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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 t1 yt1 t (NKPC) yt yt1 (rt1 t1) t (IS curve) rt r rt1 ( 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. 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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