Forecasting Sales for a Retail Firm: A Model and Some Evidence. Russell J. Lundholm Sarah E. McVay. University of Michigan

Transcription

1 Forecasting Sales for a Retail Firm: A Model and Some Evidence By Russell J. Lundholm Sarah E. McVay University of Michigan October 2003 Note to seminar participants at the University of Waterloo: his paper is extremely preliminary. We are still collecting more data, still working on the model and still estimating more regressions. Please view this as a progress report rather than a completed paper. We welcome all your comments.

2 Introduction Every financial statement forecast begins with an estimate of future sales. ypically the sales estimate is then combined with a margin forecast to estimate future income and combined with a turnover forecast to estimate future assets. Although the sales forecast is the starting point for the entire financial statement forecasting exercise, there is surprisingly little published guidance on how one should go about making this estimate. he purpose of this paper is to present a reasonably general sales forecasting model and to demonstrate its use in the retail sector. he model distinguishes between sales growth that arises from growth in the asset base (e.g. opening new stores) and sales growth that arises from increased sales from existing assets (e.g. comparable store sales growth). he model also accounts for the predictable change in sales that will result as the asset base matures. Besides describing how sales are generated in a retail firm, we document that our model is a surprisingly accurate predictor of retail sales. We develop and estimate our model in the retail sector for a number of reasons. First, the underlying sales-generating assets -- the stores -- are clearly identified for retail firms. Virtually every retail firm discloses the number of stores it operated during the year and many forecast the number of new stores they anticipate opening in the next year. Second, retail firms generally disclose the comparable store sales growth for the year, defined as the percentage growth in sales from stores that have been open for at least two full years. his gives us the two main pieces of the puzzle in our model the number of new sales-generating units and the growth in sales from existing units. he question is how should these two drivers of future sales be woven together? Finally, we focus on the retail sector because it is arguably the most closely watched barometer of consumer spending. Since personal consumption expenditures make up about two thirds of the US Gross Domestic Product, sales in the retail sector are a barometer for the whole economy. 1

3 While our model is developed with a retail firm in mind, sales forecasts for many other types of firms will have a similar flavor. Forecasting sales growth at a pharmaceutical company involves forecasting the sales growth from existing drugs and the sales growth from introducing new drugs to the market. Forecasting the sales growth for a cruise line company involves forecasting increases in fares or passenger counts on existing ships and forecasting the revenues from newly-launched ships. he retail industry offers us perhaps the best example of this type of problem because the salesgenerating units are clearly identified and relatively homogeneous. here is a growing financial statement analysis literature that examines how profit margins and asset turnover ratios evolve over time. Nissim and Penman (2001) and Fairfield and Yohn (2001) document reversion in these ratios to an economy-wide mean, and Soliman (2003) shows that an industry statistic is a more predictive mean reversion target. Penman and Zhang (2002) and Fairfield and Yohn (2001) also consider how past changes in these ratios predict future changes. Collectively these results characterize the future profitability and asset investment necessary for a given level of sales activity. But to use these results for valuation, or to forecast actual income flows or asset balances, the level of future sales activity must also be forecast. he only result related to predicting future sales is in Nissim and Penman (2001), who show that percentage sales growth tends to mean revert very quickly. Another related literature uses non-financial metrics to predict future earnings. Besides forecasting earnings rather than sales, these papers differ from our study in how closely related the non-financial measure is to the underlying sales-generating asset. For example, Amir and Lev (1996) study the product market size and market penetration in the wireless industry; Chandra, Procassini and Waymire (1999) and Fargher, Gorman and and Wilkins (1998) study shipment data in the semiconductor industry; Rajgopal, Shevlin and Venkatachalam (2003) study order backlog, Ittner and Larcker (1998) study customer satisfaction measures and rueman, Wong and Zhang 2

4 (2000) study web traffic measures. None of these measures distinguish between changes in the financial performance due to changes in existing investments and changes due to new investment. 1 Our purpose is to present a reasonably general model for forecasting sales growth in the retail industry and to test the validity of various restrictions on the model that might lead to more parsimonious representations. We also illustrate the model s flexibility to adapt to different types of retail environments. For instance, the model can distinguish between retail firms who enjoy fad status, so that their new stores earn considerably more than their more mature stores (e.g. Whole Foods), and retail firms that take a long time to reach maturity, so that their new stores earn considerably less than their more mature stores (e.g. JC Penney). Our goal is also to develop a model that can be used to forecast sales growth for a typical retail firm in a typical year. One problem we must confront is the extreme limit on the number of observations in our regressions. he estimated sales-generating rates are unique to each firm, ruling out cross-sectional estimation, and the typical retail firm has only a limited time series of annual data. Consequently, we are forced to estimate our model on relatively little data the typical firm has only nine observations. For this reason we place heavy emphasis on developing a model with few estimated parameters. Despite this constraint, the median absolute residual error for the median firm is only 2.1% of sales. In contrast, using the estimated mean reversion in sales growth (as in Nissim and Penman 2001) results in an error that is 5% of sales. 2 We also discuss how to use our model for out-of-sample prediction and examine its out-ofsample forecast errors. A common voluntary disclosure for a retail firm is to estimate the number 1 In other related research, Nagar and Rajan (2001) examine the relation between a non-financial measure and future revenue. hey show that certain quality measures at 11 plants of the same company have predictive power for future revenue beyond past sales and other financial measures. Also, Francis, Schipper and Vincent (2003) show that comparable store sales in the restaurant industry are related to market prices. 2 Improving the sales forecast by just a few percent can have enormous consequences. As an example, if a firm had an expected constant ROE of 20%, a cost of equity capital of 10% and an expected perpetual growth rate of 5%, its marketto-book ratio would be 3 (which is close to the current economy -wide value). If the growth rate was raised to 6% the firm s value would increase 17%; if the growth rate was lowered to 4% the firm s value would decrease 11%. 3

5 of new stores it will open in the following fiscal year. Our model shows exactly how to incorporate this disclosure into a sales forecast. Unfortunately, firms rarely forecast their comparable store growth rate, so this must be estimated. We develop a simple model based on mean reversion in the firm s own comparable store growth rate and the advance monthly retail sales data provided by the US Census Bureau each month. Putting these two forecasts together with an estimate from our model, we generate out-of-sample forecasts that are almost as accurate as Valueline and IBES revenue forecasts. he Model Our model of sales for a retail firm requires that we distinguish between three classes of stores. he notation is as follows: #N t = number of new stores opened in year t (i.e. new stores) #M t = #N t-1 = number of new stores opened in year t-1 (i.e. mid stores) #D t = number of stores closed in year t (i.e. dead stores) #O t = number of stores open for at least 2 years and open in year t (i.e. old stores). his notation implies two equalities concerning the numbers of different types of stores: 1) #O t = total number of stores at year end - #N t - #M t and 2) #O t = #O t-1 + #M t-1 - #D t. he average rate of sales in the fiscal year per store for each of the three classes of stores is denoted as NR t = the average sales/store rate for new stores in year t MR t = the average sales/store rate for the mid stores in year t OR t = the average sales/stores rate for the old stores in year t. With this, total sales in year t are given by Sales t = #O t OR t + #M t MR t + #N t NR t. (1) 4

6 Besides asserting that sales are generated by stores, (1) is a tautology because the sales-generating rate from each of the three classes of stores can change each period. 3 Later we impose various restrictions on the sales-generating rates that allow these rates to be estimated. he model uses three different classes of stores for a few different reasons. First, for most retail firms new stores generate sales at very different rates than old stores. Consumers may take some time to discover the new store and change their shopping habits, causing the new store sales to lag old store sales. Alternatively, the new store may blitz the market with advertisements and promotions, or may be a retailing fad, causing new store sales to exceed old store sales. And, most simply, the new stores are open only half of the fiscal year, on average, compared to the full year for old stores. he mid stores, which are last year s new stores, serve two purposes. First, as shown below, this category of store is necessary in order to precisely capture the notion of comparable store sales growth. Second, by comparing the estimated mid store rate to the estimated old and new store rates, we learn something about the speed with which the firm s stores reach maturity or, alternatively, enjoy a new store honeymoon period. he comparable store growth rate C t is the percentage increase in sales from stores that were open at the beginning of the prior fiscal year and are currently still open. Expressing this in terms of our model gives # OtOR t C t = 1. (2) (# O # D ) OR + # M MR t1 t t1 t1 t1 3 We could insert a constant term in (1) to capture sales that are not related to stores, such as internet sales. Later, however, we will estimate the differenced version of this equation so a constant would simply cancel out. 5

7 he numerator #O t OR t is the sales earned by the stores that have been open for two years, and are still open. he denominator is the sales these same stores earned a year earlier. o compute the sales from these stores in year t-1, recall that #O t = #O t-1 + #M t-1 - #D t and consider the sales that each of these types of stores generated in year t-1. here were #O t-1 old stores that were open a full year in t-1, but #D t of these stores were closed in the current year; the net of these stores generated sales at the old rate of OR t-1 in year t-1. Note that this assumes that the stores closed in the current year come from the pool of old stores in year t-1, and that they were closed at the beginning of the year. In addition, #M t-1 of the stores in the #O t total are stores that transitioned from generating sales at the mid rate MR t-1 in year t-1 to the old rate OR t in year t. Note from (2) that, even if the old store rate isn t changing over time, if MR t-1 < OR t-1 then a firm could show healthy same store growth rates as long as they keep opening new stores. As the young stores mature from earning MR t-1 to earnings OR t the comparable growth rate will be positive. However, when new store openings slow there will be precipitous drop in the comparable store growth rate. One simplification of the model that we will consider adds the constraint MR t-1 = OR t-1. hat is, after the end of the fiscal year in which a store opens, it immediately generates sales at the old store rate. his implies that ORt C t = 1. (3) OR t1 Equation (3) is the most obvious expression of same store sales growth although it is clearly a simplification. he simplification is unreasonable for two different types of stores. For stores where consumers make large but infrequent purchases or stores that require consumers to change 6

8 their shopping habits, it may well take more than a year to reach maturity, so that MR t-1 < OR t-1. Alternatively, some stores enjoy a fad status in the early months and this might extend beyond the store opening year s fiscal end, making MR t-1 > OR t-1. In our empirical tests we document some examples of store types that fit each of these descriptions. However, for much of our analysis we will use the simplifying assumption that MR t-1 = OR t-1. Because we estimate our sales model for each firm individually over time, the error term in a levels regression is unlikely to be stationary. For this reason we take first differences: Sales t = #O t OR t - #O t-1 OR t-1 + #M t MR t - #M t-1 MR t-1 + #N t NR t - #N t-1 NR t-1. (4) At this point our model is still a tautology: each sales-generating rate is allowed to change every period so that, by definition, equation 4 holds. In order to estimate the different sales rates we need to impose some restriction over time. A tempting restriction is simply to assume the three rates are constant over time. Unfortunately this assumption is incompatible with the fact that firms rarely report comparable store growth rates that are zero each period. Ignoring the complications of mid store rates versus old store rates, (3) shows that the comparable store growth rate is the change in the sales-generating rate for old stores over time; the very thing we were tempted to assume was zero. he trick in the estimation will be to use the historical comparable store growth rate for the firm to control for the known changes in the sales-generating rates over time so that we can estimate an underlying rate that is stable. Denote by the most recent year in the dataset for a particular firm. he necessary feature of any restriction we impose on the sale-generating rates is that it allows us to rewrite (4) for every period in terms of OR, MR and NR. he coefficients on these sales rate parameters are the 7

9 independent variables in the regression and, as we show next, they change to adjust for how far back in time the observation is from time. Our most general models are complicated because they estimate separate sales-generating rates for old stores, mid stores and new stores. [Insert models 1 and 2 here -- still a work in progress!] Model 3 greatly simplifies the regression by assuming that 1) MR t = OR t and 2) NR t = NR t-1 (1+C t ). Assumption 1 says that after the fiscal year in which the store opens, it immediately earns at the same rate as an old store. his in turn implies that OR t = OR t-1 (1+C t ), as discussed above. Assumption 2 says that the earn rate on new stores changes in the same way as the earn rate on the old stores; it too grows at the comparable store growth rate for the old stores. he idea behind assumption 2 is that the success of new stores is probably related to the success of the old stores. If the products being sold in the old stores are generating increasing sales dollars then it is likely that the new stores will enjoy similar increases in their sales rate. Using these two assumptions, we get the following sequence of sales changes: In the final year, Sales = (# O + # M ) OR (# O 1 + # M 1) OR 1+ # N NR # N 1NR 1. (5) We can rewrite (5) in terms of OR and NR using assumptions 1 and 2 to get 8

10 Sales (# O + # M ) (# N 1) = (# O + # M ) OR + (# N NR C. (1 ) (1 + C ) Note the different sources of changes in sales in year. Both terms are close to the change in the number of stores, either new stores in the second term or old plus mid stores in the first term. But for both terms the number of stores in year -1 is deflated by one plus the comparable store growth rate for year. By adjusting the beginning number of stores down using C like a deflator, the net change in brackets captures both the growth in the number of units and the growth in the sales-generating rate of each unit. It effectively treats 100 stores at the beginning of the year, who grow same-store sales by 10%, as having 100/(1+.10) = stores at the beginning of the year. More generally, for year -, where counts back in time to the first year of data for an individual firm, we have Sales = ( 1+ C )(# O + # M ) (# O 1 + # M 1) (1 + C )# N # N 1 OR + NR. i= (1 + C ) i i= (1 + C ) i he numerator for each term captures the change in sales due to changes in the number of stores of each type and the comparable store growth rate for that year. he denominator of each term adjusts the data each year to be stated in terms of year sales dollars. Note that we could move the denominator to the LHS of the equation and we would be inflating the historical data so that every observation is stated in terms of year sales dollars, given the firm s history of comparable store growth rates. In this way we control for the known variation in the OR t and NR t series and can estimate the parameters OR and NR. 9

11 Model 4 is a minor variation on model 3. Instead of assuming that the new store rate changes at the same rate as the comparable store growth rate, this model assumes that the new store rate is constant over time. hat is, 1) MR t = OR t and 2) NR t = NR t-1. he best argument for a constant sales-generating rate for new stores is that it is a simple assumption. We offer it as an alternative because the assumption in model 3, that the rates for both types of stores change at the same rate, might be grossly in error. For example, it could be that whenever a retail firm s old stores start suffering declining sales, so that their comparable growth rate is negative, they introduce new stores with a fresh design and new product ideas such that a new store earns about the same amount over time even while the old store rate is declining. Following the same derivation as in model 3 with this one slight variation gives Sales = ( 1 + C )(# O + # M ) (# O 1 + # M 1) # N # N 1 OR + NR. i= (1+ C ) i i= (1+ C ) i he only difference between models 3 and 4 is in the second term where model 3 adjusts the number of new stores in year - up by (1+C - ) to capture the assumed increase in the new store rate and model 4 does not. Besides the 4 models derived above, we measure the explanatory power and forecasting accuracy of a number of ad hoc approaches to sales forecasting. hese models serve as benchmarks to measure the relative improvement that comes from modeling the effects of different types of 10

12 stores and the comparable store growth rate. Model 5 assumes that next year s sales equals this year s sales: Sales - = 0. Model 6 is similar to model 5 except that we estimate the intercept α: Sales - = α + ε. Nissim and Penman (2001) document the mean reversion rate in each decile of sales growth in a large sample of firms. o use this idea for model 7 we sort the cross-section of firms in our sample into deciles of percentage sales growth in year t-1 and measure the median sales growth for each decile in year t, denoting it as SG j j=1 to 10. his gives Sales - = Sales --1 SG j. he next three models represent the crass empiricist view. Each estimates a regression of the change in sales on the changes in the different types of stores and each is estimated firm by firm, much like the derived models 1 though 4. None of the models take the comparable store growth rates into account. his means that they treat the estimated sales rate as a constant even though it is changing over time. Model 8 lumps all types of stores together, estimating the average sales rate per store: Sales - = β[(#o - + #M - + #N - ) (#O -1 + #M -1 + #N -1 )] + ε -. Model 9 distinguishes between new stores and old plus mid stores, much like model 3 above: Sales - = γ 1 [(#O - + #M - ) (#O -1 + #M -1 )] + γ 2 [#N - #N -1 ] + ε -. 11

13 Model 10 estimates a separate rate for each type of store, much like model 1 above: Sales - = η 1 [#O - #O -1 ] + η 2 [#M - #M -1 ] + η 3 [#N - #N -1 ] + ε -. he Sample o generate out-of-sample forecasts we need a sample of firms that disclose their estimated number of store openings/closings in the next fiscal year. While this is a common disclosure in the retail industry, it is not a required disclosure. Rather than randomly searching press releases and 10-K filings, we begin with the 104 retail firms on Valueline that have a store forecast in 2001, reasoning that Valueline probably got this information from the firm. In addition, to estimate our model for each fiscal year we need the number of stores at year end and the comparable store growth rate. o obtain this information we search each firm s 10-K filing for the following information: 1) number of stores at year end 2) stores opened during the year 3) stores closed during the year 4) expected number of store openings/closings for the following year 5) comparable store growth rate. In the vast majority of cases the number of stores at the end of the year and the comparable store growth rate for the year where available in the MD&A section of the 10-K. Firms disclosed the number of stores openings and closings separately 76% of the time. If this information was not disclosed we computed the change in the ending number of stores and, if the difference was positive we assumed this was the number of stores opened and none were closed, if the difference was negative we assumed this was the number of stores closed and none were opened. 12

14 We also require that the firm s fiscal year end doesn t change between 1990 and 2002 and has a minimum of six years of sequential annual data in order to estimate our model. his results in a sample of 78 firms and 691 firm-years with sufficient historical data to estimate the models discussed earlier. Of these 78 firms, 68 firms and 239 firm-years disclosed the expected number of store openings/closings in at least one year; these observations are used for out-of-sample forecasting tests. able 1 gives the list of sample firms and their sales and numbers of total stores as of fiscal able 2, panel A gives descriptive statistics for the sample. he median firm has sales of $ million and annual sales growth of 11.8%. Median comparable store sales growth is 4%, meaning that a large component of annual sales growth is due to opening new stores. he distribution of industry sales growth is similar to the comparable store sales growth, where the industry sales are taken from the US Census Bureau s Advance Monthly Sales for Retail rade (discussed in more detail later). In terms of stores, the median firm has 498 total stores, opens 44 new stores and closes 4 stores. here are a few very large firms in the sample, such as Walmart, that skew the sales and store count distributions. We estimate our model firm by firm, however, so the differences in size across firms should not influence our statistics. able 2, panel B gives the correlations between our main variables. As one might expect, sales growth is negatively correlated with the number of closed stores and positively correlated with the number of new stores opened. Sales growth is also negatively correlated with the total number of stores, implying that larger firms have lower sales growth than smaller firms. he comparable store growth rate shows a similar pattern. All the positive correlations between the numbers of different types of stores shown in the lower part of table 2 are driven by size; large firms open more stores, close more stores and have more stores. 13

15 Results for In-Sample Estimates We begin by estimating the four versions of our model (models 1-4) and the six benchmark models (models 5-10) using the entire history of available data. Each model is estimated separately for each firm based on a minimum of six observations per firm, and a median of nine observations per firm. he empirical specifications for each model are exactly as given in the model section. In particular, the dependent variable is the change in sales (in millions) each year, the independent variables are the derived changes in the number of stores in each category, adjusted for the historical and current comparable store growth rates, and there is no intercept in the regression. able 3 gives summary statistics from the in-sample regressions. Beginning with model 3, the median estimated sales rate for old+mid stores (i.e. old stores and mid stores) is $4.376 million per store and for new stores is $2.233 million per store. Given that new stores are open, on average, only half a fiscal year, the fact that the new store rate is roughly half the old+mid store rate implies these two types of stores fundamentally generate sales at about the same daily rate. But looking at the median rates across the sample can be misleading. Later we give examples of firms with radically different new store rates and old+mid store rates. he median significance of the estimated rates for model 3 is impressive given the extremely small sample in each regression. In addition, the estimated old+mid stores sales rate is positive in 77 of the 78 regressions (99%), the estimated new store rate is positive in 75 of the 78 regressions (96%), and the median adjusted R 2 is 92.9%. 4 Finally, given our goal of forecasting future sales changes, we also compute for each firm the median absolute residual error scaled by total sales for the year. he median of this statistic across our 78 firms is.020, or 2% of sales. 4 he Adjusted R 2 for a model without an intercept is slightly different from the standard definition. It is computed as the squared sample correlation between the actual values and fitted values from the regression (see Greene, page ). In addition, although we differenced the sales time series to control for non-stationarity, it is still possible that growth in sales might cause heteroskedastic errors. We test this hypothesis and reject homoskedasticity in only 1 of 78 cases at the 0.10 level. 14

16 Recall that the only difference between model 4 and model 3 is that model 4 assumes that the new store sales rate is constant over time will model 3 assumes that it changes with the comparable store growth rate. Given this small difference, it isn t surprising that the results for model 4 are very similar to model 3. Because model 3 has a slightly lower median p-value on the new store rate, a slightly higher number of positive coefficients on the old+mid store rate and has a slightly higher adjusted R 2, we will focus on model 3 in our comparisons with the benchmark models. However, as seen below, there are individual firms where model 4 is definitely superior to model 3 (still to be done). Model 3 easily beats the six benchmark models shown in the lower half of table 3. Of the three benchmark models that don t use the number of stores in their estimation, the model that estimates a constant percentage change in sales (model 6) has the lowest median residual error. But, at 4.8% of sales, this median error is more than twice as large as the error for model 3. he three benchmark models that estimate coefficients on changes in the number of stores, but do not take into account the movement between store types or the comparable store growth rates, show improvement over the other benchmark models, but are still worse than model 3. Model 8 regresses the change in sales on the change in the total number of stores, resulting in a 4.4% residual error. Model 9 regresses the change in sales on the changes in the number of old+mid stores and new stores, resulting in a 3.6% residual error. Model 9 is most comparable to model 3, yet the adjusted R 2 is still more than 10% lower than the R 2 on model 3 and the median residual error is 3.6% of sales, more the 70% greater than model 3 s residual error. For a statistical comparison between model 3 and model 9, we compute the median absolute residual error (scaled by sales) for each firm using each model. We then conduct a signed rank test of difference between the two models and find that model 3 has significantly lower errors than model 9 at the.0001 level. By taking into 15

17 account the change in different types of stores and how the comparable store growth rate affects each store type, model 3 yields significantly lower errors. he median coefficients, adjusted R 2 s and residual errors are useful statistics for assessing the overall accuracy of the different models but they give little insight into the nuances of the model at the individual firm level. able 4 gives the individual firm estimates of the new store rate and the old+mid store rate. Both estimates are usually significant at the.10 level, suggesting that the model is sufficiently flexible to work well for most firms, despite the fact that the typical regression has only nine observations. When examining the individual company estimates keep in mind that a new store is probably only open half a year so, even if the new stores and old+mid stores immediately have the same daily sales rates, the estimated annual new store rate will be half the old+mid rate. With this as a benchmark, we test the hypothesis that the new store rate is half the old store rate and cannot reject this hypothesis at the.10 level in 50 of the 78 companies. However, for 28 of the 78 firms, there is a significant difference between the new store rate and half the old store rate (as identified by the superscript F by the R 2 ). For these firms it is important to estimate separate sales rates for the two types of stores. Consider a few examples that illustrate the importance of estimating different new store rates and old+mid store rates. As a benchmark, he Gap earns $3.69 million per old+mid store and $1.81 per new store, so the new store rate is very close to half of the old+mid store rate (as shown in table 4). Assuming that the average new store is opened half way through the fiscal year, this implies that he Gap has neither a sales frenzy when they first open nor a long maturity period before their stores are at steady state. In contrast, grocery stores typically open with heavy advertising and promotions, causing the new store rate to far exceed half the old+mid store rate. Albertsons, Safeway and Whole Foods all show this effect in our sample; for each of these companies the new store rate is significantly higher than half the old store rate. he most extreme example of a new store effect is Bed, Bath and Beyond, whose new 16

18 store rate of $19.98 million per store is more than 5 times as large as the old+mid rate of $3.66 million per store. At the other extreme, companies whose old+mid rate is significantly higher than twice the new store rate are slow to mature, possibly because their stores sell products that are infrequent purchases or that require changes in customer shopping habits. In our sample, weeters, who sell high-end stereo equipment, might be the best example. heir old+mid rate is $5.47 million and their new store rate is only $0.72 million. Other examples in our sample are JC Penney and Ross Stores, both large department stores who take some time to reach maturity. In sum, our model of sales growth, with the model 3 restrictions that 1) the mid store rate equals the old store rate and 2) the new store rate changes with the comparable store growth rate, is the best model for describing changes in sales across our sample of retail firms. It is the most parsimonious of the four models we present and it fits the data significantly better than the ad hoc benchmark models. In the next section we discuss how to use this model to make out-of-sample forecasts and examine the resulting out-of-sample forecast accuracy. Results for Out-of-Sample Forecasts o use the model to forecast future changes in sales, we need three things. We need a forecast of the number of stores the firm will open or close in the next year, we need a forecast of the comparable store growth rate for the firm in the next year, and we need to estimate the salesgenerating rates for the different categories of stores from a subset of the data prior to the year being forecasted. In our sample 68 of the 78 firms disclosed their expected number of store openings/closings at least once during the sample period. In 2002, 65 firms disclose this information, but it becomes less common the further we go back in time. We also use five years of observations to estimate the model, leaving 239 out-of-sample forecasts between 1997 and

19 he most difficult ingredient to find for our model is an estimate of the comparable store growth rate for the firm in the next year. While firms will sometimes make predictions for the next month or quarter (e.g. Home Depot), it is rare to make such a prediction for a full year into the future. In table 5, we assume that the comparable store sales growth rate is equal to the previous year s rate. We then improve on this assumption in later tables. Recall that the in-sample median residual error on model 3 is 2.0% of sales, as shown in table 3. Because this error is after the regression used the realized store counts and comparable store growth rates, and optimally fit the sales rates coefficients, the 2.0% error rate is a lower bound on the out-of-sample forecast error. Not surprisingly, the out-of-sample median forecast error increases to 4.6% in table 5, where the firm s past comparable store growth rate is used as the forecast for the next year s rate. hree other benchmarks for model 3 are the errors that result when the model estimates the sales rates on five prior years of data but then uses perfect foresight for the number of store openings/closings, the comparable store growth rate, or both. hese are presented in panel B of table 5. Interestingly, perfect foresight with respect to the number of store opening/closings does not significantly reduce the error for model 3. his suggests that when managers forecast store openings or closings, these forecasts tend to be accurate. However, when the model uses perfect foresight for comparable store sales growth, the error is reduced to approximately 2.7%. hese results suggest that the key to generating a more accurate out-ofsample forecast is developing a more accurate forecast of the next year s comparable store growth rate. In table 6 we present a few alternative models of comparable store growth. We bring three sources of data to bear: the company s own history of comparable store growth rates, and two different sources of industry sales growth rates. Roughly two weeks after each month end the US Census Bureau releases the Advance Monthly Sales Report for Retail rade documenting the 18

20 seasonally adjusted (but not price adjusted) sales figures for the month from the different NAICS codes within the Retail sector. he advantage of this source of industry data is that we can match it to the specific NAICS code of each firm; the disadvantage is that it covers both private and public firms in the retail industry, not just the public firms in our sample, so it may not be representative. For this reason we also collect comparable monthly data from Walmart, the largest retailer in the industry. Approximately one week after each month end Walmart discloses their comparable store growth rate for the month. 5 In table 6, panel A, we provide a correlation matrix with comparable store sales growth, prior year comparable store sales growth and our two industry sales growth measures. Current and prior year comparable store sales growth are correlated at Industry growth is also significantly and positively correlated with current year comparable store sales growth, but Walmart comparable store sales growth is only weakly correlated with current year comparable store sales growth. his variable is, however, positively correlated with industry sales growth, consistent with the idea that Walmart is a proxy for the whole retail industry. We consider two competing models of comparable store sales growth, as follows: C t = α 0 + α 1 C t-1 + ε (model A) C t = β 1 C t-1 + (1-β 1 )R t + µ (model B) where C t is comparable store sales growth in year t and R t is equal to one of the two industry sales growth rates discussed above. Model A is a simple mean-reversion model, assuming the estimated intercept is greater than one and the estimated slope is less than one. Model B simply takes the weighted average of the prior year comparable store growth rate and the industry rate, where the weight is estimated. We estimate the regression models above in a pooled regression, and provide 5 Monthly comparable store growth rates compare the sales in stores open for the same full month in the previous year fiscal year. Consequently, they are naturally seasonally adjusted. 19