundamentals, assumed to be estimated with known precision; we also allow for uncertainty about precision. Fourth, it derives results that are general in the sense that they do not depend on any particular social welfare criterion. Each extension sheds new light on the role of central bank transparency. Focusing on the signaling role of the interest rate, we consider various degrees of transparency, ranging from full opacity, to just publishing the interest rate, to also revealing the signals and estimates of their precision. While uncertainty about the fundamentals results in the now familiar common knowledge effect, uncertainty about information precision creates a fog effect, which reduces the quality of decisions taken by the central bank and the private sector. In the absence of the fog effect, full transparency is generally not desirable, because it deprives the central bank from the ability to optimally manipulate private sector expectations. When the central bank’s fog is large, we find that full transparency is usually the best communication strategy. This result tends to survive when the private sector’s fog is large. Full opacity is only desirable when the central bank is poorly informed. Another result that emerges from our analysis is that it is usually desirable for the central bank to divulge some information, even if it is erroneous, and known to be erroneous. The reason is that, when the private sector knows that the central bank is mistaken, it needs to evaluate the extent of its mistakes.
Keywords: central bank transparency; monetary policy; information asymmetry;
JEL classification: E42, E52 E58
How Much Information Should Interest Rate-Setting Central Banks Reveal?
Pierre Gosselin, Aïleen Lotz, Charles Wyplosz
Abstract: Morris and Shin (2002) have shown that a central bank may be too transparent if the private sector pays too much attention to its possible imprecise signals simply because they are common knowledge. In their model, the central bank faces a binary choice: to reveal or not to reveal its information. This paper extends their model to the more realistic case where the central bank must anyway convey some information by setting the interest rate. This situation radically changes the conclusions. In many cases, full transparency is socially optimal. In other instances the central bank can distill information to either manipulate private sector expectations in a way that reduces the common knowledge effect or to reduce the unavoidable information content of the interest rate. In no circumstance is the option of only setting the interest rate socially optimal.
Keywords: central bank transparency.
JEL classification: E42, E52, E58.
The New Keynesian Phillips Curve in the United States and the euro area: aggregation bias, stability and robustness
Bergljot Barkbu, Vincenzo Cassino, Aileen Gosselin-Lotz, Laura Piscitelli
Abstract: In the recent past, the empirical literature on the New Keynesian Phillips Curve (NKPC) has grown rapidly. The NKPC has been shown to describe satisfactorily the relationship between inflation and marginal cost both for the United States and the euro area. However, little attention has been given so far to the stability and robustness of the parameters in the estimated NKPC. In this paper, we aim to help fill this gap. After estimating hybrid NKPCs on US and euro-area data using the generalised method of moments and having found that our results are broadly in line with previous findings, we subject our estimated NKPCs to a thorough stability analysis. We find that the estimated coefficients for the United States are stable, whereas those for the euro area are considerably less stable. We then investigate the possible reasons for this instability. One explanation, explored using the Andrews’ test, is the presence of structural breaks. Another possibility is the presence of an aggregation bias, which we investigate by estimating NKPCs for the three largest euro-area economies: Germany, France and Italy. At this disaggregated level, the fit of the NKPC improves, but the coefficients are still unstable. Furthermore, the disaggregated analysis indicates the presence of structural breaks in the three largest euro-area economies.
JEL classification: C12, C13, E31.
Structural Changes in Inflation
Abstract: The declining inflation experienced during the last decade is a common feature of both the Euro Area and other developed economies. Possible explanations have been the event of exogenous shocks, such as oil price, effictive exchange rates, and import prices. An increased globalization, leading to an increased competition in both domestic and international markets, eroding firms’ pricing power. For the United States, productivity growth, raising the rate at which the economy can grow without giving rise to inflationary pressures, has also been considered. Yet, the absence of evidence about productivity and competition improvements in the Euro area raises doubts on the validity of such views.
This project is aiming at studying the decline in inflation experienced in Europe during the last decades has raised the issue of the structural change hypothesis in such a process. I relied on structural break analysis, to assess for the changes witnessed by inflation from the seventies onward. The wage and pice inflation equations are estimated over the whole sample period, and instability is being tracked through a battery of structural break tests.
We find that the Phillips curve has been modified since 1981. From 1981 onwards, price inflation seems to have been more inertial than it was in the past. On the wage side, labor productivity, as well as unemployment gap appear to have played an ever-decreasing role in the wage inflation process. Both results tend to confirm a structural change in the standard Phillips curve. The classic trade-off existing between unemployment and wage inflation seems if not to have disappeared, yet to have significantly diminished over the past two decades.
When considering possible cause of changes in the inflationary process, it seems that trade liberalization has played no role in the lower inflation experienced within the Euro zone. On the contrary, labor market liberalization witnessed in Europe since the mid-eighties would explain some of the decrease of wage inflation.