Causal conditioning and instantaneous coupling in causality graphs

The paper investigates the link between Granger causality graphs recently formalized by Eichler and directed information theory developed by Massey and Kramer. We particularly insist on the implication of two notions of causality that may occur in physical systems. It is well accepted that dynamical causality is assessed by the conditional transfer entropy, a measure appearing naturally as a part of directed information. Surprisingly the notion of instantaneous causality is often overlooked, even if it was clearly understood in early works. In the bivariate case, instantaneous coupling is measured adequately by the instantaneous information exchange, a measure that supplements the transfer entropy in the decomposition of directed information. In this paper, the focus is put on the multivariate case and conditional graph modeling issues. In this framework, we show that the decomposition of directed information into the sum of transfer entropy and information exchange does not hold anymore. Nevertheless, the discussion allows to put forward the two measures as pillars for the inference of causality graphs. We illustrate this on two synthetic examples which allow us to discuss not only the theoretical concepts, but also the practical estimation issues.Comment: submitte

Empirical Structural Evidence on Wages, Prices and Employment in the US

In this paper, I investigate US post war price, wage and employment dynamics by identifying and estimating a price and a wage equation. I reach the following two main conclusions: Nominal wages adjust faster to prices than prices do to nominal wages. This may be taken as evidence that price inertia is more important empirically than nominal wage inertia. The wage equation implies that the effect on wage inflation of a permanent increase in unemployment, given prices, is largely temporary. This can be interpreted in various ways. One is that, if the wage equation is interpreted as a Phillips curve, both the rate of change and the level of unemployment play an important role in wage determination. The methodology of the paper is somewhat different from the traditional approach to the estimation of price and wage equations. Its spirit is to impose on the reduced form a just identifying set of restrictions. In this way, a structural interpretation is made possible, while the data are left free to speak.

Current and Anticipated Deficits, Interest Rates and Economic Activity

There is widespread feeling that current deficits, in Europe and the U.S.,may hurt rather than help the recovery. This paper examines some of the issues involved, through a sequence of three models.The first model focuses on sustainability and characterizes its determinants. It suggests that the issue of sustainability may indeed ber elevant in some countries.The second model focuses on the effects of fiscal policy on real interestrates, and in particular on the relative importance of the level of deficits andthe level of debt in determining interest rates.The third model focuses on the effects of fiscal policy on the speed of the recovery. It shows how a sharply increasing fiscal expansion might be initially contractionary rather than expansionary.

The Wage Price Spiral

This paper rehabilitates the old wage price spiral. It shows that, after an increase in aggregate demand, the process of adjustment of nominal prices and nominal wages results from attempts by workers to maintain or increase their real wage and by firms to maintain or increase their markups of prices over wages. Under continuous price and wage setting, the process of adjustment would be instantaneous ; under staggering of price and wage decisions, the adjustment takes time. The more inflexible real wages and markups are to shifts in demand, the higher is the degree of price level inertia, the longer lasting are the effects of aggregate demand on output.

Price Asynchronization and Price Level Inertia

If price decisions are taken neither continuously nor in perfect synchronization, the process of adjustment of all prices to a new nominal level will imply temporary movements in relative prices. It might then well be that, to avoid these movements in relative prices, each price setter will want to move his own price slowly compared to others. The result will be a slow movement of all prices to their new nominal level, and substantial inertia of the price level. This paper formalizes this intuitive argument and reaches four main conclusions: (1) Even small departures from perfect synchronization can generate substantial price level inertia. (2) If price decisions are desynchronized, even anticipated movements in money will usually have an effect on economic activity. It is however possible to find paths of money deceleration which reduce inflation at no cost in output. (3) Price desynchronization has implications for relative price movements as well as for the price level. Goods early in the chain of production have more price and profit variability than goods further down the chain. (4) Price inertia, if it is due to price desynchronization, may be difficult to remove. It may well be that, given the timing decisions of others, no agent has an incentive to change his own timing decision: the time structure of price desynchronization may be stable.

Debt, Deficits and Finite Horizons

Many issues in macroeconomics, such as the level of the steady state interest rate, or the dynamic effects of government deficit finance, depend crucially on the horizon of economic agents. This paper develops a simple analytical model in which such issues can be examined and in which the horizon of agents is a parameter which can be chosen arbitrarily.The first three sections of the paper characterize the dynamics and steady state of the economy in the absence of a government. The focus is on the effects of the horizon index on the economy. The paper clarifies in particular the separate roles of finite horizons and declining labor income through life in the determination of steady state interest rates.The next three sections study the effects and the role of fiscal policy.The focus is on the effects of deficit finance both in closed and open economies. The paper clarifies the respective roles of government spending, deficits and debt in the determination of interest rates.