Long-run Inflation Rate Research Articles

Volatile energy markets, consumers and energy price expectations

We conduct a survey of consumers in four EU countries (the Czech Republic, Germany, Italy and Poland) faced with supply disruptions, rising energy prices, and serious concerns about both prices and actual availability of energy inputs due to Russia's war on Ukraine. We find that people are aware of the current prices of motor fuels, and willing and able to form expectations for them in one, six, 12 and 60 months. The mean annual rate of growth of prices is positive, exceeds or is equal to the current inflation rate, is greater than the long-run inflation rate in the last 10—20 years, and declines with the length of the horizon over which the respondents are to form their expectations. At least one-third of the respondents expect the prices to decline in the future, and about one-quarter expect them to stay the same. The expectations are affected by the individual characteristics of the respondents and their beliefs about the causes of the current state of the energy markets. The behavioral responses announced by the respondents (change travel mode, reduce driving, replace their car with a more fuel-efficient one, etc.) appear to be realistic and well thought-out, and depend on the expected direction of the expected price changes, rather than their magnitude. By contrast, our respondents struggle with grasping the current prices per unit of electricity or natural gas, and envision higher, and considerably more uncertain, growth rates for them.

Optimal long-run money growth rate in a cash-in-advance economy with labor-market frictions

AbstractWe revisit the Friedman rule in a labor search model and extend Heer (2003), Cooley and Quadrini (2004), and Wang and Xie (2013) to one that allows for endogenous growth. We show that, even without a liquidity effect or a CIA constraint on firms’ wage payment, our model offers a different channel for moderate money growth to increase welfare. Intuitively, in a one-sector endogenous growth economy, the technology is of constant returns with respect to capital. When the labor market is frictional, a moderate increase in money growth induces an expansion in vacancy and employment. Labor and capital are complements in production. With an increase in employment, when the technology is neoclassical, the decreasing return in capital leads to a lower marginal product of labor. However, in an endogenous growth framework wherein the technology exhibits socially constant returns in capital, the marginal product of labor is constant. Due to a constant marginal product of labor, modest inflation raises employment, enlarges economic growth, and increases welfare. Moreover, the optimal long-run inflation rate departs from the Friedman rule, even when the Hosios rule holds. Finally, we find that our model with sustainable growth fits the data better than that without sustainable growth.

Optimal long-run inflation rate in an open economy

I analyze the long-run optimal inflation rate in the sticky price model with trend inflation and a two-country, two-good Ricardian trade structure. As in the closed-economy model, price stickiness effectively reduces an industry’s productivity under trend inflation. Contrary to the standard closed-economy models in which the optimal inflation rate is approximately zero, the model implies that the optimal rate is positive under certain conditions. Welfare gains come from manipulations of the terms of trade, and are hence associated with the loss of the trade partner. If the partner counter-acts, the allocation can be worse than what would occur under autarky.

Dynamic Analysis for Measuring the Impact of Remittance Inflows on Inflation: Evidence From Georgia

Remittance plays a critical role for small economies like Georgia as an unusual means of financing. In policy-making decisions, an understanding of the essence of the relationship between the amount of money exchanged and inflation is important. The paper studies the impact of remittance inflows, using quarterly data spanning a period (2000-2018), on the inflation rate in Georgia. The paper revealed that all independent variables have an effect on the long-run inflation rate; long-run inflation is positively associated with the leading explanatory variable remittance, and no relation is found in the short-run between remittance and inflation. The paper found that inflation's adjustment level to its equilibrium is 12% annually.

Is It Time for Some Unpleasant Monetarist Arithmetic?

Sargent and Wallace (1981) published "Some Unpleasant Monetarist Arithmetic" 40 years ago. Their central message was that a central bank may not have the power to determine the long-run rate of inflation without fiscal support.

Phillips curve and long-run inflation under commitment

PurposeThe purpose of this paper is to study the optimal long-run rate of inflation in the presence of a hybrid Phillips curve, which nests a purely backward-looking Phillips curve and the purely forward-looking New Keynesian Phillips curve (NKPC) as special limiting cases.Design/methodology/approachThis paper derives the long-run rate of inflation in a basic New Keynesian (NK) model, characterized by sticky prices and rule-of-thumb behavior by price setters. The monetary authority possesses commitment and its objective function stems from an approximation to the utility of the representative household.FindingsCommitment solution for the monetary authority leads to steady-state outcomes in which inflation, albeit small, is positive. Rising from zero under the purely forward-looking NKPC, the optimal long-run rate of inflation reaches its maximum under the purely backward-looking Phillips curve. In this case, inflation bias arises, while, under the hybrid Phillips curve, positive long-run inflation is associated with an output gain.Research limitations/implicationsThis paper serves as a clarification against the misperception that log-linearized models take as given the steady-state inflation rate rather than being capable of determining it. Analysis is sensitive to the basic NK setting, with the assumed rule-of-thumb behavior by price setters and price staggering.Originality/valueThe results are the first to quantify the optimal long-run rate of inflation in a fully microfounded model that nests different Phillips curves.

Are Central Bankers Inflation Nutters? An MCMC Estimator of the Long-Memory Parameter in a State Space Model

Inflation targeting is a common monetary policy regime. Inflation targets are often flexible in the sense that the central bank allows inflation to temporarily deviate from the target to avoid causing unnecessary volatility in the real economy. In this paper, we propose modeling the degree of flexibility using an autoregressive fractionally integrated moving average (ARFIMA) model. Assuming that the central bank controls the long-run inflation rate, the fractional integration order becomes a measure of how flexible the inflation target is. A higher integration order implies that inflation deviates from the target for longer periods of time and consequently, that the target is flexible. Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2014) show that a state-based maximum likelihood estimator is superior to other estimators, but our simulations show that their finding is over-biased for a nearly non-stationary time series. To resolve this issue, we first proposed a Bayesian Monte Carlo Markov Chain (MCMC) estimator for fractional integration parameters. This estimator resolves the problem of over-bias. We estimate the fractional integration order for 6 countries for the period 1993M1 to 2017M9. We found that inflation was integrated to an order of 0.8 to 0.9 indicating that the inflation targets are implemented with a high degree of flexibility.

The Optimal Inflation Rate with Discount Factor Heterogeneity

This paper shows that deviations from long-run price stability are optimal in the presence of price stickiness whenever profit and utility flows are discounted at a different rate. In that case, a monetary authority acting under commitment will choose a path for the inflation rate that ends with a non-zero value. Such a property is relevant in a wide range of macroeconomic environments. I first illustrate this by studying optimal monetary policy in a New Keynesian model with a perpetual youth structure. In this setting, profit flows are discounted more heavily than utility flows and the optimal inflation target is equal to 3.2 percent in a baseline calibration of the model. I also show that this property leads to a positive long-run inflation rate in models with firm entry and exit and in environments with search and matching frictions in the labor market and another form of nominal rigidity, wage stickiness.

Are common stocks a hedge against inflation in emerging markets?

This paper examines the inflation-hedging ability of common stocks in the long run for emerging market countries using monthly data on stock and goods prices over the period 1982:01–20,016:01. Johansen’s (J Econ Dyn Control 12:231–254, 1988) method of cointegration is employed for 28 countries for which the order of integration of the underlying series is the same, and Pesaran et al.’s (J Appl Econom 16:289–326, 2001) autoregressive distributed lag (ARDL) bounds test is used for 18 countries for which the order of integration is not the same. In only 10 cases is the long-run relationship established between stock and goods prices when the former test is used, whereas such a relationship is established in 7 cases when the latter test is used. The results of error-correction representations normalized on stock prices indicate that stock prices take a long time to return to their long-run equilibrium relation with goods prices. Overall, common stocks provide a good hedge against inflation in the long run in more than one-third of the cases examined. One implication that emerges from these results is that in the majority of the countries, monetary authorities are not able to control inflation by reducing the nominal interest rate. Another implication is that the monetary growth is not the key factor determining the long-run inflation rate in these countries.

Some Implications of Learning for Price Stability

Survey data on expectations of a range of macroeconomic variables exhibit low-frequency drift. In a New Keynesian model consistent with these empirical properties, optimal policy in general delivers a positive inflation rate in the long run. Two special cases deliver classic outcomes under rational expectations: as the degree of low-frequency variation in beliefs goes to zero, the long-run inflation rate coincides with the inflation bias under optimal discretion; for non-zero low-frequency drift in beliefs, as households become highly patient valuing utility in any period equally, the optimal long-run inflation rate coincides with optimal commitment ― price stability is optimal.

Some implications of learning for price stability

Survey data on expectations of a range of macroeconomic variables exhibit low-frequency drift. In a New Keynesian model consistent with these empirical properties, optimal policy in general delivers a positive inflation rate in the long run. Two special cases deliver classic outcomes under rational expectations: as the degree of low-frequency variation in beliefs goes to zero, the long-run inflation rate coincides with the inflation bias under optimal discretion; for non-zero low-frequency drift in beliefs, as households become highly patient valuing utility in any period equally, the optimal long-run inflation rate coincides with optimal commitment – price stability is optimal. The optimal state-contingent response to cost-push disturbances similarly reflects properties of optimal discretion and optimal commitment, depending on the degree of low-frequency variation in beliefs. When beliefs exhibit substantial variation in response to short-run forecast errors, optimal policy is closer to commitment.

Monetary policy and liquid government debt

We examine the conduct of monetary policy in a world where the supply of outside money is controlled by the fiscal authority–a scenario increasingly relevant for many developed economies today. Central bank control over the long-run inflation rate depends on whether fiscal policy is Ricardian or Non-Ricardian. The optimal monetary policy follows a generalized Friedman rule that eliminates the liquidity premium on scarce treasury debt. We derive conditions for determinacy under both fiscal regimes and show that they do not necessarily correspond to the Taylor principle. In addition, Non-Ricardian regimes may suffer from multiplicity of steady-states when the government runs persistent deficits.

A Note on Intrinsic Inflation Persistence and the Optimal Inflation Rate

This paper examines the implications of intrinsic inflation persistence, namely inertia that inflation inherits from its own past, on the conduct of optimal monetary policy. We study the optimal long-run rate of inflation in a basic New Keynesian model, which is augmented for intrinsic inflation persistence. We show that the commitment solution for the monetary authority leads to steady-state outcomes in which inflation is positive.

Optimal long-run inflation with occasionally binding financial constraints

This paper studies the optimal long-run inflation rate in a simple New Keynesian model with occasionally binding collateral constraints that intermediate-good firms face on hiring labor. The paper finds that the optimal long-run annual inflation rate is around 1.5% if the economy is hit by a total factor productivity (TFP) shock and nearly 2.5% if the economy is subject to a markup shock. The shadow value of the collateral constraint is akin to an endogenous cost-push shock. Differently from usual cost-push shocks, however, this shock is asymmetric as it takes non-negative values only. Since the mean of this asymmetric endogenous cost-push shock is positive, inflation is also positive on average. In addition, a binding collateral constraint resembles a time-varying tax on labor, which the monetary authority can smooth by setting a positive inflation rate. More generally, the basic result is related to standard Ramsey theory in that optimal policy smoothes distortions over time.

THE OPTIMAL INFLATION TARGET IN AN ECONOMY WITH LIMITED ENFORCEMENT

We formulate a central bank's problem of selecting an optimal long-run inflation rate as the choice of a distorting tax by a planner who wishes to maximize discounted stationary utility for a heterogeneous population of infinitely lived households in an economy with constant aggregate income and public information. Households are segmented into agents who store value in currency alone and agents who have access to both currency and loans. We show that the optimum inflation rate is positive, because inflation reduces the value of the outside option for credit agents and raises their debt limits.

Optimal monetary policy with endogenous entry and product variety

Deviations from long-run price stability are optimal in the presence of endogenous entry and product variety in a sticky-price model in which price stability would be optimal otherwise Long-run inflation (deflation) is optimal when the benefit of variety to consumers falls short of (exceeds) the market incentive for creating that variety—the desired markup; Price indexation exacerbates this mechanism. Plausible preference specifications and parameter values justify positive long-run inflation rates. However, short-run price stability (around this non-zero trend) is close to optimal, even in the presence of endogenously time-varying desired markups that distort the intertemporal allocation of resources.

Envy, guilt, and the Phillips curve

We incorporate inequality aversion into an otherwise standard New Keynesian dynamic stochastic equilibrium model with Calvo wage contracts and positive inflation. Workers with relatively low incomes experience envy, whereas those with relatively high incomes experience guilt. The former seek to raise their income and the latter seek to reduce it. The greater the inflation rate, the greater the degree of wage dispersion under Calvo wage contracts, and thus the greater the degree of envy and guilt experienced by the workers. Since the envy effect is stronger than the guilt effect, according to the available empirical evidence, a rise in the inflation rate leads workers to supply more labor over the contract period, generating a significant positive long-run relation between inflation and output (and employment), for low inflation rates. Provided that wage adjustments are costly, this tradeoff remains significant even once the degree of wage stickiness adjusts to the inflation rate. This Phillips curve relation, together with an inefficient zero-inflation steady state, provides a rationale for a positive long-run inflation rate. Given standard calibrations, optimal monetary policy is associated with a long-run inflation rate around 2%.

Are Central Bankers Inflation Nutters? A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model

Several central banks have adopted inflation targets. The implementation of these targets is flexible; the central banks aim to meet the target over the long term but allow inflation to deviate from the target in the short-term in order to avoid unnecessary volatility in the real economy. In this paper, we propose modeling the degree of flexibility using an ARFIMA model. Under the assumption that the central bankers control the long-run inflation rates, the fractional integration order captures the flexibility of the inflation targets. A higher integration order is associated with a more flexible target. Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2011) show that a state-based maximum likelihood estimator is superior to other estimators, but our simulations show that their finding is over-biased for a nearly non-stationary time series. We resolve this issue by using a Bayesian Monte Carlo Markov Chain (MCMC) estimator. Applying this estimator to inflation from six inflation-targeting countries for the period 1999 M1 to 2013 M3, we find that inflation is integrated of order 0.8 to 0.9 depending on the country. The inflation targets are thus implemented with a high degree of flexibility.

The Optimal Inflation Target in an Economy with Limited Enforcement

We formulate the central bank's problem of selecting an optimal long-run inflation rate as the choice of a distorting tax by a planner who wishes to maximize discounted stationary utility for a heterogeneous population of infinitely-lived households in an economy with constant aggregate income. Households are divided into cash agents, who store value in currency alone, and credit agents who have access to both currency and loans. The planner's problem is equivalent to choosing inflation and nominal rates consistent with a resource constraint, and with an incentive constraint that ensures credit agents prefer the superior consumption-smoothing power of loans to that of currency. We show that the optimum implied rate of inflation is positive, and the optimum implied nominal interest rate is higher than the inflation rate, if the social welfare function weighs credit agents no more than their population fraction.

Optimal monetary policy and downward nominal wage rigidity in frictional labor markets

This paper studies the optimal long-run inflation rate in a labor search and matching framework in the presence of downward nominal wage rigidity. Optimal monetary policy features positive inflation in the long run; the optimal annual long-run inflation rate for the U.S. economy is slightly below 1 percent with a money demand motive and around 2 percent otherwise. Positive inflation facilitates real wage adjustments and hence it eases job creation and prevents excessive increase in unemployment following adverse productivity shocks. The findings of the paper can also be related to standard Ramsey theory of “wedge smoothing”; with positive inflation under sticky prices, the size and the volatility of the intertemporal wedge are significantly reduced.