Time-Consistent Control in Non-Linear Models

We show how to use optimal control theory to derive optimal time-consistent Markov-perfect government policies in nonlinear dynamic general equilibrium models, extending the result of Cohen and Michel (1988) for models with quadratic objective functions and linear dynamics. We replace private agents' costates by flexible functions of current states in the government's maximization problem. The functions are verified in equilibrium to an arbitrarily close degree of approximation. They can be found numerically by perturbation or projection methods. We use a stochastic model of optimal public spending to illustrate the technique.Fiscal policy; Monetary policy framework

National Saving-Investment Dynamics and International Capital Mobility

The authors analyze the dynamics of national saving-investment relationships to determine the degree of international capital mobility. Following Coakley and Kulasi (1997), the authors interpret the close relationship between national saving and investment in the long run as reflecting a solvency constraint, rather than as evidence of limited capital mobility (Feldstein and Horioka 1980). As in Jansen (1996, 1998), the authors also examine the short-term saving-investment relationship, especially the speed at which the variables return to the long-run equilibrium relationship once they have deviated from it. The ease with which a country can borrow or lend and run current account imbalances in the short run, before it has to ultimately reverse the transaction at some future date to satisfy the solvency constraint, is interpreted as being positively related to the degree of international capital mobility. Extending the approach by Jansen, the authors apply panel error-correction techniques to data for 20 OECD countries from 1960 to 1999, and find that saving and investment display a long-run relationship that is consistent with the interpretation that a long-run solvency constraint is binding for each country. Furthermore, capital mobility has increased over time.International topics

Computing Optimal Policy in a Timeless-Perspective: An Application to a Small-Open Economy

Since the contribution of Kydland and Prescott (1977), it is well known that the optimal Ramsey policy is time inconsistent. In a series of recent contributions, Woodford (2003) proposes a new methodology to circumvent this problem, namely the timeless perspective solution. However, one main limitation is that it is not yet empirically implementable. In this paper, we develop a new methodology to compute initial values of the Lagrange multipliers in order to implement the timeless-perspective solution. In so doing, we also provide a generalization of the Ramsey and timeless-perspective problems. We apply our results to a small-open economy model in Canada.Monetary policy framework

The Implications of Transmission and Information Lags for the Stabilization Bias and Optimal Delegation

In two recent papers, Jensen (2002) and Walsh (2003), using a hybrid New Keynesian model, demonstrate that a regime that targets either nominal income growth or the change in the output gap can effectively replicate the outcome under commitment and hence reduce the size of the stabilization bias. Moreover, these two targeting regimes have been shown to outperform a regime that targets inflation, except when inflation expectations are predominantly backward looking. In this paper, the authors modify an otherwise conventional New Keynesian model to include transmission and information lags, two key problems faced by policy-makers, and they examine whether the results from the baseline model are robust to these two modifications. The authors find that the gains from commitment are considerably reduced when the model includes these two features, which implies that optimal delegation is less important. Furthermore, a regime that targets CPI inflation in a conservative manner is found to perform well and even outperforms the targeting regimes advocated by Jensen and Walsh under certain conditions.Transmission of monetary policy; Inflation targets

The Implications of Information Lags for the Stabilization Bias and Optimal Delegation.

Many papers for example Jensen (2002) and Walsh (2003) have shown that in a New Keynesian model with a significant degree of forward-looking behaviour, policy regimes that target either the change in the output-gap (speed limit targeting) or nominal income growth can considerably reduce the size of the stabilization biasÐthe inefficiency that arises when a central bank conducts policy under discretion as opposed to commitment. Inflation targeting can also reduce the size of the stabilization bias but unless inflation expectations in the model are predominantly backward-looking, this targeting regime does not perform as well as speed limit or nominal income growth targeting. Jensen (2002) and Walsh (2003) obtain their results using a New Keynesian model where changes in the policy rate affect macroeconomic variables immediately. In this paper, we compare the performance of several targeting regimes by using a New Keynesian model that includes a delayed response of monetary policy as a result of information lags. We find two results that are substantially different from Jensen (2002) and Walsh (2003). First the size of the stabilization bias is considerably reduced. Second, a regime that targets inflation outperforms a regime that targets either the change in the output-gap or the growth in nominal income even when inflation expectations are very forward-looking.Stabilization bias, Inflation Targeting, Discretion, Commitment, Information Lag

Long-memory process and aggregation of AR(1) stochastic processes: A new characterization

Contemporaneous aggregation of individual AR(1) random processes might lead to different properties of the limit aggregated time series, in particular, long memory (Granger, 1980). We provide a new characterization of the series of autoregressive coefficients, which is defined from the Wold representation of the limit of the aggregate stochastic process, in the presence of long-memory features. Especially the infinite autoregressive stochastic process defined by the almost sure representation of the aggregate process has a unit root in the presence of the long-memory property. Finally we discuss some examples using some well-known probability density functions of the autoregressive random parameter in the aggregation literature. JEL Classification Code: C2, C13

Aggregating Phillips curves

The New Keynesian Phillips Curve is at the center of two raging empirical debates. First, how can purely forward looking pricing account for the observed persistence in aggregate inflation. Second, price-setting responds to movements in marginal costs, which should therefore be the driving force to observed inflation dynamics. This is not always the case in typical estimations. In this paper, we show how heterogeneity in pricing behavior is relevant to both questions. We detail the conditions under which imposing homogeneity results in overestimating a backward-looking component in (aggregate) inflation, and underestimating the importance of (aggregate) marginal costs for (aggregate) inflation. We provide intuition for the direction of these biases, and verify them in French data with information on prices and marginal costs at the industry level. We show that the apparent discrepancy in the estimated duration of nominal rigidities, as implied from aggregate or microeconomic data, can be fully attributable to a heterogeneity bias. JEL Classification: C10, C22, E31, E52heterogeneity, Inflation persistence, marginal costs, New Keynesian Phillips curve