POTENTIAL AND OPTIMAL OUTPUT 1. Introduction

POTENTIAL AND OPTIMAL OUTPUT ALEJANDRO JUSTINIANO, GIORGIO E. PRIMICERI, AND ANDREA TAMBALOTTI Abstract. We estimate a DSGE model with imperfectly competitive products and labor markets, and sticky prices and wages. We use the model to back out two counterfactual objects. Potential output is the level of output that would prevail in the absence of ine¢ cient markup ‡uctuations. Optimal output is the level of output that would prevail under a monetary authority that maximizes welfare. We …nd that potential output is pro-cyclical, but less volatile than actual output, suggesting that postwar US business cycles involved substantial movements in the economy’s degree of ine¢ ciency. On the contrary, optimal output is more volatile than actual output, since the planner assigns a large weight to wage in‡ation stabilization in its objectives and because wage markup shocks are very volatile. These disturbances, however, are very similar to measurement errors because they are prevalent at high frequencies and wash out in di¤erent wage in‡ation measures. Under this alternative interpretation, potential and optimal output are almost identical. This suggests that a large fraction of output ‡uctuations in the postwar period should have been avoided.

1. Introduction Between 1954 and 2009, U.S. GDP grew on average at an annual rate of 3:2 percent per quarter, with a standard deviation of 3:8 percent. A sizable fraction of this variability is concentrated at business cycle frequencies. According to the NBER cronology, GDP grew on average 4:1 percent in expansions and contracted by 2 percent in recessions over the same period. The fundamental origin of these ‡uctuations in economic activity is still a matter of debate. Even more controversial is whether these ‡uctuations largely re‡ect the e¢ cient responses of households and …rms to changes in economic fundamentals, or instead departures from the e¢ cient allocation of resources that policy should attempt to counteract. Date: November 2010. PRELIMINARY, PLEASE DO NOT QUOTE. This paper replaces an earlier manuscript titled “Potential and Natural Output.” We thank Vasco Curdia, Jose Dorich, Gauti Eggertsson, Chris Erceg, Stefano Eusepi, Andrea Ferrero, Lars Svensson, Carl Walsh, and partecipants in several conferences and seminars for comments and suggestions, Ging Cee Ng for superb research assistance and especially Vasco Curdia for generously sharing his code for the computation of optimal equilibria. The views in this paper are solely the responsibility of the authors and should not be interpreted as re‡ecting the views of the Federal Reserve Bank of Chicago, the Federal Reserve Bank of New York or any other person associated with the Federal Reserve System. 1

2

ALEJANDRO JUSTINIANO, GIORGIO E. PRIMICERI, AND ANDREA TAMBALOTTI

The objective of this paper is to provide a quantitative answer to this question. To do so, we estimate a dynamic stochastic general equilibrium (DSGE) model of the U.S. economy with monopolistically competitive products and labor markets, and sticky prices and wages. At the neoclassical core of this model, markets are competitive and agents react e¢ ciently to shocks. However, the New-Keynesian features that sorround this neoclassical nucleous distort the economy’s observed equilibrium away from the e¢ cient allocation. This distortion manifests itself in the form of time-varying markups of prices over marginal cost and of wages over marginal rates of substitution, re‡ecting the monopoly power of …rms and workers. We summarize the evolution of this distortion by tracking the distance between actual GDP and the GDP that would emerge in equilibrium if markups were …xed at their steady state level. This is what we call potential GDP. In our model, potential GDP is below the e¢ cient level, since markups are positive in steady state. However, potential and e¢ cient output share identical dynamics. We center our analysis on potential, rather than on e¢ cient output because our model provides an empirically plausible account of the ‡uctuations in economy’s degree of ine¢ ciency, but it abstracts from many other distortions that are likely to be especially important in determining its absolute level.1 According to our estimates, potential GDP is pro-cyclical, but less volatile than actual GDP, so that the the output gap— the di¤erence between observed and potential GDP— is also pro-cyclical. An immediate implication of this …nding is that a substantial share of the real ‡uctuations experienced by the U.S. economy in the postwar period represents movements in its degree of ine¢ ciency, which would have not been observed in a competitive economy. A further inference that one might be tempted to draw from the relatively large ‡uctuations in the output gap that we document is that stabilization policy should have been more forceful in attempting to smooth the path of GDP. This conclusion, however, is unwarranted, because the …rst best e¢ cient allocation that would be achieved under perfect competition is infeasible in our model with nominal rigidities in both the goods and labor markets (see Erceg, Henderson, and Levin (2000)). Therefore, a policy that kept output closer to our measure of potential would have not necessarily delivered an improvement in welfare.

1 In the model, there is a small discrepancy between output and GDP, due to the presence of capital utilization costs. In the text, we sometimes refer to GDP as “output,” even if this usage is slightly imprecise in our context.

POTENTIAL AND OPTIMAL OUTPUT

3

The simple intuition for this result is that e¢ ciency requires real wages to adjust so as to maintain the marginal rate of substitution between consumption and leasure in line with their marginal rate of transformation. But these real wage movements, which must be achieved through some combination of chages in nominal prices and/or wages, produce dispersion in relative prices and hence in quantities supplied across …rms and workers. This dispersion in relative quantities, in turn, is ine¢ cient, since those productive units have identical tastes and technologies, and should therefore supply the same amount of goods and labor. As a result, stabilization policy faces a tradeo¤ between closing the output gap, on the one hand, and eliminating wage or price dispersion on the other. To evaluate quantitatively the tensions among the elements of this trilemma in our estimated model, we compute its optimal allocation and, in particular, optimal output. By comparing optimal to potential output, we can then assess whether the latter construct is a useful reference point for stabilization policy. We …nd that the answer to this question is yes, although reaching this conclusion requires a few steps. We summarize them as follows. First, in our baseline model, optimal output is signi…cantly more volatile than potential, and even than actual output. The key driver of this result are the large exogenous movements in desired markups needed to account for the observed variation in wage in‡ation. In contrast to the actual equilibrium, in the optimal allocation these markup shocks load almost entirely on quantities, since in the model the relative price dispersion caused by wage in‡ation is extremely costly. In fact, this shift away from output stabilization and towards in‡ation stabilization engineered by optimal policy is so extreme that optimal GDP resembles quite closely natural output. By natural, we refer to the level of output that would be observed in equilibrium if prices and wages were ‡exible. The distinguishing feature of the natural allocation, in which prices and quantities are independent, is that the adjustment to changes in desired markups must happen entirely through movements in quantities, with no direct spillover to prices. This full pass through of markup shocks to real allocations, and in particular to output, is also an approximate feature of the optimal equilibrium. Another interesting consequence of the preponderance of the nominal stabilization objective in the welfare function is that optimal output is virtually invariant to the interpretation of labor supply shocks as re‡ecting changes in workers’ taste for leisure or, instead, exogenous variations in their monopoly power. This …nding is important because in our model the

4


ultimate source of shifts to labor supply–tastes or desired markups–cannot be identi…ed from the data alone, but it has signi…cant implications for potential output (see Chari, Kehoe, and McGrattan (2009) and Sala, Söderström, and Trigari (2010)). Taken at face value, our results imply that policy should aim at de-stabilizing real activity. However, the ‡uctuations in wage desired markups implied by our estimates, and that drive this puzzling result, are implausibly large, as also argued by Chari, Kehoe, and McGrattan (2009). Moreover, they account for a very minor share of the variation of real variables at business cycle frequencies, and their explantory power for wage in‡ation is concentrated at high frequencies. These observations suggests that these markup shocks might in fact capture, at least in part, measurement error in the wage in‡ation series. By this term, we broadly refer to sampling and idiosyncratic errors across alternative wage series, arising from di¤erences in coverage or de…nitions. Regardless of their source, for our purpose, these shocks entail some disconnect between the model’s “wage” and its counterpart in the data (Boivin and Giannoni (2006a), Galí (2010)). To investigate this possibility, we re-estimate our model replacing the wage markup shocks with measurement errors in wage in‡ation. This speci…cation has several notable features compared to the baseline. First, it …ts the data better. Second, it produces measurement errors that are very similar to the baseline markup shocks. Third, the estimated structural parameters and potential output are almost identical in the two speci…cations. Fourth, and most important for our purposes, optimal and potential output move closely together in the speci…cation with measurement errors. Fifth, in this speci…cation, output gap and in‡ation stabilization can be approximately achieved together. This suggests that the endogenous tradeo¤ between the stabilization of quantities and prices due to the contemporanous presence of price and wage rigidities is relatively small. The similarity between optimal and potential output in the model without markup shocks con…rms that the latter are indeed the main source of the tradeo¤ between output and in‡ation stabilization that was evident in the baseline speci…cation. Moreover, this similarity, together with the more plausible interpretation and better …t of the model with measurement error, lead us to conclude that e¢ cient output is indeed a useful reference point for stabilization policy.

This paper is related to a large literature on the estimation of DSGE models (see, for instance, Rotemberg and Woodford (1997), Lubik and Schorfheide (2004), Boivin and Giannoni


5

(2006b) or Smets and Wouters (2007)). Some of these papers explicitly assume that monetary policy reacts to the di¤erence between actual and potential output, but do not focus on the model predictions about the output gap. This issue is potentially important because a number of studies have shown that it is hard to obtain model-based estimates of the output gap with clear cyclical properties (Levin, Onatski, Williams, and Williams (2005), Nelson (2005), Andrés, López-Salido, and Nelson (2005) and Edge, Kiley, and Laforte (2008)). Similar to Levin, Onatski, Williams, and Williams (2005), Nelson (2005), Andrés, López-Salido, and Nelson (2005) and Edge, Kiley, and Laforte (2008), we explicitly take on the task of estimating the theory-based output gap. However, our estimate of the output gap is closer to more conventional views of business cycles. Our result that the output gap comoves with the business cycle is similar to Gali, Gertler, and Lopez-Salido (2007) and Sala, Soderstrom, and Trigari (2008). However, Gali, Gertler, and Lopez-Salido (2007) mainly study on the gap between the consumption/leisure marginal rate of substitution and the marginal product of labor, which is proportional to the output gap only in particular cases. Moreover, we di¤er from Sala, Soderstrom, and Trigari (2008) due to our focus on the comparison between potential and optimal output. Unlike in most of the DSGE work on output gaps, in fact, we complement our estimation of potential output with that of optimal output. The comparison of the two allows us to evaluate the usefulness of potential output as a reference point for stabilization policy. On this dimension, we make contact with the normative literature in medium-scale DSGE models (e.g. Levin, Onatski, Williams, and Williams (2005), Schmitt-Grohe and Uribe (2004) and Schmitt-Grohé and Uribe (2007)). Similarly to these authors, we …nd that nominal dispersion holds the key to the normative implications of the model. Unlike them, however, we end up deemphasising the tradeo¤ between output and wage in‡ation stabilization, once we recognize that wage markup shocks are more likely to stand in for measurement error. This emphasis on wage markup shocks and labor supply shocks more in general relates our work to Chari, Kehoe, and McGrattan (2009), although they are not concerned with the estimation of the output gap, nor with the characterization of optimal policy. The rest of the paper is organized as follows. Section 2 provides the details of the theoretical model. Section 3 describes the approach to inference and the procedure to obtain a DSGEbased measure of potential output. Section 4, 5 and 6 present our estimates of potential and optimal output, and our interpretation of them. Section 7 concludes.

6


2. The Model Economy This section outlines our baseline model of the U.S. business cycle, which is similar to Christiano, Eichenbaum, and Evans (2005) and Smets and Wouters (2007). It is a mediumscale DSGE model with a neoclassical growth core, augmented with several shocks and “frictions”— departures from the simplest assumptions on tastes, technology and market structure— now common in the literature. The economy is populated by …ve classes of agents: producers of a …nal good, intermediate goods producers, households, employment agencies and a government. We now present their optimization problems. 2.1. Final good producers. At every point in time t, perfectly competitive …rms produce the …nal consumption good Yt combining a continuum of intermediate goods fYt (i)gi , i 2 [0; 1], according to the technology Yt =

Z

1

Yt (i)

1+

1 1+ p;t

p;t

.

di

0

The elasticity

p;t

follows the exogenous stochastic process log (1 +

where "p;t is i:i:d:N (0;

2 ). p

p;t )

p;t

= (1

p) p

+

p p;t 1

This is a price markup shock, since

+ "p;t ,

p;t

is the desired net markup

of prices over marginal costs for intermediate …rms. Pro…t maximization and the zero pro…t condition imply that the price of the …nal good, Pt , is a CES aggregate of the prices of the intermediate goods, fPt (i)gi Pt =

Z

1

Pt (i)

1 p;t

p;t

di

,

0

and that the demand function for the intermediate good i is

(2.1)

Yt (i) =

Pt (i) Pt

1+ p;t p;t

Yt .

2.2. Intermediate goods producers. A monopolist produces the intermediate good i using the production function (2.2)

Yt (i) = max At1

Kt (i) Lt (i)1

At F ; 0 ,


7

where Kt (i) and Lt (i) denote the amounts of capital and labor employed by …rm i: F is a …xed cost of production, chosen so that pro…ts are zero in steady state (see Rotemberg and Woodford, 1995 or Christiano, Eichenbaum, and Evans, 2005). At represents exogenous labor-augmenting technological progress or, equivalently, a neutral technology factor. The level of neutral technology is non-stationary and its growth rate (zt

log At ) follows a stationary AR(1) process zt = (1

z)

+

z zt 1

+ "z;t ,

2 ). z

with "z;t i:i:d:N (0;

As in Calvo (1983), every period a fraction

p

of intermediate …rms cannot optimally choose

their price, but reset it according to the indexation rule Pt (i) = Pt where

t

Pt Pt 1

is gross in‡ation and

p

1 (i) t 1

1

p

,

is its steady state. Our indexation scheme implies full

indexation and, therefore, no price dispersion in steady state. This assumption implies that the long-run Phillips curve is vertical and there is no long-run tradeo¤ between in‡ation and real activity. Therefore, the level of steady state in‡ation is inconsequential for welfare, which allows us to focus on the welfare consequences of cyclical ‡uctuations, abstracting from the challenging question about the optimal average level of in‡ation (Schmitt-Grohe and Uribe (2010)). The remaining fraction of …rms choose their price, P~t (i), by maximizing the present discounted value of future pro…ts Et

1 X s=0

s p

s

t+s t

nh P~t (i)

p s 1 j=0 t 1+j

p

i

Yt+s (i)

h

io Wt Lt (i) + rtk Kt (i) ,

subject to the demand function 2.1 and the production function 2.2. In this objective,

t+s

is the marginal utility of nominal income of the representative household that owns the …rm, while Wt and rtk are the nominal wage and the rental rate of capital. 2.3. Employment agencies. Firms are owned by a continuum of households, indexed by j 2 [0; 1]. Each household is a monopolistic supplier of specialized labor, Lt (j); as in Erceg, Henderson, and Levin (2000). A large number of competitive “employment agencies”combine this specialized labor into a homogenous labor input sold to intermediate …rms, according to Z 1 1+ w;t 1 . Lt = Lt (j) 1+ w;t dj 0

8


The elasticity

w;t

corresponds to the desired markup of wages over the household’s marginal

rate of substitution (MRS). For reasons that will become clear in the next subsection, we assume that log (1 +

w;t )

w;t

is i:i:d:N (0;

2 ). w

We refer to this as the wage markup shock.

Pro…t maximization by the perfectly competitive employment agencies implies the labor demand function (2.3)

Wt (j) Wt

Lt (j) =

1+ w;t w;t

Lt ,

where Wt (j) is the wage received from employment agencies by the supplier of labor of type j, while the wage paid by intermediate …rms for their homogenous labor input is Z 1 w;t 1 . Wt = Wt (j) w;t dj 0

2.4. Households. Each household maximizes the utility function (1 X Lt+s (j)1+ s (2.4) Et bt+s log (Ct+s hCt+s 1 ) 't 1+ s=0

)

,

where Ct is consumption, h is the degree of habit formation. The disturbance to the discount factor bt is an intertemporal preference shock and follows the stochastic process log bt = with "b;t

i:i:d:N (0;

2 ). b

b log bt 1

+ "b;t ,

The disturbance to the disutility of labor 't is instead an intratem-

poral preference or labor supply shock. If this shock had the same stochastic properties of the wage markup shock, it would also have exactly the same e¤ect on the household’s …rst order conditions. As a consequence, these two disturbances would not be separately identi…ed from each other, despite the fact that the markup shock induces macroeconomic ‡uctuations that are entirely ine¢ cient, i.e. that would not be observed in a perfectly competitive economy, while the labor disutility shock does not (see Chari, Kehoe, and McGrattan (2009) and Sala, Söderström, and Trigari (2010)). To disentangle these two disturbances, we model the labor supply shock as log 't = 1 + with "';t

i:i:d:N (0;

2 ), '

'

'+

' log 't 1

+ "';t ,

where the autocorrelation re‡ects our prior that labor supply

shocks should capture changes in labor force participation and other demographic developments largely unrelated to the business cycle, and should therefore be much smoother than wage markup innovations. We will return to this issue of observational equivalence in section


9

5, where we will show that interpreting labor supply shocks as ine¢ cient markup shocks is inconsequential for our estimate of optimal output. Since technological progress is non stationary, utility is logarithmic to ensure the existence of a balanced growth path. Moreover, consumption is not indexed by j because the existence of state contingent securities ensures that in equilibrium consumption and asset holdings are the same for all households. As a result, the household’s ‡ow budget constraint is Pt Ct + Pt It + Tt + Bt

Rt

1 Bt 1

+ Qt (j) +

t

+ Wt (j)Lt (j) + rtk ut Kt

1

Pt a(ut )Kt

1,

where It is investment, Bt is holdings of government bonds, Rt is the gross nominal interest rate, Qt (j) is the net cash ‡ow from household’s j portfolio of state contingent securities,

t

is the per-capita pro…t accruing to households from ownership of the …rms and Tt is lump-sum taxes and transfers. Households own capital and choose the capital utilization rate, ut , which transforms physical capital into e¤ective capital according to Kt = u t Kt

1.

E¤ective capital is then rented to …rms at the rate rtk . The cost of capital utilization is a(ut ) a00 (1) a0 (1) :

per unit of physical capital. In steady state, u = 1, a(1) = 0 and

In the log-linear

approximation of the model solution this curvature is the only parameter that matters for the dynamics. The physical capital accumulation equation is Kt = (1 where

)Kt

1

+

t

1

S

It It

It , 1

is the depreciation rate. The function S captures the presence of adjustment costs

in investment, as in Christiano, Eichenbaum, and Evans (2005). In steady state, S = S 0 = 0 and S 00 > 0.2 The investment shock

t

is a source of exogenous variation in the e¢ ciency

with which the …nal good can be transformed into physical capital, and thus into tomorrow’s capital input. Justiniano, Primiceri, and Tambalotti (2010b) show that this variation might stem from technological factors speci…c to the production of investment goods, as in Greenwood, Hercowitz, and Krusell (1997), but also from disturbances to the process by which 2 Lucca (2007) shows that this formulation of the adjustment cost function is equivalent (up to …rst order)

to a generalization of the time to build assumption.

10


these investment goods are turned into productive capital. The investment shock follows the stochastic process log where "

;t

t

=

log

t 1

+"

;t ,

2 ):

is i:i:d:N (0;

As in Erceg, Henderson, and Levin (2000) , every period a fraction

w

of households cannot

freely set its wage, but follows the indexation rule Wt (j) = Wt

zt 1 (j) ( t 1 e

1

) w ( e )1

w

.

The remaining fraction of households chooses instead an optimal wage by maximizing their utility, subject to the labor demand function 2.3. 2.5. Monetary and government policies. Monetary policy sets the short term nominal interest rate following a Taylor type rule. In particular, the rule allows for interest rate smoothing, a systematic response to deviations of annual in‡ation from a time varying in‡ation target, and deviations of observed annual GDP growth (Xt =Xt

4)

from its steady state

level:

Rt = R

20 3 Y 6B 6 R 6B s=0 6B 6B B 6@ 4

Rt 1 R

t s

!1=4 1 C C C C C A

t

(Xt =Xt e

1=4 4)

!

Y

31 7 7 7 7 7 7 5

R

e"R;t ,

where R is the steady state for the gross nominal interest rate and "R;t is an i:i:d: N (0; monetary policy shock. The Central Bank’s in‡ation target

t

2) R

evolves exogenously according

to the process log with "

;t

i:i:d:N (0;

2 );

t

= (1

) log

+

log

t 1

+"

;t ,

whose primary role is to account for the very low frequency behavior

of in‡ation (Ireland (2007)). Otherwise, these long-run ‡uctuations would imply a high degree of backward price indexation (Cogley and Sbordone (2008)). We prefer to minimize this source of in‡ation persistence because it a¤ects signi…cantly the relationship between in‡ation and welfare, but it does not seem to be supported by the micro evidence on …rms’ pricing behavior.


11

Fiscal policy is Ricardian. The government …nances its budget de…cit by issuing short term bonds. Public spending is determined exogenously as a time-varying fraction of output Gt =

1 gt

1

Yt ,

where the government spending shock gt follows the stochastic process log gt = (1 with "g;t

i:i:d:N (0;

g ) log g

+

g

log gt

1

+ "g;t ,

2 ). g

3. Model Solution and Estimation This section describes how we solve and estimate the model in order to compute potential and optimal output. The …rst step consists of rewriting the equilibrium conditions in terms of deviations of the real variables from the non-stationary technology process At . Let (3.1)

Et f

t+1 ; t ; t 1 ; e

"t

;

= 0,

denote the collection of these equilibrium conditions, in which

t,

"t and

are the vectors

of endogenous variables, exogenous i.i.d. disturbances and unknown structural coe¢ cients respectively. We then log-linearize (3.1) around the non-stochastic steady state and solve the resulting linear system of rational expectation equations by standard methods (for example Sims (2001)). This procedure yields the following system of transition equations ^ = G( )^ t t

(3.2)

1

+ M ( ) "t ,

where the “hat”denotes log deviations from the steady state, ^t is an extended version of ^t that also includes the relevant expectational variables, and G ( ) and M ( ) are conformable matrices whose elements are functions of . 3.1. Observables and data. We estimate the model using seven series of U.S. quarterly data. More precisely, we specify the observation equation dt = H ^t + d,

(3.3) where dt

[

log Xt ;

log Ct ;

log It log Lt ;

log Wt ;

t ; Rt ].

Notably, our choice of observ-

able variables implies that labor productivity and the labor share are also observed. This is important because it makes our analysis consistent with the Real Business Cycle literature, which focused on productivity shocks as sources of business cycles (e.g. Plosser (1989), King

12


and Rebelo (1999)), as well as with the literature emphasizing the role of the labor share as a driving force of in‡ation (e.g. Gali and Gertler (1999) and Sbordone (2002)). The estimation sample starts in 1954:III and ends in 2009:IV. Real GDP is nominal GDP divided by the civilian non-institutional population (16 years and older) and the GDP De‡ator.3 The real series for consumption and investment are obtained in the same manner. Consumption corresponds to the sum of non-durables and services, while investment is constructed by adding consumer durables to total private investment. For hours we use a measure for the total economy, rather than for the non-farm business sector. The series we use exhibits a less pronounced low frequency behavior because it accounts better for sectoral shifts, as noted by Francis and Ramey (2009). For consistency, our measure of compensation corresponds to hourly nominal wages for the total economy.4 In‡ation is measured as the quarterly log di¤erence in the GDP de‡ator, while for nominal interest rates we use the e¤ective Federal Funds rate. We do not demean or detrend any series. 3.2. Bayesian inference and priors. We characterize the posterior distribution of the model’s coe¢ cients by combining the likelihood function with prior information (see An and Schorfheide (2007) for a survey of Bayesian estimation of DSGE models). The likelihood function can be evaluated by applying the Kalman Filter to the linear and Gaussian state space representation of the model, given by equations (3.2) and (3.3). In the rest of this section we brie‡y discuss the speci…cation of the priors, which is reported in table 1. Two parameters are …xed using level information not contained in our dataset: the quarterly depreciation rate of capital ( ) to 0:025 and the steady state ratio of government spending to GDP (1

1=g) to 0:2, which corresponds to the average value of Gt =Xt in our sample.

Also due to lack of identi…cation, we set the steady state net wage markup to 25 percent. The priors on the other coe¢ cients are fairly di¤use and broadly in line with those adopted in previous studies, such as Smets and Wouters (2007) and Del Negro, Schorfheide, Smets, and Wouters (2007).. The prior distribution of all but two persistence parameters is a Beta, with mean 0:6 and standard deviation 0:2. The two exceptions are the autocorrelation of neutral technology shocks–whose prior is centered at 0:2, since this process already includes a unit root–and 3 Breaks in the civilian population series due to census-based population adjustments are smoothed by splicing them uniformly over a 10-year window. 4 We are grateful to Shawn Sprague, of the Bureau of Labor Statistics, for providing us the series of hours and the labor share in the total economy.


13

the autocorrelation of the in‡ation target shock, which we …x to 0:995. This value re‡ects our prior view that the in‡ation target shock should help to explain the very low frequency behavior of in‡ation. In reduced form, this disturbance might be capturing the evolution of policymakers’ beliefs and the consequent changes in the conduct of monetary policy, as suggested by some recent literature on learning (Cogley and Sargent (2004), Primiceri (2006) or Ireland (2007)). The intertemporal preference, price and wage markup shocks are normalized to enter with a unit coe¢ cient in the consumption, price in‡ation and wage equations respectively (see appendix A for details). The priors on the innovations’standard deviations are quite disperse and chosen to generate volatilities for the endogenous variables broadly in line with the data. Their covariance matrix is diagonal. 3.3. E¢ cient, Potential and Natural Output: De…nition and Estimation. The equilibrium of the model that we match with the observable variables features two deviations from perfect competition. First, the monopoly power enjoyed by …rms allows them to price goods above marginal cost. Similarly, households take advantage of the imperfect substitutability of their labor services to price them above the marginal rate of substitution. These price and wage markups over the relevant opportunity costs have two components. The …rst component, which is exogenous, corresponds to the (net) markups that would be observed in equilibrium if prices and wages were ‡exible, but …rms and workers maintained the same degree of monopoly power as in the actual economy. These net desired markups are the stochastic processes

p;t

and

w;t :.The

second component of the markups, which is endoge-

nous, depends on the presence of nominal rigidities, which prevent …rms and workers from achieving their desired markups at any given point in time. Given this structure, we de…ne three counterfactual objects. First, natural output is the level of output that would prevail in equilibrium if prices and wages were ‡exible, but monopoly power and hence desired markups continued to ‡uctuate as in the baseline economy. Potential output is equilibrium output with actual price and wage markups constant at their (positive) steady state level

p

and

w:

This would occur if prices were ‡exible and the

elasticity of goods and labor demand, and hence desired markups, were constant. Finally, e¢ cient, output is equilibrium output in the competitive economy, in which price setters face in…nitely elastic demands and hence desired markups are zero. Therefore, the only di¤erence between the potential and e¢ cient equilibria is that desired markups are positive, but

14


constant in the latter and zero in the former. As a result, the behavior of the two counterfactual economies is identical, up to a shift in the steady state that has no implications for the log-linear approximate dynamics.5 The reason for focusing on potential rather than on e¢ cient output is that the current version of our model abstracts from sources of distortions that are likely to be particularly relevant in steady state, such as taxes. Incorporating these other sources of distortions, both on average as well as over time, is an important avenue for future research. To estimate natural, potential and e¢ cient output, we must expand the system of equations (3.1) and the vector ^t to include all the additional equations and variables that are necessary to characterize the equilibria of the economy under the relevant counterfactual assumptions. For a given draw of the parameter vector , the solution of the expanded version of (3.1) delivers an expanded state space representation of the model. We then use the disturbance smoother of Durbin and Koopman (2002) to generate a sample from the conditional posterior distribution of the states. Repeating this procedure for each parameter draw enables us to characterize the posterior distributions of natural and potential output. In this way, the posterior accounts for both parameter and state uncertainty. 4. Potential Output and the Output Gap in the Estimated Model This section presents the estimation results of the baseline model, as well as our estimates of potential output and the output gap. Table 1 reports the posterior mode, mean, median and 90 percent posterior intervals for the unknown coe¢ cients. The data are quite informative about the model parameters and the estimates we obtain are generally in line with previous studies. For this reason, and given the focus of our paper on understanding the importance of the assumption of monopolistic competition and the charecterization of optimal policy, we only brie‡y comment on the coe¢ cients ralated to nominal rigidities and the conduct of monetary policy. In particular, prices and wages are re-optimized approximately every three quarters and the degree of backward indexation is very low. Moreover, monetary policy is considerably inertial and exhibits a substantial degree of activism, with interest rates responding more than 2 to 1 to in‡ation and nearly 1 to 1 to output growth. 5 The dynamic equivalence between the potential and e¢ cient economies requires that the …xed cost F is

assumed to be invariant to the assumption on the degree of competition. If the …xed cost F; whose primary role is to “absorb” the steady state pro…ts generated by the presence of monopolistic competition, is assumed to vanish as the economy becomes competitive, the dynamic properties of the e¢ cient equilibrium will of course be a¤ected. However, this e¤ect is quantitatively small, so we ignore it here.


15

Table 1. Prior distributions and posterior estimates in the baseline model Prior

Posterior

Dist

5%

Median

95%

Mode

Mean

SE

5%

Median

95%

N

0.2178

0.3000

0.3822

0.1656

0.1662

0.0062

0.1562

0.1661

0.1766

p

B

0.2526

0.5000

0.7474

0.0520

0.0647

0.0278

0.0269

0.0611

0.1144

w

B

0.2526

0.5000

0.7474

0.0761

0.0817

0.0293

0.0383

0.0791

0.1340

N

0.4589

0.5000

0.5411

0.4934

0.4929

0.0229

0.4550

0.4930

0.5305

h

B

0.4302

0.6029

0.7597

0.8430

0.8373

0.0318

0.7815

0.8400

0.8850

p

N

0.0678

0.1500

0.2322

0.2934

0.2909

0.0373

0.2291

0.2910

0.3523

N

-0.8224

0.0000

0.8224

0.0320

0.0370

0.4904

-0.7649

0.0356

0.8568

N

0.4605

0.6250

0.7895

0.6217

0.6189

0.1005

0.4552

0.6178

0.7846

G

0.1111

0.2368

0.4339

0.1170

0.1296

0.0419

0.0653

0.1268

0.2032

G

0.9454

1.9071

3.3718

1.9585

2.3210

0.6950

1.3241

2.2421

3.5643

p

B

0.4869

0.6651

0.8158

0.7702

0.7777

0.0296

0.7305

0.7766

0.8279

w

B

0.4869

0.6651

0.8158

0.7322

0.7350

0.0450

0.6582

0.7364

0.8066

G

3.4764

4.9335

6.7505

4.9496

5.1669

1.0253

3.6112

5.0982

6.9674

G

2.5090

3.9170

5.7743

3.5815

3.8625

0.7429

2.7316

3.8091

5.1585

N

1.2065

1.7000

2.1935

2.1034

2.1748

0.1987

1.8581

2.1699

2.5116

Y

N

-0.0935

0.4000

0.8935

0.9353

0.9436

0.1318

0.7329

0.9411

1.1654

R

B

0.2486

0.6143

0.9024

0.7797

0.7764

0.0272

0.7276

0.7792

0.8157

z

B

0.0976

0.3857

0.7514

0.0795

0.0949

0.0447

0.0282

0.0909

0.1755

g

B

0.2486

0.6143

0.9024

0.9951

0.9940

0.0030

0.9887

0.9944

0.9983

B

0.2486

0.6143

0.9024

0.7406

0.7243

0.0548

0.6299

0.7269

0.8094

B

0.2486

0.6143

0.9024

0.9001

0.8774

0.0505

0.7840

0.8841

0.9473

B

0.2486

0.6143

0.9024

0.9824

0.9812

0.0090

0.9650

0.9824

0.9933

b

B

0.2486

0.6143

0.9024

0.4445

0.4526

0.1080

0.2803

0.4498

0.6362

mp

IG1

0.0493

0.1021

0.3727

0.2148

0.2162

0.0115

0.1980

0.2159

0.2357

z

IG1

0.4077

0.7751

2.2455

0.9182

0.9276

0.0484

0.8519

0.9256

1.0107

g

IG1

0.1756

0.3552

1.2108

0.3657

0.3688

0.0176

0.3413

0.3680

0.3990

IG1

0.1756

0.3552

1.2108

7.0261

7.6853

1.3740

5.6646

7.5490

10.1255

IG1

0.0493

0.1021

0.3727

0.0979

0.1000

0.0108

0.0833

0.0994

0.1188

IG1

0.4077

0.7751

2.2455

2.9851

3.5276

1.0927

2.1064

3.3504

5.5488

b

IG1

0.0327

0.0679

0.2488

0.0614

0.0624

0.0169

0.0366

0.0613

0.0920

w

IG1

0.0493

0.1021

0.3727

0.2956

0.2973

0.0173

0.2697

0.2968

0.3268

IG1

0.0264

0.0439

0.0932

0.0347

0.0396

0.0088

0.0270

0.0385

0.0558

Lss

F

S

0

p

p

16


(a): DSGE GDP Gap (Median and Error Bands) 10

5

0

-5

-10

-15 1960q1

1970q1

1980q1

1990q1

2000q1

(b): HP and DSGE Gap DSGE Gap: Median HP Gap

4 2 0 -2 -4 -6 1960q1

1970q1

1980q1

1990q1

2000q1

Figure 1. Model-based output gap and the business cycle

Figure 1a plots the posterior median and 90 percent posterior interval for the modelimplied output gap, i.e. the di¤erence between actual and the DSGE-based potential output. To gauge the cyclical properties of the output gap, …gure 1b plots it together with a popular indicator of the business cycle–the deviation of GDP from a Hodrick-Prescott (HP) trend–and with shaded areas corresponding to the NBER recessions. The DSGE-based output gap has a pronounced cyclical behavior: it peaks at the cusp of expansions and declines substantially during recessions, but much less sharply than the HP output gap. Overall, the two gaps comove positively, but the DSGE-based output gap is smoother and displays a low frequency component which is eliminated by construction in the HP gap. This behavior of the DGSE gap suggests that the ine¢ ciencies associated with market power build during expansions and peak with the business cycle, but decline only slowly after that. The pattern of deviations of GDP from potential just described implies that output ‡uctuations in the postwar period would have been less pronounced if products and labor markets


17

had been perfectly competitive. In particular, …gure 1 suggests that the “twin” recessions of the early 1980s corresponded to a sharp decline in the output gap, which brought the economy back to its potential equilibrium after almost two decades of “overheating”starting in the mid-1960s. This con…rms the anecdotal evidence about the importance of “nominal” and monetary factors in driving real macroeconomic outcomes during that historical period. Our estimate of the output gap is also lower than HP-detrended output during the 1990s, implying that the steady rise of output in the 1990s can be traced to a rise in potential output. This historical account squares well with the view that the 1990s were charachterized by a considerable surge in productivity. Finally, according to our estimates, the last recession is associated with a dramatic and unprecendented fall in output relative to the DSGE-based potential. Such a decline is driven by large negative investment shocks, whose origin can be traced to …nancial disturbances further propagated by nominal rigidities, as argued in Justiniano, Primiceri, and Tambalotti (2010b). In sum, our model-based estimate of the output gap points to sizable ine¢ ciencies associated with departures from perfect competition. The historical path of these ine¢ ciencies does not exactly coincide with commonly used indicators of the business cycle, such as HP-…ltered output, but is certainly positively correlated with economic ‡uctuations, as in Gali, Gertler, and Lopez-Salido (2007) and Sala, Soderstrom, and Trigari (2008). This last result stands in contrast to the conclusions from other studies in the empirical DSGE literature, as pointed out by Walsh (2005) and Mishkin (2007). This literature has typically inferred small and acyclical DSGE-based output gaps, mainly due to modeling assumptions that seem at odds with the data. For example, Andrés, López-Salido, and Nelson (2005) calibrate the coe¢ cient of backward indexation to one and do not have price markup shocks or any other disturbance entering the Phillips curve directly. With these tight restrictions, variation in marginal costs are forced to explain the high frequency ‡uctuations in the …rst di¤erence of in‡ation. This requires a large estimate of the slope of the Phillips curve and erroneously suggests that nominal rigidities are nearly irrelevant for cyclical ‡uctuations. Edge, Kiley, and Laforte (2008) instead estimate a large scale model, starting in the early 1980s, but without an in‡ation target shock. Since the in‡ation rate exhibits a pronounced declining trend during their estimation period, their inferred output gap inherits this trend. Finally, Levin, Onatski, Williams, and Williams (2005) detrend the real series outside the model and their policy rule responds to the output gap directly. Since their estimate of the

18


output gap is small and countercyclical, this policy rule is at odds with the conventional view that the Fed tends to raise the federal funds rate during expansions, and lower it in recessions. If we impose the same restrictions assumed by these authors in our model, we can approximately replicate their results.

5. Optimal Output The e¢ cient level of output that we studied in the previous section corresponds to equilibrium output in a counterfactual economy hit by the same shocks that perturbed the U.S. economy in the last …fty years, but with perfectly competitive markets and therefore ‡exible prices and wages. In such an economy, the price and wage ‡uctuations necessary to ensure an e¢ cient movement in the real wage (i.e. such that M RS = W=P = M P L) are inconsequential for welfare since real and nominal outcomes are dichotomous and they do not result in any real distorsions. This is no longer the case, however, in an environment with nominal rigidities, such as the one that best describes the U.S. economy according to our estimates. In this environment, ‡uctuations in aggregate price and wage in‡ation produce dispersion in relative prices and wages, and therefore in the demand for goods and labor across workers and producers. Since these agents are assumed to meet the demand they face, this dispersion is ine¢ cient: agents with identical preferences and technologies end up supplying di¤erent amounts of labor and goods. An important implication of the existence of these distortions in both the goods and labor markets is that the Pareto e¢ cient allocation is not a feasible equilibrium in the sticky economy (e.g. Proposition 1 in Erceg, Henderson, and Levin (2000)). This is not to say that an equilibrium in which aggregate output is at its e¢ cient level cannot be achieved in the sticky economy, but rather that such an equilibrium and the resulting allocation are not Pareto e¢ cient. This is because the movements of prices and wages necessary to achieve such an equilibrium are incompatible with the elimination of dispersion in both prices and wages, and of the distortions that this dispersion generates. An optimal allocation in this environment will therefore tradeo¤ the costs of these distortions with the bene…ts of maintaining the aggregate real variables close to their e¢ cient level. For a more comprehensive insight into the tradeo¤s faced by the planner in our economy, we now turn to the study of the model’s optimal allocation. To compute this allocation, we


19

maximize the utility of the average household, subject to the nonlinear constraints represented by the equilibrium behavior of private agents, as illustrated in detail in Woodford (2010). We approach this normative investigation from two complementary perspectives. First, we ask to what extent the optimal allocation “resembles”the equilibrium in which output is at its e¢ cient level. The answer to this question is important to determine if e¢ cient output could be useful as a practical benchmark for stabilization policy, or if it should be regarded only as an element of an utopian equilibrium, not to be pursued on its own in the real world. Second, we compare actual and optimal output, to determine if interest rate policy could have delivered a tamer business cycle over our sample, without causing at the same time a reduction in welfare due to more in‡ation volatility. The answers to these questions are provided in …gure 2a, which compares actual, potential and optimal output. To do so in a parsimonious way, and to mantain comparability with …gure 1 above, actual and optimal output are both presented in deviation from potential output. Our …rst …nding is that the optimal output gap— optimal minus potential output— exhibits frequent and large deviations away from zero. These discrepancies between optimal and potential output suggest that the latter is not a good benchmark for stabilization policy. In addition, optimal output is more volatile than actual output, at both business cycle and higher frequencies. The reason for the excess volatility of optimal output is that this is the cost the planner is willing to pay to reduce the variability of the in‡ation rates, and thus relative price dispersion, as we can observe from …gures 2b and c.6 The large variability in output in the optimal equilibrium, relative to that in prices, points to the preponderance of the distorsions generated by nominal dispersion as a source of welfare losses in this class of models. The striking implication of our calculations is that policy should focus on minimizing these distorsions, even if this comes at the cost of de-stabilizing the real economy. This shift away from output stabilization and towards in‡ation stabilization engineered by optimal policy is so extreme that optimal GDP resembles quite closely natural output. By natural, we refer to the level of output that would prevail in a counterfactual equilibrium with ‡exible prices and wages, and it is shown in …gure 3 . One distinguishing feature of the natural allocation is that the adjustment to changes in desired markups happens entirely 6 According to our estimates, the coe¢ cients of backward price and wage indexations are small, so that price and wage in‡ation are close to a su¢ cient statistic for the amount of price and wage dispersion in the economy.

20


(a): Optimal and Observed GDP in Deviation from Potential: Baseline Optimal Actual

6 4 2 0 -2 -4 -6 1960q1

1970q1

1980q1

1990q1

(b): Price Inflation

2000q1

(c): Wage Inflation 3 Optimal Data

2.5

Optimal Data

2.5 2

2

1.5 1.5 1 1 0.5 0.5

0

0

-0.5 1960q1

1970q1

1980q1

1990q1

2000q1

1960q1

1970q1

1980q1

1990q1

2000q1

Figure 2. Optimal output in the baseline model

through movements in quantities, since the latter evolve independently from prices. This full pass through of markup shocks to real allocations, and in particular to output, is also an approximate feature of the optimal equilibrium in our baseline model. An interesting consequence of the preponderance of the nominal stabilization objective in the welfare function is that optimal output is virtually invariant to the interpretation of labor supply shocks as re‡ecting changes in workers’taste for leisure or, instead, exogenous variations in their monopoly power. This is shown in …gure 4, which plots optimal output under two alternative scenarios. In the …rst scenario, which corresponds to our baseline speci…cation, taste shocks are a priori more likely to account for any low frequency movement in labor supply, as in Justiniano, Primiceri, and Tambalotti (2010a), while markup shocks are i.i.d. In the second scenario, all exogenous variation in labor supply detected by the model is instead attributed to shifts in desired markups. In both scenarios, optimal output has very similar properties, since the strong preference of the planner for a relatively stable wage


21

Natural, Actual, and Optimal GDP in deviation from Potential GDP Natural - Potential Actual - Potential Optimal - Potential 10

5

0

-5

-10 1960q1

1970q1

1980q1

1990q1

2000q1

Figure 3. Potential, natural and actual GDP in‡ation implies that hours and output bear the brunt of the adjustment to labor supply shocks in the optimal equilibrium, regardless of their origin. This …nding is important because the ultimate source of shifts to labor supply–tastes or desired markups–cannot be identi…ed from the data alone, but it has signi…cant implications for potential output (Chari, Kehoe, and McGrattan (2009)). Sala, Söderström, and Trigari (2010), for example, show that the time-series properties of potential output in a model very similar to our are very di¤erent depending on the interpretation of labor supply shocks. The evidence in …gure 4 demonstrates that these di¤erences in potential output, need not have meaningful implications for optimal policy.

6. Wage Markup Shocks: Fact or Fiction? Our results so far suggest that stabilization policy should be mainly concerned with minimizing the real distorsions generated by price and wage dispersion, even at the cost of actively destabilizing output. In this section, we show that the key driver of this extreme

22


Optimal GDP in Deviation from Baseline Potential Baseline All Wage Markup 6

4

2

0

-2

-4

-6 1960q1

1970q1

1980q1

1990q1

2000q1

Figure 4. Optimal GDP (in deviation from the baseline potential GDP in the baseline model) with and without taste shocks in the utility function. tension between output and in‡ation stabilization is the volatility of wage markup shocks. However, these shocks closely resemble measurement errors, which can be interpreted strictly as sampling errors, or more generally as idiosyncratic disturbances across alternative wage series (arising from di¤erences in coverage, de…nition, etc.). When we model them as such, the model’s …t improves, and the tradeo¤ between in‡ation and output stabilization almost disappears. Figure 5 provides a useful perspective on the role of markup shocks. The three panels plot GDP, price and wage in‡ation in the optimal allocation of a counterfactual economy in which the volatility of wage markup shocks has been set to zero. In this economy, the deviations of optimal output from potential are much smaller and smoother then in the baseline case. Moreover, the behavior of price in‡ation is similar to that in the baseline case, while optimal wage in‡ation is even less volatile. This counterfactual experiment demonstrates that wage markup shocks are a fundamental driver of the tradeo¤ between output and wage in‡ation stabilization illustrated in the previous section. This tradeo¤ almost disappears when desired


23

(a): Optimal and Observed GDP in Deviation from Potential: No Wage Markup Shock Optimal Actual

6 4 2 0 -2 -4 -6 1960q1

1970q1

1980q1

1990q1


2000q1


2.5

Optimal Data

2.5 2

2

1.5 1.5 1 1 0.5 0.5

0

0

-0.5 1960q1

1970q1

1980q1

1990q1

2000q1

1960q1

1970q1

1980q1

1990q1

2000q1

Figure 5. Optimal output without wage markup shocks

wage markups are constant. On the contrary, the tradeo¤ between output and price in‡ation stabilization remains, although between the two objectives, the former seems to loom larger in the welfare function, as suggested by the more pronounced volatility of price than wage in‡ation in the optimal equilibrium. The fact that markup shocks play such a prominent role in the striking normative implications of our baseline estimates is troubling for at least two reasons. First, the microfoundations of these shocks are dubious (see Chari, Kehoe, and McGrattan (2009) or Shimer (2009)). Second, their explantory power is large for wage in‡ation, especially at high frequencies, but small for the real variables.7 These observations suggest that these shocks might in fact capture measurement error in the wage in‡ation series or, more in general, some disconnect between the model’s “wage”and its counterparts in the data (Boivin and Giannoni (2006a)).

7 Wage markup shocks explain only 2 percent of GDP and hours volatility over the business cycle and 1

percent of consumption and investment.

24


Nominal wage inf lation 3.5 baseline LEPRIVA

3 2.5 2 1.5 1 0.5 0 -0.5 -1 1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 6. Two measures of nominal wage in‡ation To pursue this insight, we re-estimate the model using two measures of wage in‡ation. The …rst measure is our baseline, which is based on NIPA. The second measure is the “hourly compensation of non-supervisory and production workers” (LEPRIVA), which is computed by the BLS based on the Establishment Survey and is the one recommended by Galí (2010). In the estimation, we allow both series to be a¤ected by an i.i.d. observation error, akin to the de…nition of idiosyncractic disturbances in factor analysis (see Boivin and Giannoni (2006a) for a generalization of this approach).8 Figure 6 plots the two series, which behave similarly at medium and low frequencies, but di¤er markedly at high frequencies. This illustrates the well known di¢ culties in measuring aggregate wages (e.g. Abraham, Spletzer, and Stewart (1999), Bosworth and Perry (1994), or Aaronson, Rissman, and Sullivan (2004)). The use of two wage indicators, however, should help us to distinguish markup shocks, which should produce ‡uctuations in both series, from (idiosyncratic) measurement errors— high frequency wage movements uncorrelated across the two indicators. 8 Following the literature on factor analysis, we normalize one of the loadings to one (that of the series used for our baseline estimation) and estimate the other loading. In addition, notice that we start the estimation in 1964:I, due to limited data availability.


25

Table 2 reports the posterior estimates for this alternative model. A few results stand out. First, coe¢ cient estimates are generally very similar to those of the baseline model. The main exceptions are the parameter corresponding to steady state in‡ation (which is probably a¤ected by the lower mean of the LEPRIVA wage in‡ation), and the persistence of the price markup shock, which is now substantially lower. The second important result is that the standard deviation of the wage markup shock is now much smaller than in the model with only one wage series, suggesting that most high frequency variation in wages stems from idiosyncratic shocks that a¤ect each series separately.

This intuition is con…rmed in …gure 7, in which we plot the optimal output gap for the new model. In this speci…cation, optimal GDP behaves almost exactly like potential output. This result has two important implications. First, potential output is a legitimate benchmark for stabilization policy, even if the entire e¢ cient allocation cannot be replicated. Furthermore, a stable output gap is roughly compatible with stable in‡ation. In other words, the tension between the three main objectives of policy seems fairly miniminal when wage markup shocks are not too large. The second key implication of our result comes from the comparison between the optimal and actual output gap in …gure 7. The large discrepancy between the two lines indicates that large output ‡uctuations could have been avoided without lowering welfare.

7. Conclusions We estimated a New-Neoclassical Synthesis model of the U.S. economy with macroeconomic data since 1954. In this model, workers and goods producers have some monopoly power, and markups of price over marginal cost and of wages over the marginal rate of substituion ‡uctuate due to exogoneous changes in monopoly power, as well as to the presence of sticky prices and wages. According to our estimates, U.S. GDP would have been signi…cantly less volatile in the absence of these sources of movements in markups, or, equivalently, if markets had been counterfactually competitive. However, this …nding does not imply that the average household in the economy would have been better o¤ if policy had attempted to stabilize output around its e¢ cient level. This is because the e¢ cient allocation is not feasible when prices and wages are in fact unable to adjust continously, as our estimated model suggest they are in practice. The e¢ cient level of

26


Table 2. Prior distributions and posterior estimates in the baseline model Prior

Posterior

Dist

5%

Median

95%

Mode

Mean

SE

5%

Median

95%

N

0.2178

0.3000

0.3822

0.1601

0.1607

0.0073

0.1488

0.1606

0.1728

p

B

0.2526

0.5000

0.7474

0.1455

0.1620

0.0705

0.0629

0.1531

0.2928

w

B

0.2526

0.5000

0.7474

0.0368

0.0435

0.0172

0.0188

0.0416

0.0751

N

0.4589

0.5000

0.5411

0.4726

0.4724

0.0232

0.4344

0.4724

0.5105

h

B

0.4302

0.6029

0.7597

0.8009

0.8165

0.0403

0.7458

0.8190

0.8784

p

N

0.0678

0.1500

0.2322

0.2512

0.2499

0.0412

0.1832

0.2491

0.3198

N

-0.8224

0.0000

0.8224

0.0035

0.0051

0.4890

-0.7873

0.0014

0.8046

N

0.4605

0.6250

0.7895

0.2352

0.2414

0.0688

0.1267

0.2429

0.3513

G

0.1111

0.2368

0.4339

0.1705

0.1806

0.0528

0.0994

0.1774

0.2715

G

0.9454

1.9071

3.3718

2.3598

2.7333

0.7627

1.6166

2.6661

4.1213

p

B

0.4869

0.6651

0.8158

0.8414

0.8384

0.0301

0.7888

0.8382

0.8883

w

B

0.4869

0.6651

0.8158

0.7166

0.7289

0.0438

0.6560

0.7297

0.7997

G

3.4764

4.9335

6.7505

5.1009

5.3121

1.0111

3.7685

5.2453

7.0778

G

2.5090

3.9170

5.7743

3.6359

3.9276

0.7848

2.7305

3.8747

5.3014

N

1.2065

1.7000

2.1935

2.3452

2.3246

0.2126

1.9666

2.3303

2.6587

Y

N

-0.0935

0.4000

0.8935

0.8157

0.8503

0.1445

0.6260

0.8411

1.0994

load2

N

0.1776

1.0000

1.8224

0.6502

0.6468

0.0332

0.5901

0.6482

0.6992

R

B

0.2486

0.6143

0.9024

0.6892

0.6982

0.0513

0.6046

0.7040

0.7716

z

B

0.0976

0.3857

0.7514

0.1285

0.1301

0.0566

0.0431

0.1266

0.2299

g

B

0.2486

0.6143

0.9024

0.9975

0.9961

0.0023

0.9916

0.9966

0.9991

B

0.2486

0.6143

0.9024

0.6909

0.6866

0.0539

0.5968

0.6881

0.7724

B

0.2486

0.6143

0.9024

0.2501

0.2773

0.1505

0.0842

0.2509

0.5622

B

0.2486

0.6143

0.9024

0.9780

0.9747

0.0135

0.9507

0.9770

0.9915

b

B

0.2486

0.6143

0.9024

0.6791

0.6318

0.0818

0.4890

0.6370

0.7576

mp

IG1

0.0493

0.1021

0.3727

0.2204

0.2238

0.0147

0.2003

0.2235

0.2482

z

IG1

0.4077

0.7751

2.2455

0.8556

0.8653

0.0505

0.7864

0.8631

0.9521

g

IG1

0.1756

0.3552

1.2108

0.3611

0.3648

0.0191

0.3350

0.3639

0.3973

IG1

0.1756

0.3552

1.2108

6.9844

7.5647

1.4596

5.3889

7.4450

10.1703

IG1

0.0493

0.1021

0.3727

0.1661

0.1626

0.0211

0.1245

0.1646

0.1934

IG1

0.4077

0.7751

2.2455

3.8603

4.7317

1.5790

2.8802

4.4873

7.2347

b

IG1

0.0327

0.0679

0.2488

0.0284

0.0338

0.0086

0.0222

0.0324

0.0499

w

IG1

0.0493

0.1021

0.3727

0.0533

0.0604

0.0155

0.0388

0.0584

0.0889

IG1

0.0264

0.0439

0.0932

0.0517

0.0522

0.0107

0.0357

0.0516

0.0707

mew

IG1

0.0493

0.1021

0.3727

0.4900

0.4940

0.0302

0.4468

0.4932

0.5453

mew2

IG1

0.0493

0.1021

0.3727

0.2753

0.2783

0.0245

0.2369

0.2788

0.3173

Lss

F

S

0

p

p


27

(a): Optimal and Observed GDP in Deviation from Potential: Wage Measurement Error Optimal Actual

6 4 2 0 -2

1964q2

1974q2

1984q2

1994q2


2004q2


2.5 2

2

1.5

1.5

1

1

0.5

0.5

0

0

-0.5 1964q2

1974q2

1984q2

1994q2

2004q2

Optimal Data

2.5

-0.5 1964q2

1974q2

1984q2

1994q2

2004q2

Figure 7. Optimal output in the model estimated with two measures of nominal wage in‡ation output, on the contrary, can be achieved in equilibrium, but this requires a volatility of price and wage in‡ation so high, that welfare is on net lower than in the actual allocation. The large ‡uctuations in desired wage markups that are necessary to account for the observed movements in nominal wages are the key driving force behind this strong tension between output and in‡ation stabilization. But the interpretation of these markup shocks as re‡ecting genuine shifts in monopoly power is questionable, sincethe shifts we measure are large, and concentrated at high frequencies. Therefore, we also estimate a version of the model that allows for some disconnect between the model’s “wage” and its measurement in the data. In this amended model, the wage markup shocks play a negligible role and the tradeo¤ between output and wage stabilization is minimal. As a result, optimal and e¢ cient output virtually coincide, suggesting that this latter construct can be a useful reference point for stabilization policy. An immediate corollary of this result is that the Taylor rule that we use to characterize monetary policy over our sample is suboptimal, since a setting of the interest rate closer to

28


that prescribed by the optimal policy could have delivered a smoother path of output, as well as more stable in‡ation. There are several possible explanations for this discrepancy between actual and optimal policy. First, our positive characterization of interest rate policy might be misspeci…ed. A comparison of the model’s …t under our Taylor rule and the optimal policy, or other interest rate rules closer to the optimal, would help evaluate this hypothesis. Second, the model’s welfare function might not be a good representation of the actual objectives of U.S. monetary policy. For example, wage distortions play a large role in reducing the welfare of the represenative agent in the model, but they are seldom mentioned as a direct preoccupation by policymakers. Third, we might have overlooked some relevant constraint in setting interest rates. The most obvious one in this respect is the zero lower bound on nominal interest rates. However, a preliminary exploration of this issue in the model with mesurement error suggests that this bound is not violated often in that model’s optimal equilibrium. Last, but not least, actual monetary policy might have been misguided, at least at some points in the past. This is a fairly common conclusion among researchers, especially for the period roughly between 1965 and 1980 (e.g. Clarida, Gali, and Gertler (2000), Cogley and Sargent (2004) and Primiceri (2006)). The fact that we assume a constant policy speci…cation across the entire span of our long sample prevents us from addressing this possibility with …ner historical detail, although doing so would be useful.

Appendix A. Normalization of the Shocks As in Smets and Wouters (2007), some of the exogenous shocks are re-normalized by a constant term. In particular, we normalize the price and wage markups shocks and the intertemporal preference shock. More speci…cally, the log-linearized Phillips curve is

^t =

1+

Et ^ t+1 + p

1 1+

^t

1

+ s^t + ^ p;t .

p

The normalization consists of de…ning a new exogenous variable, ^ p;t

^ p;t , and estimating

the standard deviation of the innovation to ^ p;t instead of ^ p;t . We do the same for the wage


29

markup and the intertemporal preference shock, for which the normalizations are ^

w;t

^b t

0

= @ =

(1 1 + (1 +

(1

b ) (e

e h+

w ) (1 1

w)

) (1 + ) w h

e2

b ) (e + h2

w

1

A ^ w;t

h) ^ bt :

These normalizations are chosen so that these shocks enter their equations with a coe¢ cient of one. In this way, it is easier to choose a reasonable prior for their standard deviation. Moreover, the normalization is a practical way to impose correlated priors across coe¢ cients, which is desirable in some cases. For instance, imposing a prior on the standard deviation of the innovation to ^ p;t corresponds to imposing priors that allow for correlation between and the standard deviation of the innovations to ^ p;t . Often, these normalizations improve the convergence properties of the MCMC algorithm.

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Federal Reserve Bank of Chicago Northwestern University, CEPR and NBER Federal Reserve Bank of New York