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Abstract:
This paper compares the welfare costs of business cycles in a dollarized economy to those arising in economies with different monetary arrangements. The alternative monetary policy regimes studied belong to three broad families: devaluation rate rules, inflation targeting, and money growth rate rules. The analysis is conducted within an optimizing model of a small open economy with sticky prices. The model is calibrated to the Mexican economy and is driven by three external shocks: terms of trade, world interest rate, and import-price inflation. We show econometrically that these shocks explain at a minimum 45 percent of the observed forecasting error variance of Mexican output and the Mexican real exchange rate at 8- to 16-quarter horizons. The model fits the data relatively well in the sense that it can account for the volatility and comovements of key macroeconomic indicators such as output, consumption, inflation, and the real exchange rate. The welfare comparisons suggest that dollarization is the least successful of the monetary policy rules considered: agents are willing to give up between 0.1 and 0.3 percent of their nonstochastic steady-state consumption to see a policy other than dollarization implemented.

Abstract:
The small open economy model with incomplete asset markets features a steady state that depends on initial conditions and equilibrium dynamics that possess a random walk component. A number of modifications to the standard model have been proposed to induce stationarity. This paper presents a quantitative comparison of these alternative approaches. Five different specifications are considered: (1) A model with an endogenous discount factor (Uzawa-type preferences); (2) A model with a debt-elastic interest-rate premium; (3) A model with convex portfolio adjustment costs; (4) A model with complete asset markets; and (5) A model without stationarity-inducing features. The main finding of the paper is that all models deliver virtually identical dynamics at business-cycle frequencies, as measured by unconditional second moments and impulse response functions. The only noticeable difference among the alternative specifications is that the complete-asset-market model induces smoother consumption dynamics.

Abstract:
The small open economy model with incomplete asset markets features a steady state that depends on initial conditions. In addition, equilibrium dynamics posses a random walk component. A number of modifications to the standard model have been proposed to induce stationarity. This Paper presents a quantitative comparison of these alternative approaches. Five different specifications are considered: (1) A model with an endogenous discount factor (Uzawa-type preferences); (2) A model with a debt-elastic interest-rate premium; (3) A model with convex portfolio adjustment costs; (4) A model with complete asset markets; (5) A model without stationarity-inducing features. The main finding of the Paper is that all models deliver virtually identical dynamics at business-cycle frequencies, as measured by unconditional second moments and impulse response functions. The only noticeable difference among the alternative specifications is that the complete-asset-market model induces smoother consumption dynamics.

Small open economy, stationarity, complete and incomplete asset markets

Abstract:
The small open economy model with incomplete asset markets features a steady state that depends on initial conditions. In addition, equilibrium dynamics posses a random walk component. A number of modifications to the standard model have been proposed to induce stationarity. This paper presents a quantitative comparison of these alternative approaches. Five different specifications are considered: (1) A model with an endogenous discount factor (Uzawa-type preferences); (2) A model with a debt-elastic interest-rate premium; (3) A model with convex portfolio adjustment costs; (4) A model with complete asset markets; (5) A model without stationarity-inducing features. The main finding of the paper is that all models deliver virtually identical dynamics at business-cycle frequencies, as measured by unconditional second moments and impulse response functions. The only noticeable difference among the alternative specifications is that the complete-asset-market model induces smoother consumption dynamics.

Small Open Economy, Stationarity, Complete and Incomplete Asset Markets

Abstract:
This paper studies optimal fiscal and monetary policy under sticky product prices. The theoretical framework is a stochastic production economy without capital. The government finances an exogenous stream of purchases by levying distortionary income taxes, printing money, and issuing one-period nominally risk-free bonds. The main findings of the paper are: First, for a miniscule degree of price stickiness (i.e., many times below available empirical estimates) the optimal volatility of inflation is near zero. This result stands in stark contrast with the high volatility of inflation implied by the Ramsey allocation when prices are flexible. The finding is in line with a recent body of work on optimal monetary policy under nominal rigidities that ignores the role of optimal fiscal policy. Second, even small deviations from full price flexibility induce near random walk behavior in government debt and tax rates, as in economies with real non-state-contingent debt only. Finally, sluggish price adjustment raises the average nominal interest rate above the one called for by the Friedman rule.

Abstract:
This Paper studies optimal fiscal and monetary policy under sticky product prices. The theoretical framework is a stochastic production economy without capital. The government finances an exogeneous stream of purchases by levying distortionary income taxes, printing money, and issuing one-period nominally risk-free bonds. The main findings of the Paper are: First, for a miniscule degree of price stickiness (ie. many times below available empirical estimates) the optimal volatility of inflation is near zero. This result stands in stark contrast with the high volatility of inflation implied by the Ramsey allocation when prices are flexible. The finding is in line with a recent body of work on optimal monetary policy under nominal rigidities that ignores the role of optimal fiscal policy. Second, even small deviations from full price flexibility induce near random walk behaviour in government debt and tax rates, as in economies with real non-state-contingent debt only. Finally, sluggish price adjustment raises the average nominal interest rate above the one called for by the Friedman rule.

Optimal fiscal and monetary policy, sticky prices, optimal inflation volatility, tax smoothing

Abstract:
This paper studies optimal fiscal and monetary policy under sticky product prices. The theoretical framework is a stochastic production economy without capital. The government finances an exogenous stream of purchases by levying distortionary income taxes, printing money, and issuing one-period nominally risk-free bonds. The main findings of the paper are: First, for a miniscule degree of price stickiness (i.e., many times below available empirical estimates) the optimal volatility of inflation is near zero. This result stands in stark contrast with the high volatility of inflation implied by the Ramsey allocation when prices are flexible. The finding is in line with a recent body of work on optimal monetary policy under nominal rigidities that ignores the role of optimal fiscal policy. Second, even small deviations from full price flexibility induce near random walk behavior in government debt and tax rates, as in economies with real non-state-contingent debt only. Finally, sluggish price adjustment raises the average nominal interest rate above the one called for by the Friedman rule.

Optimal Fiscal and Monetary Policy, Sticky Prices, Optimal Inflation Volatility, Tax Smoothing

Abstract:
This paper derives a second-order approximation to the solution of a general class of discrete-time rational expectations models. The main theoretical contribution of the paper is to show that for any model belonging to the general class considered, the coefficients on the terms linear and quadratic in the state vector in a second-order expansion of the decision rule are independent of the volatility of the exogenous shocks. In other words, these coefficients must be the same in the stochastic and the deterministic versions of the model. Thus, up to second order, the presence of uncertainty affects only the constant term of the decision rules. In addition, the paper presents a set of MATLAB programs designed to compute the coefficients of the second-order approximation. The validity and applicability of the proposed method is illustrated by solving the dynamics of a number of model economies.

Abstract:
Since the seminal paper of Kydland and Prescott (1982) and King, Plosser and Rebelo (1988), it has become commonplace in macroeconomics to approximate the solution to nonlinear, dynamic general equilibrium models using linear methods. Linear approximation methods are useful to characterize certain aspects of the dynamic properties of complicated models. First-order approximation techniques are not however, well suited to handle questions such as welfare comparisons across alternative stochastic of policy environments. The problem with using linearized decision rules to evaluate second-order approximations to the objective function is that some second-order terms of the objective function are ignored when using a linearized decision rule. Such problems do not arise when the policy function is approximated to second-order or higher. In this paper we derive a second order approximation to the policy function of a dynamic, rational expectations model. Our approach follows the perturbation method described in Judd (1998) and developed further by Collard and Juillard (2001). We follow Collard and Juillard closely in notation and methodology. An important difference separates this Paper from the work of Collard and Juillard. Namely, Collard and Juillard apply what they call a bias reduction procedure to capture the fact that the policy function depends on the variance of the underlying shocks. Instead, we explicitly incorporate a scale parameter for the variance of the exogenous shocks as an argument of the policy function. In approximating the policy function, we take a second order Taylor expansion with respect to the state variables as well as this scale parameter. To illustrate its applicability, the method is used to solve the dynamics of a simple neoclassical model. The Paper closes with a brief description of a set of MATLAB programs designed to implement the method.

Solving dynamic general equilibrium models, second order approximation, MATLAB code

Abstract:
This paper derives a second-order approximation to the solution of a general class of discrete-time rational expectations models. The main theoretical contribution of the paper is to show that for any model belonging to the general class considered, the coefficients on the terms linear and quadratic in the state vector in a second-order expansion of the decision rule are independent of the volatility of the exogenous shocks. In other words, these coefficients must be the same in the stochastic and the deterministic versions of the model. Thus, up to second order, the presence of uncertainty affects only the constant term of the decision rules. In addition, the paper presents a set of MATLAB programs designed to compute the coefficients of the second-order approximation. The validity and applicability of the proposed method is illustrated by solving the dynamics of a number of model economies.

dynamic general equilibrium models, perturbation methods, second-order approximation

Abstract:
This paper studies optimal fiscal and monetary policy under imperfect competition in a stochastic, flexible-price, production economy without capital. It shows analytically that in this economy the nominal interest rate acts as an indirect tax on monopoly profits. Unless the social planner has access to a direct 100 percent tax on profits, he will always find it optimal to deviate from the Friedman rule by setting a positive and time-varying nominal interest rate. The dynamic properties of the Ramsey
allocation are characterized numerically. As in the perfectly competitive case, the labor income tax is remarkably smooth, whereas inflation is highly volatile and serially uncorrelated. An exact numerical solution method to the Ramsey conditions is proposed.

Optimal Fiscal and Monetary Policy, Friedman rule, Imperfect competition

Abstract:
When a government decides to dollarize its economy, that is, to replace the domestic currency with the U.S. dollar, it automatically ceases to collect the stream of seignorage revenue, which is instead redirected toward the U.S. government. A central issue in the debate about dollarization is the distribution of seignorage between U.S. and the economies that are considering the adoption of the dollar as the sole legal tender. A pre-requisite for designing meaningful seignorage sharing rules is to asses the amount of resources that are at stake. A common misconception is that the amount of seignorage income involved is simply equal to the interest income on the amount of foreign reserves required to exchange the entire domestic money supply for dollars. This way of measuring the loss of seignorage income is in general biased for it implicitly assumes no growth in monetary assets. In this note we show that this bias can lead to enormous underestimations of the amount of seignorage revenue lost by governments of countries that dollarize.

Abstract:
A key result of a recent literature that focuses on the global consequences of Taylor-type interest rate feedback rules is that such rules, in combination with the zero-bound on nominal interest rates, can lead to unintended liquidity traps. An immediate question posed by this result is whether the government could avoid liquidity traps by ignoring the zero-bound, that is, by threatening to set the nominal interest rate at a negative value should the inflation rate fall below a certain threshold. This Paper shows that even if the government could credibly commit to setting the interest rate at a negative value, self-fulfilling liquidity traps can still emerge. That is, deflationary equilibria originating arbitrarily near the intended equilibrium and leading to low (possibly zero) interest rates and low (and possibly negative) rates of inflation cannot be ruled out by lifting the zero-bound on the monetary policy rule. This result obtains in models with flexible and sticky prices and under continuous and discrete time.

Taylor rules, liquidity traps, zero bound on nominal interest rates

Abstract:
A key result of a recent literature that focuses on the global consequences of Taylor-type interest rate feedback rules is that such rules in combination with the zero bound on nominal interest rates can lead to unintended liquidity traps. An immediate question posed by this result is whether the government could avoid liquidity traps by ignoring the zero bound, that is, by threatening to set the nominal interest rate at a negative value should the inflation rate fall below a certain threshold. This paper shows that even if the government could credibly commit to setting the interest rate at a negative value, self-fulfilling liquidity traps can still emerge. That is, deflationary equilibria originating arbitrarily near the intended equilibrium and leading to low (possibly zero) interest rates and low (and possibly negative) rates of inflation cannot be ruled out by lifting the zero bound on the monetary policy rule. This result obtains in models with flexible and sticky prices and under continuous and discrete time.

Taylor rules, liquidity traps, zero bound on nominal interest rates

Abstract:
This paper studies the role of asset-market completeness for the properties of optimal policy. A suitable framework for this purpose is the small open economy with complete international asset markets. For in this environment changes in policy represent country-specific risk diversifiable in world markets. Our main finding is that the fundamental public finance principle whereby when taxes on all final goods are available, it is optimal to tax final goods uniformly fails to obtain. In general, uniform taxation is optimal because it amounts to a nondistorting tax on fixed factors of production. In the open economy this principle fails because when households can insure against the risk of a policy reform, initial private asset holdings are contingent on actual policy and thus no longer represent an inelastically supplied source of income. Two further differences between optimal policy in the closed and open economies with complete markets are: (a) In the open economy, optimal consumption and income tax rates are unchanged in response to government purchases shocks. By contrast, in the closed economy tax rates do respond to innovations in public spending. (b) In the open economy, the Friedman rule is optimal only if the Ramsey planner has access to consumption taxes. In the absence of consumption taxes, deviations from the Friedman rule are large. On the other hand, in the closed economy, the availability of either consumption or income taxes suffices to render the Friedman rule optimal.

Abstract:
This paper studies the role of asset-market completeness for the properties of optimal fiscal and monetary policy. A suitable framework for this purpose is the small open economy with complete international asset markets. For changes in policy represent country-specific risk diversifiable in world markets. Our main finding is that the fundamental public finance principle whereby when taxes on all final goods are available, it is optimal to tax final goods uniformly fails to obtain. In general, uniform taxation is optimal because it amounts to a nondistorting tax on fixed factors of production. In the open economy this principle fails because when households can insure against the risk of a policy reform, initial private asset holdings are contingent on expected policy and not an inelastically supplied source of income. Furthermore, we find that the Friedman rule is optimal only if the Ramsey planner has access to consumption taxes.

Optimal monetary and fiscal policy, open economies, anticipated Ramsey policy

Abstract:
This Paper studies the role of asset-market completeness for the properties of optimal policy. A suitable framework for this purpose is the small open economy with complete international asset markets. For in this environment changes in policy represent country-specific risk diversifiable in world markets. Our main finding is that the fundamental public finance principle whereby when taxes on all final goods are available, it is optimal to tax final goods uniformly fails to obtain. In general, uniform taxation is optimal because it amounts to a non-distorting tax on fixed factors of production. In the open economy this principle fails because when households can insure against the risk of a policy reform, initial private asset holdings are contingent on actual policy and thus no longer represent an inelastically supplied source of income. Two further differences between optimal policy in the closed and open economies with complete markets are: (a) In the open economy, optimal consumption and income tax rates are unchanged in response to government purchases shocks. By contrast, in the closed economy tax rates do respond to innovations in public spending. (b) In the open economy, the Friedman rule is optimal only if the Ramsey planner has access to consumption taxes. In the absence of consumption taxes, deviations from the Friedman rule are large. On the other hand, in the closed economy, the availability of either consumption or income taxes suffices to render the Friedman rule optimal.

Optimal monetary and fiscal policy, open economies, anticipated Ramsey policy

Abstract:
The goal of this Paper is to compute optimal monetary and fiscal policy rules in a real business cycle model augmented with sticky prices, a demand for money, taxation, and stochastic government consumption. We consider simple policy rules, whereby the nominal interest rate is set as a function of output and inflation, and taxes are set as a function of total government liabilities. We require policy to be implementable in the sense that it guarantees uniqueness of equilibrium. We do away with a number of empirically unrealistic assumptions typically maintained in the related literature that are used to justify the computation of welfare using linear methods. Instead, we implement a second-order accurate solution to the model. Our main findings are: First, the size of the inflation coefficient in the interest-rate rule plays a minor role for welfare. It matters only insofar as it affects the determinacy of equilibrium. Second, optimal monetary policy features a muted response to output. More importantly, interest rate rules that feature a positive response of the nominal interest rate to output can lead to significant welfare losses. Third, the optimal fiscal policy is passive. The welfare losses associated with the adoption of an active fiscal stance are, however, negligible.

Optimal fiscal and monetary policy, nominal rigidities, optimal inflation volatility, second-order approximation techniques

Abstract:
The goal of this paper is to compute optimal monetary and fiscal policy rules in a real business cycle model augmented with sticky prices, a demand for money, taxation, and stochastic government consumption. We consider simple policy rules whereby the nominal interest rate is set as a function of output and inflation, and taxes are set as a function of total government liabilities. We require policy to be implementable in the sense that it guarantees uniqueness of equilibrium. We do away with a number of empirically unrealistic assumptions typically maintained in the related literature that are used to justify the computation of welfare using linear methods. Instead, we implement a second-order accurate solution to the model. Our main findings are: First, the size of the inflation coefficient in the interest-rate rule plays a minor role for welfare. It matters only insofar as it affects the determinacy of equilibrium. Second, optimal monetary policy features a muted response to output. More importantly, interest rate rules that feature a positive response of the nominal interest rate to output can lead to significant welfare losses. Third, the optimal fiscal policy is passive. However, the welfare losses associated with the adoption of an active fiscal stance are negligible.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
The goal of this paper is to compute optimal monetary and fiscal policy rules in a real business cycle model augmented with sticky prices, a demand for money, taxation, and stochastic government consumption. We consider simple policy rules whereby the nominal interest rate is set as a function of output and inflation, and taxes are set as a function of total government liabilities. We require policy to be implementable in the sense that it guarantees uniqueness of equilibrium. We do away with a number of empirically unrealistic assumptions typically maintained in the related literature that are used to justify the computation of welfare using linear methods. Instead, we implement a second-order accurate solution to the model. Our main findings are: First, the size of the inflation coefficient in the interest-rate rule plays a minor role for welfare. It matters only insofar as it affects the determinacy of equilibrium. Second, optimal monetary policy features a muted response to output. More importantly, interest rate rules that feature a positive response of the nominal interest rate to output can lead to significant welfare losses. Third, the optimal fiscal policy is passive. However, the welfare losses associated with the adoption of an active fiscal stance are negligible.

Optimal fiscal and monetary policy, nominal rigidities, optimal inflation volatility, second-order approximation techniques

Abstract:
A growing empirical and theoretical literature argues in favor of specifying monetary policy in the form of Taylor-type interest rate feedback rules. That is, rules whereby the nominal interest rate is set as an increasing function of inflation with a slope greater than one around an intended inflation target. This paper shows that such rules can easily lead to chaotic dynamics. The result is obtained for feedback rules that depend on contemporaneous or expected future inflation. The existence of chaotic dynamics is established analytically and numerically in the context of calibrated economies. The battery of fiscal policies that has recently been advocated for avoiding global indeterminacy induced by Taylor-type interest-rate rules (such as liquidity traps) are shown to be unlikely to provide a remedy for the complex dynamics characterized in this paper.

Taylor rules, chaos, periodic equilibria

Abstract:
The existing literature on the stabilizing properties of interest-rate feedback rules has stressed the perils of linking interest rates to forecasts of future inflation. Such rules have been found to give rise to aggregate fluctuations due to self-fulfilling expectations. In response to this concern, a growing literature has focused on the stabilizing properties of interest-rate rules whereby the central bank responds to a measure of past inflation. The consensus view that has emerged is that backward-looking rules contribute to protecting the economy from embarking on expectations-driven fluctuations. A common characteristic of the existing studies that arrive at this conclusion is their focus on local analysis. The contribution of this paper is to conduct a more global analysis. We find that backward-looking interest-rate feedback rules do not guarantee uniqueness of equilibrium. We present examples in which for plausible parameterizations attracting equilibrium cycles exist. The paper also contributes to the quest for policy rules that guarantee macroeconomic stability globally. Our analysis indicates that policy rules whereby the interest rate is set as a function of the past interest rate and current inflation are likely to ensure global stability provided that the coefficient on lagged interest rates is greater than unity.

Backward Looking Taylor Rules, Endogenous Cycles, Sticky Prices

Abstract:
Once the zero bound on nominal interest rates is taken into account, Taylor-type interest rate feedback rules give rise to unintended self-fulfilling decelerating inflation paths and aggregate fluctuations driven by arbitrary revisions in expectations. These undesirable equilibria exhibit the essential features of liquidity traps since monetary policy is ineffective in bringing about the government's goals regarding the stability of output and prices. This paper proposes several fiscal and monetary policies that preserve the appealing features of Taylor rules, such as local uniqueness of equilibrium near the inflation target, and at the same time rule out the deflationary expectations that can lead an economy into a liquidity trap.

Abstract:
Once the zero-bound on nominal interest rates is taken into account, Taylor-type interest-rate feedback rules give rise to unintended self-fulfilling decelerating inflation paths and aggregate fluctuations driven by arbitrary revisions in expectations. These undesirable equilibria exhibit the essential features of liquidity traps, as monetary policy is ineffective in bringing about the government's goals regarding the stability of output and prices. This Paper proposes several fiscal and monetary policies that preserve the appealing features of Taylor rules, such as local uniqueness of equilibrium near the inflation target, and at the same time rule out the deflationary expectations that can lead an economy into a liquidity trap.

Taylor rules, liquidity traps, zero-bound on nominal interest rates

Abstract:
Once the zero bound on nominal interest rates is taken into account, Taylor-type interest-rate feedback rules give rise to unintended self-fulfilling decelerating inflation paths and aggregate fluctuations driven by arbitrary revisions in expectations. These undesirable equilibria exhibit the essential features of liquidity traps, as monetary policy is ineffective in bringing about the government's goals regarding the stability of output and prices. This paper proposes several fiscal and monetary policies that preserve the appealing features of Taylor rules, such as local uniqueness of equilibrium near the inflation target, and at the same time rule out the deflationary expectations that can lead an economy into a liquidity trap.

Abstract:
Since John Taylor's (1993) seminal paper, a large literature has argued that active interest rate feedback rules, that is, rules that respond to increases in inflation with a more than one-for-one increase in the nominal interest rate, are stabilizing. In this paper, we argue that once the zero bound on nominal interest rates is taken into account, active interest rate feedback rules can easily lead to unexpected consequences. Specifically, we show that even if the steady state at which monetary policy is active is locally the unique equilibrium, typically there exists an infinite number of equilibrium trajectories originating arbitrarily close to that steady state that converge to a liquidity trap, that is, a steady state in which the nominal interest rate is near zero and inflation is possibly negative.

Abstract:
In this paper, we characterize conditions under which interest rate feedback rules whereby the nominal interest rate is set as an increasing function of the inflation rate generate multiple equilibria. We show that these conditions depend not only on the fiscal regime (as emphasized in the fiscal theory of the price level) but also on the way in which money is assumed to enter preferences and technology. We analyze this issue in flexible and sticky price environments. We provide a number of examples in which, contrary to what is commonly believed, active monetary policy in combination with a fiscal policy that preserves government solvency gives rise to multiple equilibria and passive monetary policy renders the equilibrium unique.

Abstract:
This paper analyzes the implications of a balanced budget fiscal policy rule for the determinacy of the price level in a cash-in-advance economy under three alternative monetary policy regimes. It shows that in such stylized models with flexible prices and a period-by-period balanced budget requirement the price level is determinate under a money growth rate peg and is indeterminate under a pure nominal interest rate peg. Under a feedback rule whereby the nominal interest rate is set as an increasing function of the inflation rate, the price level is determinate for intermediate values of the inflation elasticity of the feedback rule and is indeterminate for both very low and very high values of the inflation elasticity. Finally, regardless of the particular monetary policy specification, a rational expectations equilibrium consistent with the optimal quantity of money may not exist.

Abstract:
In this paper, we study Ramsey-optimal fiscal and monetary policy in a medium-scale model of the U.S. business cycle. The model features a rich array of real and nominal rigidities that have been identified in the recent empirical literature as salient in explaining observed aggregate fluctuations. The main result of the paper is that price stability appears to be a central goal of optimal monetary policy. The optimal rate of inflation under an income tax regime is half a percent per year with a volatility of 1.1 percent. This result is surprising given that the model features a number of frictions that in isolation would call for a volatile rate of inflation-particularly non-state-contingent nominal public debt, no lump-sum taxes, and sticky wages. Under an income-tax regime, the optimal income tax rate is quite stable, with a mean of 30 percent and a standard deviation of 1.1 percent.

Ramsey policy, inflation stabilization, tax smoothing, time to tax

Abstract:
This paper generalizes the standard habit-formation model to an environment in which agents form habits over individual varieties of goods as opposed to over a composite consumption good. We refer to this preference specification as deep habit formation. Under deep habits, the demand function faced by individual producers depends on past sales. This feature is typically assumed ad hoc in customer-market and brand-switching-cost models. A central result of the paper is that deep habits give rise to countercyclical mark-ups, which is in line with the empirical evidence. This result is important, because ad hoc formulations of customer-market and switching-cost models have been criticized for implying procyclical and hence counterfactual mark-up movements. Under deep habits, consumption and wages respond procyclically to government-spending shocks. The paper provides econometric estimates of the parameters pertaining to the deep-habit model.

Abstract:
This Paper generalizes the standard habit formation model to an environment in which agents form habits over individual varieties of goods as opposed to over a composite consumption good. We refer to this preference specification as 'deep habit formation'. Under deep habits, the demand function faced by individual producers depends on past sales. This feature is typically assumed ad-hoc in customer market and brand switching cost models. A central result of the Paper is that deep habits give rise to counter cyclical mark-ups, which is in line with the empirical evidence. This result is important because ad-hoc formulations of customer-market and switching-cost models have been criticized for implying pro-cyclical and hence counterfactual mark-up movements. The Paper also provides econometric estimates of the parameters pertaining to the deep habit model.

Habit formation, customer market models, switching cost models, time varying mark-ups, business cycles

Abstract:
This paper generalizes the standard habit formation model to an environment in which agents form habits over individual varieties of goods as opposed to over a composite consumption good. We refer to this preference specification as 'deep habit formation'. Under deep habits, the demand function faced by individual producers depends on past sales. This feature is typically assumed ad-hoc in customer market and brand switching cost models. A central result of the paper is that deep habits give rise to countercyclical markups, which is in line with the empirical evidence. This result is important because ad-hoc formulations of customer-market and switching-cost models have been criticized for implying procyclical and hence counterfactual markup movements. The paper also provides econometric estimates of the parameters pertaining to the deep habit model.

Abstract:
As the millennium draws to an end, the threat posed by the Year 2000 (Y2K) computer problem is inducing vast private and public spending on its remediation. In this paper, we model the Y2K problem as an anticipated, permanent loss in output whose magnitude can be lessened by investing resources in advance. We embed the Y2K problem into a dynamic general equilibrium framework and show that our model replicates three observed characteristics of the dynamics triggered by the Y2K bug: (1) Precautionary investment: investment in solving the Y2K problem begins before the year 2000; (2) Investment delay: although economic agents have been aware of the Y2K problem since the 1960s, investment did not begin until recently; (3) Investment acceleration: as the new millennium approaches, the amount of resources allocated to solving the Y2K problem increases. Furthermore, the model predicts that Y2K investment peaks at the end of 1999 and that consumption growth is not negatively affected by Y2K, whereas investment in physical capital is.

Abstract:
This paper explores the macroeconomic consequences of preferences displaying a subsistence point. It departs from the existing related literature by assuming that subsistence points are specific to each variety of goods rather than to the composite consumption good. We show that this simple feature makes the price elasticity of demand for individual goods procyclical. As a result, markups behave countercyclically in equilibrium. This implication is in line with the available empirical evidence.

Non-homothetic preferences, time-varying markups, business cycles

Abstract:
This paper explores the macroeconomic consequences of preferences displaying a subsistence point. It departs from the existing related literature by assuming that subsistence points are specific to each variety of goods rather than to the composite consumption good. We show that this simple feature makes the price elasticity of demand for individual goods procyclical. As a result, markups behave countercyclically in equilibrium. This implication is in line with the available empirical evidence.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
In this paper, we perform a structural Bayesian estimation of the contribution of anticipated shocks to business cycles in the postwar United States. Our theoretical framework is a real-business-cycle model augmented with four real rigidities: investment adjustment costs, variable capacity utilization, habit formation in consumption, and habit formation in leisure. Business cycles are assumed to be driven by permanent and stationary neutral productivity shocks, permanent investment-specific shocks, and government spending shocks. Each of these shocks is buffeted by four types of structural innovations: unanticipated innovations and innovations anticipated one, two, and three quarters in advance. We find that anticipated shocks account for more than two thirds of predicted aggregate fluctuations. This result is robust to estimating a variant of the model featuring a parametric wealth elasticity of labor supply.

Abstract:
This paper studies optimal fiscal and monetary policy under imperfect competition in a stochastic, flexible-price, production economy without capital. It shows analytically that in this economy the nominal interest rate acts as an indirect tax on monopoly profits. Unless the social planner has access to a direct 100 percent tax on profits, he will always find it optimal to deviate from the Friedman rule by setting a positive and time-varying nominal interest rate. The dynamic properties of the Ramsey allocation are characterized numerically. As in the perfectly competitive case, the labor income tax is remarkably smooth, whereas inflation is highly volatile and serially uncorrelated. An exact numerical solution method to the Ramsey conditions is proposed.

Abstract:
This Paper studies optimal fiscal and monetary policy under imperfect competition in a stochastic, flexible-price, production economy without capital. It shows analytically that in this economy the nominal interest rate acts as an indirect tax on monopoly profits. Unless the social planner has access to a direct 100% tax on profits, he will always find it optimal to deviate from the Friedman rule by setting a positive and time-varying nominal interest rate. The dynamic properties of the Ramsey allocation are characterized numerically. As in the perfectly competitive case, the labour income tax is remarkably smooth, whereas inflation is highly volatile and serially uncorrelated. An exact numerical solution method to the Ramsey conditions is proposed.

Imperfect Competition, Optimal Fiscal and Monetary Policy, Ramsey Equilibria

Abstract:
In this paper, we study Ramsey-optimal fiscal and monetary policy in a medium-scale model of the U.S.\ business cycle. The model features a rich array of real and nominal rigidities that have been identified in the recent empirical literature as salient in explaining observed aggregate fluctuations. The main result of the paper is that price stability appears to be a central goal of optimal monetary policy. The optimal rate of inflation under an income tax regime is half a percent per year with a volatility of 1.1 percent. This result is surprising given that the model features a number of frictions that in isolation would call for a volatile rate of inflation---particularly nonstate-contingent nominal public debt, no lump-sum taxes, and sticky wages.Under an income-tax regime, the optimal income tax rate is quite stable, with a mean of 30 percent and a standard deviation of 1.1 percent. Simple monetary and fiscal rules are shown to implement a competitive equilibrium that mimics well the one induced by the Ramsey policy. When the fiscal authority is allowed to tax capital and labor income at different rates, optimal fiscal policy is characterized by a large and volatile subsidy on capital.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
A growing empirical and theoretical literature argues in favor of specifying monetary policy in the form of Taylor-type interest rate feedback rules. That is, rules whereby the nominal interest rate is set as an increasing function of inflation with a slope greater than one around an intended inflation target. This paper shows that such rules can easily lead to chaotic dynamics. The result is obtained for feedback rules that depend on contemporaneous or expected future inflation. The existence of chaotic dynamics is established analytically and numerically in the context of calibrated economies. The battery of fiscal policies that has recently been advocated for avoiding global indeterminacy induced by Taylor-type interest-rate rules (such as liquidity traps) are shown to be unlikely to provide a remedy for the complex dynamics characterized in this paper.

Abstract:
This paper characterizes Ramsey-optimal monetary policy in a medium-scale macroeconomic model that has been estimated to fit well postwar U.S.\ business cycles. We find that mild deflation is Ramsey optimal in the long run. However, the optimal inflation rate appears to be highly sensitive to the assumed degree of price stickiness. Within the window of available estimates of price stickiness (between 2 and 5 quarters) the optimal rate of inflation ranges from -4.2 percent per year (close to the Friedman rule) to -0.4 percent per year (close to price stability). This sensitivity disappears when one assumes that lump-sum taxes are unavailable and fiscal instruments take the form of distortionary income taxes. In this case, mild deflation emerges as a robust Ramsey prediction. In light of the finding that the Ramsey-optimal inflation rate is negative, it is puzzling that most inflation-targeting countries pursue positive inflation goals. We show that the zero bound on the nominal interest rate, which is often cited as a rationale for setting positive inflation targets, is of no quantitative relevance in the present model. Finally, the paper characterizes operational interest-rate feedback rules that best implement Ramsey-optimal stabilization policy. We find that the optimal interest-rate rule is active in price and wage inflation, mute in output growth, and moderately inertial. This rule achieves virtually the same level of welfare as the Ramsey optimal policy.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
This paper identifies optimal interest-rate rules within a rich, dynamic, general equilibrium model that has been shown to account well for observed aggregate dynamics in the postwar United States. We perform policy evaluations based on second-order accurate approximations to conditional and unconditional expected welfare. We require that interest-rate rules be operational, in the sense that they include as arguments only a few readily observable macroeconomic indicators and respect the zero bound on nominal interest rates. We find that the optimal operational monetary policy is a real-interest-rate targeting rule. That is, an interest-rate feedback rule featuring a unit inflation coefficient, a mute response to output, and no interest-rate smoothing. Contrary to existing studies, we find a significant degree of optimal inflation volatility. A key factor driving this result is the assumption of indexation to past inflation. Under indexation to long-run inflation the optimal inflation volatility is close to zero. Finally, we show that initial conditions matter for welfare rankings of policies.

Abstract:
The existing literature on the stabilizing properties of interest-rate feedback rules has stressed the perils of linking interest rates to forecasts of future inflation. Such rules have been found to give rise to aggregate fluctuations due to self-fulfilling expectations. In response to this concern literature has focused on the stabilizing properties of interest-rate rules whereby the central bank responds to a measure of past inflation. The consensus view that has emerged is that backward-looking rules contribute to protecting the economy from embarking on expectations-driven fluctuations. A common characteristic of the existing studies that arrive at this conclusion is their focus on local analysis. The contribution of this paper is to conduct a more global analysis. We find that backward-looking interest-rate feedback rules do not guarantee uniqueness of equilibrium. We present examples in which for plausible parameterizations attracting equilibrium cycles exist. The paper also contributes to the quest for policy rules that guarantee macroeconomic stability globally. Our analysis indicates that policy rules whereby the interest rate is set as a function of the past interest rate and current inflation are likely to ensure global stability provided that the coefficient on lagged interest rates is greater than unity.

Abstract:
A number of empirical studies document that marginal cost shocks are not fully passed through to prices at the firm level and that prices are substantially less volatile than costs. We show that in the relative-deep-habits model of Ravn, Schmitt-Grohé, and Uribe (2006), firm-specific marginal cost shocks are not fully passed through to product prices. That is, in response to a firm-specific increase in marginal costs, prices rise, but by less than marginal costs leading to a decline in the firm-specific markup of prices over marginal costs. Pass-through is predicted to be even lower when shocks to marginal costs are anticipated by firms. In our model unanticipated firm-specific cost shocks lead to incomplete pass-through (or a decline in markups) of about 20 percent and anticipated cost shocks are associated with incomplete pass-through of about 50 percent. The model predicts that cost pass-through is increasing in the persistence of marginal cost shocks and U-shaped in the strength of habits. The relative-deep-habits model implies that conditional on marginal cost disturbances, prices are less volatile than marginal costs.

cost pass-through, deep habits, markups

Abstract:
A number of empirical studies document that marginal cost shocks are not fully passed through to prices at the firm level and that prices are substantially less volatile than costs. We show that in the relative-deep-habits model of Ravn, Schmitt-Grohe, and Uribe (2006), firm-specific marginal cost shocks are not fully passed through to product prices. That is, in response to a firm-specific increase in marginal costs, prices rise, but by less than marginal costs leading to a decline in the firm-specific markup of prices over marginal costs. Pass-through is predicted to be even lower when shocks to marginal costs are anticipated by firms. In our model, unanticipated firm-specific cost shocks lead to incomplete pass-through (or a decline in markups) of about 20 percent and anticipated cost shocks are associated with incomplete pass-through of about 50 percent. The model predicts that cost pass-through is increasing in the persistence of marginal cost shocks and U-shaped in the strength of habits. The relative-deep-habits model implies that conditional on marginal cost disturbances, prices are less volatile than marginal costs.

Abstract:
We compare two ways of modeling Calvo-type wage stickiness. One in which each household is the monopolistic supplier of a differentiated type of labor input (as in Erceg, et al., 2000) and one in which households supply a homogenous labor input that is transformed by monopolistically competitive labor unions into a differentiated labor input (as in Schmitt-Grohe and Uribe, 2006a,b). We show that up to a log-linear approximation the two variants yield identical equilibrium dynamics, provided the wage stickiness parameter is in each case calibrated to be consistent with empirical estimates of the wage Phillips curve. It follows that econometric estimates of New Keynesian models that rely on log-linearizations of the equilibrium dynamics are mute about which type of wage stickiness fits the data better. In the context of a medium-scale macroeconomic model, we show that the two variants of the sticky-wage formulation give rise to the same Ramsey-optimal dynamics, which call for low volatility of price inflation. Furthermore, under both specifications the optimized operational interest-rate feedback rule features a large coefficient on price inflation and a mute response to wage inflation and output.

Abstract:
This paper proposes a novel international transmission mechanism based on the assumption of deep habits. The term deep habits stands for a preference specification according to which consumers form habits on a good-by-good basis. Under deep habits, firms face more elastic demand functions in markets where nonhabitual demand is high relative to habitual demand, creating an incentive to price discriminate. We refer to this type of price discrimination as pricing to habits. In the presence of pricing to habits, innovations to domestic aggregate demand induce a decline in markups in the domestic country but not abroad, leading to a departure from the law of one price. In this way, the proposed pricing-to-habit mechanism can explain the observation that prices of the same good across countries, expressed in the same currency, vary over the business cycle. Furthermore, it can account for the empirical fact that in response to a positive domestic demand shock, such as an increase in government spending, the real exchange rate depreciates, domestic consumption expands, and the trade balance deteriorates.

Abstract:
The existing literature on the stabilizing properties of interest-rate feedback rules has stressed the perils of linking interest rates to forecasts of future inflation. Such rules have been found to give rise to aggregate fluctuations due to self-fulfilling expectations. In response to this concern, a growing literature has focused on the stabilizing properties of interest-rate rules whereby the central bank responds to a measure of past inflation. The consensus view that has emerged is that backward-looking rules contribute to protecting the economy from embarking on expectations-driven fluctuations. A common characteristic of the existing studies that arrive at this conclusion is their focus on local analysis. The contribution of this Paper is to conduct a more global analysis. We find that backward-looking interest-rate feedback rules do not guarantee uniqueness of equilibrium. We present examples in which for plausible parameterizations attracting equilibrium cycles exist. The Paper also contributes to the quest for policy rules that guarantee macroeconomic stability globally. Our analysis indicates that policy rules whereby the interest rate is set as a function of the past interest rate and current inflation are likely to ensure global stability provided that the coefficient on lagged interest rates is greater than unity.

Backward-looking Taylor rules, endogenous cycles, sticky prices

Abstract:
This Paper identifies optimal interest-rate rules within a rich, dynamic, general equilibrium model that has been shown to account well for observed aggregate dynamics in the post-war United States. We perform policy evaluations based on second-order accurate approximations to conditional and unconditional expected welfare. We require that interest-rate rules be operational, in the sense that they include as arguments only a few readily observable macroeconomic indicators and respect the zero bound on nominal interest rates. We find that the optimal operational monetary policy is a real-interest-rate targeting rule. That is, an interest-rate feedback rule featuring a unit inflation coefficient, a mute response to output, and no interest-rate smoothing. Contrary to existing studies, we find a significant degree of optimal inflation volatility. A key factor driving this result is the assumption of indexation to past inflation. Under indexation to long-run inflation the optimal inflation volatility is close to zero. Finally, we show that initial conditions matter for welfare rankings of policies.

Monetary policy evaluation, inflation stabilization, business cycles

Abstract:
Using panel structural VAR analysis and quarterly data from four industrialized countries, we document that an increase in government purchases leads to an expansion in output and private consumption, a deterioration in the trade balance, and a depreciation of the real exchange rate (i.e., a decrease in the domestic CPI relative to the exchange-rate adjusted foreign CPI). We propose an explanation for these observed effects based on the deep habit mechanism. We estimate the key parameters of the deep-habit model employing a limited information approach. The predictions of the estimated deep-habit model fit well the observed responses of output, consumption, the trade balance, and the real exchange rate to an unanticipated government spending shock. In addition, the deep-habit model predicts that in response to an anticipated increase in government spending consumption and wages fail to increase on impact, which is consistent with the empirical evidence stemming from the narrative identification approach. In this way, the deep-habit model reconciles the findings of the SVAR and narrative literatures on the effects of government spending shocks.

Countercyclical Mark-ups, Deep Habits, Government Spending Shocks, Real exchange rate movements

Abstract:
Using panel structural VAR analysis and quarterly data from four industrialized countries, we document that an increase in government purchases leads to an expansion in output and private consumption, a deterioration in the trade balance, and a depreciation of the real exchange rate (i.e., a decrease in the domestic CPI relative to the exchange-rate adjusted foreign CPI). We propose an explanation for these observed effects based on the deep habit mechanism. We estimate the key parameters of the deep-habit model employing a limited information approach. The predictions of the estimated deep-habit model fit well the observed responses of output, consumption, the trade balance, and the real exchange rate to an unanticipated government spending shock. In addition, the deep-habit model predicts that in response to an anticipated increase in government spending consumption and wages fail to increase on impact, which is consistent with the empirical evidence stemming from the narrative identification approach. In this way, the deep-habit model reconciles the findings of the SVAR and narrative literatures on the effects of government spending shocks.

Abstract:
This paper computes welfare-maximizing monetary and fiscal policy rules in a real business cycle model augmented with sticky prices, a demand for money, taxation, and stochastic government consumption. We consider simple feedback rules whereby the nominal interest rate is set as a function of output and inflation, and taxes are set as a function of total government liabilities. We implement a second-order accurate solution to the model. Our main findings are: First, the size of the inflation coefficient in the interest-rate rule plays a minor role for welfare. It matters only insofar as it affects the determinacy of equilibrium. Second, optimal monetary policy features a muted response to output. More importantly, interest rate rules that feature a positive response to output can lead to significant welfare losses. Third, the welfare gains from interest-rate smoothing are negligible. Fourth, optimal fiscal policy is passive. Finally, the optimal monetary and fiscal rule combination attains virtually the same level of welfare as the Ramsey optimal policy.

Abstract:
This paper characterizes Ramsey-optimal monetary policy in a medium-scale macroeconomic model that has been estimated to fit well postwar US business cycles. We find that mild deflation is Ramsey optimal in the long run. However, the optimal inflation rate appears to be highly sensitive to the assumed degree of price stickiness. Within the window of available estimates of price stickiness (between 2 and 5 quarters) the optimal rate of inflation ranges from -4.2 percent per year (close to the Friedman rule) to -0.4 percent per year (close to price stability). This sensitivity disappears when one assumes that lump-sum taxes are unavailable and fiscal instruments take the form of distortionary income taxes. In this case, mild deflation emerges as a robust Ramsey prediction. In light of the finding that the Ramsey optimal inflation rate is negative, it is puzzling that most inflation-targeting countries pursue positive inflation goals. We show that the zero bound on the nominal interest rate, which is often cited as a rationale for setting positive inflation targets, is of no quantitative relevance in the present model. Finally, the paper characterizes operational interest-rate feedback rules that best implement Ramsey-optimal stabilization policy. We find that the optimal interest-rate rule is active in price and wage inflation, mute in output growth, and moderately inertial.

Ramsey policy, interest rate rules, nominal rigidities, real rigidities

Abstract:
More than half of U.S. currency circulates abroad. As a result, much of the seignorage income of the United States is generated outside of its borders. In this paper we characterize the Ramsey-optimal rate of inflation in an economy with a foreign demand for its currency. In the absence of such demand, the model implies that the Friedman rule—deflation at the real rate of interest—maximizes the utility of the representative domestic consumer. We show analytically that once a foreign demand for domestic currency is taken into account, the Friedman rule ceases to be Ramsey optimal. Calibrated versions of the model that match the range of empirical estimates of the size of foreign demand for U.S. currency deliver Ramsey optimal rates of inflation between 2 and 10 percent per annum. The domestically benevolent government finds it optimal to impose an inflation tax as a way to extract resources from the rest of the world in the form of seignorage revenue.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
A policy issue central banks are confronted with is whether inflation targets should be adjusted to account for the systematic upward bias in measured inflation due to quality improvements in consumption goods. We show that in the context of a Ramsey equilibrium the answer to this question depends on what prices are assumed to be sticky. If nonquality-adjusted prices are assumed to be sticky, then the Ramsey plan predicts that the inflation target should not be corrected. If, on the other hand, quality-adjusted (or hedonic) prices are assumed to be sticky, then the Ramsey plan calls for raising the inflation target by the magnitude of the bias.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
This paper proposes a novel international transmission mechanism based on the assumption of deep habits. The term deep habits stands for a preference specification according to which consumers form habits on a good-by-good basis. Under deep habits, firms face more elastic demand functions in markets where nonhabitual demand is high relative to habitual demand, creating an incentive to price discriminate. We refer to this type of price discrimination as pricing to habits. In the presence of pricing to habits, innovations to domestic aggregate demand induce a decline in markups in the domestic country but not abroad, leading to a departure from the law of one price. In this way, the proposed pricing-to-habit mechanism can explain the observation that prices of the same good across countries, expressed in the same currency, vary over the business cycle. Furthermore, it can account for the empirical fact that in response to a positive domestic demand shock, such as an increase in government spending, the real exchange rate depreciates, domestic consumption expands, and the trade balance deteriorates.

Countercyclical markup, deep habits, government spending, Law of one price, real exchange rate

Abstract:
This paper examines whether asset and goods market trade alone can explain the transmission of short term economic fluctuations between national economies. Three alternative mechanisms by which disturbances are transmitted are analyzed. One mechanism operates through variations in the rate of return on international financial assets, the second through changes in the terms of trade due to variations in the export demand and in the third mechanism variations in export demand affect not only the terms of trade but also equilibrium markups, because export producers have market power and collude as in (Rotemberg and Woodford, 1992). Empirically testable quantitative models of the effects on Canadian output, investment and employment of shocks to the U.S. economy are developed. The empirical success of the three mechanisms is tested by comparing impulse responses estimated from vector autoregressions to the quantitative predictions of the theoretical models for hypothetical parameter configurations suggested in the literature on (international) real business cycles. For all transmission channels considered, a central discrepancy between predicted and observed transmission is that the models can explain quantitatively the observed increase in real variables like investment, output and hours only in combination with a substantially higher terms of trade appreciation than is in fact observed.

Abstract:
A common argument against a balanced-budget fiscal policy rule is that it would tend to amplify business cycles, inducing tax increases and public expenditure cuts during recessions and inducing the reverse during booms. This paper suggests an additional source of instability that may arise from this type of fiscal policy rule. It shows, within the standard neoclassical growth model, that a balanced-budget rule can make expectations of higher tax rates self-fulfilling if the fiscal authority relies heavily on changes in labor income taxes to eliminate short-run fiscal imbalances. Calibrated versions of the model show that this result is empirically plausible for the U.S. economy and other G-7 countries.

Abstract:
This paper studies four models which allow for aggregate fluctuations due to self-fulfilling expectations. It compares the minimum degree of increasing returns to scale necessary to make such equilibria possible and the ability of these models to explain the observed co-movements in macroeconomic time series at business cycle frequencies. The four models discussed are Gali (1994), Rotemberg and Woodford (1992), Benhabib and Farmer (1994) and Baxter and King (1991). These economies are modified, if necessary, to be presented in a unified framework and calibrated uniformly using King, Plosser, and Rebelo (1988) values. Beyond those parameters each model has up to three additional free parameters. For three models necessary and sufficient conditions for the existence of stationary sunspot equilibria are derived analytically, and for each model a numerical example is given to show for which values of these additional parameters stationary sunspot equilibria exist. I find that the two models with variable markups (i.e., Gali and Rotemberg and Woodford) require a lower degree of increasing returns to allow for endogenous fluctuations than do the two models of fixed markups. However, endogenous fluctuations in all four models occur only for markup values in the upper range of available empirical estimates. I also show that persistent output fluctuations are not a necessary property of these models of the business cycle when the only source of fluctuations are changes in people's expectations about the future path of the economy.