text:
стр. 2
Note that the right-hand side of (1.36) is the the reciprocal of the steady-state "value-added markup"
or inefficiency wedge resulting from market power that Rotemberg and Woodford (1995) contrast with
the steady-state "gross-output markup" or firm-level markup of price over marginal cost µ. Distinguishing
between the two is essential in calibrating an imperfectly competitive model that abstracts from the existence
of intermediate inputs.
This would correspond to a materials share of 54 percent, if we assume Оё = 10 as do Chari et al. Note
that Basu (1995) suggests that a share parameter as high as sm = 0.9 could be reasonable, on the ground
that the share of intermediate inputs in marginal cost could be substantially higher than their share in
average cost. Under such an assumption this correction would be much more important than under the
calibration suggested here; for example, the assumption sm = 0.9 combined with an assumption Оё = 10
would imply that О¶ = 0. But such a calibration is not easy to interpret. If, for example, one proposes that a
large fraction of primary input purchases represent fixed or "overhead" costs, this would imply substantial
increasing returns (average cost much higher than marginal cost), which would in turn not be consistent
with equilibrium in the absence of an implausibly high degree of market power.
Table 3.1: The value of О¶ under alternative assumptions.
Пѓ в€'1 = 1, П‰ = 1.25 Пѓ в€'1 = .16, П‰ = .47
ОёВµ Вµsm homo. factor spec. factor homo. factor spec. factor
0 0 2.25 0.17 0.63 0.11
1 0 1.13 0.16 0.32 0.09
0 .6 0.90 0.15 0.25 0.09
1 .6 0.45 0.13 0.13 0.06
this implies that О¶ is reduced by a factor of 2.5 (i.e., it is multiplied by 0.4). This is again
a significant reduction, and if this effect is combined with the degree of variation in the
desired markup argued for above, the value of О¶ is only one-п¬Ѓfth the size indicated by the
baseline calculation of Chari et al. — 0.45 instead of 2.25, which is to say well below 1
(implying strategic complementarity) rather than being well above 1 (implying strategic
substitutability). On the other hand, in the case of specific factor markets, this correction
matters much less, unless sm is assumed to be much closer than Вµв€'1 than seems realistic.
Using the calibration discussed above, assuming Вµsm = 0.6 rather than zero reduces О¶ from
0.17 to 0.15 (in the constant-markup case), or from 0.16 to 0.13 (in the variable-markup
case). These reductions make no dramatic difference in one's conclusions about the degree
of strategic complementarity.
Our conclusions about the effects of these several corrections, in the case of the calibra-
tions just discussed, are summarized in Table 3.1. The left side of the table gives the value
of О¶ under the assumption that П‰ = 1.25, Пѓ = 1, and Оё = 10, as assumed by Chari et al.,
under eight different cases, representing three binary choices. These are the assumption of
homogeneous factor markets (sy = 0, sY = ω + σ −1 ) versus specific factor markets (sy = ω,
sY = Пѓ в€'1 ); the assumption of a constant desired markup ( = 0) versus a realistic degree
of markup variation (Оё mu = 1); and the assumption of no intermediate inputs (sm = 0)
versus a realistic intermediate input share in costs (Вµsm = 0.6). In each case, the simple
assumption made in the baseline case of Chari et al. is the one least favorable to strategic
complementarity. Changing any of these assumptions individually reduces О¶ substantially
relative to their baseline case. However, it is the allowance for factor specificity that matters
most, if one accepts that this is the more realistic assumption. For while each of the other
two corrections makes a significant difference in the case of homogeneous factor markets, and
together they make an even larger difference (as stressed by Bergin and Feenstra), in the
case of specific factor markets even their combined effect is not at all dramatic. Furthermore,
factor specificity alone reduces the value of ζ much more than the other two factors combined
do, if the importance of these latter factors is calibrated in what seems a reasonable way.
The right side of the table offers a similar comparison, when instead lower values are
assumed for both Пѓ в€'1 and П‰. The values suggested here are those obtained by Rotemberg
and Woodford (1997) when a slightly more complicated version of this pricing model is
п¬Ѓt to U.S. time series, as discussed further in chapter 4. The higher value of Пѓ (implying
much greater interest-sensitivity of private expenditure) is needed in order to account for the
observed size of the effects of an identified monetary policy shock on real aggregate demand;
the lower value of П‰ (implying much more elastic labor supply) is needed in order to account
for the observed modest declines in real wages that accompany such a large decline in output.
Under these alternative assumptions regarding preferences, О¶ < 1, implying a modest degree
of strategic complementarity, even in the case of homogeneous factor markets, Dixit-Stiglitz
preferences, and no intermediate inputs. But once again the degree of real rigidity is increased
by modifying any of these last three assumptions. It is interesting to observe in this case
that even under the assumption of homogenous factor markets, we obtain a value of О¶ = .13,
if we make realistic assumptions about the other two sources of real rigidity. Thus a value
of О¶ in the range between 0.10 and 0.15 does not require implausible assumptions. This is
a value that implies substantial strategic complementarity, and as we shall see, enough to
explain roughly the observed degree of sluggishness of aggregate price adjustment in response
to variations in nominal expenditure, given the observed frequency of price adjustment in
economies like that of the U.S.
2 Inflation Dynamics with Staggered Price-Setting
An unsatisfactory feature of the "New Classical" aggregate supply relation derived above
is its implication that only unanticipated fluctuations in nominal spending have any effect
upon real activity, and that equilibrium fluctuations in the output gap must be completely
unforecastable. These strong predictions were the occasion of a great deal of discussion and
criticism during the 1970s and early 1980s (see, e.g., Sheffrin, 1996, chap. 2). They imply
that only the immediate effects of a monetary policy shock upon nominal expenditure should
have any consequences for real activity; delayed effects (effects on nominal spending after
the "period" in which the shock occurs) should not affect output at all, only the price level.
And such real effects of a monetary policy shock as occur must be purely transitory, i.e.,
must last no longer than the "period" for which the sticky prices are fixed in advance.
These predictions are quite inconsistent with the effects identified in the "structural VAR"
literature. As an example, Figure 3.2 plots the impulse response of nominal GDP to an
identified monetary policy shock, according to the structural VAR model of Christiano et al.
(2001).24 There is practically no measurable effect of an unexpected interest-rate reduction
in quarter zero upon nominal GDP until the second quarter following the monetary policy
shock, though there is a strong increase in nominal GDP at that time.25 But this means
that according to the "New Classical" aggregate-supply relation, monetary shocks should
have no effect upon real activity at all, unless the "period" for which sticky prices are fixed
in advance is longer than six months.
Figure 3.3 next shows the estimated impulse response of real GDP to the same shock in
This particular impulse response is not reported in their paper, though the point estimates here are
implied by the inflation and real GDP responses that are reported there. I thank Charlie Evans for supplying
the data plotted in this and subsequent п¬Ѓgures. The impulse responses implied by this particular VAR study
are representative of those found in many others; see Christiano et al. (1999) for a review.
The fact that there is zero effect upon nominal GDP in quarter 0 is an artifact of the authors' iden-
tification scheme, which assumes that any contemporaneous correlation between interest-rate innovations
and innovations in either real GDP or inflation is due to feedback from the latter variables to the current
interest-rate operating target, as under a Taylor rule. However, the estimated effect in quarter 1 is in no
way constrained by the identification scheme; the fact that neither output nor inflation is estimated to be
significantly affected in quarter 1 provides some support for the assumption relied upon in the identification
0 5 10 15 20 25 30
Figure 3.2: Impulse response of nominal GDP to an unanticipated interest-rate reduction
in quarter 0. Periods on horizontal axis represent quarters, while the vertical axis measures
the effect on log nominal GDP in percentage points. Source: Christiano, Eichenbaum and
Evans (2001).
quarter zero. Contrary to the suggestion just mentioned, there is a substantial real effect
of the shock. (Note that in both п¬Ѓgures, the monetary policy shock is normalized so that
the long-run effect on nominal GDP is an increase of one percentage point.) Furthermore,
the effect occurs with a substantial delay; there is essentially no effect on output until the
second quarter following the policy shock,26 and the peak output effect occurs only in the
sixth quarter following the shock. The estimated effect is still more than two standard errors
greater than zero two full years after the shock, and (at least according to the point estimate)
the effect is still at more than a third of its maximum level ten quarters after the shock.
It may be wondered why we assert that the shock actually occurs in quarter zero, given that there is
no effect on nominal expenditure until quarter two. The occurrence of the policy shock is indicated by the
substantial decline in the federal funds rate in quarter zero; see Christiano et al. (2001) for a plot of this
0 5 10 15 20 25 30
Figure 3.3: Impulse response of real GDP to the same monetary policy shock as in Figure
3.2. The vertical axis measures the effect on log real GDP in percentage points. Source:
Christiano, Eichenbaum and Evans (2001).
Such long-lasting effects are inconsistent with the "New Classical" aggregate-supply relation,
unless the "period" for which prices are fixed in advance is longer than two years. But survey
evidence on price changes (e.g., Blinder et al., 1998) п¬Ѓnds that the majority of п¬Ѓrms change
their prices more frequently than once per year, so that more than half of all prices should
have been adjusted at least once within the п¬Ѓrst two quarters following a shock.
This undesirable feature of the model can be avoided, however — without abandoning
the assumption that prices are set optimally (under rational expectations) when they are
adjusted, and without assuming counterfactually long intervals between price changes — by
assuming that the intervals over which the prices of different goods remain fixed overlap,
rather than being perfectly synchronized. As Phelps (1978) and Taylor (1979a, 1980) п¬Ѓrst
pointed out,27 such staggering of price changes can lead to a sluggish process of adjustment
of the overall price level, even when individual prices are adjusted relatively frequently.
This is because, if individual suppliers' pricing decisions are strategic complements, then
the fact that some prices are not yet being adjusted will restrain the degree to which prices
are changed by those suppliers that do adjust their prices. At a later date, the adjustment of
the prices that earlier were sticky will in turn be restrained by the fact that the prices that
earlier were adjusted were not changed very much. As a result of this process, the level of
prices prior to a shock can continue to have a significant effect on the general level of prices
even after most prices have been adjusted at least once since the shock. If the strategic
complementarity between pricing decisions is great enough, the adjustment of the general
level of prices can be quite slow, even though individual price adjustments are frequent. The
consequence will be prolonged effects on real activity of a sustained change in the level of
nominal spending.
As we shall see, this theory of pricing can again justify an aggregate supply relation that
takes the form of an "expectations-augmented Phillips-curve" relation. However, in this
variant case, the kind of inflation expectations that determine the location of the short-run
Phillips curve are current expectations regarding future inflation, rather than past expecta-
tions regarding current inflation. This might seem a small difference (given the degree of
serial correlation in inflation expectations, at least in recent decades), but it is a crucial one;
for the aggregate supply relation, together with rational expectations, no longer exclude the
possibility of forecastable variations in the output gap. With this modification, the model
becomes consistent with the occurrence of prolonged fluctuations in real activity following a
monetary policy shock, of at least roughly the kind estimated in the VAR literature.
These п¬Ѓrst applications of the idea assumed that wages, rather than prices, were п¬Ѓxed for a period
of time (owing to wage contracts), and thus concerned the effects of staggered wage negotiations rather
than staggered price-setting. But as Blanchard (1983) pointed out, the same principle can be applied to
2.1 The Calvo Model of Price-Setting
Here we present a particular example of a model with staggered price-setting, a discrete-
time variant of a model proposed by Guillermo Calvo (1983).28 In this model, a fraction
0 < О± < 1 of goods prices remain unchanged each period, while new prices are chosen for
the other 1 в€' О± of the goods. For simplicity, the probability that any given price will be
adjusted in any given period is assumed to be 1 в€' О±, independent of the length of time since
the price was set, and independent of what the particular good's current price may be.
These last assumptions are plainly unrealistic, but they are very convenient in simplifying
the analysis of equilibrium inflation dynamics, as they greatly reduce the size of the state
space required to characterize those dynamics. Because each supplier that chooses a new
price for its good in period t faces exactly the same decision problem, the optimal price pв€—
is the same for each of them, and so in equilibrium, all prices that are chosen in period t
have the common value pв€— . The remaining fraction О± of prices charged in period t are simply
a subset of the prices charged in period t в€' 1, with each price appearing in the period t
distribution of unchanged prices with the same relative frequency as in the period t в€' 1 price
distribution. (For this last argument it is crucial that each price has an equal probability
of being adjusted in a given period.) Then the Dixit-Stiglitz price index (1.3) in period t
1 1
Pt1в€'Оё в‰Ў pt (i)1в€'Оё di = (1 в€' О±)pв€—1в€'Оё + О± ptв€'1 (i)1в€'Оё di,
0 0
so that
О±)pв€—1в€'Оё 1в€'Оё 1в€'Оё
Pt = (1 в€' + О±Ptв€'1 . (2.1)
It follows that in order to determine the evolution of this price index, we need only know
its initial value, and the single new price pв€— that is chosen each period. The determination of
See also Rotemberg (1987) for discussion of this model, and the similarity of its implications for aggregate
dynamics to those of a model with convex costs of price adjustment. The п¬Ѓrst use of a discrete-time version
of Calvo's model of price-setting, in the context of a complete intertemporal equilibrium model of aggregate
fluctuations, was in the work of Yun (1996). Other early applications of the same device include Woodford
(1996), King and Watson (1996), King and Wolman (1996), and Goodfriend and King (1997). Kimball (1995)
also assumes Calvo pricing, albeit in continuous time, in another important early study of an intertemporal
equilibrium model with sticky prices.
pв€— , in turn, depends upon current and expected future demand conditions for the individual
good, but (1.11) implies that other prices affect the demand curve for good i only through
the value of the price index Pt . Thus we can determine the equilibrium value of the index Pt
as a function of its previous period's value, the expected future path of this same index, and
current and expected future values of aggregate real variables. There is no need for reference
to additional information about past prices.29
A supplier that changes its price in period t chooses its new price pt (i) to maximize
О±T в€'t Qt,T [О i (pt (i))] ,
Et (2.2)
T =t
by analogy with (1.16), where once again nominal profits each period are given by
О i (p) = [Yt PtОё p1в€'Оё в€' wt (i)f в€'1 (Yt PtОё pв€'Оё /At ). (2.3)
Here the factor О±T в€'t multiplying the stochastic discount factor indicates the probability
that price pt (i) will still be charged in period T .30 The price pt (i) is chosen on the basis
of information available at date t so as to maximize this expression, given the expected
state-contingent values of the random variables Qt,T , YT , PT , wT (i) and AT for all dates
T ≥ t.
Corresponding to (1.18) we obtain in this case the п¬Ѓrst-order condition
О±T в€'t Qt,T YT PT [pt (i) в€' ВµST (i)] = 0.
Et (2.4)
T =t
Thus there is again a sense in which the price pt (i) is set equal to Вµ times a weighted average
of the levels of marginal costs expected to prevail in the various future states, and at the
This is only precisely true in the case of our baseline model, with specific factor markets, since in this case
the real marginal cost of supplying a given good depends only upon the quantity supplied of that good yt (i),
aggregate output Yt , and the vector of aggregate shocks Оѕt . If we instead assume common factor markets,
as in Yun (1996), real marginal cost depends upon an alternative output aggregate (the one that determines
aggregate demand for factors), and not solely upon the Dixit-Stiglitz aggregate Yt (that determines the
utility value of output). This means that the equilibrium conditions for the evolution of Pt also involve a
second price index, as shown by Yun. However, even in that case, up to a log-linear approximation the
equilibrium conditions can be written solely in terms of the index Pt .
Note that (2.2) reduces to (1.16) if the factor О±T в€'t is replaced by one that takes the value 1 if T = t + 1
and the value zero for all other T .
various future dates, at which the price pt (i) applies. But once again, (2.4) does not give a
closed-form expression for the optimal price, since ST (i) will depend upon the price of good
i.31 Substituting the demand function (1.11) into the real marginal cost function defined in
(1.9), and using this to replace ST (i) in (2.4), and again substituting the solution for the
stochastic discount factor from equation (xx) of chapter 2, we obtain
(О±ОІ)T в€'t uc (YT ; ОѕT )YT PT [pв€— в€' ВµPT s(YT PT pв€—в€'Оё , YT ; ОѕT )] = 0
Оёв€'1 Оё
Et (2.5)
t t
T =t
as an equation that implicitly defines the optimal price p∗ . Note that the monotonicity of s
in its п¬Ѓrst argument implies that the left-hand side of this expression is increasing in pв€— , so
that the optimal price is uniquely defined by this condition. The value of p∗ then determines
the evolution of the price index Pt through (2.1).
Once again, we may usefully approximate the equilibrium dynamics of inflation in the case
of small enough disturbances Оѕt by considering a log-linear approximation to these equations.
Лњ ВЇ
If ξt = 0 and Yt = Y at all times, equations (2.1) and (2.5) have a solution with zero inflation,
in which Pt = p∗ = Pt−1 each period. In the case of small enough fluctuations in ξt and Yt
around these values, we accordingly look for a solution in which Pt /Ptв€'1 and pв€— /Pt remain
always close to 1, though the (log) price level may contain a unit root.32 The fluctuations
in these two stationary variables must approximately satisfy a log-linear approximation to
Authors such as Yun (1996) or Goodfriend and King (1997), who assume common factor markets, are
instead able to solve for the optimal price pв€— in closed form. However, the assumption of common factor
markets results in an unrealistic estimate of the likely degree of strategic complementarity in price-setting,
as discussed above.
Our algebra at this point is simplified by log-linearizing around a steady state with a zero inflation
rate, rather than some other constant inflation rate. The resulting log-linear structural equations thus apply
only to the determination of equilibrium in the case of a policy rule that does in fact generate inflation
near zero at all times. This does not mean, however, that we can consider only policy rules that make the
average inflation rate exactly zero, or that involve a "target" inflation rate of zero. It is only necessary
that the average inflation rate be sufficiently small (technically, of order O(||ξ||), if we want the error in
our characterization of the evolution of inflation and other variables to be of order O(||ξ||2 ), where ||ξ|| is a
bound on the size of the disturbances). As we shall argue (see chapter 6) that desirable policies do imply
a low average inflation rate, this does not seem an inconvenient restriction, from the standpoint of our goal
of characterizing optimal policy. Characterization of the effects of policy in a high-inflation economy might
require a more accurate approximation. But the Calvo pricing model itself is implausible as a model of
pricing under such circumstances, as many individual prices are likely to be indexed to some broader price
index (or to an exchange rate). The model with backward-looking price indexation, discussed in section xx
below, would likely be more realistic for such purposes.
1в€'О± в€—
ПЂt = p,
where pв€— в‰Ў log(pв€— /Pt ). They must also approximately satisfy a log-linear approximation to
Л†t t
(2.5), given by пЈ± пЈј
пЈІ пЈЅ
в€ћ T
(О±ОІ)T в€'t пЈіpв€— в€' [Л†t,T +
Et Л†t s ПЂП" ]пЈѕ = 0, (2.7)
П" =t+1
T =t
where st,T denotes the deviation (from its steady-state value) of the log of real marginal cost
in period T for a supplier whose price is pв€— . (The term in square brackets in (2.7) is thus
the deviation of the log of
(PT /Pt )s(YT PT pв€—в€'Оё , YT ; ОѕT )
from its steady-state value of Вµв€'1 . There are no terms in (2.7) corresponding to stochastic
variation in the discount factors in (2.5), because the steady-state value of the term in square
brackets in that equation is zero.)
Under our characterization (1.14) of the dependence of marginal supply cost upon a
producer's own level of output, the variable st,T can furthermore be approximated by
st,T = sT в€'
Л† Л† pt в€' ПЂП" ],
П" =t+1
where sT denotes the deviation of the log of the average level of real marginal cost (real
marginal cost for a good with output yT (i) = YT ) from its steady-state value. Substituting
this into (2.7), we can solve for
в€ћ T
pв€— T в€'t в€'1
Л†t = (1 в€' О±ОІ)Et (О±ОІ) [(1 + П‰Оё) sT +
П" =t+1
T =t
в€ћ в€ћ
1 в€' О±ОІ
(О±ОІ)T в€'t Et sT + (О±ОІ)T в€'t Et ПЂT .
1 + П‰Оё T =t T =t+1
Thus the relative price chosen by those suppliers who adjust their prices in period t is a
purely forward-looking function of aggregate conditions at that date.
This last expression in turn can be quasi-differenced to yield
1 в€' О±ОІ
pв€— = st + О±ОІEt ПЂt+1 + О±ОІEt pв€— .
Л†t Л† Л†t+1
1 + П‰Оё
Then using (2.6) to substitute for pв€— on both sides of the above, we obtain a stochastic
difference equation for the inflation rate,
ПЂt = ОѕЛ†t + ОІEt ПЂt+1 ,
s (2.8)
1 в€' О± 1 в€' О±ОІ
Оѕв‰Ў > 0.
О± 1 + П‰Оё
Writing this alternatively as
∆ log Pt = ξ[log St − log Pt + log µ] + βEt ∆ log Pt+1 , (2.9)
we see that we have an equation that can be solved for the predicted path of the price
index Pt , given the evolution of the average level of nominal marginal cost St . Specifically,
if {log St } is a difference-stationary process, there is a unique solution for the price index
process such that {log Pt } is also difference-stationary (i.e., inflation is a stationary process),
given by
О»в€'j [log Вµ + Et log St+j ],
О»в€'1 )
log Pt = О»1 log Ptв€'1 + (1 в€' О»1 )(1 в€' (2.10)
where 0 < О»1 < 1 < ОІ в€'1 < О»2 are the two roots33 of the characteristic polynomial
ОІО»2 в€' (1 + ОІ + Оѕ)О» + 1 = 0. (2.11)
This prediction of the Calvo pricing model is in fact independent of any specification of
the determinants of average marginal costs; the only feature of the marginal cost function
used in deriving (2.8) was the fact that the elasticity of an individual supplier's marginal
cost with respect to its own output is equal to П‰ > 0. Tests of the empirical adequacy of
this theory of pricing are therefore appropriately focused upon this prediction, rather than
upon the accuracy of the "New Keynesian" aggregate supply relation derived below (which
depends as well upon the details of one's theory of supply costs). This is the approach
The roots can be shown to be real and to satisfy the inequalities just stated, as long as 0 < ОІ < 1 and
Оѕ > 0.
ULC growth
1965 1970 1975 1980 1985 1990 1995
Figure 3.4: U.S. inflation (quarterly change in GDP deflator, in percentage points of equiv-
alent annual rate) compared to growth rate of unit labor cost. Source: Sbordone (2002).
taken by Sbordone (1998, 2002), who uses data on the average level of unit labor cost in the
U.S. economy as a measure of nominal marginal cost.34 She estimates a small atheoretical
VAR model with which to forecast the future path of unit labor costs, using quarterly U.S.
data over the period 1960-1997. This then allows one to construct an implied series for the
forward-looking terms on the right-hand side of (2.10), for any assumed values of ОІ and Оѕ
(which then imply values for О»1 and О»2 ). Starting from an initial condition for the price level
(given by its historical value in the initial quarter), one can then simulate (2.10) to obtain
a predicted time path for the price level, given the observed path of unit labor costs (and of
forecasted future labor costs). One can then compare this prediction to the actual path of
Note that according to the model developed here, average marginal supply cost should be proportional
to average unit labor cost under the assumption of a production technology with a constant elasticity of
output with respect to the labor input (e.g., the familiar Cobb-Douglas specification). See Rotemberg and
Woodford (1999b) for further discussion of this common measure of marginal cost and alternatives.
в€'0.03 predicted
1965 1970 1975 1980 1985 1990 1995
Figure 3.5: Actual path of price/ULC ratio (quarterly U.S. data, reported as log deviation
from mean) compared to prediction of the Calvo pricing model. Source: Sbordone (2002).
the aggregate price level over the same period.
Note that in the case of flexible prices (the ξ → ∞ limit of the above model), the predicted
price series would simply be given by log Pt = log µ + log St , so that predicted inflation would
be given by the percentage growth in nominal unit labor costs from one quarter to the next.
As shown in Figure 3.4, this would be quite a poor explanation of actual U.S. inflation; in
particular, one observes that inflation has been much less volatile than the growth rate of
unit labor costs. Alternatively, as shown in Figure 3.5, there has been substantial variation
in the ratio of price to unit labor cost from year to year, whereas the model implies that
this should be constant. In the case of sticky prices (Оѕ п¬Ѓnite), the model implies less volatile
inflation, and in fact, for a certain value of ξ, it predicts a path for the price level quite
similar to its actual path. Figure 3.5 compares the actual path of the (demeaned, log)
price/ULC ratio to the model's prediction in the case that ξ = .055.35 The fit is quite good;
the mean squared error of the predicted price/ULC series is only 12 percent as large as the
variance of the actual price/ULC series. And even this statistic fails to emphasize the extent
to which the model succeeds in explaining the timing of quarterly changes in the ratio; the
discrepancy between the predicted and actual series is mainly at quite low frequencies. Figure
3.6 similarly compares the actual path of U.S. inflation (measured by growth in the GDP
deflator) with the path predicted by the model. The fit is again quite good (which is another
way of seeing that the discrepancy in Figure 3.5 is almost entirely at low frequencies).36
These results provide persuasive evidence for price stickiness of roughly the sort implied
by the Calvo pricing model. The degree to which the model fits U.S. inflation dynamics is
perhaps surprising, given that the assumption of a п¬Ѓxed probability of price change for all
suppliers has been chosen for analytical convenience rather than out of any belief that it
ought to be realistic. Probably this reflects the fact that, given the small value of ξ implied
by Sbordone's estimates (and hence the high degree of smoothing of marginal cost in the
price dynamics), the details of the distribution of intervals between price changes does not
matter much for the evolution of the aggregate price index, but only the average rate at
which prices are revised. But the п¬Ѓt of the model does clearly depend upon the existence of
staggered price changes of the kind assumed by Calvo. The "New Classical" pricing model
considered above, for example, would imply that fluctuations in the ratio of price to marginal
cost should be unforecastable, so that the predicted P/ULC series would necessarily exhibit
no serial correlation. The significant serial correlation of the P/ULC series shown in Figure
3.5, and the closely similar degree of serial correlation of the series predicted by the Calvo
Sbordone selects this value as her estimate, on the ground that it minimizes the mean-squared error of
the model's predicted path for log Pt , when β is assigned a value of 1. Note that she actually reports the
value of Оѕ в€'1 = 18.3.
Gali and Gertler (1999) obtain similar results for U.S. inflation, using an alternative, instrumental-
variables strategy for estimating equation (2.8). Gali and Gertler п¬Ѓnd that they can statistically reject this
baseline pricing model in favor of a generalization in which some price-setters use a backward-looking "rule of
thumb", discussed further below in section xx. However, they find that the baseline model already explains
historical inflation dynamics quite well, as Figure 3.6 shows; and the validity of the standard errors used to
determine that the rejection of the baseline model is statistically significant might also be questioned. Batini
et al. (2000) similarly find that the Calvo pricing model can explain U.K. inflation dynamics, while Gali et
al. (2001) obtain similar results for several European countries.
8 predicted
1965 1970 1975 1980 1985 1990 1995
Figure 3.6: Actual path of inflation (quarterly U.S. data) compared to prediction of the
Calvo pricing model. Source: Sbordone (2002).
model,37 suffices to show that the kind of price stickiness allowed in that model cannot
similarly explain the U.S. data. Perhaps more surprisingly, Sbordone shows that the U.S.
price index cannot be п¬Ѓt nearly as well by any purely backward-looking moving average of
unit labor costs, either; the kind of smoothing reflected in the figures depends importantly
upon the presence of the forward-looking terms on the right-hand side of (2.10), and not
simply upon the partial-adjustment term.38
One might, of course, doubt the accuracy of the simple unit-labor-cost measure of
marginal cost, for various reasons that are reviewed by Rotemberg and Woodford (1999b).
The autocorrelation functions of both series, with standard errors for the data series, are presented in
Sbordone (1998, 2002).
Sbordone shows this formally by separately estimating the weights О»1 and О»в€'1 in (2.10), without imposing
the restriction that they correspond to the two roots of (2.11). She finds not only that both coefficients are
significantly positive, but that the values that yield the best fit are nearly equal in size, as the Calvo pricing
model would imply. (Note that the two roots of (2.11) necessarily satisfy О»1 О»2 = ОІ в€'1 .)
But it seems fortuitous that such a simple model of price-setting can explain actual inflation
dynamics so well, if unit labor cost is not in fact a fairly accurate measure of variations
in marginal cost, at least at moderate frequencies.39 In fact, Sbordone experiments with a
number of possible corrections to her simple measure of marginal cost, and п¬Ѓnds that none of
them improves the п¬Ѓt of the pricing model. One might also wonder whether forecasts based
on a VAR model with constant coefficients fit to the entire period 1960-97 should correspond
very closely to people's expectations, even assuming that their expectations were rational,
on the ground that the dynamics of unit labor costs need not have been constant over this
period. (One might think, for example, that inflation dynamics have been substantially
different since the disinflation of the early 1980s; but this would imply that unit labor cost
dynamics should have been different as well.) But, once again, the close fit of the model,
and the fact that it п¬Ѓts equally well both before and after the 1979-82 period, suggest that
the hypothesis of a common (and at least roughly unbiased) forecasting rule over the entire
period is not too inaccurate.
2.2 A "New Keynesian" Phillips Curve
We can use the model of optimal price-setting just derived to obtain an aggregate supply
relation — i.e., a structural relation between inflation dynamics and the level of real activity
— by adjoining to our above pricing equation a theory of how real marginal costs depend
upon the level of real activity. The simple model used earlier in this chapter (recall equation
(1.14)) implies that
st = (П‰ + Пѓ в€'1 )(Yt в€' Ytn ).
Substituting this into (2.8) then yields an aggregate supply relation of the form
ПЂt = Оє(Yt в€' Ytn ) + ОІEt ПЂt+1 , (2.13)
Because of the degree of smoothing involved in (2.10), high-frequency error in the measure of marginal
cost will have relatively little effect upon the predicted path for prices. And Figure 3.5 itself indicates at
least a small amount of low-frequency specification error, which might be due to low-frequency error in the
measure of marginal cost.
(1 в€' О±)(1 в€' О±ОІ) П‰ + Пѓ в€'1
Оє в‰Ў (П‰ + Пѓ )Оѕ = > 0.
О± 1 + П‰Оё
Alternatively, the slope coefficient can be written as
(1 в€' О±)(1 в€' О±ОІ)
Оє= О¶, (2.14)
where ζ is defined in (1.22). This is what Roberts (1995) calls the "New Keynesian Phillips
Curve," as this specification, or one similar to it, is implied by a variety of simple models
of optimal price-setting.40 From (2.14) we observe once again that the short-run Phillips
curve is flatter (for any given inflation expectations) the smaller the value of ζ, and thus the
greater the degree of strategic complementarity in price-setting. It is also flatter the larger
is О±, which is to say, the longer the average time interval between price changes.
Our aggregate supply relation again has the form of an expectations-augmented Phillips
curve, but now the inflation expectations that shift the curve are current expectations of
future inflation, rather than past expectations of the current inflation rate, as in (1.23). The
difference turns out to be crucial for the model's ability to allow for forecastable fluctuations
in the output gap. It is now possible for non-zero values of Yt в€' Ytn to be forecasted at some
earlier date t в€' j; this simply requires that Etв€'j ПЂt not equal ОІEtв€'j ПЂt+1 .
2.3 Persistent Real Effects of Nominal Disturbances
We return now to the question of the persistence of the real effects of disturbances to nominal
spending. Once again, we assume a given stochastic process for aggregate nominal spending
Yt , and consider what processes for Pt and Yt are then implied by the aggregate supply
relation (2.13). As a simple example, suppose that an unexpected disturbance permanently
increases log Y by a unit amount at date zero, which is then expected to maintain the higher
Notably, the same form of aggregate supply relation, up to our log-linear approximation, is implied
by a model with convex costs of price adjustment, as shown by Rotemberg (1987). Note that in Roberts'
presentation of the "New Keynesian Phillips Curve," the discount factor β is set equal to one. This simpli-
fication may seem appealing, in that it implies a vertical "long-run" inflation-output tradeoff. But correctly
accounting for the presence of the discount factor in (2.13) has important consequences for the analysis of
optimal policy, as is shown in chapters 6 and 7.
value. Thus
E0 log Yt = 1 (2.15)
for all t ≥ 0, where log Yt is measured as a deviation from the constant level that would
have been expected in the absence of the disturbance. Let us consider the expected paths
E0 log Pt and E0 log Yt that are consistent with (2.13), given the initial condition log Pв€'1 = 0,
where log Pt and log Yt are also measured as deviations from the levels that would have been
maintained but for the shock. We assume that the shock (a purely nominal disturbance)
involves no change in the constant expected level for the natural rate of output.
Let pt denote E0 log Pt в€'1, the extent to which the expected price-level response in period
t differs from exact proportionality to the permanent increase in nominal spending. Then
we must have E0 log Yt = −˜t for each horizon t ≥ 0; substituting this into (2.13), we find
that the price-level responses must satisfy
ptв€'1 в€' (1 + ОІ + Оє)Лњt + ОІ pt+1 = 0
Лњ p Лњ (2.16)
for each t ≥ 0, starting from the initial condition p−1 = −1. The unique bounded solution is
easily seen to be given by
pt = в€'О»t+1 ,
Лњ (2.17)
where 0 < О» < 1 is the smaller of the two real roots41 of the characteristic equation
P (О») в‰Ў ОІО»2 в€' (1 + ОІ + Оє)О» + 1 = 0. (2.18)
Since E0 log Pt = 1 + pt , we observe that the log price level is expected to rise monotonically,
asymptotically reaching a level proportional to the increase in nominal spending. Since
E0 log Yt = в€'Лњt , we observe that output increases in the period of the disturbance, by an
amount less than (though possibly close to) proportional to the increase in nominal spending,
then decays monotonically back to its original level. (These impulse responses of the price
level and of output are plotted in Figure 3.7, for the illustrative parameter values ОІ = .99
and Оє = .024.42 )
nominal GDP
real output
price level
0 5 10 15 20
Figure 3.7: Impulse responses to an immediate permanent increase in nominal GDP.
The degree of persistence of the effect upon real activity is thus dependent upon the size
of the root О»; the closer О» is to one (its theoretical upper bound), the longer the time it takes
for real activity to return to its "potential" level following a nominal disturbance. (Note that
λ also determines the size of the initial effect upon real activity in period zero, as well. Thus
the same factors that increase the amplitude of the effect upon real activity — by making
aggregate price adjustment more sluggish — also make the effect more persistent.) It is
easily seen, in turn, that the smaller root of P (О») varies inversely with the size of Оє, with a
value that approaches zero in the case of very large Оє, and a value that approaches one for Оє
near zero. Thus a small value of κ (a flat short-run Phillips curve) is required for significant
persistence. This in turn could occur either as a result of О± being near one (infrequent price
Since P (0) > 0, P (1) < 0, P (ОІ в€'1 ) < 0, and P (О») > 0 for all large enough О» > 0, it is evident that the
equation has two real roots, 0 < О» < 1 and another root greater than ОІ в€'1 .
These values are taken from the estimates of Rotemberg and Woodford (1997), discussed further in
chapter 4.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Figure 3.8: Persistence of real effects of an increase in nominal spending as a function of
the frequency of price adjustment, for alternative degrees of strategic complementarity in
changes) or О¶ being small (strong strategic complementarity).
It is perhaps most interesting to observe that the degree of strategic complementarity
can have a considerable effect upon the degree of persistence, holding fixed the frequency of
price changes. Note that for any value of О±, the value of Оє can be made arbitrarily small,
or arbitrarily large, through assignment of an appropriate value to ζ. The effects of α and
О¶ upon the degree of persistence are shown quantitatively in Figure 3.8, where the implied
value of О» is plotted as a function of these two parameters, assuming the value ОІ = .99.
One observes that О» > О± if and only if О¶ < 1, i.e., if and only if pricing decisions are
strategic complements in the sense discussed above. This can be shown analytically by
observing that
P (О±) = (1 в€' О±)(1 в€' О±ОІ)(1 в€' О¶),
where we have used (2.14) to substitute for Оє. Thus P (О±) > 0, so that О± < О» < 1, if and
only if О¶ < 1. It is in this case that the rate of adjustment of the aggregate price index is
slower than would be expected mechanically as a result of the fact that not all prices have
yet had an opportunity to be updated since the occurrence of the shock. (The fraction of
prices in period t that have not yet been adjusted even once since the shock is given by О±t .)
In this case, Taylor (1980) speaks of the existence of a "contract multiplier" as a result of the
staggering of price adjustments.43 Such a multiplier depends upon the existence of strategic
complementarity among different suppliers' pricing decisions, so that the fact that other
prices have not fully adjusted makes an individual supplier adjust its own price less. In the
case of strategic substitutes (О¶ > 1), there is actually even less persistence than one would
expect for purely mechanical reasons (О» < О±), because the п¬Ѓrst prices that are adjusted
actually over-adjust in reaction to the failure of other prices to adjust in proportion to the
increase in nominal spending.
In fact, the connection between the value of О¶ and the value of Оє indicated by (2.14)
continues to hold when additional sources of strategic complementarity are introduced, such
as non-CES preferences over differentiated goods, or intermediate inputs. If we generalize
our assumptions about demand and production costs in both of these directions, as in section
xx above, nominal profits are instead of the form
О i (p) = [pYt d(p/Pt ) в€' wt (i)f в€'1 ((1 в€' sm )d(p/Pt )Yt /At ) в€' sm Pt Yt d(p/Pt ),
generalizing (2.3). Here d(pt (i)/Pt ) is the relative demand ct (i)/Ct implied by (1.27). The
corresponding п¬Ѓrst-order condition for optimal price-setting by a п¬Ѓrm that chooses its price
at date t is then
О±T в€'t Qt,T YT d(pt (i)/PT )[pt (i) в€' ВµT (i)ST (i)] = 0,
T =t
generalizing (2.4). Here the desired markup is given by ВµT (i) = Вµ(d(pt (i)/PT )), where the
function µ(x) is again defined by (1.30), and marginal cost is now given by (1.35). As before,
In Taylor's original formulation, it is actually the staggered negotiation of wage contracts that gives rise
to the "multiplier".
we may log-linearize this to obtain
(О±ОІ)T в€'t {Л†t,T в€' [Л†t,T + st,T ]} = 0,
Et p Вµ Л† (2.19)
T =t
generalizing (2.7). Here we introduce the notation
pt,T =
Л† Л†t в€' ПЂП"
П" =t+1
for the (log) relative price at date T of a п¬Ѓrm that has set its price at date t, yt,T for its (log)
output relative to steady state, and
Вµt,T =
Л† Вµ (Л†t,T
y в€' YT )
for its (log) desired markup relative to steady state.
Noting that
+ sy )(Л†t,T в€' YT ) в€' (sy + sY )(YT в€' YTn )
pt,T в€' [Л†t,T + st,T ] = pt,T в€' (
Л† Вµ Л† Л† y
+ sy )]Л†t,T в€' (sy + sY )(YT в€' YTn ),
= [1 + Оё( p
we observe that (2.19) can equivalently be written
(О±ОІ)T в€'t pв€— в€' О¶(Yt в€' Ytn ) = 0,
Et Л†t (2.20)
T =t
where О¶ is now given by (1.37). This in turn allows once again to derive an aggregate supply
relation of the form (2.13), where Оє is again given by (2.14). Thus it continues to be the
case that the degree of strategic complementarity is a crucial determinant of the degree of
persistence of the real effects of an increase in nominal spending; each of the factors discussed
above that increase strategic complementarity increases persistence.
Can staggering of price changes give rise to an empirically realistic degree of persistence,
assuming an empirically realistic average interval between price changes? Chari, Kehoe and
McGrattan (2000) argue that it cannot. However, their conclusion depends both upon an
exaggeration of the size of the "contract multiplier" that would be needed, and an under-
estimate of the empirically plausible degree of strategic complementarity. They define the
contract multiplier as "the ratio of the half-life of output deviations after a monetary shock
with staggered price-setting to the corresponding half-life with synchronized price-setting"
(p. 1152). In our analysis above of the response of output under Calvo price-setting to
a monetary shock that permanently increases the level of nominal GDP,44 we have shown
that the level of output returns to its steady-state level following a shock as О»t , where О»
is the smaller root of (2.18). Thus the "half-life" with staggered price setting would equal
log 2/ log О»в€'1 periods.
By the corresponding half-life "with synchronized price-setting", Chari et al. mean the
case in which each price that is revised after the shock occurs is immediately adjusted
all the way to the new expected long-run price level, so that the fraction of the eventual
aggregate price adjustment that has occurred at any time is equal to the fraction of prices
that have been revised at least once since the occurrence of the monetary shock. In the case
of the Calvo pricing model, the fraction of prices that have not yet been adjusted k periods
following a shock is αk+1 , so that the "half-life with synchronized price-setting" would equal
log 2/ log О±в€'1 .45 The contract multiplier implied by the Calvo pricing model is then equal to
log О±в€'1 / log О»в€'1 . It follows from our results above that the multiplier is greater than one if
and only if О¶ < 1, which is to say if and only if there is strategic complementarity in the
pricing decisions of different suppliers.46 In fact, in the continuous-time limit of the Calvo
This is not exactly the form of monetary shock considered by Chari et al., who instead assume an
exogenous process for the money supply, and consider its implications within a complete general-equilibrium
model of the monetary transmission mechanism. However, in their analysis of a "stripped-down version" of
their baseline model, they assume a static money demand function according to which nominal GDP is at
all times proportional to the money supply, and also assume a random walk for the (log) money supply; this
is thus an experiment of exactly the kind we consider here.
Chari et al. instead assume п¬Ѓxed-length price commitments, as a result of which this half life is equal
to N/2 periods, where is the number of periods that each price remains п¬Ѓxed.
As noted in the previous two footnotes, Chari et al. consider a different model of staggered pricing, but
obtain this same conclusion; their finding that the multiplier is necessarily less than one in their "stripped-
down" model follows from the fact that ζ is necessarily greater than one, for the reasons that we have
discussed above. (They call this parameter Оі; their equation (34) shows that it must exceed one.) In their
analysis, as here, the question of whether a contract multiplier much greater than one is possible amounts
largely to a consideration of whether О¶ can plausibly be much less than one.
model, one can show that the contract multiplier is equal to
, (2.21)
[4aв€— (aв€— + 1)О¶ + 1]1/2 в€' 1
where aв€— is the ratio of the (continuous) rate of price adjustment to the (continuous) rate
of time preference, independent of the values of the other parameters.47 In the case that
aв€— >> 1, this is approximately О¶ в€'1/2 , regardless of the size of aв€— ; this provides an analytical
explanation for the п¬Ѓnding of Chari et al. that the predicted contract multiplier in a model
with staggered price-setting depends little upon the assumed length of time between price
Chari et al. argue that a very large multiplier would be needed in order for staggered
price-setting to account for observed persistence. They п¬Ѓt a univariate ARMA model to de-
trended real GDP for the postwar U.S., and conclude that the half-life of output fluctuations
around trend is approximately 10 quarters. At the same time, they argue that a reasonable
length of time to assume that prices are п¬Ѓxed would be only one quarter, implying a half-life
with synchronized price-setting of only half a quarter. Thus they argue that a contract mul-
tiplier of 20 would be needed; this would be possible only if О¶ were quite small (.004 in the
case of our continuous-time limit).48 Instead, they п¬Ѓnd that their baseline parameter values
imply a value of О¶ well above one, and so a contract multiplier less than one; and while
alternative parameter values can raise the multiplier somewhat, they argue that it cannot
plausibly be greater than two. They conclude that one must believe that prices remain п¬Ѓxed
for many years in order to account for observed persistence.
However, this way of identifying the persistence of the output effects of monetary shocks
assumes that all fluctuations of output around a deterministic trend path are due to monetary
shocks. There is no reason to assume this; indeed, a central contention of this study is
Here we fix ζ and let α and β decrease with ∆, the period length, so that as ∆ → 0, log β −1 /∆
and log α−1 /∆ both approach positive constants, ρ and a respectively. Then, expanding the characteristic
polynomial (2.18) in powers of ∆, one can show that log λ−1 /∆ approaches a positive constant n as well,
which depends upon О¶ and the ratio aв€— в‰Ў a/ПЃ. The multiplier (2.21) is then equal to a/n.
This value follows from (2.21) under the assumption that aв€— = 33, a value suggested by survey evidence
on the frequency of price change in the U.S. economy, as discussed below. Note, however, that a similarly
small value of О¶ is required in the case of any large value for aв€— .
that the task of monetary policy is to respond appropriately to a large variety of types of
real disturbances to which economies are subject. One may attribute great importance to
monetary policy without holding that any large fraction of the overall variability of output
is due (in the sense of ultimate causation) to the random component of monetary policy; for
systematic monetary policy can greatly change the effects of real disturbances. For example,
the estimated model of Rotemberg and Woodford (1997), discussed in section xx of chapter
4, attributes only a few percent of the overall variance of real GDP around trend over the
sample period to monetary policy shocks; yet the counter-factual simulations reported in
that paper show that alternative systematic monetary policies would have implied greatly
different paths of real as well as nominal variables.
One needs, then, to identify the real effects of monetary policy shocks alone in order
to determine the relevant half-life. This may be much shorter than the one estimated by
Chari et al., without any implication that monetary policy is unimportant for business
fluctuations. For example, the impulse response reported in Figure 3.3 above shows that
only three quarters after the peak output response, the level of (log) output has already
returned halfway to the level that would have been expected prior to the shock; and two
quarters after that, the response has fallen to only 20 percent of its peak level. This suggest a
"half-life" of only 2.5 to 3 quarters. The structual VAR of Rotemberg and Woodford (1997),
discussed in chapter 4, yields an output response that involves more nearly exponential decay
after the quarter in which output is first substantially affected; this response, shown in Figure
xx below, exhibits a "half-life" of only about 3 quarters.49
Furthermore, survey evidence indicates that many prices remain unchanged for longer
than a quarter on average. For example, the survey of Blinder et al. (1998) indicates an aver-
age time between price changes (for a representative sample of U.S. п¬Ѓrms) of 9 months.50 This
As shown in Figure xx, the peak (and first significant) output contraction occurs two quarters following
a contractionary policy shock; log output has returned about half-way to its trend level by the п¬Ѓfth quarter
following the shock. Nonetheless, the model of Rotemberg and Woodford is fully consistent with the ob-
served degree of persistence of the deviations of output from trend; compare the predicted and estimated
autocorrelation functions reproduced in Figure xx below.
See Rotemberg and Woodford (1997) for discussion of other survey evidence from studies of smaller
sectors of the economy.
suggests that the continuous rate of price change should be parameterized as approximately
0.33/quarter, implying a half-life of 2.08 quarters. Thus the required contract multiplier is
only 1.44, within the range that Chari et al. п¬Ѓnd to be possible. In the continuous-time limit
of the Calvo pricing model derived above,51 this requires only that О¶ = 0.49, and (as shown
in Table 3.1 above) a value this low or even lower is easily consistent with the assumptions
about preferences and technology made by Chari et al., once we allow for non-CES prefer-
ences and intermediate inputs, or alternatively for at least some degree of factor specificity.52
A larger value of Пѓ makes this even easier, and as we shall argue in chapter 4, it is most
reasonable to calibrate this model with a value of Пѓ much larger than one.
In fact, our discussion above has indicated that a variety of plausible assumptions can
justify a value of О¶ in the range of 0.10-0.15. This would imply a contract multiplier (in
the continuous-time limit of our model) in the range of 2.6 to 3.3, or a "half-life" for the
output response (assuming the rate of price adjustment indicated by the survey evidence)
between 5.5 and 6.8 quarters. This is a degree of persistence of the effects on real activity of
an increase in nominal expenditure considerably greater than the one indicated by the VAR
evidence cited by Rotemberg and Woodford, but is comparable to the degree of persistence
indicated by some other studies of the effects of identified monetary shocks.53
Here we use (2.21), assuming that a = 0.33/quarter and ПЃ = 0.01/quarter, so that aв€— = 33.
In fact, the model of Rotemberg and Woodford is not able to reproduce their estimated impulse response
function for real GDP in response to a monetary policy shock without a considerably smaller value of О¶,
approximately 0.13. The difference is obtained because their model is a discrete-time model with "periods" of
length three months (which results in a degree of persistence somewhat different than that in the continuous-
time limit), because they set О± = 2/3 (so that exactly one-third of all prices are changed each quarter, rather
than the fraction 1 в€' eв€'a = 0.28 implied by integration of the continuous-time model), and because their
identified monetary policy shock does not result in an immediate, permanent increase in nominal GDP as
assumed above.
The real effects of the identified monetary policy shocks obtained by Rotemberg and Woodford (1997)
are less persistent than those obtained in some other VAR studies, mainly using longer sample periods. For
example, in the baseline results of Christiano et al. (1999), using quarterly data and identifying monetary
policy shocks with innovations in the federal funds rate (п¬Ѓrst column of their Figure 2), the peak contraction
in real GDP following an unexpected monetary tightening occurs only п¬Ѓve to six quarters after the shock,
while output has returned half-way to its original trend path by the eleventh quarter following the shock;
this would indicate a "half-life" of five to six quarters. The later results of Christiano et al. (2001) indicate
a half-life of less than three quarters, however, as noted above.
2.4 Consequences of Persistence in the Growth of Nominal Spend-
We have thus far considered only the response of real activity to an unexpected, permanent
increase in nominal spending. While this particular thought experiment allows us a clear
definition of the degree of persistence, such a perturbation of the expected path of nominal
spending has little similarity to the estimated responses of nominal spending to the monetary
policy shocks identified in the VAR literature; thus the model's predictions for this case
cannot be directly compared to any empirical estimates. Identified monetary policy shocks
tend to affect nominal spending only slightly (if at all) in the first few months, with an effect
that increases cumulatively over a period of several quarters, eventually bringing expected
future nominal spending to a new permanent level.
As a simple case that allows for shocks of this kind, let us assume that the growth rate
of nominal spending follows a п¬Ѓrst-order autoregressive process,
∆ log Yt = ρ∆ log Yt−1 + (2.22)
with 0 < ПЃ < 1, where is an i.i.d. random variable, assumed for simplicity to have
mean zero. This process implies that an innovation increases the conditional expectation
Et log Yt+j by an amount (1 в€' ПЃ)в€'1 (1 в€' ПЃj+1 ) t which increases monotonically with j, asymp-
totically approaching a permanent effect that is (1 − ρ)−1 > 1 times as large as the initial
effect.54 Let us consider the impulse response to a positive innovation = 1 − ρ, which
results in a unit increase in the expected long-run level of nominal spending. Again letting
pt denote E0 log Pt в€' 1, we п¬Ѓnd that the price-level responses must satisfy
ptв€'1 в€' (1 + ОІ + Оє)Лњt + ОІ pt+1 = ОєПЃt+1 ,
Лњ p Лњ (2.23)
a generalization of (2.16), again starting from initial condition pв€'1 = в€'1. (Because nominal
spending does not immediately jump to its expected long-run value, we now have E0 log Yt =
This form of stochastic process is used as a rough approximation of actual U.S. time series in Rotemberg
[E0 log Yt в€' 1] в€' pt = в€'(Лњt + ПЃt+1 ).) The unique bounded solution to (2.23) is given by the
Лњ p
solution to the п¬Ѓrst-order equation,
ПЃt+1 ,
pt = О»Лњtв€'1 в€'
Лњ p в€'1 в€' ОІПЃ
again starting from the given value for p−1 , where 0 < λ < 1 is again defined as in (2.17).
(Note that in the limiting case ПЃ = 0, this reduces to the same solution (2.17) as before.)
Then using the relations
E0 log Pt = pt + 1,
E0 log Yt = в€'(Лњt + ПЃt+1 ),
we can compute the impulse responses of the price level and of aggregate output to an inno-
vation in the nominal spending process. These are plotted in Figure 3.9, for the illustrative
parameter values ОІ = .99, Оє = .024, and ПЃ = .4, along with the impulse response of nominal
spending itself.55 We observe that in this case innovation in nominal spending results in an
increase in real activity, that continues to grow larger, reaching its peak only in the second
and third quarters after the shock, and then declines monotonically back to its original level.
This "hump-shaped" output response is predicted in the case of any large enough value of
ρ, specifically, for any value such that λ + ρ > 1. The responses yt ≡ E0 log Yt satisfy
(1 в€' ПЃL)(1 в€' О»L)Лњt = 0
for all t ≥ 1, starting from initial values y−1 = 0 and
(1 в€' ПЃ)(1 в€' ОІПЃ)
y0 =
Лњ > 0.
(О»в€'1 в€' ОІПЃ)
A second-order difference equation of this kind has a solution that either decays monotoni-
cally back to zero after a peak in the period of the shock, or that п¬Ѓrst increases to a peak,
and then decays monotonically back to zero. Since y2 = (О» + ПЃ)Лњ1 , the second case occurs if
Лњ y
and only if О» + ПЃ > 1.
The figure also shows the impulse response of the inflation rate, here measured in annual percentage
points, so that the inflation rate plotted is defined as 4 ∆ log Pt . The dynamics of the inflation rate are
discussed further in section xx below.
nominal GDP
real GDP
price level
в€'2 0 2 4 6 8 10 12 14 16 18 20
Figure 3.9: Impulse responses to an innovation in nominal GDP, in the case of persistence
in nominal GDP growth.
The reason for such an equilibrium response is simple. Even though prices do not change
much immediately following the shock, the increase in output is not initially large, because
nominal spending has not yet increased much. As nominal spending increases further, real
output increases as well. Eventually, prices adjust, and real activity falls back to its original
level (or, in a model with trend output growth, back to its original trend).
The "hump-shaped" output response shown in Figure 3.9 is at least roughly of the kind
typically estimated using structural VAR methodology (see, e.g., Figure 3.3 above). Indeed,
Cochrane (1996) finds that a slightly modified version of the "New Keynesian" aggregate
supply relation (2.13) can more closely match the estimated response of output to a monetary
policy shock than any of the other simple aggregate supply relations that he considers.56 A
particular advantage of this specification is that it can allow significant output effects of
The form used by Cochrane is actually equation (3.2), with a delay d = 1 quarter.
a nominal disturbance even when there is little immediate effect upon nominal spending.
This can be seen by considering the above calculation in the case that ПЃ is close to 1. In
such a case, there is little increase in nominal spending in period zero (log Y0 increases only
by 1 − ρ, yet the peak output effect may be an arbitrarily large fraction of 1. (For small
enough Оє, the value of О» may be made arbitrarily close to 1, so that the adjustment of prices
is slow compared to the rate at which expected nominal spending approaches its long-run
value.) This contrasts sharply with the prediction of the "New Classical" aggregate supply
relation (1.23), which implies that the peak output effect (which must occur in period zero)
is bounded above by 1 − ρ, no matter how flat the short-run Phillips curve may be.
2.5 Consequences of Sectoral Asymmetries
Thus far we have considered only a completely symmetric model, in the sense that all pref-
erences and production relations would remain the same if we interchanged the labels of
different goods. In particular, we have assumed that all real disturbances affect supply and
demand conditions for all goods in exactly the same way: technical progress lowers the cost
of producing each good in exactly the same proportion, and so on. In reality, of course, there
are many kinds of disturbances that differentially affect various sectors of the economy. Here
we briefly consider an extension of the basic model with staggered pricing that allows for
several kinds of asymmetries. One reason for interest in this extension is that in the presence
of such asymmetries, it is no longer generally the case that stabilization of an aggregate price
index and stabilization of an aggregate output gap are equivalent policies (an important but
obviously special implication of the "New Keynesian" Phillips curve (2.13)). Allowing for
sectoral asymmetries is also especially important in analyzing monetary policy for an open
economy (where, for example, one will want to consider the consequences of shocks that
affect the terms of trade), though we do not develop that extension here.57
Instead of assuming that the consumption index Ct that enters the utility function of the
стр. 2


text:
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Medical secretaries
- Cheryl Moore
- The Elms Crede Lane Bosham Chichester PO18 8NX
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GMC registration
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Recording and reporting on electromyography and nerve conduction studies (EMG); CTS (Bilateral upper limb only) or peripheral neuropathy - (5-50)
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subset: commoncrawl


text:
The How-To Guide to Digital Operations
Digitizing manufacturing operations is imperative—yet immensely difficult. Companies that have tried have seen mixed results. We've identified factors that separate leaders from laggards.
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Digitizing manufacturing operations is imperative—yet immensely difficult. Companies that have tried have seen mixed results. We've identified factors that separate leaders from laggards.
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Industrialized AM will become a reality only if key stakeholders—including materials suppliers, equipment providers, and end users—act now to define their differentiated strategies.
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Incremental reductions won't cut it in today's business environment. CPG companies must fundamentally change the way they manage their supply chain costs.
Tariff wars may dominate the news, but changing cost structures will have a longer-term impact on where the world's goods are made.
Not if the underlying process is broken. To realize the promise of new technologies, you must first step back to identify and fill capability gaps.
Uberization is about to transform supply chains everywhere, as companies increasingly rely on the supply chain capabilities of external, platform-based ecosystems instead of building their own.


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August 30th, 2018
Good day. I am excited to announce our West Parry Sound Economic Development Summit – "Own the Space" – Hosted by WPS Economic Development Office, local municipalities and various business people/organizations scheduled for September 28th 2018.
Our Goal is to Spur future growth and development in West Parry Sound.
The West Parry Sound Economic Development Summit aims to gather business people to learn more about the opportunities that exist in the area and promote future development. The theme of the event is "Own The Space" which refers to the opportunities that exist in West Parry sound including both physical space and market space to be owned.
We would like to ask you to invite one or more friends/business associates from "away" to join us on a familiarization tour and introduction to the region including a select number of business tours with the hopes that they may consider investing/locating in our region.
We have arranged a bus tour, lunch and a fun cruise on the Island Queen free for your guest, as part of the event package. There will be a networking opportunity with members of the Chamber of Commerce at the fun night social on the Island Queen hosted by the Chamber of Commerce.
This is an excellent opportunity to build our community together and I look forward to your support as we continue to shape our future together for a great place to live and work!!
Please contact us if you would like a copy of the Itinerary and Registration forms for you to forward to your colleagues whom you feel would benefit and enjoy our event.
Many thanks,
Glen Barnden
Regional Economic Development Officer
Representing the Municipalities of Whitestone, Carling, McDougall, Parry Sound, Sequin, Archipelago
Parry Sound Area Community Business & Development Centre
1A Church Street
Parry Sound, ON P2A 1Y2
Like us on Facebook
Follow us on Twitter
1A Church Street, Parry Sound, Ontario, P2A 1Y2, Phone: 705-746-4455 Fax: 705-746-4435


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1. Kindly see that your child does not take leave from the school without very genuine need.
2. Once attendance is marked no student shall be given leave without an extra ordinary reason.
3. Appointments with doctor's, dentist etc. should not be arranged during the school hours.
4. No leave will be granted without leave application. Leave application may be written in Punjabi, Hindi or in English. The leave must be written by the parent/guardian with the proper signature and date. Such application written by students will not be accepted in any case. Special attention in this regard will help the school to have a check on your ward's sincerity.
5. A student on returning to school after contagious or infectious disease should produce a physical fitness certificate from an authorised and govt. approved medical practitioner permitting him to do attend the school. The school shall be held liable if a student is obliged to return home during class hours who failed to produce such certificate prior to the attendance.
6. All are expected to attend school on the re-opening day after each of the vacations. students of std. L.K.G to V who fail to mark their attendance on the day of re-opening after holiday will be fined Rs.20/- for each day of the absence made and similarly Rs.30/- will be fined to students of classes vi to x up to 15 consecutive working days.
7. Every student who absent because of sickness must present a medical certificate from a govt. medical practitioner before they are admitted to class. Absence for more than fifteen class days renders the student liable to be struck off the rolls. re-admission, if granted, will be done on payment of a re-admission fee of Rs.5000/-


text:
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About LucyMormont
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Dragonheart reacted to a post in a topic: [Spoilers] Rant & Rave without Repercussion, Final edition
RYShh reacted to a post in a topic: Why the Night King Didn't Fight Jon
LucyMormont reacted to a post in a topic: Excellent article on the show's shift from sociological to psychological storytelling
LucyMormont reacted to a post in a topic: [Poll] How would you rate episode 806?
Nightwish reacted to a post in a topic: Jon killing Dany doesn't work for me
Jon killing Dany doesn't work for me
LucyMormont replied to Tyrion1991's topic in E06: The Iron ThroneWell, Bran actually DID usurp his brother's right, didn't he? Or because Jon wasn't really his brother, this is less questionable and treacherous? And that, after making look like the most important thing was that Jon had to know that he was the "true heir" to the throne. In fact, also Sansa betrayed Jon, it all looked like Sansa and Bran teamed up to manipulate Jon to get rid of Danaerys, and then throw him under the bus.
JagLover reacted to a post in a topic: Jon killing Dany doesn't work for me
Rose of Red Lake reacted to a post in a topic: Jon killing Dany doesn't work for me
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Jon killing Dany doesn't work for me
LucyMormont replied to Tyrion1991's topic in E06: The Iron ThroneI couldn't agree more. It's disgusting that "mad queen" Cersei gets to die having the consolation of someone who loves her and comes back to try to save her or die with her; and "mad queen" Daenerys dies, in a treacherous way, at the hands of the man she loves. NO WAY. Cersei was way worse than Dany, never did a single selfless thing, and didn't torch all the people that opposed her just because SHE DIDN'T HAVE a dragon. Sansa, gets rewarded with a kingdom, after becoming Littlefinger 2. Tyrion, gets rewarded with being Hand of the King, after being the proven worst Hand of the King in the histoty of Westeros, not to mention highly responsible for the carnage of King's Landing population. Sam, a coward oathbreaker and manipulator, gets rewarded with a position in the King's Counsel. Bran, who to this very moment we don't know if he is just an autistic tree or the worst villain of all, gets the throne. And Jon, the only character that always acted with the greater good in mind -albeit cluelessly- gets exiled and banished. This is a very dark hopeless story. And no, this is nothing like real life. There are tragedies in real life, but life is also full of beauty, of good, of true heroism. It's full of people who fall and get up again, who fight their demons and adictions and succeed, and then help others to do the same. It's full of selfless people who do the right thing when the easy way is to do the opposite. Some people in this forum think that the end doesn't matter, that what matters is the journey. So I understand that they are willing to read the remaining books, even when the end is so unsatisfactory. But for me, the only thing that gives meaning to a "journey", is it's destination. From this story, I only got frustration, I don't need more of that.
Jon killing Dany doesn't work for me
LucyMormont replied to Tyrion1991's topic in E06: The Iron ThroneI love Jon Snow, and he killing Daenerys does not work for me either. Or maybe I should say that I used to love him. He and Arya were my favorite characters. I liked Dany, but not to the extent I loved those two. And then, just before the finale, I've reached the point where I couldn't care less for any of the characters. They were all pretty disgusting to me. The show has taken from the characters almost all "likeable" qualities, those that made them who they used to be. ShowJon was made a mindless clueless fool manipulated by everyone, and Dany "madness" was not built up. I could see her progresively becoming more entitled, more power hungry, more arrogant. But not more illogical, or more paranoid (like some people say -it's not paranoia when the people surrounding you are plotting against you and treat you badly for NO reason-), or more willing to destroy innocent human lives indiscriminately. Narratively, you can't jump from A to Z without passing through B,C,D, and so on. She was depicted as a heroine, although a troubled and flawed one, practically up to 2 episodes before. Anyway, I don't think the show wants to put you in Jon's shoes, because it never depicts what "Jon's shoes" are. His POV is hidden from us practically the whole season. We don't know whether he loved her or he used her, we don't know if he bent the knee because he truly believed she was going to be a good queen, or because he was just infatuated with her. We don't know how he felt about his Targaryen heritage and all its implicances. The show just makes no sense; it made all characters act out of character, stupidly, incoherently or evil (even Dany herself) to make Danaerys feel isolated and "doom" her. Tyrion the Smart oh-so-big-mind made the stupidest of plans; Varys the Great Spy schemmed and plotted in the open for everyone to see, Sansa betrayed her brother; Dany "forgot" the Iron Fleet -and apparently likes to fly looking up and not down-; the dragons are flying cows that anybody can take down or the most powerful weapons against which all defense is useless, and so on. And how can be Jon the protagonist? He is a moron, they don't even made him take by himself the decision that Daenerys had to be taken down. After seeing all the destruction, he was still "she's everyone's queen" and "we are done with the war now". And then he changed his mind because Tyrion said so! He was manipulated by Tyrion, My grief is that the characters I used to love are nowhere to be found, and that the moral of this story is that nothing makes sense. All those years following it, absolutely for nothing.
shameeka reacted to a post in a topic: People's reaction to Dany turning Mad Queen says something about us as humans
People's reaction to Dany turning Mad Queen says something about us as humans
LucyMormont replied to A man doesn't have a name's topic in E06: The Iron ThroneI believe that what you say is not exclusive to Daenerys. I've seen people justifying many other character's wrong deeds, Many fans praised Littlefinger for his "intelligence and manipulating skills", for example, instead of rejecting him as the piece of s**t of human being he was. It's not so much about idolizing, as it is about not having a clear moral compass. Sadly, many people justify carnages for some reason of another.
[Spoilers] Rant & Rave without Repercussion, Final edition
LucyMormont replied to Ran's topic in E06: The Iron ThroneAtcually, not "the Lannisters", but only Tyrion. And Sansa wasn't included in the "origianl 5" either, just Bran, Jon, Arya, Danaerys and Tyrion.
The purpose of R+L=J?
LucyMormont replied to anjulibai's topic in E06: The Iron ThroneNothing in this show had any purpose. It was all pointless and for nothing.
[Spoilers] Rant & Rave without Repercussion, Final edition
LucyMormont replied to Ran's topic in E06: The Iron ThroneI couldn't even pass through Tyrion's speech... the moment he said that there's nothing more powerful than a good story and that no enemy can defeat it, I felt that I could not stomach a minute more. Maybe in some days I'll bring myself to watch the rest of the episode. But nothing can redeem this ending for a show once was great and should have remained so.
"Bittersweet" can't happen in the show
LucyMormont replied to Hodor's Dragon's topic in E06: The Iron ThroneTolkien did not do the same thing. I don't care how GRRM describes Tolkien's work, it's not "a powerful sadness" for me and for many millions of people.
"Bittersweet" can't happen in the show
LucyMormont replied to Hodor's Dragon's topic in E06: The Iron ThroneIf this is his goal, he is a sadistic petty and small man, whose only contribution on this earth was to make life worse for some of his fellow human beings. I believe that he'll have created a powerful disgust, and a healthy advise for many people to stay far away from anything related to him.
How should Jon kill Dany
LucyMormont replied to MagicPen's topic in E06: The Iron Throne??? How can anybody say this is beyond me. Dany is not the rightful ruler, and even if she was, she had no right to put KL or any city to sword/dragon fire. That act alone takes away all "rightfulness" she might have had. No, he wouldn't be loyal to a mass murderer. The thing that he repeated all the time to those that opposed her is "she is not his father". Well, now he was proven wrong, she is like his father and worse. There is no way that Jon can give a pass to what Dany did.
Have people given up all hope?
LucyMormont replied to LearnToBeNoOne's topic in E05: The BellsI am not particularly good at math, but I just noticed the petition to "remake season 8 with competent writers" has crossed half million signatures. I predict that by the time of the series finale release, it will reach a million. And it will continue to grow. Episode 5 was watched by 12.48 million viewers. Let's say that multi-platform figures rise to 18 million. The fact that right now there are at least 3% of the viewership that thinks season 8 is that bad as to put their signatures into a petition to remake the whole season, speaks volumes. https://www.change.org/p/hbo-remake-game-of-thrones-season-8-with-competent-writers By the way, I do think that this season is crap, I am severely disappointed, and yet I didn't sign that petition. I didn't because I feel really sorry for all the people who worked so hard. But the writers and HBO deserve the blame, and it won't fade away the fact that so many people are voicing their disappointment
I wholeheartedly agree. and more, do we need a piece of literary fiction to remind us that power corrupts, and that the weakest more innocent ones are always who suffer the most?? If I wanted to be "reminded" of that, I'd read a newspaper... or read about history... or just look around; from Syria to Venezuela, right now, we are surrounded by glaring "reminders" of that every single day. Apparently, GRRM doesn't know what bittersweet means.
1) He should be very angry with Sansa, what she did was totally wrong. He might forgive her eventually, with time (if he admits that after all, Sansa was right in distrusting Dany -although she had no objective reason to distrust her, so all this is inconsistent, unless we are shown that Bran knew something that he told her sisters but not Jon-), but he'll never trust her, ever again. 2)Things between Jon and Dany will go south in a heartbeat from now on. Jon knows now he was mistaken about Dany, Jon bent the knee to her because he needed her to save the North AND because he believed she'd be a worthy queen, "better than Cersei". It turned out the North is saved from the Dead, but in danger from Dany's forces,. No matter her former good intentions, she proved to be worse than Cersei. Although to be fair, we don't know what would Cersei have done if she had dragons. And Dany will not trust Jon, not anymore. She knows he won't go against his Stark family, but worse, she knows that his Targaryen heritage is now out in the open, so he is a threat to her, because there will always be people willing to conspire in the same way Varys did. And since marriage is not an option because he isn't willing to do so, I think that her next move is to kill him. In the same sense, his only move is to letting himself be killed, and thus allowing her to go against his sisters, or try to stop her. But the problem I see is that he can't just kill her, because the inestability won't stop with Dany out of the way, it could potentially get worse, with the Unsullied, Dothrakis and Drogon on the loose, with nobody able to keep control over them. He has to figure out a way to deal with Dany's armies and dragon. But since show Jon is stupid, he might just kill her and then watch like a dumbfounded fool how they wipe out all the remaining living inhabitants of Westeros, the ones he worked so hard to keep alive. 3) If Tyrion has just ONE working brain cell left, he should begin to run away as quickly as his short legs allow him. He betrayed Dany, and also broke Sansa's trust; so even in the slightest chance that Stark team wins, he'd have to face the Stark sisters.
I am a classic fantasy fan, so I never worshipped GRRM for it. Actually, I stopped reading the books after Ned's beheading, and I missed the Red Wedding when he wrote it. When the show came out, I started watching and only by the end of episode 1 I was like "This story looks familiar"... I continued watching the show because I was curious, and ten years had passed since that first reading of "A game of Thrones". Obviously, time and life change people, I wasn't entirely the same person I was then; and now I thought I could bear Ned's beheading if the story would go to a satisfactory end. After the first season, I decided to continue reading the books. I found the last two of a great lesser quality than the first three (literary wise). Anyway, I fell in love with some characters, and wanted to see where their stories go. While the show started its downhill path after season 4, I still wanted to know were the stories of the characters I used to care go, and above all, the main thing that kept me going was that I was promised a "bittersweet" ending, Lord of the Rings style. So I thought that at least, all that suffering will be worth it. But no, all that suffering was pointless, only followed by more suffering. Now I feel completely cheated. The story was all along nothing more than a monumental nihilistic pointless junk. Yes, the show made it worse, full of plot holes, character inconsistency, horrid resources typical of cheap writers, But even if the books make it beliavable, I won't like or enjoy it.


text:
We embarked on a marathon interview with DJ Aero Manyelo of Herbal 3 Record
Eric Manyelo AKA DJ Aero Manyelo is quickly establishing himself as a strong brand in the music industry. He is a DJ, Producer, Composer and Record label boss. He was born in Zebediela in Limpopo Province and moved to Tembisa, East of Johannesburg when he was five. His music career started when he was just seven years old. After completing grade 12 and struggling to finance his further studies, he decided to get a job in order to earn the funds to enroll in his dream course. While at work in a retail shop one day, he received a call that changed his life − Soul Candi Institute of Music were offering him a bursary to study for a diploma in Advanced Sound Engineering. "Regardless of the financial constraints one of the things that I want people to take into consideration is that they must have positive self-esteem. I know that my journey to the top will only come from hardworking and dedication to my studies, work and being pro-active", says Manyelo.
He has worked with Mash.O, Oluhle, Ntira, Oskido, Mono T, Sugar House (Greece), Leva Meksraityte (UK), Wunmi (USA) and Teki Letex (France) just to name few. "I love and live for music as it allows me to be myself and stretch my mind." He credits his two-year bursary at Soul Candi for sharpening his production skills and introducing him to established talents, like Oskido − "He calls me and he wanted to feature one of my track called Mexican girl on his album."
In addition to Oskido, Aero gained inspiration from Booka Shades and Ryan Murgatryd in terms of business and music. "I didn't give up my dream because of financial woes, but obstacles made me more determined to succeed. I know that success is not going to be handed to me on a silver platter, but I have to work hard and hard work really pays off." His ravenous zeal for music is slowly paying off and his lack of money never represses this talented musician. Today DJ Aero is the proudly owner of Herbal 3 Records which released a smash album by Mash.O, Drum Herbalist.
In August 2012, he was touring France, England, Germany and Switzerland with the 'Kasi Vibes' tour. Kasi Vibes is also the name of the album Herbal 3 Records released together with the German label OUTHERE RECORDS in April 2013. "Aero Manyelo – Kasi Vibes" is available on iTunes.
"The best part of the tour was me playing at the same Festival with the likes of Ame, Phonique and other top European music composers. I grew up listening to their music [and] being at the same festival with them is something else. The Fusion Festival is attended by more than 60,000 people every year [and] playing for that crowd was also amazing," says Manyelo.
"I've learned that most of my songs that I released in 2009 are still playing that side. Some of the songs made this tour possible. I had a lot of people asking me about 'Mexican Girl', for example, which was released in 2008 on Oskido's 7th Commandment album. It is really amazing how music takes time to reach other continents – thanks to the Herbal 3 Records team for their hard work," added Aero.
"I also need to put more effort in my sound quality, in terms of mastering and mixing. Europeans take sound quality very serious – your song can be nice but if the sound quality is weak, then it is a problem. They might end up not playing your song in clubs or radio or any other place. Sound quality is very important. First of all, be humble at the border – they might reject your entry if you are big-headed. When it comes to performing, be yourself – you are there because they love your work, so do it like you do it here at home. No need to change. The more natural you are, the better performance you will give. And be prepared for people asking you about Nelson Mandela.
I would really like to thank Spoek Mathambo, Crazy White Boy, Ryan Murgatroyd, DJ Mujava etc. who paved a way for guys like us to be recognized in the European market. The Kasi Vibes tour was a success and after the tour my Europe agent was getting a lot of booking requests so I did another tour in October 2013 to late November 2013. Between those dates I also played in France (at a digital arts and modern music centre they call LaGaîté Lyrique) for a concert sponsored by the South African National Art Council, called 'SHARP SHARP JOHANNESBURG'," says Aero.
"My future plan is to grow Herbal 3 Records and open doors to upcoming DJs, producers, vocalists and composers. I've learned the music business, like how to protect my music, market it and how to make money." Between building and marketing Herbal 3 Records and signing fresh new Djs and producers, he does not miss out on recording. He released an album for Soul Candi Institute of music (SCIM) and his mixes are currently playing on international Internet radio.


text:
Human behavior
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Applied behaviour analysis
Applied behavior analysis
Behavior or behaviour (see spelling differences) is the range of actions and mannerisms made by individuals, organisms, systems, or artificial entities in conjunction with themselves or their environm...
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Behavioural sciences
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Collective behavior
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52+ Dofollow Social Bookmarking Sites List 2019 [High DA]
When we talk about off-page search engine optimization, there are a lot of options which we can use to improve our ranking and domain authority. One of the most popular methods is social bookmarking. ...
52+ Dofollow Social Bookmarking Sites List 2019 [High DA]
When we talk about off-page search engine optimization, there are a lot of options which we can use to improve our ranking and domain authority. One of the most popular methods is social bookmarking. ...
How to create an app like TikTok: Features, Business Model, Cost
This guide will tell you how to adopt a TikTok success pattern and develop a social media app.
Trying not to offend people in 2019
Jordan Peterson Political Correctness and Postmodernism
Peterson Doesn't Have All The Answers - Only Most!
A One-Day Starvation Secret Got the Nobel Prize
You probably know that most tissues in your body regularly replace their cells with new ones. Different organs need their own time to renew completely. And some tissues don't replace their cells at al...
Boeing's Diversity and Inclusion Pronouncements Should Make Us All Uneasy
Boeing should be in the business of building planes that fly, not in creating a future utopia.
Modern Educayshun
The follow up to Equality, Modern Educayshun delves into the potential dangers of a hypersensitive culture bred by social media and political correctness. Written and Directed by Neel Kolhatkar Insta...
Eating behaviors
Play may refer to:Play may also refer to:
Human sexuality is the capacity to have erotic experiences and responses. A person's sexual orientation may influence their sexual interest and attraction for another person. Sexuality may be exp...
Human behavior
Human behavior refers to the array of every physical action and observable emotion associated with individuals, as well as the human race as a whole. Some behavior changes with age. While specific tra...
Cat behavior
Cat behavior refers to the behaviors and habits of domestic cats, including body language, elimination habits, aggression, play and communication. Cat behavior varies among breeds and individuals, a...
Cat behavior - Wikipedia
Dog behavior
Dog behavior refers to the collection of behaviors by the domestic dog, Canis lupus familiaris, and is believed to be influenced by genetic, social, situational and environmental causes. The domestic ...
Dog behavior - Wikipedia
Horse behavior
Horse behavior is best understood from the view that horses are prey animals with a well-developed fight-or-flight response. Their first reaction to a threat is often to flee, although sometimes they...
Horse behavior - Wikipedia
Spider behavior
Spider behavior refers to the range of behaviors and activities performed by spiders. Spiders are air-breathing arthropods that have eight legs and chelicerae with fangs that inject venom. They are t...
Ethology is the scientific and objective study of animal behaviour, usually with a focus on behaviour under natural conditions. Behaviourism is a term that also describes the scientific and objective...
Behaviorism (or behaviourism) is an approach to psychology that combines elements of philosophy, methodology, and theory. It emerged in the early twentieth century as a reaction to "mentalistic" psyc...
Behavioural sciences
Behavioral science is the systematic analysis and investigation of human and animal behaviour through controlled and naturalistic observation, and disciplined scientific experimentation. It attempts t...
Behavior modification
Behavior modification is the traditional term for the use of empirically demonstrated behavior change techniques to increase or decrease the frequency of behaviors, such as altering an individual's be...
Collective behavior
The expression collective behavior was first used by Robert E. Park (1921), and employed later by Herbert Blumer (1939), Ralph Turner and Lewis Killian (1957), and Neil Smelser (1962) to refer to soci...
The 4 Brain Superpowers You Need to Be a Successful Leader, According to Neuroscience
Leaders who understand how brains work can make themselves and their teams more nimble, innovative, and resilient.