Taylor Type Rules And Permanent Shifts In Productivity Growth
Research Division
Federal Reserve Bank of St. Louis
Working Paper Series
Taylor-Type Rules and Permanent
Shifts in Productivity Growth
William T. Gavin
Benjamin D. Keen
and
Michael R. Pakko
Working Paper 2009-049A
http://research.stlouisfed.org/wp/2009/2009-049.pdf
September 2009
FEDERAL RESERVE BANK OF ST. LOUIS
Research Division
P.O. Box 442
St. Louis, MO 63166
______________________________________________________________________________________
The views expressed are those of the individual authors and do not necessarily reflect official positions of
the Federal Reserve Bank of St. Louis, the Federal Reserve System, or the Board of Governors.
Federal Reserve Bank of St. Louis Working Papers are preliminary materials circulated to stimulate
discussion and critical comment. References in publications to Federal Reserve Bank of St. Louis Working
Papers (other than an acknowledgment that the writer has had access to unpublished material) should be
cleared with the author or authors.
Taylor-Type Rules and Permanent Shifts in Productivity Growth
William T. Gavin, Federal Reserve Bank of St. Louis
Benjamin D. Keen, University of Oklahoma
Michael R. Pakko, University of Arkansas at Little Rock
September 16, 2009
ABSTRACT:
This paper examines the impact of a permanent shock to the productivity growth rate in a New
Keynesian model when the central bank does not immediately adjust its policy rule to that shock.
Our results show that inflation and productivity growth are negatively correlated at business
cycle frequencies when the central bank follows a Taylor-type policy rule that targets the output
gap. We then demonstrate that inflation is more stable after a permanent productivity shock
when monetary policy targets the output growth rate (not the output gap) or the price-level path
(not the inflation rate). As for the welfare implications, both the output growth and price-level
path rules generate much less volatility in output and inflation after a productivity shock than
occurs with the Taylor rule.
JEL Codes: E30, E42, E58
Keywords: Inflation Dynamics, Permanent Productivity Shocks, Nominal Interest Rate Rules
The views expressed in this paper are those of the authors and do not necessarily represent official
positions of the Federal Reserve Bank of St. Louis or the Federal Reserve System. Corresponding author:
William T. Gavin, at gavin@stls.frb.org
1. Introduction
During the 1990s, inflation rate averaged 3 percent per year in the United States, well below the
5- to 10-year-ahead forecasts of 5 percent made in 1989. In retrospect, the surprisingly low
inflation of the 1990s is attributable to a permanent rise in productivity growth. Orphanides et al.
(2000) likewise argue that rising U.S. inflation from 1965 to 1980 was the result of real-time
errors in the measurement of potential output.1 They contend that a productivity slowdown
reduced the actual growth rate of potential output below its perceived growth rate, which led
policymakers inadvertently to follow an inflationary policy. This paper investigates one source
of the negative correlation between inflation and productivity growth to determine whether
policymakers can prevent an unintentional change in monetary policy after a productivity growth
shock.
Taylor (1993) outlines a simple monetary policy rule in an attempt to describe how the
Federal Reserve has conducted monetary policy in recent years. The Taylor rule says that the
nominal interest rate target adjusts according to deviations of output from its potential and the
inflation rate from its target rate. Recently, researchers also have examined how well the Taylor
rule achieves the objectives of the monetary authority. Although it is not usually the optimal
monetary policy rule, researchers find that the Taylor rule performs relatively well in a variety of
macroeconomic models under alternative assumptions about potential output and real interest
rates.2 We, however, find that the Taylor rule does not work well when there is a permanent shift
in the productivity growth rate that is not immediately observed by policymakers.
1 See also Orphanides (2003a, 2003b). Edge, Laubach, and Williams (2007) investigate a model in which agents
learn about shifts in long-run productivity growth.
2 See, for example, the papers collected in Taylor (1999b) and on the “Monetary Policy Rule Home Page” website:
http://www.stanford.edu/~johntayl/PolRulLink.htm.
1
This paper examines the impact of a permanent shock to the productivity growth rate in a
standard New Keynesian model under alternative monetary policy rules. Our results indicate that
a permanent rise in productivity growth causes an unstable decline in inflation when the central
bank follows the standard Taylor rule and does not immediately observe the shock. The negative
correlation between productivity growth and inflation, however, is specific to the Taylor rule.
When the central bank targets the output growth rate or the price-level path instead of the level
of output, we show that inflation initially rises and eventually returns to its target without any
intervention by the central bank. Furthermore, inflation and the output gap vary much less when
the output growth rate or the price-level path is the target of monetary policy as opposed to the
level of output, which is used in the Taylor rule. Those results suggest that the Taylor rule has it
backwards. That is, we find that the monetary authority should target the output growth rate and
the price-level path instead of the level of output and the inflation rate as suggested by Taylor
(1993).
The paper proceeds in the following manner. Section 2 outlines a conventional New
Keynesian model with a permanent productivity growth shock. Section 3 examines how the
economy responds to a permanent productivity growth shock under various monetary policy
rules. To assess the welfare implications of the alternative policy rules, Section 4 examines the
volatility of inflation and output over horizons ranging from 1 quarter to 5 years after a
permanent productivity shock. Section 5 concludes.
2. The
Model
We use a standard New Keynesian model with infinitely lived households who maximize utility
over consumption and leisure. Our model features include Calvo-style price setting, capital
2
adjustment costs, monopolistically competitive firms, a role for money via a “shopping-time”
constraint, and alternative nominal interest rate rules for implementing monetary policy. In our
model, the central bank’s optimal policy is to stabilize the inflation rate at its steady state to
eliminate the sticky price distortion.
Our analysis evaluates the effects of a permanent shift in the productivity growth rate on
the economy under alternative monetary policy rules.3 An abbreviated version of our model is
presented below, whereas the entire model is outlined in the appendix.4
2.1
Households
Households are infinitely lived agents who seek to maximize their expected utility from
consumption, ct, and leisure, lt,
∑
ln
(1)
subject to the following budget constraint, time constraint, and capital accumulation equation:
/
/
/
/
/ , (2)
1, and
(3)
/
, (4)
where Pt is the price level, it is investment, Mt is the nominal money stock, Bt is government
bonds, wt is the real wage, nt is labor, qt is the capital rental rate, kt is the capital stock, dt is the
firms’ real profits remitted to the households, Rt is the gross nominal interest rate from period t to
t+1, Tt is a transfer from the monetary authority, E0 is the expectational operator at time 0, β is
the discount factor, δ is the depreciation rate, χ and ω are preference parameters, and st represents
3 See Pakko (2002) for a richer discussion of the transitional effects associated with a permanent change in the
growth rate of technological progress.
4 Our model is a modified version of the model in Gavin, Keen, and Pakko (2005).
3
the shopping-time costs of holding money balances: st = ζ(Ptct/Mt)γ. The parameter φ(·)
represents capital adjustment costs that are given by it – φ(it/kt)kt. We assume that the average
and marginal capital adjustment costs are zero around the steady state (i.e., φ(it/kt) = i/k and
φ΄(it/kt) = 1).
2.2 Firms
Each firm produces a heterogeneous good in a monopolistically competitive market.
Specifically, firm f produces its output, yf,t, according to the following production function:
,
,
,
, (5)
where nf,t is firm f’s labor demand, kj,t is firm f’s capital demand, Zt is an economy-wide
productivity factor, and 0 < α < 1. The differentiated output of all the firms is then combined to
generate aggregate output:
/
/
,
,
(6)
where –ε is the price elasticity of demand for yf,t and yt = ct + it. The productivity factor, Zt,
evolves such that its growth rate follows a random walk:
ln
⁄
ln
⁄
, (7)
where vt ~ N(0,σ2). Initially, productivity grows at a deterministic rate of . Following Calvo
(1983), the probability that a firm can set a new price is η, and the probability that a firm cannot
change the price that it charged last period is (1 – η).5
2.3 Calibrating
the
Model
Our calibration of the parameters is consistent with that of the literature. The household discount
5 Since the steady-state inflation rate is zero in our model, indexation is not included in the price-setting rule.
4
factor, β, is set to 0.99 and the preference parameter, χ, is set so that the steady-state labor
supply, , equals 0.3. In the steady state, shopping time, , equals 1 percent of the time spent
working. The other preference parameter, ω, is calibrated to 7/9, which implies that the elasticity
of labor supply with respect to the real wage is approximately equal to 3.6 The shopping-time
parameter, γ, is set to unity, so that the interest rate elasticity of money demand equals –0.5.7 The
capital share of output, α, is set to 0.33 and the capital stock is assumed to depreciate at 2 percent
per quarter. The price elasticity of demand, , is set equal to 6, which is consistent with a steady-
state markup of 20 percent. We calibrate the probability of price adjustment, η, equal to 0.25.
That parameterization implies that firms change prices on average once a year. Capital
adjustment costs are calibrated so that the elasticity of the investment-to-capital ratio with
respect to Tobin’s q, [(i/k)φ″(·)/φ′(·)]-1, is equal to 5. The steady-state gross inflation rate, , is 1.
Finally, we consider the specification and calibration of various monetary policy rules.
2.4
The Monetary Authority
The monetary authority targets the nominal interest rate, R, as follows:
1
̂ , (8)
where θπ ≥ 0, θy ≥ 0, θg ≥ 0, θP ≥ 0, pt is the log of the price level, and gt is the growth rate of
output. The symbol ‘^’ indicates the variable’s percentage deviation from its steady state
observed before the permanent shift in productivity growth. Equation (8) then resembles a Taylor
(1993) rule in which θg and θP are set = 0. In our sticky price model, the optimal monetary policy
rule, if it were implementable, prevents the inflation rate from deviating from its target by setting
θπ = ¥. We initially analyze the effects of a permanent productivity growth shock on key
6 The elasticity of labor supply with respect to the real wage equals 1
/
.
7 The interest rate elasticity of money demand is approximately equal to 1/ 1
.
5
economic variables under the optimal policy rule and then use those results to evaluate
alternative and more politically feasible monetary policies.
3.
Monetary Policy’s Response to a Productivity Growth Shock
This section examines the impact of a permanent shock to the productivity growth rate for
various parameterizations of the monetary policy rule given in Equation (8). We assume that
productivity increases at 0.4 percent per period (or quarter) and then a productivity shock (v1 =
0.1) permanently raises the productivity growth rate to 0.5 percent per period. Impulse response
functions for capital stock growth, the inflation rate, real and nominal interest rates, real wage
growth, real marginal cost, hours worked, and output growth to that productivity growth shock
are shown for each monetary policy rule considered.
3.1
The Optimal Policy
Our initial objective is to establish the optimal monetary policy for comparison with alternative
monetary policy rules. King and Wolman (1999), Woodford (2003), and Canzoneri, Cumby, and
Diba (2004) find that a monetary policy rule that eliminates the distortions caused by nominal
frictions, such as sticky prices, is approximately optimal. That rule is approximately optimal
because distortions due resulting from real features, such as monopolistic competition and the
shopping-time costs, are small relative to distortions associated with nominal rigidities. In our
model, price stickiness is the only nominal friction and the distortions caused by it can be
eliminated by perfectly stabilizing inflation.
The solid line in Figure 1 shows the impulse responses of key economic variables to a
permanent productivity growth shock in which the monetary authority follows the optimal policy
6
rule (θπ = ∞, and all the other θis equal zero). That shock immediately causes households’
permanent income to rise, which in turn leads to an upward spike in consumption and a decline
in hours worked as households increase their leisure time. Furthermore, firms raise their demand
for labor which, when combined with the decline in labor supply, causes hours worked to fall
and the real wage to spike upward.8 That instantaneous decline in labor dominates the rise in
productivity, so that output initially falls. The decrease in output and the rise in consumption
require that investment sharply declines and the growth rate of capital stock slows. The capital
stock response, however, is not unexpected. According to the Solow model, a rise in technology
growth causes capital per effective unit of labor to decline as the economy transitions to its new
balanced growth path. The increase in productivity raises future capital rental rates, so that the
real interest rate jumps on impact. Under the optimal policy rule, the nominal interest rate
response mimics the real interest rate because inflation remains unchanged. Finally, the central
bank’s policy of keeping inflation constant guarantees that firms’ price markup and real marginal
cost remain unchanged.
In subsequent periods, the economy begins to transition to its new steady state.
Consumption growth moderates to a degree consistent with the real interest rate. Faster
productivity growth raises the growth rate of the real wage, which encourages households to
substitute away from leisure and toward more work. The increase in hours worked and the
growth rate of productivity raises the growth rates of output and investment. Both real and
nominal interest rates continue to rise as the returns to capital increase.
Although placing an extreme weight on inflation (i.e., θπ = ∞) is theoretically the optimal
monetary policy, most central banks are unable politically to implement such a policy. Therefore,
8 Basu, Fernald, and Kimball (2006) and Francis and Ramey (2005) provide empirical evidence that hours worked
declines after a positive technology shock.
7
we will measure how close alternative monetary policy rules, which are more politically feasible,
come to the optimal policy.
3.2
The Weak Inflation Rule
We begin by considering a policy in which the central bank weakly targets the deviation of
inflation from its target. Specifically, the monetary authority sets its nominal interest rate target
in response to changes in the inflation rate:
1
, (9)
where θπ > 0 is a necessary condition for the model to have a stable and unique solution.9 The
longer dashed lines in Figure 1 depict the impulse responses to a 0.1 percent permanent increase
in the productivity growth rate when the monetary authority follows the weak inflation rule (θπ =
0.5). The key difference between the weak inflation rule and the optimal rule (θπ = ∞) is that a
permanent productivity growth shock causes inflation to increase and the rise in the nominal
interest rate to be greater with the weak inflation rule. To understand that result, substitute the
long-run Fischer equation,
, into a long-run version of Equation (9), so that
inflation can be solved as a function of the long-run real interest rate:
/ . (10)
Since the 0.1 percent increase in productivity growth boosts the long-run real interest rate by
approximately the same amount, long-run inflation rises by 0.2 percent with the weak inflation
rule, whereas it remains unchanged under the optimal policy rule.10 The long-run nominal
interest rate then increases by 0.3 percent with the weak inflation rule according to the Fischer
9 This condition, sometimes referred to as the “Taylor principle” [Taylor (1999a)], states that a percentage point
change in the nominal interest rate target must exceed the corresponding change in the inflation rate.
10 The one-for-one relationship between productivity growth and the real interest rate is due to our assumption that
utility is a function of the logarithm of consumption.
8
equation but by only 0.1 percent with the optimal policy.
The inflation caused by the permanent productivity growth shock with the weak inflation
rule also affects real variables, albeit only slightly. Firms, which can adjust their prices only
infrequently, raise their prices aggressively whenever given the opportunity because they expect
long-run inflation to increase. Those higher prices further dampen output growth, which then
causes the real marginal cost to fall modestly and capital stock growth and hours worked to
decline even more.
The results for Equation (10) also illustrate the effect of θπ on both the inflation rate and
the nominal interest rate. Specifically, a lower value for θπ implies that the endogenous response
of the inflation rate and the nominal interest rate to an exogenous shock will be higher and those
variables will fluctuate more. An economy with a central bank that aggressively responds to
inflation (i.e., θπ is large) will not observe large nominal interest rate fluctuations unless there
are similarly large movements in the real interest rate.
3.3 The
Taylor
Rule
The shorter dashed lines in Figure 1 show the impulse responses for the Taylor (1993) rule in
which the nominal interest rate target responds to both the inflation rate and the level of output:
1
, (11)
where θπ = 0.5 and θy = 0.5. The impulse responses in Figure 1 demonstrate that setting θy > 0 in
the Taylor (1993) rule has a dramatic effect on both nominal and real variables. To understand
the impact of θy, Equation (11) is solved for the long-run inflation rate using the same procedure
as for Equation (10):
. (12)
9
The 0.1 percent increase in the productivity growth rate affects inflation by boosting both the
long-run real interest rate and the output growth rate by 0.1 percent each. The inflation rate in
Equation (12), however, responds to the deviation of output from its potential, which is now
growing faster. If the policymaker’s response to the change in the underlying productivity
growth rate is slow, then the Taylor rule generates a negative correlation between inflation and
productivity growth at business cycle frequencies.11 Specifically, the long-run output gap in
Equation (12) will get progressively larger each period, which corresponds to a continually
falling inflation rate. The persistent decline in inflation highlights a critical problem with the
Taylor rule. That is, a permanent productivity growth shock causes an unstable response when
the monetary authority follows the Taylor rule but fails to adjust that rule to the productivity
shock’s effect on potential output.
Firms’ pricing decisions are affected by the original Taylor rule’s endogenous response to
a permanent productivity shock. The prospect of a declining inflation rate forces firms, which
can infrequently adjust their prices, to select a lower price than they otherwise would if they
could adjust their prices every period. Those lower prices lead to higher output demand, a
smaller price markup, and a rise in the real marginal cost compared with the weak inflation rule
and the optimal policy rule. To raise production, firms increase their demand for inputs, which
raises the real wage and the rental rate of capital and dampens the decline in hours worked and
the capital stock growth rate. The higher capital rental rate then boosts the real interest rate. The
nominal interest rate initially rises with the real interest rate, but then declines in subsequent
periods as expected inflation falls. Therefore, our results indicate that the Taylor rule generates a
negative correlation between inflation and real output growth after a permanent productivity
11 Kiley (2003) provides detailed evidence about this negative correlation. He uses an elementary aggregate
demand/aggregate supply model in which the Federal Reserve targets constant money growth to explain this
empirical regularity.
10
growth shock.
3.4
An Output Growth Rule
Figure 2 displays the impulse responses to the optimal policy and two proposed policy rules that
improve on Taylor’s rule. The output growth rule (θπ = 0.5 and θg > 0) replaces the output gap in
the Taylor rule with the change in the output gap.12 This specification is appealing because
output growth converges to a constant growth rate after a permanent productivity shock, whereas
the output gap grows into perpetuity if the monetary authority does not recognize the shock. To
understand why the monetary authority should target the output growth rate, consider the
intertemporal Euler equation from the households’ problem. For simplicity, we abstract from the
complications introduced by the shopping-time specification and assume that consumption enters
the utility function in logged form. The resulting intertemporal Euler equation relates the growth
rate of consumption to the real interest rate:
/
1 . (13)
Since long-run consumption grows at the steady-state productivity growth rate, , Equation (13)
shows that the real interest rate is positively related to :
1
/
1 .
That is, a long-run increase in the productivity growth rate of 0.1 percent will permanently raise
the real interest rate by 0.1 percent. As a result, we set θg = 1.
The output growth rule assumes that the monetary authority’s nominal interest rate target
responds to both the inflation rate and to the output growth rate:
1
. (14)
12 Several authors, including Orphanides and Williams (2002) and Walsh (2003), have recommended replacing the
output gap with the growth rate of the output gap.
11
Using the long-run Fischer equation, we can show that the inflation rate is related to the real
interest rate and the growth rate of output:
.
Since both the real interest rate and output grow at the same long-run rate and θg = 1, the
inflation rate will equal zero.
The longer dashed lines in Figure 2 illustrate the impulse responses of key economic
variables to a permanent productivity growth shock when the monetary authority follows our
output growth rule. Initially, the increase in the real interest rate dominates the small rise in
output growth, so inflation rises. Over the next several periods, the inflation rate falls as output
grows faster than the real interest rate. Falling inflation expectations induce price-adjusting firms
in our sticky price model to set their prices lower than they would in the absence of price
rigidities. The lower prices stimulate output demand, dampen the decline in capital stock growth,
and raise the real marginal cost relative to their responses with the optimal policy. The higher
demand for output raises firms’ labor demand, relative to the optimal policy, which increases real
wage growth and dampens the fall in hours worked. Furthermore, the reduced decline in the
capital stock limits the increase in future capital rental rates, which leads to a smaller rise in the
real and nominal interest rates when compared with the optimal policy.
Within two years, the impulse responses for the real variables under the output growth
rule converge to the responses with the optimal policy: The output growth target in the policy
rule indirectly captures the changes in the long-run real interest rate. Therefore, a permanent
shock to productivity growth does not have any long-run effects on inflation.
A comparison of Figures 1 and 2 reveals that inflation is more than 5 times more variable
with either the weak inflation rule or the Taylor rule than it is with the output growth rule.
12
Specifically, inflation under the output growth rule rises by slightly less than 0.02 percent and
falls by less than 0.03 percent. That small variation compares favorably with the optimal
monetary policy in which inflation remains constant.
3.5
A Price-Level Path Rule
Another monetary policy rule that improves on the Taylor rule is one that responds to deviations
of the deterministic price level from its target path. 13 Svensson (1999) shows that the discretion
solution to a model with a price-level path target is equivalent to the commitment solution to that
same model with an inflation target.14 The key difference between a price-level path target and
an inflation target is the policy response when inflation rises above its target. A price-level path
target automatically forces inflation to fall below its target to “undo” the previous inflation,
whereas an inflation target ignores previous deviations and simply seeks to return the inflation
rate to its target. Our price-level path rule assumes that the nominal interest rate target moves
one-to-one with the inflation rate and also responds to deviations of the price level from its long-
run price path:
̂ . (15)
By substituting ̂
̂
into Equation (15), the long-run link between inflation and the
real interest rate under a price-level path rule can be expressed as follows:
. (16)
The shorter dashed lines in Figure 2 show the impulse responses of key variables to a
13 The target price-level path grows at the target inflation rate. A price-level path target is essentially a long-run
inflation target.
14 Gaspar, Smets, and Vestin (2007) survey the literature on price-level path rules, and Gorodnichenko and Shapiro
(2007) show that including a price-level path target in the policy rule generally improves the performance of the
economy in the presence of temporary shifts in productivity growth.
13
permanent productivity growth shock when policymakers implement a price-level path rule
(θp = 1).15 The productivity shock initially raises the real interest rate faster than the lagged price
level, so the inflation rate rises. In subsequent periods, the increase in the lagged price level
catches up with the higher real interest rate. Therefore, inflation gradually returns to its steady
state. Price stickiness prevents some firms from raising their prices, so those firms must
accommodate the higher demand for their goods by raising their output. The higher output
increases firms’ demand for factor inputs, which raises hours worked, capital stock growth, and
real wage growth above their respective levels with the optimal policy. The higher capital stock
growth then dampens the rise in the capital rental rate, which leads to a more modest rise in the
real interest rate. The impulse responses of those real variables with the price-level path rule,
however, are closer to their respective responses with the optimal policy than with either the
output growth rule or the Taylor rule. The nominal interest rate mimics the optimal policy almost
perfectly because the smaller short-run rise in the real interest rate is offset by the higher
inflation rate.
4.
Inflation and Output Volatility: A Measure of Welfare
Researchers have shown that monetary policy minimizes welfare losses when it eliminates the
output fluctuations caused by nominal frictions. That result indicates that the welfare loss in our
model is proportional to the variance of the output gap (the deviation of output from its path in
the absence of nominal rigidities).16 Although welfare loss is properly measured using current-
quarter output volatility, our New Keynesian model, like most other models, does not incorporate
15 Our calibration of θp is based roughly on the relationship between Hodrick-Prescott-filtered data on the price level
and the nominal interest rate. Specifically, volatility of the percent deviation of the Consumer Price Index from its
long-run trend is similar to that of the federal funds rate over the past two decades.
16 This definition of the output gap is suggested by Neiss and Nelson (2003).
14
characteristics of the real economy that make the long-term horizon relevant. For example, our
model does not include long-term loans or long-term planning problems which, although
difficult to model, are essential to the real economy. Since central banks are concerned about the
long-run consequences of their policy decisions, we examine the impact of permanent
productivity growth shocks on the long-term volatility of the output gap and inflation under the
Taylor rule, the output growth rule, and the price-level path rule.17
Our analysis focuses on the output and inflation fluctuations over forecast horizons as
long as 5 years because we believe that interval is a reasonable time for policymakers to
recognize changes in the balanced growth trend. We assume that the economy begins at its
steady state and then simulate 5 years of permanent productivity growth shocks over 1,000 times
in which the standard deviation of the productivity shock is 0.1 percent per quarter. At each
forecast horizon, we calculate the average deviation of the annual inflation rate and the output
gap from their respective values under the optimal policy.
Figure 3 shows the impact of permanent productivity growth shocks on the standard
deviations of inflation and output growth from the optimal policy over forecast horizons of 1
quarter, 1 year, 2 years, 3 years, 4 years, and 5 years ahead. The upper panel displays the results
for the inflation rate. When comparing the three rules, inflation varies the most at all forecast
horizons with the Taylor rule. Inflation volatility in that model is modestly high in the short-run
forecast horizons, declines over the 2- and 3-year horizons, and then skyrockets in later years. As
for the other two monetary policy rules, inflation variability is modestly lower with the output
growth rule for the 1-quarter- and 1-year-ahead forecast, whereas inflation fluctuates the least
with the price-level path rule at forecast horizons of 2 years and beyond. In fact, inflation
17 The long-term volatility of the output gap and inflation is considered because many papers measure welfare loss
as a weighted average of the fluctuations in the output gap and inflation.
15
volatility continues to fall with the price-level path rule after 2 years, while it keeps rising with
the output growth rule. Our results suggest that, on average, a price-level path rule minimizes
inflation fluctuations after a permanent productivity growth shock.
The bottom panel of Figure 3 depicts the impact of permanent productivity growth
shocks on output growth over a forecast horizon ranging from 1 quarter to 5 years. Our findings
reveal that the relative ranking of the alternative policies remains the same over the full horizon.
Specifically, the growth rate of the output gap fluctuates the most under the Taylor rule and the
least under the price-level path rule. The distinction among the three policy rules in Figure 3 is
due mostly to the differences in the impulse responses of output growth in the first two years
after a productivity growth shock. During that time, output growth under the price-level path rule
is closest to the optimal policy, whereas it is farthest under the Taylor rule. The longer-run
differences among the policy rules in Figure 3 persist because they are averages that include the
short-run effects.
5. Conclusion
Empirical evidence suggests that the inflation rate rises when the productivity growth rate
permanently decreases and vice versa. Orphanides (2003a) argues that the central bank does not
immediately observe a decline in productivity growth, so it does not correspondingly lower the
money growth rate, which results in higher inflation. Our paper analyzes the impact of a
permanent productivity growth shock when the central bank fails to immediately adjust its policy
rule to that shock. We find that the negative correlation between inflation and productivity
growth occurs because the central bank follows a Taylor-type rule, which responds to the level of
the output gap.
16
Our paper shows that a permanent increase in productivity growth affects inflation
differently with either the output growth rule or the price-level path rule than with the Taylor
rule. Specifically, the Taylor rule causes inflation to continually decline after a permanent rise in
productivity, whereas inflation initially rises and eventually returns to its target under both the
output growth rule and the price-level path rule. The output growth rule and the price-level path
rule also generate less variation in inflation and the output gap than the Taylor rule after a
permanent shift in productivity growth. Those findings indicate that the central bank should
target the price-level path and the output growth rate, which is the direct opposite of that
advocated by Taylor (1993). In particular, the Taylor rule targets the growth rate of the price
level and the level of output, whereas we find that the central bank should target the price level
and the growth rate of output. Our result is practical because policymakers can easily observe
and target a price-level path in real time but must estimate the output gap, which can result in
large errors that persist for many years.
Our finding that a price-level path target reduces the volatility of inflation and the output
gap due to uncertainty about the growth rate of potential output further complements a growing
literature on targeting the price-level path. Svensson (1999), Roisland (2006), and Vestin (2006),
among others, argue that price-level path targeting is preferable to inflation targeting. On the
other side, Lebow, Roberts, and Stockton (1992), Haldane and Salmon (1995), and Black,
Macklem, and Rose (1997) contend that the transition costs to a price-level path target and
backward-looking expectations greatly reduce the benefits from price-level path targeting. One
drawback to all such models is that they fail to incorporate realistic features such as risk and the
interaction between risk-taking and the monetary policy rule. Building dynamic stochastic
17
general equilibrium models with those characteristics will enable researchers to better address a
wider set of problems confronting policymakers.
18
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21
Appendix
A.1 Nonlinear
Equations
A.1.1
a
A.1.2
a
A.1.3
a
1
A.1.4
a
A.1.5
βE
1
δ
A.1.6
1 A.1.7
A.1.8
A.1.9
A.1.10
A.1.11
A.1.12
1
A.1.13
1
/
A.1.14
∑
A.1.15
∑
A.1.16
A.1.17
A.1.18
A.1.19
22
A.2 Steady-State
Equations
A.2.1
A.2.2
A.2.3
A.2.4
1
A.2.5
1
A.2.6
1 A.2.7
1
A.2.8
A.2.9
A.2.10
A.2.11
A.2.12
1
A.2.13
A.2.14
1 A.2.15
23
A.3 Linearized
Equations
A.3.1
A.3.2
̂
̂
0 A.3.3
̂
A.3.4
ı̂
k
τ
λ A.3.5
τ
E
q
ı̂
k
q
τ
A.3.6
̂
0 A.3.7
ı̂
1
δ
k
gk
A.3.8
̂
̂ A.3.9
̂
̂
A.3.10
1
A.3.11
1
A.3.12
1
A.3.13
A.3.14
1
̂ A.3.15
̂
̂
A.3.16
A.3.17
1
A.3.18
24
Figure 1. Responses to a Permanent 0.1% Increase in Productivity Growth Under Optimal Policy,
Weak Inflation Rule, and a Taylor Rule
Capit
a
a
pit l
a Stoc
St
k
oc Grow
Gr
th
ow
Inflat
a ion
0.06
0.2
d
0.15
d
d
n
Taylo
Ta
r
ylo Ru
R l
u e
n
n
0.04
0.1
T
r
e
T
r
e
Weak Inflation Rule
m
0.05
m
m
0.02
f
ro
0
f
ro
f
ro
n
n
0.
0 05
0
Op
O tima
tim l
a Po
P lic
o
y
t
i
o
0
t
i
o
i
a
0.
0 1
i
a
i
a
v
v
e
e
D
0.
0 15
D
1
0.
0 02
0
D
t
t
n
0.
0 2
n
n
e
e
rc
0.
0 04
0
rc
0.
0 25
2
e
e
Taylo
Ta
r
ylo Ru
R l
u e
e
P
Weak Inflation Rule
P
0.
0 3
e
0.
0 06
0
0.
0 35
3
0
1
2
3
4
5
6
7
8
9 10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
0
1
2
3
4
5
6
7
8
9 10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
Re
R al
e
Int
In eres
t
t
eres Rat
Ra e
t
Nominal In
I t
n er
t e
er s
e t
s Rat
Ra e
t
0.08
0.25
Taylo
Ta
r
ylo Ru
R l
u e
Weak Inflation Rule
d
0.2
d 0.07
d
n
07
n
n
0.15
T
r
e
0.06
T
r
e
06
m
0.1
m
m
Optimal Pol
P icy
m
f
ro 0.05
0.05
05
f
ro
n
n
0
t
i
o 0.04
t
i
o
i
a
0.05
i
a
i
a
0
i
a
v
v
e 0.03
e
D
0.
0 1
D
D
t
t
n 0.02
0.15
02
n
1
n
e
e
rc
rc
0.
0 2
e 0.01
e
P
01
P
P
0.25
2
Taylo
Ta
r
ylo Ru
R l
u e
0
0.
0 3
0
1
2
3
4
5
6
7
8
9
10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
0
1
2
3
4
5
6
7
8
9 10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
Re
R al
e
Wag
W
e
ag Grow
Gr
th
ow
Re
R al
e
Marg
ar inal Cos
o t
s
0.3
0.25
d
d
n
Taylo
Ta
r
ylo Ru
R l
u e
n
n
0.2
0.25
T
r
e
T
r
e
Taylo
Ta
r
ylo Ru
R l
u e
T
r
e
0.15
m
m
0.2
f
r
o
ro
f
r
o
ro
n
n
0.1
on
on
ti
t
i
o 0.15
ti
t
i
o
a
a
i
a
i
0
0.05
05
v
v
e
e
D
0.1
D
Optimal Policy
t
t
0
n
n
e
e
rc 0.05
rc
e
e
0.05
P
P
Weak Inflation Rule
0
0.1
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Hours Worked
Output Growth
0.3
0.15
Taylor Rule
0.2
d
0.1
d
Taylor Rule
0.1
T
r
e
n
T
r
e
n
0.05
m
m
0
f
r
o
f
r
o
n
0
n
o
o
0.1
ati
ati 0.05
Optimal Policy
Optimal Policy
0.2
Devi
Devi
t
t
0.1
0.3
P
e
r
c
e
n
P
e
r
c
e
n
0.4
0.15
Weak Inflation Rule
Weak Inflation Rule
0.5
0.2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Optimal Policy
=
Weak Inflation Rule
= 0.5
Taylor Rule
= 0.5 and y = 0.5
25
Figure 2. Responses to a Permanent 0.1% Increase in Productivity Growth Under Optimal Policy,
Output Growth Rule, and a Price Level Path Rule
Capit
a
a
pit l
a Stoc
St
k
oc Grow
Gr
th
ow
Inflat
a ion
0.03
0.025
d
0.02
0.02
02
d
n
n
0.015
Pr
P ice Leve
Le
l
ve Pa
P t
a h Rule
T
r
e
0.01
T
r
e
m
0.01
m
m
0
f
ro
0.005
f
ro
f
ro
n
0.
0 01
0
n
0
t
i
o
t
i
o
i
a
0.
0 02
0.005
02
i
a
v
v
Op
O tima
tim l
a Po
P lic
o
y
v
e
e
D
0.
0 01
D
0
0.
0 03
0
D
t
t
n
0.015
n
n
e
0.
0 04
0
e
Output Gr
G owth Rule
rc
rc
0.
0 02
0
e
e
P
0.
0 05
0
P
0.025
0.
0 06
0
0.
0 03
0
0
1
2
3
4
5
6
7
8
9 10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
0
1
2
3
4
5
6
7
8
9 10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
Re
R al
e
Int
In eres
t
t
eres Rat
Ra e
t
Nominal In
I t
n er
t e
er s
e t
s Rat
Ra e
t
0.08
0.08
d 0.07
d
n
07
0.07
n
n
Pr
P ice Leve
Le
l
ve Pa
P t
a h Rule
T
r
e
0.06
T
r
e
06
0.06
m
m
f
ro 0.05
f
ro 0.05
Optimal Pol
P icy
n
n
t
i
o 0.04
t
i
o 0.04
i
a
i
a
v
v
e 0.03
e 0.03
D
D
t
t
n 0.02
n
Output Gr
G owth Rule
e
0.02
e
e
rc
rc
e 0.01
e
P
01
0.01
P
P
0
0
0
1
2
3
4
5
6
7
8
9
10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
0
1
2
3
4
5
6
7
8
9
10
1
11
1
12
1
13
1
14
1
15
1
16
1
17
1
18
1
19
1
20
2
Re
R al
e
Wag
W
e
ag Grow
Gr
th
ow
Re
R al
e
Marg
ar inal Cos
o t
s
0.35
0.25
d
d
n
0.3
n
0.2
T
r
e
T
r
e
Output Gr
G owth Rule
T
r
e
0.25
m
m
0.15
f
r
o
ro
f
r
o
ro
n
0.2
n
on
on
ti
t
i
o
ti
t
i
o
0.1
a
a
i
a 00.15
i
15
Pr
Price
ice Leve
Le
l
ve Pa
P t
a h Rule
v
v
e
e
D
D
0.05
t
0.1
t
n
n
e
e
rc
rc
0
e 0.05
e
P
P
Optimal Policy
0
0.05
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Hours Worked
Output Growth
0
0.1
0.05
d
d 0.05
T
r
e
n
0.1
T
r
e
n
Output Growth Rule
m
m
f
r
o
0
f
r
o
0.15
n
n
o
o
ati
ati
0.2
0.05
Devi
Devi
Price Level Path Rule
t
t
0.25
0.1
P
e
r
c
e
n
0.3
P
e
r
c
e
n
Optimal Policy
0.35
0.15
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Optimal Policy
=
Output Growth Rule
= 0.5 and g = 1
Price Level Path Rule
= 0 and p = 1
26
Figure 3. Root Mean Square Deviations (from the Optimal Path)
Inflat
In
ion
0.008
0.0298
0.03
0.03
0.0297
0.0292
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
1‐quarter
1‐year
r
2‐year
r
3‐year
4‐year
r
5‐year
r
Forecasts
Output Gr
owth
Gr
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
1‐quarter
1‐year
2‐year
3‐year
4‐year
5‐year
Forecasts
Taylor Rule
θπ = 0.5 and θy = 0.5
Output Growth Rule
θπ = 0.5 and θg = 1
Price‐Level Path Rule
θπ = 0 and θp = 1
27
