DETECTING AND MEASURING SHIFTS IN THE DEMAND FOR DIRECT MAIL

Transcription

1 Chapter 3 DETECTING AND MEASURING SHIFTS IN THE DEMAND FOR DIRECT MAIL 3.1. Introduction This chapter evaluates the forecast accuracy of a structural econometric demand model for direct mail in Canada. Direct mail also known as advertised admail is used to provide advertising to consumers through the mail system. My original model was developed in March 1986 and was based on the period ending January 1996 using twelve years of historical monthly data. A complete discussion of the original regression model original is provided in Dubin (1998). In this chapter, I update the regression results for the April 1989 through January 1996 period revised and provide new results from twenty additional monthly observations for the period of February 1996 through September 1997 updated. In Section 3.2, I present the original, revised, and updated regression models for direct mail. In Section 3.3, I discuss the shift in demand for direct mail in Canada and the accuracy of the structural economic model. Section 3.4 provides my estimates of forecast accuracy and conclusions Comparison of Original, Revised, and Updated Direct Mail Models To review, my econometric model for addressed admail used seasonal dummy variables (seasonal indicators), real paper and printing prices, real product price, real retail sales, and trend to explain historical demand. A variable glossary is presented in Table 3.1. Table 3.2 presents the results of the direct mail regression models (as originally estimated) for short-long (standard business), oversized (non-standard business size), and combined admail demand for the period ending in January 51

2 52 EMPIRICAL STUDIES IN APPLIED ECONOMICS Table 3.1. Variable Glossary (1) constant term s1-s11 month dummy variables pi mnppr/cpi real paper and printing cost index all sl v short-long advertised admail volume all us v oversized advertised admail volume all ad v combined advertised admail volume all sl p short-long advertised admail price all os p oversized advertised admail price all ad p combined advertised admail price ret m al/cpi real retail sales index trend time trend Generally the fit of the model was quite good and the explanatory factors were significant and in accord with economic theory. In Table 3.3, I re-estimate the regression models for the time period ending in January As there were revisions to the Canadian historical time-series direct mail data and revisions to the Statistics Canada macroeconomic data, these models differ from my original reported model. I use the revised data regressions in the forecasts of admail demand for the 20-month period that occurred between my 1996 study (Dubin 1998)) and this study. Generally, these models are very similar to the models as originally estimated and, therefore, I do not discuss them in significant detail. A complete discussion is provided in Dubin (1998). For instance, the original price elasticity of the demand for admail was estimated to be and was re-estimated using the revised data to be. I note that the new estimate using the additional 20 months of data is Comparison of Revised and Updated Models I present the updated regression models for Addressed Admail in Table 3.4. These models for short-long, oversized, and total admail are very similar to the models as originally estimated. The regression fit is approximately the same as in the original model, with values at roughly 87 percent. The estimates for the elasticity of total admail demand with respect to paper and printing prices fell from to, the retail sales elasticity fell from 0.7 to 1 For data sources and variable construction see Dubin (1998).

3 Shifts in the Demand for Direct Mail , and the estimated trend effect was approximately the same. The price elasticity for total admail rose slightly from my previous estimate of to the current estimate of. The short-long price elasticity fell from to and the oversize price elasticity estimate rose from to. In sum, the changes in the estimated regression models are small and the general conclusions I previously reached remain unaltered. Specifically, the demand for addressed admail is still growing, still responsive to paper and printing costs, still moves pro-cyclically with the Canadian economy, and still reveals inelastic price elasticity Addressed Admail Specific Results Paper and printing costs remained steady in real terms until the rapid increase and subsequent fall in The estimated price elasticity of real paper and printing costs is estimated to be ( -stat ) indicating that an increase in the real cost of paper and printing causes the demand for addressed admail to decline. Moreover, customers are captive to this cost since the elasticity is less than one. Retail sales have a positive and statistically significant effect on admail demand. A percentage increase in retail sales leads to a 0.61 percentage increase in the demand for addressed admail. As noted above, the estimated price elasticity of ( -stat ) shows that an increase in the real price of admail causes admail volumes to decline. The inelasticity estimated by the model indicates that an increase in the price of Canadian addressed admail products will result in lower volume, but higher overall revenues at a higher price level. Profitability is also predicted to increase as costs decline with lower total volumes. In order to examine the separate price elasticities for specific types of admail, I specified and estimated two additional models. I present these models using the updated data in Table 3.4. The first model considers short-long admail. The own-price elasticity is estimated at ( -stat ). Thus, it is less elastic than both oversized or combined addressed admail with elasticities of and, respectively. Short-long admail is also revealed to have grown more rapidly than oversized admail after controlling for other factors. Paper and printing costs have a negative effect on both short-long and oversized volumes. Given the estimated elasticities, it is likely that a uniform increase in the price of all addressed admail types will create a greater volume decline in oversized pieces than in short-long pieces. These conclusions, therefore, remain unchanged relative to my 1996 study (Dubin (1998)) The Shift in Demand Between 1995 and 1996 The average price of addressed admail in fiscal year 1995 was $0.261 per piece. In fiscal year 1996, this rose to $0.289 per piece. Volumes on an annual

4 54 EMPIRICAL STUDIES IN APPLIED ECONOMICS basis rose from 1,458,510 to 1, pieces. Additionally, between fiscal year 1995 and fiscal year 1996, several key explanatory factors showed important changes. First, the Canadian economy improved. Second, the real cost of paper and printing fell. Third, other trend effects caused demand to rise. These shifts would have combined to increase demand even if addressed admail prices had remained constant. Therefore, the price increase between fiscal years 1995 and 1996 caused a movement along the demand curve while other factors caused a shift in the demand curve. I illustrate this using the estimated demand curve for fiscal years 1995 and 1996 as depicted in Figure 3.1. The figure shows the consequences of the price increase as a movement along the demand curve from Point A to B. The movement from Point B to C represents the shift in the demand curve. Hence, the move between fiscal years 1995 and 1996 (the movement between Points A and C) has two components the price component (A to B) and the shift component (B to C). Between fiscal years 1995 and 1996, average addressed admail prices rose from $0.261 to $0.289 per piece. In nominal terms, this was an 10.7 percent price increase. In real terms, the price increase was lower, at 8.8 percent as average inflation in Canada between the two fiscal years was approximately 1.8 percent. During this same period, volumes increased about 3.5 percent. As a consequence of the price increase, volumes fell (the movement along the demand curve). At the same time, general trend effects increased demand for addressed admail while improvements in retail sales caused a further increase in demand. The substantial decline in real paper and printing costs of 14 percent caused demand to increase substantially. Thus, the change in volume due to increased admail price per piece was almost fully offset by lower paper and printing costs. Therefore, the shift in demand from Point B to Point C was due to three factors: retail sales improvements; decline in real costs of paper and printing; and general trend effects. Using the estimated regression model, I find that approximately 7 percent of the shift was due to the improvement in the Canadian economy, 38 percent of the shift was a result of lower paper and printing costs, and the remaining 55 percent of the shift was due to general trends causing admail demand to increase each year Comparing Forecast Accuracy In Figure 3.2, I display the ex post forecast of total addressed admail for the period February 1996 through September This forecast is based on the revised regression for total addressed admail presented in Table 3.3, column 3. This is an ex post forecast since it relies on the realized volumes of the explanatory factors. The plot in Figure 3.2 reveals some variation between forecasted and actual values.

5 P Figure 3.1: Shift in Demand Between Fiscal Years 1995 and % Retail Sales B A 1,458,510 38% Printing FY 95 55% Trend C 1,510,016 FY 96 Q Shifts in the Demand for Direct Mail 55

6 56 EMPIRICAL STUDIES IN APPLIED ECONOMICS Figure 3.2: Forecasted Volume Versus Actual Volume Year.Month Volume (million Pieces) Actual Volume Forecasted Volume

7 BA BA Shifts in the Demand for Direct Mail Forecasting Addressed Admail Volume To predict the value of model recall that. The forecast error is The forecast variance is: associated with a regressor vector under the is the minimum variance linear unbiased estimator of 8! I estimate the forecast variance using " in place of. The estimated standard error of the forecast variance is denoted by " $#. A confidence interval for is formed using % : ". For the log-linear demand models used in this study, the forecast confidence interval is: & ('*),+ $-./ / / 7 $-./ / - 99 Salkever (1976) suggested a method for combining the computation of forecasts and standard errors using an expanded regression. Suppose that the esti- observa- mation is based on ; observations and that we desire to forecast ; tions, < = : Construct an augmented regression: >?@ C> C A F?. B F. ED >? G >? BA or < In the augmented regression, there are ; new observations and a set of ; new variables. Each column in the second part of is a dummy variable that takes the value minus one for the new observations and zero otherwise. Using this expanded regression model, Salkever (1976) shows that the least squares regression of on produces the coefficient vector (H, where is the original OLS coefficient vector and H are the predictions of ; the residuals

8 ; ; ; 58 EMPIRICAL STUDIES IN APPLIED ECONOMICS from this regression are, for the first ; observations, the original least squares residuals and for the last ;, zero; and the estimated covariance matrix for the expanded vector of coefficient estimates contains, in its upper left block, the covariance matrix for the least squares estimates of and, in its lower block, the covariance matrix for the forecasts. The th diagonal element of the covariance matrix in the lower block is: Est Var H Est Var " Measures of Forecast Accuracy Various measures have been proposed for assessing the predictive accuracy of forecasting models. Most of these measures are designed to evaluate ex post forecasts, that is, forecasts in which the exogenous variables do not themselves have to be forecasted. A common measure based on the residuals from the forecasts is the root mean squared error: where ; is the number of forecasted periods. This has an obvious scaling problem as it depends on the magnitude of. Several measures without scaling problems are based on the Theil statistic: 2 Large values of Theil s statistic indicate poor forecasting performance. In order to examine the model s ability to track turning points it is possible to replace the levels, with either absolute change,, or percentage changes. The statistics are calculated below Forecast Results Confidence Intervals In Table 3.5, I show the estimated 95 percent confidence intervals for the addressed admail model. The estimation period ends in January 1996, which was the last available data point in my previous study. The period from February 1996 through September 1997 was forecasted ex post (i.e., using the realized values of exogenous factors appearing in the model, including paper and printing costs, retail sales, admail prices, and so forth). In Figure 3.3, I show the 95 percent confidence interval, the forecasted point estimates, and the realized actual values for this period. I note that only two 9 2 See Theil (1961).

9 Shifts in the Demand for Direct Mail 59 of twenty values fall outside the estimated intervals. Therefore, the estimated confidence intervals contained the true values 90 percent of the time Forecast Results Conclusions The 95 percent confidence intervals range in volume by plus 23 percent and minus 19 percent of typical monthly volumes. The total addressed admail volume for the 20-month period was 2,505,951,000 pieces. The model s prediction for this period was 2,574,181,000 pieces. The difference is approximately a 2.7 percent error. Hence, the model is quite good at forecasting the overall volume even if there are some substantial monthly errors. The total addressed admail volume for fiscal year 1996/1997 was 1,510,016,000 pieces. The model s prediction for this period was 1,556,070,000 pieces. Hence, the model over-predicted the results for fiscal year 1996/1997 by approximately 3.0 percent. 3 Finally, I have calculated Theil statistics for the forecast period based on levels, differences, and percentage changes. The statistic for levels is on the order of 11 percent, while the statistics for differences or percentage changes is about 55 percent. These statistics reveal that the direct mail demand model does a better job at predicting levels than turning points. 3 The point estimates were within as little as 2.3 percent of actual monthly volume and were off by as much as 28 percent in one month. Apparently, the model is particularly poor in forecasting the extreme swings that occur in the summer months. The model tends to under-predict the June highs and the July lows.

10 60 EMPIRICAL STUDIES IN APPLIED ECONOMICS Figure 3.3: Estimated Confidence Interval for Addressed Admail Year.Month Actual Volume Forecasted Volume Lower Bound Upper Bound Volume (million Pieces)

11 Shifts in the Demand for Direct Mail 61 Table 3.2. Addressed Admail (Original) Admail S/L Admail O/S Admail All Dep Variable: (log(all sl v)) (log(all os v)) (log(all ad v)) (1) s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 (log(pi mnppr/cpi)) (log(all ad p/cpi)) (log(all os p/cpi)) (log(all ad p/cpi)) (log(ret m al/cpi)) (log(trend)) Observations Corrected -squared Mean of Dep Variable statistics in parenthesis

12 62 EMPIRICAL STUDIES IN APPLIED ECONOMICS Table 3.3. Addressed Admail (Revised) Admail S/L Admail O/S Admail All Dep Variable: (log(all sl v)) (log(all os v)) (log(all ad v)) (1) s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 (log(pi mnppr/cpi)) (log(all sl p/cpi)) (log(all os p/cpi)) (log(all ad p/cpi)) (log(ret m al/cpi)) (log(trend)) Observations Corrected -squared Mean of Dep Variable statistics in parenthesis

13 Shifts in the Demand for Direct Mail 63 Table 3.4. Addressed Admail (Updated) Admail S/L Admail O/S Admail All Dep Variable: (log(all sl v)) (log(all os v)) (log(all ad v)) (1) s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 (log(pi mnppr/cpi)) (log(all ad p/cpi)) (log(all os p/cpi)) (log(all ad p/cpi)) (log(ret m al/cpi)) (log(trend)) Observations Corrected -squared Mean of Dep Variable statistics in parenthesis

14 64 EMPIRICAL STUDIES IN APPLIED ECONOMICS Table 3.5. Addressed Admail 95% Confidence Intervals Confidence Actual Forecasted Confidence Interval Volume Volume Interval Period (lower bound) (1,000 s) (1,000 s) (upper bound) February 96 95, , , ,394 March , , , ,952 April 96 90, , , ,583 May 96 91, , , ,998 June 96 84, , , ,529 July 96 75,987 87, , ,809 August 96 86, ,374 94, ,684 September , , , ,337 October , , , ,115 November , , , ,926 December , , , ,077 January , , , ,705 February , , , ,226 March , , , ,152 April , , , ,861 May , , , ,969 June 97 95, , , ,155 July 97 88,024 88, , ,661 August 97 95, , , ,964 September , , , ,087