Download Review of theoretical literature on price setting in macroeconomics

Review of price setting theories based on pricing
conduct in South Africa 2001-2007
Kenneth Creamer*
Introduction
Assumptions on pricing conduct play an important role in macroeconomics.
Woodford (2003) compares macroeconomics’ perfect case – where there are no
pricing rigidities - to a physicist’s study of the pure laws of motion in a frictionless
environment. He states that: “It may well simplify the analysis [of] basic issues in the
theory of monetary policy to start from the frictionless case, just as a physicist does
when analyzing the motion of a pendulum or the trajectory of a cannonball.”1 Just as
prevailing winds impact on aerodynamics, when monetary policy is studied in the
context of actual pricing conduct then a close analysis of the workings of underlying
pricing frictions is important to understanding the impact of such policy.
The study of pricing microdata is emerging in the literature as an important avenue of
enquiry into understanding actual pricing conduct. Studies of the large price data sets
used to compile CPI and PPI measures have been undertaken in a number of countries
including Israel (Baharad et al, 2003), Spain (Alvarez et al (2004)), France (Baudry et
al (2004)), the Euro Area (Alvarez et al (2005a)), the United States (Bils and Klenow
(2005)), Portugal (Dias et al (2005)), Germany (Stahl (2005)), Luxemburg
(Lunnemann (2005)), Austria (Baumgartner et al (2005)), Sierra Leone (Kovanen
(2006)), Italy (Sabbatini et al (2006)), Denmark (Hansen et al (2006)), Brazil (Gouvea
(2007)), France (Gautier (2007)), Finland (Kurri (2007)), Slovakia (Coricelli and
Horvath (2008)), Colombia (Julio et al (2008)) and South Africa (Creamer and
Rankin (2008)).
Alternative methodologies for establishing pricing conduct include surveys of price
setting conduct, such as Blinder et al’s seminal survey of price setters in the United
States (Blinder et al 1998). Other surveys of price setting behaviour that have been
*
1
School of Economic and Business Sciences, University of the Witwatersrand
Woodford (2003), p.32
1
conducted include in France (Loupias and Ricart (2004)), Sweden (Apel et al
((2005)), Austria (Kwapil (2005)), Spain (Alvarez et al (2005a)), Portugal (Martins
(2005)), Luxemburg (Lunnemann (2006)), Canada (Amirault et al (2006)), Holland
(Hoebrichts et al (2006)) and Turkey (Sahinoz et al (2008)).
Some studies of price setting conduct, utilising price data sets based on supermarket
scanner data, have also been undertaken, such as, in the United States (Chevalier et al
(2000)) and in the United Kingdom (Bunn and Ellis (2009)).
This paper makes use of previous studies of South African CPI and PPI microdata in
order to discuss:
-
firstly, how pricing conduct in South Africa compares with the assumptions
underlying various theories of pricing conduct prevalent in the literature, and,
-
secondly, a basic framework for understanding some of the possible
implications of such pricing conduct for monetary policy.
It is useful to start with a summary of the key findings on pricing conduct in South
Africa from Creamer and Rankin (2008), Creamer (2009a) and Creamer (2009b).
These findings are based on studies of the microdata sets used in compiling South
Africa’s CPI and PPI measures over the period 2001m12 to 2007m12.
Summary of key findings regarding pricing conduct
Based on a study of the large CPI data set comprising 3 930 977 price records over
the period 2001m12 to 2007m12, there is evidence of:
-
a varying frequency of price changes, and related price durations, over time,
with an unweighted average monthly price change frequency of 16,8% over
the period, and a maximum monthly price change frequency of 23,9% in
2003m6 and a minimum monthly price change frequency of 11,6% in
2004m12
-
asymmetry in pricing as price increases (10,8%) occur more frequently than
price decreases (6%)
-
heterogeneity in pricing across goods and services and across various product
categories, with goods prices increasing with a frequency of 10,8% and
2
decreasing with a frequency of 6,1%, and services prices increasing with a
frequency of 11,4% and decreasing with a frequency of 3,5%
-
psychological, or attractive, pricing with 62,7% of all prices ending in either
99 cents, 95 cents, 50 cents or 00 cents
-
sizeable magnitudes in price changes, which are larger than the prevailing
inflation rate, as for those prices that rose, the average magnitude of price
increases was 12,1% and for those prices that declined, the average magnitude
of price decreases was -14,9%
-
seasonality in pricing (or time-dependent pricing)2 is evidenced in that the
frequency of price increases rises during the month of March, during April and
June there is also some evidence of a higher frequency of price increases
although this is at lower statistical confidence than the finding for March,
June is the only month of the year where there is some evidence of seasonality
of price decreases
-
further seasonality is evidence by the fact that December is the month with the
highest magnitude of price increases
-
state-dependency in pricing3 is evidenced by a positive association between
the frequency of price increases and the rate of inflation both in real time and
after a three-month lag
-
further state-dependency in pricing is evidenced by the fact that a currency
appreciation is associated with a decline in the frequency of price increases
both in real time and after a three-month lag
-
further state-dependency in pricing is evidenced by the fact that after a three
month lag an increase in the repo rate is associated with an increase in the
frequency of price decreases, although there is no such effect in real-time
-
further state-dependency in pricing is evidenced by the fact that an increase in
inflation expectations – measured using bond spreads and surveys of inflation
expectations - is associated with a higher frequency of price increases
-
with regard to the magnitude of price changes, there is no clear evidence that
changes in the repo rate and exchange rate effect price change magnitudes, but
2
Where price-setters adopt time-dependent pricing then the timing of the price review and possible
price adjustment is exogenous and does not depend on the state of the economy.
3
Where price-setters adopt state-dependent pricing then prices are reviewed based on changes in the
prevailing economic conditions, for example, when a shock occurs. Time-dependent pricing is likely
to lead to stickier pricing than state-dependent pricing if the economy experiences shocks on a more
frequent basis, than the period which elapses between time-based price reviews.
3
there is some evidence of state-dependency in that when the rate of inflation
rises the magnitude of price decreases is smaller (in absolute terms)
Based on a study of the large PPI data set comprising 381 861 price records over the
period December 2001 to December 2007, there is evidence of:
-
a varying frequency of price changes, and related price durations, over time,
with an unweighted average monthly price change frequency of 20,2% over
the period, and a maximum monthly price change frequency of 34,9% in
2007m10 and a minimum monthly price change frequency of 10,8% in
2004m12.
-
asymmetry in pricing as price increases (12,2%) occur more frequently than
price decreases (8,1%)
-
heterogeneity in pricing across various product categories, with the frequency
of price changes for imported products over the period (23,2%) being higher
than the frequency of price changes for local products (18,8%) and for
exported products (18,7%).
-
sizeable magnitudes in price changes, which are larger than the prevailing
inflation rate, as for those prices that rose, the average magnitude of price
increases was 14,6% and for those prices that declined, the average magnitude
of price decreases was -16,8%
-
seasonality in pricing (or time-dependent pricing) is evidenced in that the
month of April has the highest frequency of price increases and there is some
evidence of an rise in the magnitude of PPI price increases in June
-
state-dependency in pricing is evidenced by a positive association between the
frequency of price increases and the rate of inflation both in real time and after
a three-month lag
-
further state-dependency in pricing is evidenced by the fact that in real time,
and after a three-month lag, a currency appreciation is associated with a
decline in the frequency of price increases and is associated with an increase
in the frequency of price decreases
-
further state-dependency in pricing is evidenced by the fact that increases in
the repo rate are associated with statistically significant real-time and threemonth lagged decreases in the frequency of price and with increase in the
frequency of price decreases
4
-
with regard to the magnitude of price changes, an increase in the PPI inflation
index is associated with a real-time and three-month lagged decrease in the
magnitude of price decreases (in absolute terms), a currency appreciation is
associated with a real-time and a three-month lagged decrease in the
magnitude of price increases, and after a three-month lag an increase in the
repo rate is associated with an absolute increase in the magnitude of price
decreases
Understanding pricing rigidities
An analysis of these main findings on pricing conduct indicate that South Africa’s
unweighted CPI price change frequencies for 2001-2007 (16,8%) are broadly similar
to findings for Spain 1993-2001 (15%), the Euro Area 1996-2001 (15,1%) and France
1994-2003 (18,9%). The United States economy would appear to have a significantly
greater frequency of price changes 1998-2003 (24,8%) and Brazil has experienced a
significantly higher frequency of price changes 1996-2006 (37%).4
Such relative price stickiness in South Africa and Europe can arise for various
reasons.
Altissimo et al (2006) suggest that: “[I]n an stable macroeconomic
environment, where agents trust in price stability, there is less need to change prices.
On the other hand, there might be structural inefficiencies that can prevent firms from
changing prices.”5 Another factor that would impact on cross-country differences in
average price change frequencies are differences in the structure of consumption in
various economies. Where food products, which have a relatively high price change
frequency enjoy a relatively large weighting in the consumption basket, then ceteris
paribus higher average price change frequencies would be expected.
According to Altissimo et al (2006), such structural factors limiting immediate price
adjustments include long term relationships with customers, explicit contracts which
are costly to renegotiate, and co-ordination problems arising from the fact firms prefer
not to change prices unless their competitors do so. Such arguments are similar to the
4
Data for Euro Area is from Dhyne et al (2005) and for the United States is from Bils and Klenow
(2004) and from Klenow et al (2005). Data on Spain is from Alvarez et al (2004). Data on France is
from Baudry (2004). Data on Brazil is from Gouvea (2007). Due to the adoption to differing
methodologies in the various studies, not all results are strictly equivalent, yet the results allow for
general comparisons of pricing conduct in a number of economies.
5
Altissimo et al (2006) p.5-6
5
survey findings of Blinder et al (1998), in their survey of 200 US-based firms, that
price-setters scored highest the following theories for price stickiness (in the
following order): (1) coordination failure – where firms hold back on price changes,
waiting for other firms to go first (Ball and Romer (1991)), (2) cost-based pricing
with lags – where price rises are delayed until costs rise (Gordon (1981) and
Blanchard (1983)), (3) delivery lags and service variation – where firms prefer to vary
other elements of the ‘vector’ such as delivery lags, service or product quality
(Carlton (1990)), and (4) implicit contracts – where firms tacitly agree to stabilize
prices, perhaps our of ‘fairness’ to customers (Okun (1981)).
Whereas a survey of price-setting conduct in South Africa would need to be
undertaken to establish the reasons for the pricing rigidities evidenced by the
microdata, it is conceivable that similar structural impediments to more flexible
pricing exist within the South African economy, which in certain sectors exhibits high
levels of concentration and a lack of competitive forces. A recent report argues that
the lack of competition impedes efficient development in terms of productivity and
innovation with negative spill-over effects for the whole economy (OECD (2008)).
Another possible reason for the lower price change frequencies in the South African
economy during the 2001-2007 period, is that this was a period of relative
macroeconomic stability. Some scholars have characterised this period as the ‘great
moderation’, stretching from 1986 to the onset of the financial crisis in 2008, due
mainly to the period’s sharply reduced output and inflation variability as compared to
previous periods (see, for example, Bernanke (2004) and Summers (2005)).
For South Africa specifically, although there was a relatively high degree of exchange
rate volatility for the South African Rand during the 2001-2007 period under review,
output and inflation volatility was relatively contained. Exchange rate volatility did
not translate into a high degree of interest rate volatility, mainly because, the inflation
targeting framework, which was formally put in place from the year 2000, replaced
the previous eclectic approach adopted by the South African Reserve Bank. Inflation
targeting allowed for a free floating exchange rate, whereas the eclectic approach
made use of interest rate adjustments in its attempts to target the exchange rate.
During the Asian crisis in the late 1990’s, the policy interest rates rose above the 20%
6
level in an attempt to counter currency deprecation forces. (Aron and Muellbauer
(2005) offer a comprehensive review of this period of South African macroeconomic
policy).
Understanding heterogeneity in pricing conduct
The heterogeneity in pricing conduct across various product categories and across
various economic sectors is explained in the literature by a number of factors.
Altissimo et al (2006) make the argument that prices change less frequently for
products with a larger share of labour input, indicating that persistence in wage
developments can be a cause of price stickiness. On the other hand, prices change
more frequently with rising shares of raw material input. Furthermore, it is argued
that sectors in which there is a high degree of competition are likely to have less price
stickiness.6
For South Africa, as with other countries, services prices are more sticky than goods
prices, which may be indicative both of high labour input costs in services, as well as
low levels of competition in the services sector. However, in the South African
situation, high degrees of price stickiness for goods such as footwear and clothing
(which have amongst the lowest price change and price increase frequencies) may be
indicative of increased import competition in those sectors. In this case, increased
competition may result in reduced price increases, where prices are fixed at a specific
level and price increases are avoided in the context of increased import competition.
Hazard functions – showing probability of price changes
An estimated hazard function shows the probability of price adjustments, conditional
on the price having been unchanged for a certain number of periods. 7 An upward
sloping hazard function would indicate that the longer the period of time that has
passed since a price has changed, the greater is the likelihood that the price will
change. As outlined in Appendix ‘B’, for a variety of specific consumer products at
specific stores hazard functions are broadly upward sloping, indicating the expected
result that the likelihood of price changes increase with the passing of time.
6
Altissimo et al (2006) p.30
Where the hazard rate (h)k is expressed as the probability that a price (pt) will change after k periods
conditional on having remained constant during the previous k-1 periods, that is: h(k) =Pr{pt+k ≠pt+k1|pt+k-1 = pt+k-2 =… =pt}
7
7
However, a an aggregated level, for the South African CPI and PPI microdata (see
Fig.1 and Fig.2), and in the literature more widely, it is found that estimated hazard
functions tend to by downward sloping. Alvarez et al (2005b) have shown that such
downward sloping hazard functions occur as a result of the aggregation of a wide
range of heterogenous data. Intuitively this is because: “The probability of observing
price changes is lower for firms with sticky price schemes than for firms following
flexible pricing rules, while the aggregate hazard considers price changes for all
firms. Therefore, when the aggregate hazard function is obtained, the share of price
changes corresponding to firms with more flexible pricing rules decreases as the
horizon increase and, consequently, the hazard rate also decreases”.8
For the CPI data, the hazard function (Fig.1 below) shows the probability of a price
change for each price duration, that is, the probability of a price change since the
previous price change.9 In this study both censored spells and uncensored spells
(which include both the beginning and end of a price spells) are used. The shape of
the hazard function is downward sloping with a small peak at 12 months. This would
seem to indicate further evidence of some time-dependency, or seasonality, in pricing
conduct in the form of annual pricing for consumer prices. The small peak at between
40 and 50 months is based on a very small sample, and is unlikely to indicate any
significant generalized finding on pricing conduct in South Africa.
Fig. 1 Hazard function using CPI microdata
Smoothed hazard estimate (CPI)
0,4
0,3
0,2
0,1
0
0
10
20
30
40
50
analysis time
8
Alvarez et al (2005b), p.9
The methodology (using STATA) for estimating the CPI and PPI hazard functions is outlined in the
“Appendix – Code for estimating hazard functions”.
9
8
For the PPI data, the hazard function (Fig. 2) is also downward sloping with a small
peak at 12 months, indicating evidence of annual pricing for producer prices. The
small peak at between 40 and 50 months is based on a very small sample, and is
unlikely to be of any significance.
Fig. 2 Hazard function using PPI microdata
Smoothed hazard estimate (PPI)
0,5
0,4
0,3
0,2
0,1
0
0
10
20
30
40
50
analysis time
Relationship between price duration and the magnitude of price changes
For both the CPI and PPI micro data there is a positive relationship between the
duration of prices and the magnitude of price changes, as per Fig.3 below.
Fig. 3 Relationship between price duration and magnitudes of price changes
Such a positive relationship – where price changes are found to be of a larger
magnitude if a longer period has passed since the previous price change – is regarded
as being indicative of price stickiness. As per Bunn and Ellis (2009): “If prices can be
9
set in each period there is no reason to expect price changes to be larger if more time
has passed since the price last changed. But if some constraint exits which allows or
incentivises firms to set prices at infrequent intervals, there is more scope for a firm’s
actual price to differ from its optimal price as the duration since the previous price
change increases. Examples of such constraints might include contracts of fixed
length or costs of price adjustment.”10
Outline various theoretical models of price setting
The various pricing models used in the macroeconomic literature can be grouped into
six broad categories. These are sticky information models, menu costs models, time
dependent models, costs of adjustment models and customer anger models.11
Sticky information models
Sticky information models, such as, those developed by Lucas (1973), Fischer (1977),
Mankiw and Reis (2002), Reis (2006) and Mackowiack and Wiederholt (2007) imply
continuous price adjustment.
Therefore, the hazard rate, or probability of price
changes, is one for each period, and there is no heterogeneity across firms in the
frequency of price changes.
In Lucas (1973) – sometimes referred to as the ‘islands model’ due to the focus on
price-output responses in a number of separate product markets - price setters are
required to solve a signal extraction problem as they cannot be sure whether to
interpret price increases for their product as a resulting from general or relative price
changes, hence rising prices are associated with rising output. There is some increase
in output in partial response to a positive price signal, which may be interpreted as
providing an increase in relative demand. This partial response in a multitude of
product markets, aggregates to a generalized increase in aggregate demand.
In Fischer (1977) and Mankiw and Reis (2002) prices are assumed to be predetermined rather than fixed. The key difference being that for Fischer prices are
10
Bunn and Ellis (2009), p.34
This taxonomy broadly follows Alvarez (2007) in which a review of theoretical literature on price
setting is outlined.
11
10
deterministically pre-specified for a number of periods, such as, contracts which fixed
prices and stated price adjustments over a number of periods, whereas for Reis and
Mankiw prices change stochastically for each period. In both models, a given fraction
of price setters computes a new path of optimal prices based on past and current
information about the economy.
In Reis (2006) price setters must pay a cost to acquire, absorb and process
information. In Mackowiack and Wiederholt (2007) firms decide what to observe.
When what the writers term “idiosyncratic conditions” – or conditions pertaining to a
particular product market - are more relevant than aggregate conditions, then firms
pay more attention to idiosyncratic conditions.
Menu Costs models
The key characteristic of menu cost models is that firms must incur a cost to change
nominal prices. Firms, therefore, do not change prices continuously, but will change
prices when such price changes are profitable.
In Danziger (1999) the expected duration of prices is positively associated with higher
menu costs, but negatively associated with increased idiosyncratic shocks and
increased money supply.
In the model developed by Dotsey et al (1999), firms face different menu costs, but
for all firms there is a positive relationship between inflation and the benefit of
adjusting prices. The hazard rate is increasing up to a point t*, where t*=1 and where
t* is negatively related to the trend inflation, that is, the value of the t* threshold is
lower for higher levels of trend inflation.12
Nakamura and Steinsson (2008) allow for idiosyncratic productivity shocks to
influence price-setting conduct. They find that the hazard function is upward sloping
12
Such state dependency models are referred to as Ss pricing models, as whenever a price setter makes
a price adjustment, he or she sets it so that the difference between the actual price and the optimum
price at that time, pi - pi*, equals a target level S, that is, S = pi - pi*. The nominal price is then kept fixed
at pi until economic conditions, such as a money stock increase, have raised p i* to the point at which pipi* falls to a trigger level s. The price-setter then resets pi-pi* to equal S and the process begins again
with prices remaining fixed until economic conditions require that prices are reset. (See Romer (2001)
at p.296 for a fuller description of this process.)
11
in the initial periods, and continues to be upward sloping in the absence of
||||idiosyncratic productivity shocks. Such shocks lead to pricing changes, resulting in
a flattening of the hazard function.
Time dependent models
Taylor (1980) and Calvo (1983) have offered seminal models of time dependent
pricing. For Taylor, prices are set by multiperiod contracts and remain fixed for the
period of the contract duration. As a result, the hazard rate is zero up to the end of the
contract at time t#, at which time the price must change so that the hazard is one.
For Calvo, there is a constant probability (  ) that any given price setter will change
its price in any period and, therefore, there is a constant hazard rate. Wolman (1999)
modifies this, and introduces a truncated Calvo model, by stipulating that after a given

period, of Calvo-like constant probability of price change, then all firms must adjust
their prices, where the hazard rate becomes one.
Heterogeneity can be introduced into time dependent models whereby different
groups of firms experience different durations of price contracts (Taylor (1993)), or
through an annualised model whereby a constant hazard rate is introduced every 12
months, 24 months and 26 months (Alvarez et al (2005)).
In Gali and Gertler (1999) model, it is assumed that there is a constant probability that
a firm will change its price in a given period, but a fraction of the firms set prices
according to a backward looking ‘rule of thumb’, and the rest of firms are forward
looking. So current inflation depends on past and expected future inflation. In this
model the hazard rate is constant.
In the Dynamic Stochastic General Equilibrium (DSGE) model developed by
Christiano et al (2005) prices adjust continuously. In periods of optimal pricing a
constant probability of price change Calvo-style assumption applies. During that
fraction of the time when non-optimal pricing pertains, then firms are assumed to
index their prices using lagged inflation rates.
Cost of adjustment models
12
In Rotemberg (1982) prices are set so as to minimise deviations from an optimal price
subject to the frictional costs of price adjustment. As a result, the hazard rate is one as
all firms are assumed to adjust prices continuously and there is no heterogeneity in the
frequency of price adjustments.
Customer Anger models
In Rotemberg (2005) firms are reluctant to change prices as customers react
negatively to price increases which they perceive to be unfair.
The model depends
on the evolution of customers’ beliefs on fair pricing. If customer beliefs are constant
then pricing in the model is equivalent to Calvo style pricing, but as customer beliefs
vary then firms price setting varies over time. As a result, the hazard rate depends on
the time-varying distribution of consumer beliefs.
Comparing South Africa’s data finding to the theoretical models
It is instructive to compare the hazard functions suggested by various theoretical
models of price setting conduct to the empirical hazard functions for South Africa’s
CPI and PPI microdata sets. The schematic comparison of the various theoretical
hazard functions and the empirically measured hazard functions is outlined in Fig.4.
As noted, whereas the hazard function for the aggregate data are downward sloping,
the hazard functions for the disaggregated data are generally upward sloping, as the
probability of price changes increases as the period since the last price change
lengthens (See Appendix ‘B’).
13
Fig. 4 Schematic of various theoretical and empirical hazard functions
A number of issues require further analysis as there is a disjuncture between the
theoretical models and the evidence of South Africa’s microdata:
-
Firstly, whereas a number of the theoretical models assume continuous price
evaluations by price-setters, the relatively low frequency of price changes
would indicate that price-setters do not review their pricing plans on a
continuous basis.13
-
Secondly, whereas a number of models are based on the assumption of
homogeneity of pricing conduct across firms, the data reveals significant
heterogeneity in pricing across various sectors. In addition to direct evidence
of heterogeneity of pricing conduct across the numerous sub-categories of the
CPI and PPI, the downward sloping hazard functions also provide evidence of
a heterogeneous mix firms, some following sticky pricing rules and others
following flexible pricing rules. There are certain models that are designed to
deal in a limited manner with pricing heterogeneity, such as, Carvalho (2006),
13
In various country studies this finding is also supported by survey data, for example Blinder et al
(1998) and Lunnemann et al (2006).
14
which assumes that each of a number of sectors re-prices based on its own
Calvo rate.
-
Thirdly, a number of pricing models do not incorporate seasonality, or timedependence. Both regression analysis and hazard analysis of South Africa’s
the CPI and PPI microdata reveal evidence of seasonality in pricing.
In
particular, the twelve-month spike in the hazard function would indicate
evidence of annual pricing conduct.
A basic macro framework for analysing the implication of various degrees of
price stickiness and backward indexation of prices
The development of a basic macroeconomic simulation model facilitates a formal
comparative discussion of how the conduct of monetary policy is affected by various
degrees of price stickiness and various degrees of backward-looking indexation of
prices. The model is not estimated specifically for any particular economy, but rather
provides a theoretical framework for understanding the implications of particular
forms of pricing conduct for the conduct of monetary policy, or more specifically for
interest rate setting.
The model defines prices as being sticky where such prices respond in a
comparatively muted manner to changes in the output gap. In general the positive
relationship between inflation and the output gap is maintained, but a high degree of
price stickiness means a lower degree of inflation responsiveness to the changes in the
output gap.
Furthermore, the model defines the degree of backward-looking
indexation as being positively associated with the proportion of price-setters who base
the current period’s prices on the previous period’s level of inflation.
The three-equation model includes a New Keynesian Phillips curve (NKPC), an
Investment-Savings (IS) curve and a Taylor rule. The NKPC relates current inflation
to its own lag, the previous period’s output gap and a cost push shock. The IS curve
links the current output gap to its own lagged value, the real interest rate and a
demand shock. The behaviour of the policy-maker is reflected in terms of a Taylor
rule, by which the nominal policy interest rate is set, based on the interest rate in the
15
previous period, if there is a degree of interest rate smoothing, and where the interest
rate depends positively on deviations from the inflation target and the output gap.
The model is outlined as follows14:

 t   t1  yt1  t
(NKPC)
yt  yt1   (rt1   t1)  t
(IS curve)
rt  r rt1   ( t   * )  y y t
(Taylor rule)

Where:

π = inflation,
y = output gap,
r = the policy interest rate,
 = cost push shock,
ε = demand shock,
 = degree of backward indexation in pricing,

κ = degree of price stickiness indicating inflation responsiveness to output gap and to
cost shock,

 = output persistence ,
σ = degree of output responsiveness to real interest rate changes,
r = extent of interest rate smoothing by authorities,

  = degree of responsiveness of policy interest rate setting to the deviation of current
inflation from the inflation target (  *), and

 y = degree of responsiveness of policy interest rate setting to the output gap


The parameters are calibrated as follows15:

14
Although this model omits forward-looking aspects, it offers the proper intuition for understanding
the comparative effects of cost shocks on inflation, output and interest rates of varying degrees of price
stickiness and price indexation. Moreover, the results suggested by this model, regarding the impact
of cost shocks and the related policy implications, are broadly similar to those of the backward and
forward looking model developed by Altissimo et al (2006), in their study of inflation persistence and
price setting in the European Union. One difference is that Altissimo et al (2006) finds negligible
difference in inflation persistence for various degrees of price stickiness, but, as with the current study,
Altissimo et al (2006) show, in the context of relatively sticky prices, that there are persistent output
effects and that there is a reduced need for aggressive interest rate responses.
15
Altissimo et al (2006) based calibrations on Smets (2004) where κ = 0,18,  =0,48,  = 0,44, σ =
0,06,  r = 0,0,   = 1,5 and  y = 0,5





16
κ = variously calibrated at 0,3, 0,5 and 0,7 to compare degrees of price stickiness with
stickier prices being indicated with a smaller κ values
 = variously calibrated at 0,9, 0,6 and 0,3 to compare degrees of backward
indexation in pricing with higher degrees of indexation being indicated by larger 
values

 = 0,9 indicating a high degree of output persistence

σ = 0,06 indicating output responsiveness to real interest rate changes
r = 0,2 indicating a limited degree of interest rate smoothing

  = 1,5 as per Taylor (1993)
 y = 0,5 as per Taylor (1993)


For purposes of comparing the effects of cost shocks given various degrees of price

stickiness, then it is assumed that the degree of backward indexation is fixed at  =
0,9. In isolating the comparison of various degrees of backward indexation then price
stickiness is fixed at κ=0,5.

Comparing degrees of price stickiness
Positive cost shock
The model responds to a positive cost-push shock  as follows: an increase in prices
due to  leads to an increase in inflation  (NKPC); the increase in  lead to an

increase in the policy interest rate r (Taylor rule); this leads to a restraining of output

growth y (IS curve); which ultimately leads to reduced pricing and containment of
inflation (NKPC).
Stickier prices, that is, prices of lower change frequency, or longer durations, are
associated with smaller κ values. As outlined in Fig.5, the model has different
outcomes depending on whether the degree of price stickiness in the economy is high
(long price duration and smaller κ values), medium (medium price duration and
medium κ values), or low (short price duration and larger κ values). The more rigid
prices are, the less responsive is inflation to changes in proximate determinants such
as the output gap, hence the smaller κ values.
17
Fig. 5 Comparing the effect of varying degrees of price stickiness and responses to a positive cost
shock
In summary, for a positive cost shock, if prices are relatively sticky (lower κ) then the
following time paths are observed for the various key macroeconomic variables:
Inflation – For relatively sticky prices, inflation increases, but by less than if prices
are more flexible, and above trend inflation persists for a longer period (about 3 to 4
months) than for more flexible prices.
Output – For relatively sticky prices, the negative deviation from trend output is lower
than for more flexible prices, and this negative deviation from trend output persists
for longer (by about to 5 to 7 months).
Nominal and real interest rates – For relatively sticky prices, there is a lower positive
interest rate response than if prices are more flexible, but the above trend interest rate
continues for a longer period (by about 2 to 3 months longer).
A higher degree of price stickiness implies a less aggressive, but more persistent,
monetary policy reaction. The required increase in the policy interest rate is smaller,
but lasts for longer, if prices are relatively sticky. This is because if prices are of a
18
relatively long duration then, in response to a positive cost shock µ, the increase in
nominal and real interest rates required to keep inflation in check is less than would
be required if price durations were relatively short and price increases were larger.
The smaller size of the interest rate response is due to the fact that with small κ values
the impact of the positive cost shock µ will result in lower levels of inflation. The
longer period over which the interest rate response must operate is due to the higher
inflation persistence associated with relatively sticky prices.16
Negative cost shock
As outlined in Fig.7, the model responds to a negative cost-push shock  as follows: a
decrease in prices due to negative  leads to an decrease in inflation  (NKPC); the
decrease in  lead to an decrease in the policy interest rate r (Taylor rule); this leads to


It is instructive to compare the situation of relative price stickiness (κ=0,3, 0,5, and 0,7) and
backward indexation (  =0,9) to the ‘no price rigidity case’ where prices adjust immediately (κ=1) and
where there is no backward indexation (  =0). As indicated in Fig.6 below, in the ‘no price rigidity
case’ a positive cost shock results in a perfect inflationary response in the first period and then inflation
returns rapidly and sharply to its long run trend level. Flexible prices result in a minimal deviation
from trend
inflation and output levels. This is due to the fact that the strong inflation response (not
mediated by any price stickiness or backward indexation) results in strong response in the policy

interest rate (via the Taylor rule). This leads to a rapid decline in inflation which means in turn that the
policy interest rate and real interest rates decrease more rapidly than in the ‘sticky price case’. As a
result of this lack of persistence in inflation and elevated interest rates the negative deviation in output
is also minimised. In sum, the ‘sticky price case’ is shown to include greater levels of inflation
persistence, more prolonged nominal and real interest rates responses, and larger deviations in output
than the ‘no price rigidity case’. In the ‘no price rigidity case’ outlined in Figure. 6 there is assumed to
be no interest rate smoothing (  r =0).
16
Fig. 6 No price rigidity case

19
a stimulation of output growth y (IS curve); which ultimately leads to higher pricing
and return to trend inflation (NKPC).
Fig. 7 Comparing the effect of varying degrees of price stickiness and responses to a negative cost
shock
In summary, for a negative cost shock, if prices are less flexible (lower κ) then the
following time paths are observed for the various key macroeconomic variables:
Inflation – For relatively sticky prices, prices decrease, but by less than if prices are
more flexible. Furthermore, for stickier prices, such deflation persists for a somewhat
longer period (by about 3 to 4 months longer than for more flexible prices).
Output – For relatively sticky prices, the positive deviation from trend output is lower
than for more flexible prices, and this positive deviation persists for a longer period
(by about 5 to 6 months longer than for more flexible prices).
Nominal and real interest rates – For relatively sticky prices, there is a smaller
negative interest rate response than if prices are more flexible, but such negative
interest rate reponse continues for longer (by about 3 to 4 months longer than for
more flexible prices).
20
A higher degree of price stickiness implies a less aggressive monetary policy reaction,
in the sense that the required decrease in the policy interest rate is smaller if prices are
relatively sticky, but the lower interest rate persists over a longer period.
This is
because if prices are of a relatively long duration then, in response to a negative cost
shock µ, the stimulatory decrease in nominal and real interest rates is less than would
be required if price durations were relatively short and price decreases were larger.
This is due the fact that with small κ values the impact of the negative cost shock µ
will result in lower levels of deflation and this will require less of an interest rate
response. The longer period over which the interest rate response must operate is due
to the higher deflation persistence associated with relatively sticky prices
Comparing degrees of backward looking price indexation
Positive cost shock
The model defines the degree of backward-looking indexation as being positively
associated with the proportion of price-setters who base the current period’s prices on
the previous period’s level of inflation. Higher values of  indicate higher degrees of
indexation as a larger proportion of price-setters set current prices based on inflation
in the previous period.

As outlined in Fig.8, the model has different responses to a positive cost shock
depending on whether the degree of price indexation in the economy is high (high 
values), medium (medium  values), or low (low  values).



21
Fig. 8 Comparing the effect of varying degrees of backward looking price indexation and
responses to a positive cost shock
In summary, for a positive cost shock, if price indexation in the economy is relatively
high (high  values) then the following time paths are observed for the various key
macroeconomic variables:
Inflation – For relatively high backward indexation, inflation increases, but by less

than if backward indexation is less prevalent. For high levels of backward indexation,
above trend inflation persists for a longer period (by about 5 to 7 months longer than
if there is less backward indexation).
Output – For relatively high backward indexation, the negative deviation from trend
output is larger than if backward indexation is less prevalent. This negative deviation
from trend output persists for a longer period (by about 3 to 4 months longer than if
there is less backward indexation).
Nominal and real interest rates – The level of nominal and real interest rate responses
is more or less the same for various degrees of backward indexation. However, both
nominal and real interest rates increases persist for a longer period where there is
relatively high degree of backward indexation (by about 5 to 7 months longer than if
there is less backward indexation).
22
For high degrees of backward indexation the monetary policy response to a positive
cost shock is more persistent, but no less aggressive than for low degrees of backward
indexation. The reason is that with a higher degree of backward indexation, inflation
is more persistent in response to a positive cost push shock and therefore there is an
increased need to respond to positive cost push shocks. For low degrees of backward
indexation, the impact of a positive cost shock will be dampened and inflation will be
less persistent. As a result the policy nominal interest rate and the real interest rate
responses will be less persistent.17
Negative cost shock
As outlined in Fig.9, the model has different responses to a negative cost shock
depending on whether the degree of price indexation in the economy is high (high 
values), medium (medium  values), or low (low  values).

Fig. 9 Comparing the effect of varying degrees of backward looking price indexation and
responses to a negative
 cost shock

Altissimo et al (2006) come to the similar finding that: “The benefit of a low degree of inflation
persistence is an improved inflation-output variability trade-off and a much reduced need to respond to
cost-push shocks.” (p.34)
17
23
In summary, for a negative cost shock, if price indexation in the economy is relatively
high (high  values) then the following time paths are observed for the various key
macroeconomic variables:
Inflation – For relatively high backward indexation, there is deflation as prices fall,

but prices fall more steeply if there are low levels of backward indexation. For high
levels of backward indexation, deflation persists for a longer period (by about 5 to 7
months longer than if there is less backward indexation).
Output – For relatively high backward indexation, the positive deviation from trend
output is larger than if backward indexation is less prevalent.
Nominal and real interest rates – For relatively high backward indexation, there is
less of a reduction in the nominal policy interest rate than if there are low levels of
backward indexation.
The level of real interest rate responses is more or less the
same for various degrees of backward indexation. However, both nominal and real
interest rates reductions persist for a longer period where there is relatively high
degree of backward indexation (by about 5 to 7 months longer than if there is less
backward indexation). A higher degree of backward indexation implies a monetary
policy reaction where the policy rate decrease is smaller, but more persistent, than it
would be for low levels of backward indexation.
Summary
A key implication of the model is that interest rate responses to cost shocks will have
to be more persistent, but less aggressive, if prices are relatively sticky. If there is a
relatively high degree of backward indexation of prices, then the interest rate response
24
will have to more persistent, but equally aggressive as compared to a relatively low
degree of backward indexation.
By more persistent, it is understood that interest rate increases, in response to positive
cost shocks, and interest rate decreases, in response to negative cost shocks, will take
place over a longer period. By less aggressive, it is understood that the size of interest
rate changes will need to be relatively smaller if prices are sticky.
Conclusion
This paper has highlighted two key issues.
Firstly, research, which makes use of pricing microdata to better understand pricing
conduct, provides a rich, but somewhat complex, set of stylised facts against which to
assess the micro foundations of macroeconomic models. A fruitful future avenue of
research would be to apply the findings of this microdata research in the development
of an estimated open economy model of the South African economy.18
Secondly, variations in pricing behaviour has implications for the conduct of
monetary policy, as relatively high degrees of price stickiness can be shown, with the
aid of a basic model, to entail less aggressive, but more persistent, interest rates
responses to cost shocks in the context of a medium term monetary policy framework.
Similarly, a relatively high degree of backward indexation of prices, can be shown to
require a more persistent, but no less aggressive, interest rate response as compared to
situations of relatively low backward indexation
18
Relevant to this endeavour would be recent research being undertaken in this regard by the South
African Reserve Bank (see Steinbach R et al (2009)), in which partial indexation of prices, as well as
staggered price setting is assumed. The challenge would be to find a way of using the micro founded
facts on pricing conduct in the South African economy to guide the estimation of pricing parameters
for the relatively sophisticated general equilibrium model, which is in the process of being constructed.
25
References
Amirault, D, C Kwan, G Wilkinson (2006) ‘Survey of Price-Setting Behaviour of
Canadian Companies’, Bank of Canada, Working Paper 2006-35, 2006
Altissimo, F, M Ehrmann and F Smets (2006) ‘Inflation Persistence and Price-Setting
Behaviour in the Euro Area: A Summary of the IPN Evidence’ European Central
Bank, Occasional Paper Series No.46
Alvarez, L. and Hernando, I. (2005a) ‘The Price setting behaviour of Spanish Firms:
Evidence from Survey Data’, European Central Bank Working Paper No.538,
October 2005
Alvarez, LJ, P Burriel and I Hernando (2005b) ‘Do decreasing hazard functions for
price changes make any sense?’ Banco de Espana, Working Paper No. 0508
Alvarez, LJ (2007) ‘What do micro price data tell us on the validity of the new
Keynesian Phillips Curve’, Banco de Espana, Documentos de Trabajo No.0729,
Apel, A, R Friberg and K Hallsten (2005) ‘Micro Foundations of Macroeconomic
Price Adjustment: Survey Evidence from Swedish Firms’, Journal of Money, Credit
and Banking, 37(2), 313-38
Aron, J and J Muellbauer (2005) ‘A review of Monetary Policy in South Africa
during 1994-2004’, Center for Economic Policy Research, Discussion Paper No. 5831
Baharad E and E Benjamin (2003), ‘Price Rigidity and Price Dispersion: Evidence
from Microdata’, August 2003
Ball, L and Romer D (1991), ‘Sticky prices as coordination failure’, American
Economic Review, 81(June), 539-52
Baudry, L, Le Bihan, H, Sevestre, P and Tarrieu, S (2007) ‘What do thirteen million
price records have to say about consumer price rigidity?’, Oxford Bulletin of
Economics and Statistics, 69(2), pp. 139-183, 2007
Baumgartner, J, E Glatzer, R Rumler and A Stiglbauer (2005) ‘How frequently do
consumer prices change in Austria? Evidence from Micro CPI Data’, European
Central Bank Working Paper No. 523
Bernanke, BS (2004) ‘The Great Moderation: Remarks by Governor Ben S
Bernanke’, Meetings of the Eastern Economic Association, Washington, DC,
February 20, 2004
Bils, M. and Klenow, P. (2004) ‘Some evidence on the importance of sticky prices’,
Journal of Political Economy, 112, pp.947-985, 2004
Blanchard OJ (1983) ‘Price synchronization and price level inertia’ in Inflation, debt
and indexation, eds. R Dornbusch and M Simonsen, 3-24, Cambridge MIT Press
26
Blinder, A, E Canetti, D Lebow and J Rudd (1998) Asking about Prices: A New
Approach to Understanding Price Stickiness, New York, United States of America,
Russell Sage Foundation
Bunn, P and C Ellis (2009) ‘Price-setting behaviour in the United Kingdom: a
microdata approach’, Bank of England Quarterly Bulletin 2009 Q1
Calvo, GA (1983) ‘Staggered Pricing in a Utility Maximizing Framework’, Journal of
Monetary Economics, 12, 383-398
Carlton DW (1990) ‘ The theory and the facts of how markets clear: Is industrial
organization valuable for understanding macroeconomics?’ Handbook of industrial
organization eds. R Schmalensee and R Willig, Amsterdam, North-Holland
Carvalho, C (2006) ‘Heterogeneity in Price Setting and the Real Effects of Monetary
Shocks’, Frontiers of Macroeconomics, Vol.2:Iss1. Article 1.
Chevalier, J, Kashyap, A and Rossi, P (2000) ‘Why don’t prices rise during periods of
peak demand? Evidence from scanner data’, NBER Working Paper no. 7981
Christiano, LJ, M Eichenbaum and CL Evans (2005) ‘Nominal rigidities and the
dynamic effects of a shock to Monetary Policy’, Journal of Political Economy,
113(1), 1-45
Coricelli, F. and Horvath, R. (2008) ‘Price setting and market structure: an empirical
analysis of microdata’, Institute of Economic Studies, Charles University in Prague,
IES Working Paper 23, 2008
Creamer, K (2009a) ‘Price setting in South Africa 2001 to 2007 based on PPI
microdata’, mimeo, University of the Witwatersrand
Creamer, K (2009b) ‘Regression analysis of time-dependency and economic statedependency in South Africa’s price setting conduct 2001 to 2007’, mimeo, University
of the Witwatersrand
Creamer, K and N Rankin (2008) ‘Price Setting in South Africa 2001 to 2007 –
Stylised facts using consumer price microdata’, Journal of Development Perspectives,
4(1), 93-118
Danziger, L (1999) ‘A Dynamic Economy with Costly Price Adjustments’, American
Economic Review, 89(4), 878-901
Dennis, R (2006) ‘The Frequency of Price Adjustments and New Keynesian Business
Cycle Dynamics’, Federal Reserve Bank of San Francisco, August 2006
Dias, D. Marques, C. and Silva, J. (2005) ‘Time or state dependent price setting rules
– Evidence from Portuguese micro data’, European Central Bank, Working Paper
Series, No. 511, August 2005
27
Fischer, S (1977) ‘Long-Term Contracts, Rational Expectations, and the Optimal
Money Supply Rule’, Journal of Political Economy, 85(1), 191-205
Gali, J and M Gertler (1999) ‘Inflation Dynamics: A structural econometric analysis’,
Journal of Monetary Economics, 44(2), 195-222
Gali, J (2008) Monetary Policy, Inflation and the Business Cycle: An introduction to
the New Keynesian Framework, Princeton, Unite States of America, Princeton
University Press
Gautier, E (2007) ‘The behaviour of producer prices: Some evidence from the French
PPI micro data’, Empirical Economics
Gordon R (1981) ‘Output fluctuations and gradual price adjustment’, Journal of
Economic Literature 19(June), 493-530
Gouvea, S (2007) ‘Price Rigidity in Brazil: Evidence from CPI Micro Data’, Banco
Central Do Brasil, Working Paper Series 143, September 2007
Greenslade, J and M Parker (2008) ‘Price-setting behaviour in the United Kingdom’,
Bank of England Quarterly Bulletin, 2008 Q4
Hansen, B and N Hansen (2006) ‘Price-setting behaviour in Denmark, A Study of CPI
micro data 1997-2005’, Denmark’s National Bank, Working Paper 39
Hoebrichts, M and A Stockman (2006) ‘Pricing behaviour in Dutch companies:
results of a survey’, European Central Bank, Working Paper No. 607
Julio, J and H Zarate (2008) ‘The price setting behaviour in Colombia: Evidence from
the PPI micro data’, Borradores de Economia, Banco de la Republica, Colombia
Kovanen, A. (2006) ‘Why do prices in Sierra Leone Change So Often? A Case Study
Using Micro Level Price Data’, IMF Working Paper WP/06/53
Kurri, S (2007) ‘Price changes in Finland: some evidence from micro CPI data’,
European Central Bank Working Paper No. 728
Kwapil, C, J Baumgartner and J Scharler (2005) ‘The price-setting behaviour of
Austrian Firms: Some Survey Evidence’, European Central Bank Working Paper No.
464
Loupias C and Ricart R (2004) ‘Price Setting in France: New evidence from Survey
Data’, European Central Bank, Working Paper Series, No. 423, December 2004
Lucas, RE (1972) ‘Expectations and the Neutrality of Money’, Journal of Economic
Theory, 4 (April), 103-24
Lucas, RE (1973) ‘Some International Evidence on Output-Inflation Tradeoffs’,
American Economic Review, 63(3), 326-34
28
Lunnemann P and T Matha (2005) ‘Consumer price behaviour in Luxemburg:
Evidence form micro CPI data’, European Central Bank Working Paper No. 541
Lunnemann P and T Matha (2006) ‘New Survey evidence on the pricing behaviour of
Luxemburg firms’, European Central Bank Working Paper No. 617
Mackowiak, B and M Wiederholt (2007) ‘Optimal Sticky Prices under Rational
Inattention’, CPER Discussion Papers 6243
Mackowiak, B. and F Smets (2008) ‘On implications of micro price data for macro
models’, European Central Bank, Working Paper Series, No 960
Martins, F (2005) ‘The price-setting behaviour of Portuguese firms: Evidence form
survey data’, European Central Bank Working Paper No. 562
Mankiw, NG and R Reis (2002) ‘Sticky Information versus Sticky Prices: A Proposal
to replace the New Keynesian Phillips Curve’, Quarterly Journal of Economics, 117,
1295-1328
Mathuloe, PT and MR Steinbach (2008) ‘A closed economy New Keynesian DSGE
model for South Africa’, South African Reserve Bank Discussion Paper, DP/08/03
Nakamura, E and J Steinsson (2008) ‘Five Facts about Prices: A Reevaluation of
Menu Cost Models’, mimeo, Harvard University, forthcoming in Quarterly Journal of
Economics
OECD (2008) ‘Economic Assessment of South Africa 2008’, OECD Economics
Surveys, July 2008, Volume 2008/15, Organisation for Economic Cooperation and
Development
Okun, A (1981) ‘Prices and quantities: A macroeconomic analysis’, Washington
D.C., Brookings Institute
Reis, R (2006) ‘Inattentive Producers’, Review of Economic Studies, 73, 793-821
Romer, D (2001) Advanced Macroeconomics, Second Edition, McGraw-Hill
International Edition
Rotemberg, J (1982) ‘Monopolistic Price Adjustment and Aggregate Output’, Review
of Economic Studies, 49, 517-531
Rotemberg, J (2005) ‘Customer Anger at Price Increases. Changes in the Frequency
of Price Adjustments and Monetary Policy’, Journal of Monetary Economics, 52,
829-852
Sabbatini, R, S Fabiani, A Gatulli and G Veronese (2006) ‘Producer Price Behaviour
in Italy: Evidence from micro PPI data’, mimeo, Banca d’Italia
Sahinoz, S and B Saracoglu (2008) ‘Price setting behaviour in Turkish industries:
Evidence from survey data’, Turkish Economic Association, Discussion Paper 2008/3
29
Summers PM (2005) ‘What caused the Great Moderation: Some cross-country
evidence’, Economic Review, Federal Reserve Bank of Kansas City
Smets, F (2004) ‘Maintaining price stability: How long is the medium term?’, Journal
of Monetary Economics, 50, 1293-1309
Smets, F and R Wouters (2003) ‘An estimated stochastic dynamic general equilibrium
model of the Euro Area’, Journal of European Economic Association, 1(5), 11231175
Stahl, H (2005) ‘Price setting in German manufacturing: Evidence from new survey
data’, Discussion Paper, Deutsche Bundesbank, No. 43/2005
Steinbach R, P Mathuloe and B Smit (2009) ‘An open economy New Keynesian
DSGE model of the South African economy’, South African Reserve Bank Working
Paper, WP/09/01
Svensson, L (1997a) ‘Inflation forecast targeting: implementing and monitoring
inflation targets’, European Economic Review, 41(6), 1111-1146
Svensson, L (1997b) ‘Optimal Inflation Targets, ‘Conservative’ Central Banks and
Linear Inflation Contracts’, American Economic Review, 87, March, 98-111
Taylor, J (1980) ‘Aggregate Dynamics and Staggered Contracts’, Journal of Political
Economy, 88(1), 1-23
Taylor, JB (1993) ‘Discretion versus policy rules in practice’, Carnegie-Rochester
Conference Series on Public Policy 39, 195-214, North-Holland
Taylor, JB (1993a) Macroeconomic Policy in a World Economy: From Econometric
Design to Practical Operation, W.W. Norton
Taylor, JB (1999) “Staggered Price and Wage setting in macroeconomics,” in J.B.
Taylor and M. Woodford (eds.), Handbook of Macroeconomics, chap. 15, 1341-1397,
New York, United States of America, Elsevier
Wolman, A.L (1999) “Sticky Prices, Marginal Cost, and the Behaviour of Inflation”,
Economic Quarterly, Federal Reserve Bank of Richmond, 85(4), 9-48
Woodford, Michael (2003) Interest and Prices: Foundations of a Theory of Monetary
Policy, Princeton, United States of America, Princeton University Press
30
Appendix ‘A’ – Code for estimating hazard functions
STATA code used for estimating the hazard functions using the CPI and PPI
microdata sets:
gen firstobs=0
replace firstobs=1 if id~=l.id
gen observed_time=0 if firstobs==1
replace observed_time=l.observed_time+1 if firstobs~=1
gen duration_all=duration
replace duration_all=observed_time if duration==.
snapspan id edate2 change changedummy duration duration_uncensored
duration_all observed_time lnprice changelnprice absolutechange
price, gen(date0) replace
stset duration_all, failure(changedummy)
sts graph, hazard width(1)
sts graph, hazard width(0.5)
sts graph
stset duration, failure(changedummy)
sts graph, hazard width(1)
sts graph, hazard width(0.5)
stdes
31
Appendix ‘B’ Dissaggregated Hazard functions for a variety of specific products
and at specific stores
0
.2
.2
.4
.4
.6
.6
.8
Smoothed hazard estimate
.8
Smoothed hazard estimate
0
5
10
15
1
2
3
analysis time
analysis time
Brown Bread
4
5
15
20
Oranges
Smoothed hazard estimate
0
0
.2
.2
.4
.4
.6
.6
.8
.8
Smoothed hazard estimate
0
2
4
analysis time
6
8
Instant Coffee
0
5
10
analysis time
Imported Whisky
Smoothed hazard estimate
0
0
.02
.2
.04
.4
.06
.6
.08
.8
Smoothed hazard estimate
3
4
5
6
7
analysis time
Packet of 20 Virginia Type Cigarettes
8
4
5
6
7
8
9
analysis time
Soccer ball
32
0
0
.02
.2
.04
.4
.06
.6
.08
.1
Smoothed hazard estimate
.8
Smoothed hazard estimate
11
11.5
12
analysis time
12.5
13
Cinema tickets
0
2
4
analysis time
6
8
Dog Food Pellets
Smoothed hazard estimate
0
.5
.05
.6
.1
.7
.15
.8
.2
.25
.9
Smoothed hazard estimate
1
1.5
2
analysis time
2.5
3
2
4
6
8
10
12
analysis time
Magazines
Dental Floss
0
.2
.4
.6
.8
Smoothed hazard estimate
0
5
10
15
analysis time
Toilet Paper
33