Optimal Monetary Policy with r* < 0
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Roberto Billi and
Jordi Gali
Journal of Monetary Economics, Volume 142, March 2024
Abstract
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We study the optimal monetary policy problem in a New Keynesian economy with a zero lower bound (ZLB) on the nominal interest rate, and in which the steady state natural rate (r*) is negative. We show that the optimal policy aims to approach gradually a steady state with positive average inflation. Around that steady state, inflation and output fluctuate optimally in response to shocks to the natural rate. The central bank can implement that optimal outcome by means of an appropriate state-contingent rule, even though in equilibrium the nominal rate remains at zero most (or all) of the time. In order to establish that result, we derive sufficient conditions for local determinacy in a more general model with endogenous regime switches.
Flattening of the Phillips curve with state-dependent prices and wages
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James Costain and
Borja Petit
The Economic Journal, Volume 132, No. 642, February 2022, 546-581
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We study monetary transmission in a model of state-dependent prices and wages based on "control costs". Stickiness arises because precise choice is costly: decision-makers tolerate errors both in the timing of adjustments, and in the new level at which the price or wage is set. The model is calibrated to microdata on the size and frequency of price and wage changes. In our simulations, money shocks have less persistent real effects than in the Calvo framework; nonetheless, the model exhibits a substantial degree of non-neutrality, driven mainly by wage rigidity. State-dependent nominal stickiness implies a flatter Phillips curve as trend inflation declines, because price and wage adjustments become less frequent, making short-run inflation less reactive to shocks. Our model can explain almost half of the observed decline in the slope of the Phillips curve since 2000.
Effectiveness and addictiveness of quantitative easing
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Peter Karadi
Journal of Monetary Economics, Volume 117, January 2021, 1096-1117
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This paper analyzes optimal asset-purchase policies in a macroeconomic model with banks, which face occasionally-binding balance-sheet constraints. It proves analytically that asset-purchase policies are effective in offsetting large financial disturbances, which impair banks’ capital position. It warns, however, that the policy can remain ineffective after non-financial shocks and might offer no substitute for interest rate policy when the latter is constrained by the lower bound. Furthermore, the asset-purchase policy is addictive because it flattens the yield curve, reduces the profitability of the banking sector, and therefore slows down its recapitalization. Consequently, the optimal exit from large central bank balance sheets is gradual.
Logit price dynamics
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James Costain
Journal of Money, Credit and Banking, Volume 51, Issue 1, February 2019, 43-78
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We model retail price stickiness as the result of costly, error-prone decision making. Under our assumed cost function for the precision of choice, the timing of price adjustments and the prices firms set are both logit random variables. Errors in the prices firms set help explain micro facts related to the size of price changes, the behavior of adjustment hazards, and the variability of prices and costs. Errors in adjustment timing increase the real effects of monetary shocks, by reducing the “selection effect.” Allowing for both types of errors also helps explain how trend inflation affects price adjustment.
Precautionary price stickiness
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James Costain
Journal of Economic Dynamics and Control, Volume 58, September 2015, 218-234
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This paper proposes a model in which retail prices are sticky even though firms can always change their prices at zero cost. Instead of imposing a “menu cost”, we assume that more precise decisions are more costly. In equilibrium, firms optimally make some errors in price-setting, thus economizing on managerial time. Both the time cost of choice, and the resulting risk of errors, give firms an incentive to leave their prices unchanged until they perceive a sufficiently costly deviation from the optimal price. We show that this error-prone “control cost” framework helps explain many puzzling observations from microdata. However, on the macroeconomic side, pricing errors do little to explain the real effects of monetary shocks.
Learning from experience in the stock market
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Galo Nuno
Journal of Economic Dynamics and Control, Volume 52, March 2015, 224-239
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New evidence suggests that individuals “learn from experience,” meaning they learn from events occurring during their lives as opposed to the entire history of events. Moreover, they weigh more heavily recent events compared to events occurring in the distant past. This paper analyzes the implications of such learning for stock pricing in a model with finitely lived agents. Individuals learn about the rate of change of the stock price and of dividends using a weighted decreasing-gain algorithm. As a result of waves of optimism and pessimism, the stock price exhibits stochastic fluctuations around the rational expectations equilibrium. Conditional on the historical path of dividends, the model produces a price–dividend ratio which is in line with the evidence for the last century, except for the “dot-com” bubble in the 1990s.
Optimal monetary policy with state-dependent pricing
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Carlos Thomas
International Journal of Central Banking, September 2014, 49-94
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This paper studies optimal monetary policy from the timeless perspective in a general model of state-dependent pricing. Firms are modeled as monopolistic competitors subject to idiosyncratic menu cost shocks. We find that, under certain conditions, a policy of zero inflation is optimal both in the long run and in response to aggregate shocks. Key to this finding is an "envelope" property: at zero inflation, a marginal increase in the rate of inflation has no effect on firms' profits and hence on their probability of repricing. We offer an analytic solution that does not require local approximation or efficiency of the steady state. Under more general conditions, we show numerically that the optimal commitment policy remains very close to strict inflation targeting.
Saudi Arabia and the oil market
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Galo Nuno
The Economic Journal, Volume 123, Issue 573, December 2013, 1333–1362
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In this study, we document two features that have made Saudi Arabia different from other oil producers. First, it has typically maintained ample spare capacity. Second, its production has been quite volatile even though it has witnessed few domestic shocks. These features can be rationalized in a general equilibrium model in which the oil market is modeled as a dominant producer with a competitive fringe. We show that the net welfare effect of oil tariffs on consumers is null. The reason is that Saudi Arabia’s monopolistic rents fall entirely on fringe producers.
Distributional dynamics under smoothly state-dependent pricing
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James Costain
Journal of Monetary Economics, Volume 58, Issues 6-8, September 2011, 646–665
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Starting from the assumption that firms are more likely to adjust their prices when doing so is more valuable, this paper analyzes monetary policy shocks in a DSGE model with firm-level heterogeneity. The model is calibrated to retail price microdata, and inflation responses are decomposed into “intensive”, “extensive”, and “selection” margins. Money growth and Taylor rule shocks both have nontrivial real effects, because the low state dependence implied by the data rules out the strong selection effect associated with fixed menu costs. The response to sector-specific shocks is gradual, but inappropriate econometrics might make it appear immediate.
Price adjustments in a general model of state-dependent pricing
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James Costain
Journal of Money, Credit and Banking, Volume 43, Issue 2-3, March 2011, 385–406
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We study the distribution of retail price adjustments under the assumption that firms are more likely to adjust their prices when doing so is more valuable. Our setup nests Calvo (1983) at one extreme and a fixed menu cost model at the other; all parameterizations are ranked by a measure of state dependence. High state dependence implies, counterfactually, that there are no small price changes and that the variance of price changes falls sharply with trend inflation. The parameterization that best fits microdata has low state dependence, implying a Phillips curve coefficient 60% as large as that of the Calvo model, but is nonetheless well behaved at high inflation rates.
Monetary policy trade-offs with a dominant oil producer
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Andrea Pescatori
Journal of Money, Credit and Banking, Volume 42, Issue 1, February 2010, 1–32
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We model oil production decisions from optimizing principles rather than assuming exogenous oil price shocks and show that the presence of a dominant oil producer leads to sizable static and dynamic distortions of the production process. Under our calibration, the static distortion costs the U.S. around 1.6% of GDP per year. In addition, the dynamic distortion, reflected in inefficient fluctuations of the oil price markup, generates a trade-off between stabilizing inflation and aligning output with its efficient level. Our model is a step away from discussing the effects of exogenous oil price variations and toward analyzing the implications of the underlying shocks that cause oil prices to change in the first place.
Oil and the Great Moderation
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Andrea Pescatori
The Economic Journal, Volume 120, Issue 543, March 2010, 131–156
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We assess the extent to which the greater US macroeconomic stability since the mid-1980s can be accounted for by changes in oil shocks and the oil elasticity of gross output. We estimate a DSGE model and perform counterfactual simulations. We nest two popular explanations for the Great Moderation: smaller (non-oil) real shocks and better monetary policy. We find that oil played an important role in the stabilization. Around half of the reduced volatility of inflation is explained by better monetary policy alone, and 57% of the reduced volatility of GDP growth is attributed to smaller TFP shocks. Oil related effects explain around a third.
Jackknife instrumental variables estimation: replication and extension of Angrist, Imbens, and Krueger
Journal of Applied Econometrics, Volume 25, Issue 6, September 2010, 1063–1066
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I replicate most of the results in Angrist, Imbens, and Krueger (Journal of Applied Econometrics 1999; 14: 57–67), point to a possible error in and re-estimate Model 3, and analyze some simple extensions. The programming code, data, and results are available under "Codes" above.
Monetary effects on nominal oil prices
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Max Gillman
North American Journal of Economics and Finance, Volume 20, Issue 3, February 2010, 1–32
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The paper presents a theory of nominal asset prices for competitively owned oil. Focusing on monetary effects, with flexible oil prices the US dollar oil price should follow the aggregate US price level. But with rigid nominal oil prices, the nominal oil price jumps proportionally to nominal interest rate increases. We find evidence for structural breaks in the nominal oil price that are used to illustrate the theory of oil price jumps. The evidence also indicates strong Granger causality of the oil price by US inflation as is consistent with the theory.
Optimal and simple monetary policy rules with zero floor on the nominal interest rate
International Journal of Central Banking, Volume 4, Issue 2, June 2008, 73–127
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Recent treatments of the issue of a zero floor on nominal interest rates have been subject to some important methodological limitations. These include the assumption of perfect foresight or the introduction of the zero lower bound as an initial condition or a constraint on the variance of the interest rate, rather than an occasionally binding non-negativity constraint. This paper addresses these issues, offering a global solution to a standard dynamic stochastic sticky-price model with an explicit occasionally binding non-negativity constraint on the nominal interest rate. It turns out that the dynamics and sometimes the unconditional means of the nominal rate, inflation, and the output gap are strongly affected by uncertainty in the presence of the zero lower bound. Commitment to the optimal rule reduces unconditional welfare losses to around one-tenth of those achievable under discretionary policy, while constant price-level targeting delivers losses that are only 60 percent larger than those under the optimal rule. Even though the unconditional performance of simple instrument rules is almost unaffected by the presence of the zero lower bound, conditional on a strong deflationary shock, simple instrument rules perform substantially worse than the optimal policy.
Granger causality of the inflation-growth mirror in accession countries
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Max Gillman
The Economics of Transition, Volume 12, Issue 4, December 2004, 653-681
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The paper presents a model in which the exogenous money supply causes changes in the inflation rate and the output growth rate. While inflation and growth rate changes occur simultaneously, the inflation acts as a tax on the return to human capital and in this sense induces the growth rate decrease. Shifts in the model's credit sector productivity cause shifts in the income velocity of money that can break the otherwise stable relationship between money, inflation, and output growth. Applied to two accession countries, Hungary and Poland, a VAR system is estimated for each that incorporates endogenously determined multiple structural breaks. Results indicate Granger causality positively from money to inflation and negatively from inflation to growth for both Hungary and Poland, as suggested by the model, although there is some feedback to money for Poland. Three structural breaks are found for each country that are linked to changes in velocity trends, and to the breaks found in the other country.
A revised Tobin effect from inflation: relative input price and capital ratio realignments
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Max Gillman
Economica, Volume 70, Issue 129, August 2003, 439-450
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The paper studies the realignments induced by inflation within an endogenous growth monetary economy. Accelerating inflation raises the ratio of the real wage to the real interest rate, and so raises the use of physical capital relative to human capital across all sectors. We find cointegration evidence for the US and UK economies consistent with a general equilibrium, Tobin-type, effect of inflation on input prices and capital intensity, even while the growth rate of output is reduced by inflation.
