testing for pricing asymmetries in customer markets

TESTING FOR PRICING ASYMMETRIES IN CUSTOMER MARKETS*

J.N.LYE and H. SIBLY

University of Melbourne Universio of Tasmania

I. INTRODUCTION

The stickiness of retail prices has been widely regarded as an important aspect of both agricultural economics and macroeconomics. The empirical studies of Marceau (1967), Griffith (1974), Griffith (1986), Naughtin and Quilkey (1979), Gfi i th , Green and Duff (1991) and Griffith, Jamandre and Pigot (1991) have found evidence that retailers in Australian meat and fresh vegetable markets both ‘average’ and ‘level’ retail prices.’ Other empirical support is provided by McClements (1972), using UK meat prices; Shonkwiler and Taylor (1988), using data from the US market on canned frozen concentrated orange juice and McDonald and Spindler (1987) who consider wholesale and retail price indices for the US, UK and Australia. More recently, asymmetric price stickiness in a wide range of retail markets has been investigated (see for example, McClements, 1972; Young, 1980; Ward, 1982; Rutherford, Hocking and Ingham, 1985; Kinnucan and Forker, 1987; Shonkwiler and Taylor, 1988; Hahn, 1990, Pick, Karrenbrock and Carman, 1990; Sumner, 1990; Hannan and Berger, 1991; Karrenbrock, 1991 and Manning, 1991).

Previous studies of asymmetric pricing have not been based on well developed theory. In particular, the specifications of the estimated equations in studies of pricing asymmetries have been ad hoc. The aim of this paper is to draw on the theory of customer markets (particularly Okun, 1981; McDonald and Spindler, 1987; McDonald, 1990 and Sibly, 1992a) to develop a test for pricing asymmetries in retail markets. The test is then used to investigate pricing asymmetries in Australian retail meat and vegetable markets. Specifically, Section II presents a discussion of pricing asymmetries in customer markets. Section III develops a model of a customer market which incorporates the pricing asymmetries identified in Section II. In Section IV data from the Australian meat and vegetable markets is used to empirically estimate the model and in Section V the empirical conclusions are briefly summarised.

* The authors are particularly grateful to Ian McDonald for many helpful comments; to Donald McKlaren for providing useful references; to Gary Griffith for supplying the data; to Jeff Borland and two anonymous referees for helpful comments.

Prices are averaged when a retailer varies margins across goods to maintain stability of the price of each item. Prices are levelled when a retailer varies the margin on an item across time in order to stabilise its price.

240 AUSTRALIAN ECONOMIC PAPERS

a. PRICING AsYMMEnUEs IN CUSTOMER MARKELS

DECEMBER

Okun (1981, pp.138-142) defines a customer market as a retail market in which there is an ongoing relationship between buyers and sellers. Repeat purchasing arises in response to the shopping costs faced by customers. Customers benefit from continuity because it avoids repeatedly incurring the switching costs associated with changing supplier. Firms also benefit by having a stable demand for their output.

Okun argues that, because customers face switching costs when changing suppliers, they seek a supplier that is dependable. Once customers are satisfied that their current retailer is a reliable supplier, the mutually beneficial relationship between buyers and sellers will persist indefinitely. Firms will be reluctant to raise price above the level expected by customers for fear of appearing unreliable. If the f m did unexpectedly raise price, some customers (particularly those ‘loyal’ customers who value reliability highly) will seek another, more dependable, firm to patronise. After this, it will be difficult for the firm to attract these customers back to it. The f m would need to convince them that, in spite of its past behaviour, it is indeed a reliable supplier (that is, one which will not raise price unexpectedly). Convincing the customer of this, either through advertising or discounts, is likely to be costly for the firm. Thus the firm would expect that, if it raises price today, it will incur costs in the future when it attempts to expand customer numbers.

Customer markets also exhibit an information asymmetry that was first identified, and systematically analysed, by Scitovsky (1952). Customers are informed of the price set by their regular firm at each purchase, but less frequently informed by the price set by other firms in the market. In such an environment firms do not immediately attract customers when they lower price as prospective customers are not aware of the price change. If the firm is to haease its patronage it must either advertise (Kling, 1982) or must rely on word of mouth (Phelps and Winter, 1970; Sibly, 1992a, 1992b). In the former case the firm must pay advertising expenses. In the latter case customer numbers build up slowly following a price fall. If initially the firm’s price is below the price which maximises profit per customer under perfect information (which is above the perfect information monopoly price), it will suffer a temporary fall in revenue as customer numbers build up. Thus, whether the firm relies on word of mouth or advertising to inform prospective customers of its lower price, its discounted profits will be lower than under perfect information.

Therefore the theory of customer markets suggests it will be costly for retailers to vary price relative to customers’ expectations. When raising price firms will be concerned that their loyal customers will view them as unreliable and attempt to seek another more dependable supplier. Firms will also be concerned that lowering price will not increase customer numbers as prospective customers will not be aware of the price fall. As a result retail prices will be less flexible than suggested by the frictionless textbook microeconomic theory. However, as the costs of raising and lowering price arise for different reasons, the possibility exists that retail price inflexibility will be asymmetric.

1994 TESTING FOR PRICING ASYMMETRIES IN CUSTOMER MARKETS 24 1

111. THE MODEL

In this section a model which captures the economic behaviour of a retailer in a customer market (see McDonald and Spindler, 1987; McDonald, 1990 and Sibly, 1992a) is developed. The model is used to develop the pricing equation that is estimated in the following section.

First consider retailers in a market where customers can costlessly move between firms. This ‘frictionless’ market is assumed to be characterised by monopolistic competition. Output in this market is assumed to be differentiated (e.g. due to location) in such a way that each firm faces a downward sloping demand curve. Following Chamberlin (1933), the number of firms in the market is sufficient to eliminate strategic interaction. The details of a representative firm’s demand curve are now specified.

Each period this firm is assumed to attract m (p, p) customers, where p is the real price it sets and p is the average industry real price. Each customer purchases one unit of output. The firm faces constant real marginal cost p,. The firm’s real profits, ?rf(p, p), are given by

Consider the case where all firms have demand.curves given by

The first component of demand, m,(p -p ) , depends on the firm’s relative price. It can be interpreted as the number of customers the firm attracts from other firms when it sets a given price. The second component, m,(p), depends only on the firm’s real price. It can be interpreted as the number of customers the firm attracts from purchasing other goods when it sets price P . ~

Although it is assumed that changes in the firm’s price will not influence other firms’ price or average industry price? we do allow firms to conjecture that a change in the cost facing all firms will influence average industry price. The firm uses its own optimal price response to a change in marginal cost as a guide to the change in average industry price in the following way! Suppose that there is an increase of marginal cost of $1. Assume the firm conjectures that, in moving to the new equilibrium, average industry price will change by p of its change in price. Thus

* This functional form for demand is fairly general in that it allows for these two components. However the additive nature of the functional form means that there is no interaction effect on total demand between those customers who come to the firm from other firms and those who switch from purchasing other goods.

Because there are sufficient firms to eliminate strategicinteraction between firms, the firm’s choice of price will not influence (noticably) any other firm’s demand curve. Hence other firm’s price, and consequently average industry price, is insensitve to the firm’s choice of price.

to itself. Thus its own response to the cost shock is a guide to the response of other firms. Intuitively the firm expects that all firms face similar (but possibly not identical) demand and cost conditions

242 AUSTRALIAN ECONOMIC PAPERS DECEMBER

Hence it is assumed that relative price is given by

This specification allows firms to conjecture that (i). by setting 8 = 0, the ratio of its price to the average industry price will not change in response to a cost shock once the market has returned to equilibrium and, (ii), by setting p = 0, industry price will not change in response to a shock. By substituting (2) and (4) into (I), the fm’s profit function, d ( p , p ) , is given by

The frictionless monopoly price, p’. solves a d ( p , p ) / a p = 0 where p is given by equation (4).

As discussed in Section 11, in a customer market buyers do not move freely between firms. Consequently, the above frictionless model needs two modifications. First, as argued by Okun (1981), there is value to the firm in retaining current customers. If the fm sets its price, p , above customers’ expected price, pc, it is assumed that the firm immediately moves up its demand curve and loses m (p) - m (p) customers. As a consequence of the price rise these customers may view their original firm as unreliable and, after switching patronage, may not readily return to the firm in the future. The firm therefore looses the opportunity, if marginal cost were to fall, to costlessly increase profits by selling to these customers. It is assumed that the expected cost to the firm arising from the loss of customers if it sets price p > p c is given by c,(m@3 - m(p) ) . This functional form captures the possibility that m @’) - m ( p ) customers might be driven away from the firm for a period longer than the price increase.

The second modification to the frictionless model introduces a cost of lowering price. Customers that do not patronise the firm are not instantaneously aware of the price set by the firm. Hence following a price fall, f m s must either advertise or rely on word of mouth to inform prospective customers. Both these mechanisms will impose a cost on the firm (see for example Sibly, 1992a). If the f m sets a price below the customers expected price it is assumed that the cost to the firm of gaining new customers is c,(rn(p) - m(pe)). This form of the cost function is chosen because the cost of attracting customers from other firms is likely to depend on the number of customers the f m wishes to attract.

Following these modifications to the frictionless model, the fm’s profit function, n, is given by

The firm’s optimal price is obtained from (6) by setting a d a p = 0. However, to develop an empirically testable model, it is necessary to adopt specific functional forms for m,(p - p ) , m,(p) and ci(.), i = 1,2. For simplicity we take

and

1994 TESTING FOR PRICING ASYMMETRIES IN CUSTOMER MARKETS 243

Using (5). the frictionless monopoly price, p'. is

p' = g + ( 9 ) P w (9)

where a = a, + a2 + b,8 and b = 2(b, + b,) - pb,. We also adopt

where A, and A , are constants. Equation (10) is the simplest specification which allows a continuous profit function. Substituting (7). (8) and (10) into (6) and differentiating gives

a ,+a2-2 (b ,+ b J p + b,P+(b,+ b,)P,-2(b1+ b,)2Al(p-pC) f o r p > p c

~ , + ~ , - 2 ( b , + b , ) p + b , p + ( b , + b2)Pw-2(bl+ b2)'A,(p-pC) forp<pc( l l )

Profit maximising price is given by a d a p = 0 where p i s given by (4). Thus the optimal price is given by

(1 - p')P' + p ' P C

(1 - P3P' + PP'

for p > p c

for p I p c P = (

Observe that if A, > A, then p' > p-.

The dynamics of the model will be determined by customer expectations. In this paper it will be assumed that the expected growth rate of retail prices is equal to the previous period's growth rate. In a world where wholesale prices are shocked frequently and are costly to observe, this may reflect a near-rational strategy on the part of the customers. Under these circumstances

where the prefix r in front of a price denotes the growth rate of that price over the real price in the previous period. For example, rp: =(pf - p,.,)Ip,.,.


N. EMPIRICAL RESULTS

In order to empirically estimate the model presented in Section 111, data from the fresh vegetable and the livestock and meat market in the state of New South Wales in Australia are used. In both these markets the cost of search is likely to be significant when compared with the price of the good. As a result, customers are likely to find it optimal to purchase from a reliable supplier rather than conduct frequent search across suppliers. Therefore these markets may be modelled as customer markets.

Before estimating the asymmetric price equation presented in Section 111, a preliminary investigation is performed to examine the existence of price rigidity in these retail price series. If price rigidity exists then this suggests that the retail price series will fluctuate less than the wholesale price series. Such behaviour is consistent with the behaviour predicted in customer markets.

a) Preliminary investigation

Vegetables There are two sectors of the Australian vegetable industry - fresh and processed. In this study

data will be used from the fresh market since in the processed sector of the industry there have been significant structural changes which have not occurred in the fresh market .

Fresh vegetables are subject to perishability and seasonal production patterns, (see, for example, Watson and Parish, 1982, p.351). Consequently, fresh vegetable producers in New South Wales have seen the prices received for their produce fluctuate substantially from season to season and from month to month, due to numerous climatic changes including the amount of rainfall, occurrence of floods etc. For example, ‘Cauliflowers, which in March were fetching from $10 to $16 a carton, this week were averaging only $3.20 a carton, while broccoli has slipped from $12- $16 a carton to between $2.50 and $7.00 a carton’ (Middlebrook and Jones, 1991). In spite of these season fluctuations, a comparison of the coefficient of variation reported in Table I for the retail and wholesale price series for the four major fresh vegetables in the New South Wales market illustrate that the degree of variability in the retail price of these vegetables is considerably less than in the wholesale price. Also, in their study of this market, Griffith et al. (1991) find some evidence of price levelling, where price levelling refers to the practice of retailers holding prices relatively stable when wholesale prices are fluctuating either upwards or downwards.

TABLE I The Coeficient of Variation for the Vegetable Series

Wholesale Retail

carrots 45.39 39.63 Onions 50.78 41.84 Potatoes 38.53 33.48 Tomatoes 3 1.74 28.12

Note: Coefficient of Variation = (Standard DeviationlMean) x 100


Meat market Prices of livestock in the Australian market vary during each year and from year to year under

the influence of climatic and market conditions. For example, when pastures are deteriorating during periods of dry weather supply is increased as fat stock are hastened to the market, causing wholesale prices to decline. Alternatively, with the arrival of rain, livestock may be withheld from the market for fattening or breeding purposes causing wholesale prices to increase. Changes in wholesale prices can be substantial. For example beef prices fell dramatically in 1974 (Campbell, 1982).

While the Australian consumer appears responsive in switching between different meats when price changes occur, (for example, the consumption of beef jumped from 41.1 kg per head in 1973-4 to 64.3 kg the following year in response to the sudden decline in beef that occurred in 1974-75), the overall level of consumption of total carcass meat shows no obvious trend over the last thirty years (see for example Longworth, 1982, p.309). The coefficient of variation statistics reported in Table I1 for the beef and lamb retail and wholesale prices in the New South Wales market indicates that the degree of variability in the retail price series is less than that in the wholesale price series. Furthermore, previous studies using meat price retail data for Australia, (see for example Griffith, 1974, Griffith, 1986 Griffith et al., 1991) have found evidence to support the hypothesis of price levelling.

TABLE I1

The Coeficient of Variation for the Meat Series

Wholesale Retail

Beef 10.06 9.24 Lamb 12.02 8.88

Note: Coefficient of Variation = (Standard Devia t ioaean) x 100

Empirical model According to the Prices Justification Tribunal (1978, p.91) purchase of wholesale meat

accounts for at least 75 per cent of operating costs for meat retailers in Australia. Similar comments can also be made about the fresh vegetable market, see for example Griffith et al. (1991). Therefore, wages and wholesale prices are considered as the two main operating costs in the retail market for our data sets. Hence, from (9), the frictionless monopoly price, p*. is given by,

p' = a. + a,wp + a2 wage. (14)

Using a dummy variable to denote asymmetries around consumers' expectations, the asymmetric retail price equation presented in (13), Section I11 can be written as,

24.6 AUSTRALIAN ECONOMIC PAP= DECEMBER

0, = 1. if rp: > rp: ;O otherwise.

For estimation purposes, the specification given in (15) is used assuming a normally distributed error term. Data are used on real monthly retail (rp) and real monthly wholesale prices (wp) for: beef and lamb prices in the New South Wales meat and livestock market; and for potatoes, carrots, tomatoes and onion quarterly prices in the New South Wales fresh vegetable market. Real labour costs are proxied in each of these markets by the variable wage (wage). The sources and details of all of this data are given in Appendix I.

A potential problem with the data is that monthIy and quarterly observations may be too infrequent to test for the presence of price rigidity in these markets. and more frequently spaced observations such as weekly observations may be more appropriate. However, the results of a Monte Carlo experiment indicate that price rigidity would still be evident in the empirical analysis even if more frequent observations are averaged and then used as the data. The results of this Monte Carlo experiment are outlined in Appendix II.

Given the nonlinearity of the asymmetric price equation specified in (15), numerical iterative optimisation procedures are required to estimate the regression parameters. The Newton-Raphson algorithm in conjunction with the Bemdt-Hall-Hall-Hausman algorithm are adopted here. All derivatives are computed numerically with the computations being performed by the program Maxlik in Gauss. The results are presented in Tables 111 to V.

In each case, parameter estimates for wage and wp have the appropriate sign, although in the case of potatoes, tomatoes and onions the t-statistic associated with the wage variable is less than one. In all the markets the values of the 1-statistics associated with the estimated coefficient is significant which implies that there is a upward price adjustment cost. On the other hand the value of the t-statistic associated with the estimated coefficient p- is less than one, in all markets with the exception of lamb. This results implies that in general there is an insignificant downward price adjustment cost.

These results suggest that the well documented retail price rigidity in Australian meat and vegetable markets is consistent with the analysis of retail markets by Okun (1981). Specifically, it appears that retailers attempt to avoid alienating their regular customers by not immediately passing on wholesale price increases. On the other hand, there is little evidence that the information asymmetry originally identified by Scitovsky (1952) causes downward price rigidity in these markets. This finding could be attributed to the layout of modem shopping centres and shopping malls in which retailers are often in close proximity to one another. Thus, many customers may be aware of all prices in their neighbourhood and consequently the price asymmetry may not be significant in retailers pricing policy.

The finding of asymmetries in retail price adjustment has implications for other theories of price rigidity. For example, consider the menu cost theory (Mankiw, 1985). This theory

1594 TESTING FOR PRICING AS- IN CUSTOMER MARKETS 241

conjectures that firms face costs when changing price. The same cost is incurred whether the firm raises or lowers price. Thus menu costs could cause price to be symmetrically rigid. Hence the findings of this paper suggest that menu costs are not the cause of price rigidity.5

The robustness of these results to various assumptions on consumers expectations was examined by specifying more general autoregressive models to represent the expectations equation. It was found that the general results were not affected.

V. CONCLUSIONS

The empirical results reported suggest that retail price is sticky relative to wholesale price in both the New South Wales meat and livestock market and fresh vegetable market. In both the fresh vegetable and meat and livestock market the empirical results indicate that retail price adjustment is typically more rigid upward than downward.

From a more general perspective, customer market analysis provides a theoretical basis for asymmetric price adjustment. We have presented a model which captures the essence of this theory, by describing its asymmetric effects in terms of upward and downward cost of price adjustment, and emphasising the role of consumer expectations in price setting. The analytic framework developed in this paper has the advantage that it can be implemented empirically. Furthermore, the approach allows de teha t ion of the source of price rigidity as the theory of customer markets predicts downward price rigidity and upward price rigidity occur for different reasons.

TABLE III

New South Wales Maximum Likelihood Estimates

Lamb

Parameter estimates t-ratios Parameter estimates t-ratios

0.8765 0.941 0.1401 0.183

0.9480 16.056 1.1418 14.725

a2 0.4128 1.558 0.4838 2.03 1

a+ -0.3964 -3.645 -0.6699 -9.482

a- -0.3273 -3.728 -0.1804 -0.700

Log Likelihood Value 197.633 205.507

It should be noted, however, that menu cost predicts rigid nominal price, whereas the customer market theories which form the basis of th is paper suggest that price is rigid with respect to customers’ expectation of price.


TABLE IV


Potatoes carrots


a 0 -0.0045 -0.466 -0.0178 -1.162

a1 0.5333 2.65 1 0.788 1 2.198

a 2 0.2814 3.827 0.7783 1.484

s+ -0.6274 -4.361 -0.4273 -2.363

s- -0.1265 -0.408 -0.1590 -1.052

Log Likelihood Value 16.133 12.753

TABLE V


Tomatoes Onions


a 0 -0.0324 -0.848 -0.0215 -0.848

a1 1.6841 3.581 1.1485 3.581

a 2 1.4056 0.983 0.8549 0.983

s+ -0.2300 -1.969 -0.4142 - 1.969

6- -0.0706 -0.322 -0.07 12 -0.372

Log Likelihood Value 18.011 -6.8502


APPENDIX I

Meat Price Data

New South Wales: The data for individual meat products are monthly and cover the period January 1971 to August 1987. The source of the data is the Division of Rural and Resource Economics of New South Wales Agriculture and Fisheries. The wholesale price series is a monthly weighted average wholesale price, in centdkg of composite beef and lamb carcasses sold at Homebush saleyards and adjusted for shrinkage. The retail price series is a monthly composite retail price, in centslkg of beef and lamb at selected retail outlets in Sydney. The procedures for adjusting and weighting these prices are outlined in Griffith, Strong, Green and Freshwater (1990). Each of these series is converted to a real series by dividing them by the consumer price index.

Vegetable Price Data New South Wales: The prices refer to fresh vegetables. The retail prices are average quarterly prices for Sydney, $/kg . The source of the data is the Australian Bureau of Statistics Catalogue 6403.0. The wholesale prices are average quarterly prices collected from the Flemington Wholesale Markets, Sydney, $/kg. The source of the data is Griffith et al. (1991). The data covers the period of the f i s t quarter 1980 to the first quarter in 1990. Each of these series is converted to a real seiies by dividing them by the consumer price index.

Wage Series

New South Wales/meat: To obtain a proxy of the labour costs of retail butchers in New South Wales, weighted average minimum weekly rates payable for a full week’s work (excluding overtime) for adult males in New South Wales in the wholesale and retail trade sector are used as prescribed in awards determinations and collective agreements. The series is monthly and obtained from various issues of the Australian Bureau of Statistics Catalogue 6312.0.

New South Waleshegetables: The average weekly earnings series for males reported in the ak databank was used to obtain a proxy of the labour costs associated with selling fresh vegetables in the New South Wales region. This data is quarterly. Each of these series is converted to a real series by dividing them by the consumer price index.

Consumer Price Index New South Walesheat: A monthly consumer price index series is constructed by interpolation of the quarterly observations from the consumer price index for Sydney. The growth rate of the monthly series in the first and last month in each quarter was adjusted to smooth the series. Results presented are insensitive to extent of smoothing in the interpolation. This quarterly cpi series is obtained from the database dx.

New South Waleshegetables: The quarterly food consumer price index for Sydney is used. This series is obtained from the database dx.

250 AUSTRALIAN ECQNOMIC PAPERS DECEMBER

The data used in the empirical section is based on monthly and quarterly observations. However, it may be that these observations are too lndrequent to be used to test for the presence of price rigidity and more frequently spaced observations may be required. To examine this possibility a Monte Carlo experiment is performed based on the structure of equation (15).

Consider the following equation

y,=a+d,x,+a-(l-d,)x,+u* t = l , ..., 120 W.1)

where u, is assumed to be a normally distributed disturbance, x, is assumed to be a stationary variable and d, is a dummy variable that takes the value one if x, > 0 and the value zero otherwise.

However, x , and yr are not observed, but rather the data is averaged so that x ; and y : are observed where

[ Y, + Y~+I + Yr+z ) 3 Y,* =

Then the equation which is estimated is

(A2.2)

where d ; is a dummy variable that takes the value one if x: > 0 and the value zero otherwise.

Equation (A2.1) was generated for lo00 replications using the GAUSS program and assuming x to be a standard normal variable. Then using this generated data (A2.2) was estimated for a range of a+ and a- values. A sample of the results are presented in Table AI where a+ and a- are the true values and &+ and (Y are the mean estimates of A2.2 from loo0 replications. The results presented in this table illustrate that asymmetry is still evident in the averaged data.

TABLE AI

Monte Carlo Results

a+ a- a+ a'

0.5 0.5 0.49 0.49 0.6 0.4 0.67 0.37 0.7 0.3 0.85 0.25 0.8 0.2 0.98 0.12

1994 TESTING FOR PRICING ASYMMETRlES IN CUSTOMER MARKETS 25 1

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testing for pricing asymmetries in customer markets

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