Shopping hours and price levels in the retailing industry: a theoretical and empirical analysis.

Tanguay, Georges A. ; Vallee, Luc ; Lanoie, Paul 等

I. INTRODUCTION

The debate surrounding shopping laws is very much the same regardless of the country in which it occurs. The traditional objectives of regulating store opening hours can be divided into four categories: (i) to guarantee access to essential goods and services; (ii) to promote and protect a certain way of life; (iii) to protect small businesses; and (iv) to assure a day of rest for everyone. Despite these concerns, the recent trend in Canadian provinces is to extend store opening hours in the retailing industry. For instance, in July 1990, the Quebec government allowed retail stores to stay open on Wednesday nights and on Sundays. The recent deregulation was prompted by changes in lifestyles and increasing constraints on the time people can devote to shopping activities. Perhaps the most significant are that the number of one-parent families is increasing, as is the number of couples in which both spouses work.

There is evidence that changes in opening hours influence the structure of the retailing industry. Morrison and Newman [1983] show that there is a redistribution of sales from small stores to large stores after deregulation. An empirical study by Moorehouse [1984] shows that in the United States those states that strictly regulate store opening hours do have a smaller proportion of large stores. Building on their work, we examine the short-term impact of extended shopping hours on prices at large stores to determine whether consumers have to pay higher prices for greater shopping flexibility. To our knowledge, this issue has not been addressed in the literature.

First, we develop an extension of Morrison and Newman's [1983] theoretical model. Inspired by Becker [1965] and location models pioneered by Hotelling [1929], Chamberlin [1951; 1962], Lancaster [1966] and Salop [1977], we deem the price of a good to have two components: the price itself and the time spent by the consumer to purchase the good. Thus opening hours and store location play a role in the determination of prices. We explore the effect of increased opening hours on the demand faced by stores of different sizes and thus on their price levels.

Among other things, our model predicts that, after deregulation, price levels at large stores will increase because of a demand shift in favor of large stores at the expense of small stores. We then test this prediction using pooled time-series and cross-section data (prices of five products for thirty-one weeks) collected before and after the deregulation of store hours in Quebec on July 8, 1990. The data were collected at three major food stores in the Montreal area. We obtain estimates of price equations using the "pooling" method developed by Kmenta [1986]. The results support our view that prices have increased at large stores since the deregulation.

The rest of the paper is organized as follows. In section II we develop our analytical framework. Section III presents the data and the estimation strategy. Since a price increase may signal an increase in costs rather than an increase in demand, we deal explicitly with this issue in that section of the paper. We discuss the empirical results in section IV, and we conclude in section V.

II. THE MODEL

The following analysis extends that of Morrison and Newman [1983]. A brief initial overview of their work is needed to develop the necessary notation and to set up the problem. In their model, Morrison and Newman make two simplifying, yet standard, assumptions. They assume a single, perfectly divisible, homogeneous commodity and only two types of stores: large and small. Thus consumers choose to shop at small or large stores to minimize the total cost (TC) of purchasing the commodity on a given shopping trip. The total cost includes the cost of the bundle of goods ([P.sub.j]B, where [P.sub.j] is the price per unit at store j and B is the bundle size) a consumer intends to buy and his own valuation of the time needed to travel to the store ([a.sub.j] V, where [a.sub.j] is the travel time and V is the value of a unit of that time). Equation (1) indicates the total cost of buying a given bundle at small (S) and large (L) stores:

(1) [TC.sub.J] = [P.sub.J] B + [a.sub.J] V; j = S,L.

In this model, V is likely to fall with changes in store opening hours (i.e., deregulation), because it will be more convenient for some people to shop during new opening hours rather than at the former restricted hours. Furthermore, in contrast to other authors,(1) we let the price of a unit of the good, [P.sub.j], and travel time, [a.sub.j], vary across stores of different sizes. Since small stores (e.g., corner stores) are generally more accessible than large stores, which are usually downtown or in suburban malls, it is assumed that [a.sub.s] [less than] [a.sub.L]. We also state now that [P.sub.s] [greater than] [P.sub.L], which we will show to hold in equilibrium.(2)

Consumers are thus expected to go to large stores (cheaper but farther away) to benefit from lower unit prices only when the quantity justifies the trip, whereas we expect them to shop at the corner store when buying just a few items. In terms of the model, a consumer will feel indifferent about shopping in a small store or a large store if [TC.sub.S] = [TC.sub.L]. Thus, from equation (1), we can find the critical bundle size, [B.sub.C], for which the full cost at both stores is the same:

(2) [B.sub.C] = V [center dot] ([a.sub.L] - [a.sub.S]) / ([P.sub.S] - [P.sub.L]).

Figure 1 illustrates the consumer's decision. For batch sizes greater (smaller)than [B.sub.C], the large (small) store is preferred. The reduction in V will lead to a downward shift in the two curves. But because travel time is a more important component of the cost of shopping at large stores than at small ones, the shift in [TC.sub.L] will be larger than the shift in [TC.sub.S], moving [B.sub.C] to the left. Thus the volume of sales will increase at large stores and will decrease at small stores.

Next, we present our extension of the Morrison-Newman model. We abstract from the location problems taking as and [a.sub.L]. as given. We also assume that large and small stores are single units that compete across size categories, but not within a size category.(3) Our analysis incorporates the following steps: we derive the demand functions faced by small and large stores, we maximize the profit function of each store, and we solve for the Cournot equilibrium.

Our setting allows us to explore the relationship between changes in shopping hours and prices. Like Morrison and Newman, we assume that, during a given time period, n shopping trips are made and that the size of the bundle of goods bought on each trip is determined randomly.(4) For simplicity, [B.sub.i] is assumed to follow a uniform distribution U[Mathematical Expression Omitted]. Thus the expected sales E(X) of the different stores for each trip made by a consumer are expressed as follows:

[Mathematical Expression Omitted],

[Mathematical Expression Omitted].

Substituting (2) into (3) and (4), and given that there are n shopping trips, we find that the respective demands faced by each store E(Q) are

[Mathematical Expression Omitted]

and it follows that

[Delta]E([Q.sub.S])/[Delta][P.sub.S] [less than] 0, [Delta]E([Q.sub.S])/[Delta][P.sub.L][greater than] 0, [Delta]E([Q.sub.S])/[Delta]V [greater than] 0

and

[Mathematical Expression Omitted]

and it follows that

[Delta]E([Q.sub.L])/[Delta]([P.sub.L]) [less than] 0, [Delta]E([Q.sub.L])/ [Delta][P.sub.S] [greater than] 0, [Delta]E([Q.sub.L])/[Delta]V [greater than] 0.

The objective of each store is to choose its price level so as to maximize profits. The maximization problem of a store of size j is thus

[Mathematical Expression Omitted];

j = S, L,

where [C.sub.J] is the store's average variable cost and is assumed to be constant, and [F.sub.J] is the store's fixed cost. Each store's cost structure is thus characterized by increasing returns to scale or falling average costs, and constant average variable costs.

Substituting (5) into the maximization problem of the small store, assuming Cournot competition, and taking the first derivative of the profit function of the small store with respect to [P.sub.S], we obtain the following reaction function (after simplifying):(5)

(8) [P.sub.S] = 2[C.sub.S] - [P.sub.L].

Similarly, substituting (6) into the maximization problem of the large store, we obtain its reaction function (after simplifying):

[Mathematical Expression Omitted]

Finally, using (8) and (9), we derive the equilibrium price (after simplifying):

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

If we assume that large stores benefit from economies of scale when purchasing products ([C.sub.s] [greater than] [C.sub.L]), it is clear that [P.sub.s] [greater than] [P.sub.L] and that [Delta][P.sub.L]/[Delta]V [less than] 0 and [Delta][P.sub.S] [Delta]V [greater than] 0.

An increase in shopping hours, which leads to a reduction in V, will therefore lead to an increase in prices at large stores and to a decrease in prices at small stores. The reason is relatively straightforward: because of the larger store's lower prices ([P.sub.L] [less than] [P.sub.S]), the flexibility provided by the liberalization of opening hours prompts some consumers to substitute purchases at the small store for purchases at the large store. This increases the demand faced by the large store and reduces the demand faced by the small store. Given the market power of each store, these shifts in demand lead, in turn, to the price changes described above.

III. DATA AND SPECIFICATION OF THE PRICE EQUATION

As a result of data constraints, we concentrate our analysis on the theoretical prediction related to the evolution of price levels at large stores only. However, in November 1992, we questioned thirty-five small-store owners about their reaction to the deregulation. These stores were all located in the same neighborhood as the large food retailers in which we collected our original data (see below). A short questionnaire was distributed to all owners and twenty of them returned it. It is noteworthy that fifteen out of twenty respondents felt that deregulation had a negative effect on their business, namely that the number of their customers had decreased. Out of these fifteen owners, ten reacted by reducing prices or introducing rebates. Furthermore, eight respondents noticed that other corner stores closed their doors in the immediate neighborhood following deregulation. Of those, all claimed to have benefited from their rivals' misfortune.(6) Altogether, this partial evidence supports our theoretical implication concerning the pricing behavior of small stores. Furthermore, Cloutier [1992] reports that one of the most important corner store chains in Quebec has lost 6 percent of its sales since deregulation. This suggests that quantities sold or prices have fallen (or a combination of both phenomena) in small stores.

These results are consistent with our conclusion and also constitute indirect evidence that the price increase in large stores following deregulation should be attributed to an increase in demand at large stores rather than to an increase in costs. Other evidence also suggests that the empirical findings presented below are due to an increase in demand rather than an increase in costs (often cited as an alternative hypothesis to explain a price increase in large stores following the extension of opening hours). We will deal explicitly with this issue before proceeding with the estimation.

Ingene [1986] and Ferris [1990] argue theoretically that deregulation should lead to higher operating costs for stores and thus to higher prices. Yet Kay and Morris [1987] have found, through a simulation, that costs may not increase. Moreover, before deregulation in Quebec, Desormeaux, Nantel and Amesse [1988] predicted that supermarket operating costs would increase by a few percent, but not by enough to cause prices to increase. The authors argue that a greater volume of sales at these stores might even reduce average costs.

The most common concern is that the extension of opening hours increases the total number of hours worked (especially overtime hours) and thus leads to higher costs. However, Table I shows that deregulation (which occurred in July 1990) did not increase the number of overtime hours worked by employees.(7) The pattern of overtime hours clearly remains constant following deregulation and is very similar to the pattern of overtime hours of the previous year at the same period.

Further discussion with specialists in the food retailing industry allowed us to understand better why deregulation did not increase the number of overtime hours. In their opinion, the total number of hours did not increase, but the distribution of working hours was changed among existing employees. Because of the higher number of customers on Sundays, some other periods during the week are now less busy, and it is not necessary to have as many workers as before during the week. Moreover, since the law requires that there be no more than four employees present in the store on Sundays, redistribution of hours without granting extra overtime was possible most of the time. When it was difficult to get employees to work on Sundays, part-time employees were hired. Since they were most often students working for lower wages, they contributed to a reduction in the average hourly salary rather than an increase.

TABLE I

Average Number of Overtime Hours per Week in Quebec Food Stores

 Before Deregulation After Deregulation
 1989 1990

August .1 .1
September .2 .1
October .2 .1
November .2 .1
December .3 .4

 1990 1991

January .2 .1
February .2 .1
March .1 .2
April .2 .2
May .2 .2
June .2 .2
July .2 .2

Source: Statistics Canada, Employment, Earnings and Hours,
Catalogue no. 72-002.

We also asked these specialists if they thought it was more costly to stay open on Sundays. Their opinion suggested the opposite, that it was expensive to close on Sundays. Since most operating costs other than wages (electricity, insurance, maintenance, etc.) are fixed and independent ofthe number of working hours, the average fixed costs per unit sold are reduced by opening on Sundays if sales increase (at worst they stay constant). Moreover, opening on Sundays allows stores to manage their stocks better, especially those of highly perishable goods like fruits and vegetables. Now that stores are open on Sundays, less produce is wasted and last minute sales are less frequent (i.e., by staying open on Sundays, managers do not have to sell products at very low prices on Saturday afternoon to get rid of whatever could not last until Monday morning).

Finally, the following theoretical argument is also appealing. Since cost increases usually reduce, whatever the industry structure, overall profits for every individual firm, why would large stores lobby so intensively (see for instance Cloutier [1992]) for the extension of opening hours? A logical answer must be that the benefits (the demand effects) outweigh the costs (the cost effects). In fact, this has been confirmed by Desormeaux, Nantel and Amesse [1988]. On the basis of these findings and arguments, we feel confident that any price increase in large stores following the extension of shopping hours reflects an increase in demand rather than in costs.

Our data-collection process among large stores was inspired by Glazer [1981]. The prices (per kilogram) of five different goods were collected at weekly intervals from April 30, 1990 to November 26, 1990 at three major food retailers in the same Montreal neighborhood. These three retailers represent the three largest food store chains in the province. The deregulation of opening hours took effect on July 8, 1990. The analysis period is intentionally short so as to capture, in conformity with our model, short-run effects and not changes in the industry's structure, such as the entry of new firms. As Quebec's food market is dominated by three supermarket chains and as each store belongs to one of the chains, we assumed that its pricing behavior reflects that of the other stores in the same chain, and thus limited our sample to these three stores.

The selected goods were bananas, red apples, yellow onions, lean beef and fresh chicken. These goods were chosen because they are sold in large volumes, they were available for the entire study period and because, as suggested by Glazer [1981], their prices can be altered easily. It is important to stress that the quality of each of the five products was homogeneous throughout the relevant period, and each product's category and variety remained the same during the experiment at all stores.

Our sample comprises 155 observations, or five goods over a period of thirty-one weeks. The price series for each good is based on the weekly average of price charged at the three different stores. Two reasons motivated this choice. First, we are not interested in explaining price variations across large stores, but in determining general price trends at these stores before and after deregulation. Second, as some data were not available for certain weeks before deregulation, the averaging process allowed us to account for these missing values.(8)

To test the implication of our theoretical model, the following linear price equation was estimated:

(12) Ln[PRICE.sub.it] = [[Beta].sub.0] + [[Beta].sub.1] [center dot] BANANA

+ [[Beta].sub.2] [center dot] APPLE + [[Beta].sub.3] [center dot] ONION

+ [[Beta].sub.4] [center dot] BEEF + [[Beta].sub.5] [center dot] Ln[COST.sub.it]

+ [[Beta].sub.6] [center dot] [H.sub.1] + [[Epsilon].sub.it],

where [[Epsilon].sub.it] is a random error term.

The variable Ln[PRICE.sub.it] is the natural logarithm of the price per kilogram of product i at time t. As in Glazer [1981], BANANA, APPLE, ONION, and BEEF are dummy variables for each product under study intended to capture products' specific effects (CHICKEN is the default product). In contrast with Glazer, however, we were able to obtain the cost per kilogram of each product. In the specification, we use the natural logarithm of this variable: Ln[COST.sub.it]. Given the large seasonal price variations of these products, we view the inclusion of this variable as essential to avoid misspecification of the equation. Moreover, our model strongly suggests that this variable must be included in the equation; recall equation (10). The expected sign of its coefficient is positive. If large retailers benefit from some market power, increases in the average variable cost will not be passed on to consumers in their entirety, and we should expect the coefficient of this variable to be smaller than one. [H.sub.1] is a dummy variable equal to one for each observation after July 8, 1990, and zero otherwise. The sign of the coefficient of this variable should be positive if prices increased upon deregulation.

We estimate equation (12) using a generalized least-squares procedure based on the cross-sectionally heteroscedastic and time-wise autoregressive model presented in Kmenta [1986, 616-25]. In a previous investigation, one regression was run for each product, using the seemingly unrelated regression method suggested by Zellner [1962], and the results were very similar to those presented here.(9)

IV. EMPIRICAL RESULTS

The results are presented below:

Ln[Price.sub.it] = 0.520 + 0.069 BANANA (4.66) (0.44)

+ 0.351 APPLE + 0.090 ONION (3.19) (0.41)

- 0.141 BEEF + 0.851 Ln[Cost.sub.it] (-3.04) (8.40)

+ 0.047 [H.sub.1] (2.72)

[Mathematical Expression Omitted] = .968 (t-ratios are in parentheses).

As predicted by the model, there is an increase in prices after deregulation.(10) This can be seen by the positive and significant coefficient of the dummy variable [H.sub.1]. The increase is about 5 percent. The coefficient of the cost variable LnCOST has the expected sign and is statistically significant. Interestingly, a change in cost is not passed on to consumers in full, since the coefficient of LnCOST is smaller than one. As already stated, this is consistent with each store having some market power over its customers. Finally, the product dummies indicate that there are specific product effects. It appears that the pricing of beef and apples is different from the pricing of onions, chicken and bananas for which another pricing scheme seems to be used.

V. CONCLUSION

This paper has examined price changes occurring at retailers of different sizes after deregulation of store opening hours. First, we presented a theoretical model to explore the effect of extended shopping hours on the prices charged by stores of various sizes. Notably, the model predicted that price levels at large stores would increase after deregulation of shopping hours. This prediction was then tested with a set of pooled time-series and cross-section data collected before and after the deregulation of opening hours in the province of Quebec. The results support the view that prices have increased at large stores since deregulation, suggesting that consumers have to (and are willing to) pay for greater shopping flexibility.

Other aspects of this matter deserve further research, in particular the potential entry of new firms attracted by higher prices, and the change in the optimal capacity of stores as a result of better distribution of sales over time after deregulation.

1. Ingene [1986], Kay and Morris [1987] and Ferris [1990].

2. We also expect this inequality to hold because small stores have a local monopoly during those hours when large stores are closed. See Nooteboom [1982] for further discussion.

3. Extensions relaxing these assumptions might prove to be interesting, but are beyond the scope of this paper. We also believe they would not change the nature of our analysis. To our knowledge, there do not exist models capable of taking into account both across- and within-size competition. The choice of which type of competition model to focus on has thus been determined by the current debate about whether allowing large stores to open on Sundays will favor them at the expense of smaller ones.

4. We also assume that the total number of shopping trips, as well as their distribution, is determined exogeneously.

5. Tanguay et al. [1992] show that the necessary second-order conditions are satisfied for the maximization problems of small and large stores.

6. One should also note that, often, those who did not suffer from deregulation or lower prices also benefited from the closing of neighboring small stores.

7. Data on the average number of overtime hours per week in Quebec food stores are published on a monthly basis by Statistics Canada. These data reflect the situation prevailing in stores of all sizes. However, given that large stores are highly represented in the survey used to produce these data, an increase in overtime hours in large stores would be reflected in the data even if overtime hours were reduced in small stores.

8. For one store, the price series were not available for all weeks in May 1990. The mean and standard deviation of the different variables are available in Tanguay et al. [1992].

9. Complete results are available upon request.

10. Tanguay et al. [1992] show that this result is robust to the choice of the specification of the equation (e.g., linear PRICE and COST instead of logarithms). Again, complete results are available upon request.

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GEORGES A. TANGUAY, LUC VALLEE, and PAUL LANOIE, Institut d'economie appliquee, Ecole des Hautes Etudes Commerciales, 5255, avenue Decelles, Montreal, H3T 1V6. Financial support from the Fondation du Pret d'Honneur of the Societe St-Jean-Baptiste and the Fonds FCAR is gratefully acknowledged. The authors wish to thank Pierre Lasserre for his helpful comments and two anonymous referees for helping to improve the paper substantially.