APLICACIONES Maniobras de conexión,

t j t j 1E p

∞

= −

∑ t

₀

time

E_tp_t^* Announced Shift in Monetary Policy

* t j t j 1E p

∞

= −

∑

time

Figure 4: Price Setting under Sticky Information Phillips Curve

Of course one might critically ask whether this conclusion applies to a scenario where the central bank conducts inflation targeting by means of manipulating the real interest rate . In a regime of interest rate targeting lower inflationary expectations might give a restrictive monetary impulse as expected real interest rates increase. Typically in a purely New Keynesian IS-framework a real balance effect is not present unless one deviates from the assumption that money and consumption enter the utility function separately (see Woodford, ch. 4, pp. 301). The fact that the SIPC does not have more adherents can be traced back to extensions of the basic Calvo model. Within the next section we will highlight these extensions.

2.1.1.5 Hybrid New Keynesian Phillips Curve

The NKP C combines elements of the “Real Business C ycle” framework w ith Keynesian elements of monopolistic compe tition and sticky prices. Nevertheless it has its problems when it meets the data . Therefore extensions have been developed to reconcile the virtues of micro foundation with stylized facts. These Phillips curves are labeled as “Hybrid New Keynesian Phillips Curves” (HNKPC) as they combine forward looking elements with backward looking behavior. Gali, Gertler and Salido Lopez (2001) propose the following derivation for a

HNKPC. The log price index pt can be defined as a weighted average of last period’s prices pt -1 and those prices that are reset in the current period:

( )

^*

t t 1 t

p = θp₋ + −θ1 p ^{. (2.112)}

Those prices p^*_t that are reset in the current period can be decomposed intop^rat_t , where the index (rat) denotes forward looking andp^b_t, where the index (b) denotes backward looking.

Clarida, Gali and Lopez-Salido (2001) propose the following updating scheme for backward looking price setters:

b *

t t 1 t 1

p =p₋ + π₋ . (2.113)

Accordingly backward looking firms update p^*_{t 1−} by last periods inflation rate. Of course alternative rules of thumb are thinkable and actually implemented (see C hristiano, Eichenbaum and Evans 2005). So for instance one might assume that backward looking agents update their prices by steady state inflation.

* 1 b

t t

p =p− +π. (2.114)

Generally rule-of-thumb behavior has become a very common theme in monetary macroeconomics as it is a straightforward way to introduce inertia in macroeconomic models.

Rule -of-thumb behavior can be rationalized by a broad list of arguments (Amato and Laubach (2003)). It does not produce any computational costs as the information needed to update prices is assumed to be publicly available. The fraction of firms that updates by rule -of-thumb implicitly learns as yesterdays inflation rate incorporates the pricing decisions of those agents that optimize. In steady state rule-of-thumb setters will set prices equal to those who do Calvo pricing. Under the assumption of Calvo pricing forward looking firms set prices according to the following rule:

( ) ( ) (

^k

)

rat

t k 0 t ˆ t t k

p = −βθ1

∑

^∞₌ βθ E mc +p₊ ^{. (2.115)} Equation (2. 112) can be rewritten as follows:

(

^*

)

t t t

1− θ p p

 

π = θ  − . (2.116)

Equation (2. 116) can be simplified by substituting out the reset price p^*_t by the weighted average of those price setters that follow a rule of thumb and those that optimize.

( ) (

^rat

) (

^b

)

t t t t t

1− θ 1 p p p p

   

π = θ   −ω − + ω −  (2.117)

Based on the seminal work of Sbordone (2002) one can derive the following expression for average marginal costs if firms implement a CES technology

( )

where α% denotes the labor share and ε the elasticity of demand. Accordingly marginal costs are given by ^{MCt =}

( (

^{W Pt t}

) (

^{/ 1−α%}

)(

^{Y Nt/ t}

) )

in levels. In order to obtain a Phillips curve in terms of inflation and deviations of marginal costs from their flex-price values we need to substitute out

(

^{ptrat −pt}

)

^and

(

^ptb−pt

)

in (2.117). The distance between the price set by forward looking agents and the log price level can be stated as follows by substituting out (2. 18) in (2. 115):

With this expression at hand it will have to hold that:

( ) ( )

^k

Combining these expressions yields:

Collecting variables and multiplying the equation by the forward operator

(

^1−βθF

)

^yields:

( )

This can ultimately be written in the standard form of a H NKPC:

t fEt t 1₊ b t 1₋ mct t

The hybrid specification nests the purely backward looking NKPC as well as the purely forwar d looking one. Therefore it bridges the gap between the old style accelerationist type of Phillips curve and the New Keynesian one. Although the HNKPC is intrinsically inertial it is

common practice in applied work (Smets and Wouters ((2005)); Rabanal and Rubio-Ramirez (2003)) to augment equation (2. 125) by a serially correlated error term. This indicates that the HNKPC is still not able to generate enough inertia out of their structural relationships. Based on this notion of the Phillips curve we will explore the true degree of forward-lookingness γ_f and backw ard-lookingness γ_b nested in the data. Equation (2.125) nests the case of a purely backward looking Phillips curve (γ_b =1) as well as the standard NKPC (γ_b =0). The dynamics enshrined in the NKPC crucially depend on two relations. On the one hand on the relative magnitude of γ_b in relation to γ_f. On the other hand on ^'

κ which depicts the p

responsiveness of inflation to deviations of marginal cost from its steady state level. The relative size of γ_b in relation to γ_f critically determines the persistence of the inflation process. The higher the degree of backward-lookingness the higher will be the persistence of the inflation process as embedded in the autocorrelation functions. The degree of backward lookingness depends in particular on the percentage of price setters that update by rule of thumb and the share of Calvo-price setters in the economy. The second crucial parameter κ^'_p denotes the sensitivity of inflation with respect to marginal cost and indirectly over the production function to output. Therefore the parameter κ^'_p can be interpreted as the slope of the Phillips Curve. Note in particular that the parameter κ depends negatively on the degree ^'_p of Calvo-price setters. Hence the more economic agents are able to adjust prices to changing economic conditions the looser becomes the link between changes in the economic cycle and the inflation process itself. Given the absolute magnitudes of γ γ_b, _f and κ^'_p it is easy to see that by far the most important variable in explaining the inflation process is the inflation rate itself and not the deviation of marginal costs from its flex-price equilibrium. In section (4.3) we will systematically evaluate the implications of variations in the degree of forward and backward lookingness and its implication for the model dynamics. To summarize. This section analyzed the price setting behavior of firms. We saw that firms are only called at random intervals to reset prices. This type of price stickiness leads to price dispersion in the economy, which has detrimental effects on consumer welfare. Therefore the non vertical (NKPC) curve leaves a meaningful role to a central bank that smoothes out the impact of macroeconomic shocks on welfare.

In document SUBTERRÁNEA EN MEDIA TENSIÓN Y CENTROS DE (página 180-190)