This study estimates a structural model of demand and supply for the US digital camera market, where there is considerable product turnover and prices have dropped significantly and persistently over time. Forward-looking consumers expect the price to fall and choose an optimal time to enter the market. While most recent studies modeling such dynamics in the demand for new durable products use a dynamic programming approach, this is at the cost, due to computational constraints, of more restrictive assumptions and limitations on the data used. This paper analyzes the dynamic issue using a simple adaptation of the standard static structural model. This enables including a rich set of characteristics and a flexible specification of the heterogeneity of consumers, as reflected by allowing randomness in the coefficients of more characteristics. The coefficient on age can be interpreted as tracking the evolution of the changing consumer mix associated with firms inter-temporally price discriminating. Hence, the
purchase time associated with each particular camera directly reveals consumers’ willingness-to-pay. Alternatively, the age variable can also control for supply side dynamics in, for example, advertising. We find introducing the age variable overcomes the problems identified for the static demand models, by yielding more reasonable coefficient estimates and markups. Furthermore, our results suggest the consequences of ignoring the ageing effect are substantial with over-estimates of price elasticities, technological progress and underover-estimates of markups. Our approach is relatively easy to implement, with a significantly reduced computational burden. It is suitable for applications where allowing for rich patterns of substitution are more important than controlling explicitly for inter-temporal choice, or as a first step in estimating a full dynamic differentiated product demand system.
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Table 1. Sales and market share of the top six brands in the US P&S market Brand Observations Units Market Share
within Six Brands
Overall Market Share
CANON 924 8,508,226 25.91% 21.71%
SONY 946 7,677,646 23.38% 19.59%
KODAK 695 6,711,926 20.44% 17.13%
OLYMPUS 761 4,064,932 12.38% 10.37%
NIKON 470 3,615,261 11.01% 9.23%
FUJIFILM 457 2,256,409 6.87% 5.76%
Total 4253 32,834,400 100.00% 83.79%
Source: NPD Market Research Company. The reported sales for each brand is the sum over a 41-month period from January 2003 to May 2006. The sales volume of the overall market is calculated upon observations of all P&S cameras by 46 brands listed in the original dataset, which takes up above 80% of overall sales in the US market during this period.
Table 2. Product characteristics of P&S cameras Time Resolution
(MP)
Optical Zoom
LCD (Inch)
Size (Inch^3)
Weight (Oz)
Age (Months) All Observations
4.20 3.03 1.80 14.77 6.80 8.31
Monthly Observations
200301 2.81 2.72 1.69 24.56 9.65 9.90
200307 3.30 2.87 1.60 18.61 8.19 8.01
200401 3.66 2.93 1.59 18.51 8.33 10.65
200407 3.86 3.03 1.70 15.21 7.17 7.53
200501 4.33 3.12 1.78 14.59 6.86 9.34
200507 4.66 3.34 1.92 13.07 6.29 7.40
200601 5.10 3.29 2.04 12.33 6.18 9.05
200605 5.59 3.41 2.19 11.33 5.49 6.55
All statistics reported in the table are the means of the characteristics of products weighted by their sales within each month.
Table 3. Demand estimation results from the logit model
OLS 2SLS
Variable (1) Without Age (2) With Age (3) Without Age (4) With Age
Price -0.0023* -0.0024* -0.0042* -0.0014*
(0.0003) (0.0003) (0.0008) (0.0006)
Constant -12.2940* -11.4826* -12.3054* -11.4960*
(0.2937) (0.2728) (0.2957) (0.2740)
Resolution 0.4430* 0.1226* 0.5534* 0.0184
(0.0279) (0.0284) (0.0556) (0.0454)
LCD 0.4312* 0.2572* 0.5032* 0.1761*
(0.0838) (0.0777) (0.0908) (0.0818)
Opt. Zoom 0.2593* 0.1606* 0.2735* 0.1264*
(0.0175) (0.0166) (0.0197) (0.0181)
Size 0.5318* 0.1023* 0.4620* -0.0338
(0.0581) (0.0560) (0.0629) (0.0651)
Weight -0.3399* -0.0625* -0.2916* -0.0031
(0.0249) (0.0252) (0.0291) (0.0310)
Dig. Zoom 1.5882* 1.8483* 1.5548* 1.8831*
(0.2007) (0.1855) (0.2021) (0.1863)
Age - -0.0906* - -0.0988*
- (0.0034) - (0.0035)
Canon 0.2681* 0.1114* 0.3070* 0.0385
(0.0507) (0.0472) (0.0556) (0.0503)
Fujifilm -0.8201* -0.5834* -0.8593* -0.4976*
(0.0746) (0.0694) (0.0785) (0.0721)
Kodak -0.0492 -0.1307* -0.1009 -0.0813
(0.0585) (0.0541) (0.0642) (0.0573)
Nikon -0.3560* -0.0923 -0.2446* -0.0796
(0.0747) (0.0697) (0.0851) (0.0773)
Olympus -0.4503* -0.2350* -0.4396* -0.1790*
(0.0559) (0.0522) (0.0566) (0.0534)
Sony 0.7096* 0.5040* 0.6646* 0.4461*
(0.0576) (0.0537) (0.0595) (0.0566)
R2 0.18 0.301 - -
Adjusted R2 0.169 0.292 - -
1. The standard errors are reported in parentheses below each parameter estimate.
2. * Coefficient significantly different from zero at the 1% level.
3. Time dummies are included in the estimation but their parameter estimates are not reported for the sake of space.
Table 4. Demand estimates from the random coefficient model Variables Parameter
Estimate
Standard Error
Parameter Estimate
Standard Error (1) Without Age (2) With Age Alpha: Term on Price
ln(y-p) 0.6707* (0.0702) 0.3240* (0.1157)
Beta: Mean Coefficient Constant -8.0837* (0.6283) -7.4278* (0.5955) Resolution 0.7970* (0.0672) 0.3825* (0.1187)
LCD 0.5038 (0.4310) 0.2472 (0.1427)
Opt. Zoom 0.4133* (0.0201) 0.2492* (0.0297)
Size 0.0930 (0.1226) -0.2577* (0.1250)
Weight -0.2799* (0.0331) 0.0232 (0.0621) Dig. Zoom 1.4859* (0.3142) 1.5229* (0.5736)
Age - - -0.2253* (0.0130)
Canon 0.5201* (0.0570) 0.2401* (0.0620)
Fujifilm -1.2024* (0.0797) -0.8256* (0.0879)
Kodak -0.2639* (0.0693) -0.3068* (0.0705)
Nikon -0.1197 (0.0819) 0.0984 (0.0861)
Olympus -0.5003* (0.0604) -0.2324* (0.0572)
Sony 0.7287* (0.0651) 0.5277* (0.0627)
Sigma: Standard deviation of Beta
Constant 0.8375 (0.6661) 0.8424 (1.1050) Resolution 0.0664 (0.1497) 0.0372 (0.3615)
LCD 1.0195* (0.3029) 0.2922 (0.2031)
Opt. Zoom 0.0256 (0.0520) 0.0052 (0.0987)
Size 0.2461* (0.0701) 0.1809 (0.1037)
Weight 0.0228 (0.0227) 0.0774 (0.0529)
Dig. Zoom 0.9169 (1.0149) 1.5235* (0.5015)
Age - - 0.0950* (0.0058)
1, The standard errors are reported in parentheses; * denotes the 1% significance level.
2, Time dummies are included in the estimation, but their estimates are not listed for the sake of space.
Table 5. Cost estimation results from the random coefficients model Variable Parameter
Estimates
Standard Error
Parameter Estimates
Standard Error (1) Without Age (2) With Age
Canon 3.0067* (0.1201) 1.7735* (0.2125)
Fujifilm 2.9557* (0.1175) 1.7951* (0.2103)
Kodak 2.9285* (0.1164) 1.7158* (0.2132)
Nikon 3.2716* (0.1108) 2.1474* (0.2006)
Olympus 3.0672* (0.1147) 1.9107* (0.2120)
Sony 2.8673* (0.1239) 1.6834* (0.2218)
Ln(Resolution) 0.6490* (0.0322) 0.4333* (0.0958)
Ln(LCD) 0.6113* (0.0558) 0.4187* (0.0457)
Opt. Zoom 0.0473* (0.0073) 0.0191* (0.0084) Ln(Size) -0.5667* (0.0300) -0.6601* (0.0394) Ln(Weight) 0.9598* (0.0591) 1.4230* (0.0791) Dig. Zoom -0.4850* (0.0765) -0.0114 (0.1618)
Trend -0.0204* (0.0010) -0.0122* (0.0019)
The standard errors are reported in parentheses; * denotes significant at the 1% level.
Table 6a. Own-price elasticity and the sum of cross-price elasticities
Model Price Own-price elasticity Sum of cross-price elasticity
OLYMPUS -0.965 0.558
(1) D425 $74.07 The upper entries in each row are elasticities when the ageing effect is excluded while the lower entries are elasticities when the ageing effect is included in the calculation.
Table 6b: Semi-price elasticity
Semi-cross-price elasticity
Model Price
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) OLYMPUS -13.030 0.019 0.002 0.016 0.000 0.005 0.001 0.001 0.097 0.181 0.002 0.003 0.005 0.012 0.003 (1) D425 74.07
-9.646 0.063 0.038 0.003 0.005 0.107 0.006 0.015 0.015 0.157 0.014 0.069 0.005 0.001 0.058
KODAK 0.072 -13.788 0.002 0.017 0.000 0.005 0.001 0.002 0.094 0.178 0.002 0.004 0.006 0.013 0.003 (2) C300 90.55
0.002 -7.245 0.010 0.001 0.000 0.027 0.000 0.001 0.001 0.042 0.006 0.039 0.008 0.001 0.001 CANON 0.065 0.017 -11.759 0.015 0.000 0.004 0.001 0.001 0.101 0.182 0.002 0.003 0.004 0.010 0.002 (3) PSA400 102.78
0.008 0.080 -11.390 0.002 0.004 0.094 0.001 0.007 0.006 0.146 0.013 0.064 0.006 0.001 0.009 FUJIFI 0.072 0.019 0.002 -13.844 0.000 0.005 0.001 0.002 0.093 0.177 0.002 0.004 0.006 0.013 0.003 (4) FINEPIXA400 135.29
0.007 0.066 0.034 -16.079 0.006 0.122 0.001 0.008 0.006 0.203 0.015 0.062 0.004 0.001 0.006 NIKON 0.020 0.005 0.001 0.005 -4.294 0.001 0.000 0.000 0.070 0.099 0.000 0.001 0.001 0.002 0.000 (5) COOLPIXL4 147.46
0.016 0.048 0.060 0.006 -19.975 0.211 0.002 0.020 0.014 0.336 0.021 0.072 0.002 0.000 0.020 FUJIFI 0.077 0.021 0.002 0.018 0.000 -15.623 0.001 0.002 0.086 0.172 0.003 0.005 0.007 0.015 0.003 (6) FINEPIXA500 155.38
0.007 0.069 0.031 0.003 0.005 -14.038 0.001 0.007 0.006 0.173 0.014 0.060 0.004 0.001 0.007 NIKON 0.044 0.011 0.001 0.010 0.000 0.003 -12.766 0.001 0.062 0.115 0.001 0.003 0.004 0.011 0.002 (7) COOLPIXL3 182.58
0.021 0.053 0.025 0.001 0.003 0.063 -6.478 0.015 0.017 0.086 0.010 0.069 0.005 0.001 0.101 OLYMPU 0.050 0.014 0.001 0.013 0.000 0.004 0.001 -18.719 0.046 0.098 0.002 0.005 0.007 0.016 0.003 (8) SP310 220.11
0.022 0.055 0.055 0.004 0.010 0.170 0.006 -13.156 0.020 0.254 0.018 0.078 0.003 0.001 0.066 KODAK 0.047 0.012 0.001 0.010 0.001 0.003 0.000 0.001 -7.715 0.175 0.001 0.001 0.002 0.005 0.001 (9) C340BD 245.59
0.023 0.056 0.046 0.003 0.007 0.136 0.007 0.021 -10.765 0.197 0.016 0.074 0.004 0.001 0.087 SONY 0.054 0.014 0.001 0.012 0.001 0.003 0.001 0.001 0.108 -9.106 0.001 0.002 0.002 0.007 0.001 (10)
DSCW70 292.03
0.006 0.067 0.029 0.003 0.004 0.106 0.001 0.007 0.005 -14.955 0.013 0.058 0.004 0.001 0.005 OLYMPU 0.061 0.017 0.001 0.015 0.000 0.005 0.001 0.002 0.048 0.108 -20.569 0.006 0.009 0.019 0.004 (11)
STYLUS710 321.45
0.005 0.079 0.022 0.002 0.002 0.071 0.001 0.004 0.003 0.115 -11.331 0.055 0.006 0.001 0.005 SONY 0.051 0.014 0.001 0.013 0.000 0.004 0.001 0.002 0.045 0.097 0.003 -19.426 0.007 0.016 0.003 (12)
DSCT9 389.65
0.004 0.086 0.018 0.001 0.001 0.051 0.001 0.003 0.003 0.080 0.009 -8.806 0.007 0.001 0.004 FUJIFI 0.066 0.019 0.001 0.017 0.000 0.006 0.001 0.003 0.044 0.104 0.004 0.006 -23.465 0.021 0.005 (13)
FINEPIXE900 392.80
0.001 0.082 0.008 0.000 0.000 0.018 0.000 0.001 0.001 0.028 0.004 0.033 -5.445 0.001 0.001 OLYMPU 0.051 0.014 0.001 0.013 0.000 0.004 0.001 0.002 0.044 0.096 0.003 0.005 0.007 -19.647 0.003 (14)
C7000 453.51
0.003 0.085 0.013 0.001 0.001 0.032 0.001 0.002 0.002 0.050 0.007 0.046 0.008 -6.624 0.003 CANON 0.060 0.017 0.001 0.015 0.000 0.005 0.001 0.002 0.052 0.113 0.003 0.005 0.008 0.018 -19.123 (15) 485.00
Figure 1. P&S sales volume and price of top six brands
0 500 1000 1500 2000 2500 3000 3500
Quantity '000
$220
$240
$260
$280
$300
$320
$340
$360
Price
Jan03 Jul03 Jan04 Jul04 Jan05 Jul05 Jan06 Jul06
Price (dollar) Quantity in thousand
Based on 4253 observations, covering all P&S cameras of top six brands (Canon, Fujifilm, Kodak, Nikon, Olympus and Sony). The sales figures plotted are the monthly sum. The prices are sales weighted average prices in US dollars.
Figure 2a. Evolution of characteristics: resolution, optical zoom and LCD screen
1.5 2 2.5 3 3.5 4 4.5 5 5.5
Jan03 Jul03 Jan04 Jul04 Jan05 Jul05 Jan06 Jul06 Resolution (mega pixel) Optical zoom
LCD (inch)
Figure 2b. Evolution of camera characteristics: size, weight and age
6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5
Age
6 8 10 12 14 16 18 20 22 24
Weight & Size
Jan03 Jul03 Jan04 Jul04 Jan05 Jul05 Jan06 Jul06
Weight (oz.) Size (inch^3) Age (month)
Figure 3. Average sales and prices at different ages
$180
$200
$220
$240
$260
$280
$300
$320
Price
0 2000 4000 6000 8000 10000 12000 14000 16000 18000
Quantity
0 10 20 30 40
Average sales for each age group Price
1. The age reported for each model is determined upon the actual first on-market date, not subject to the first-time observed sales in the dataset. The information regarding actual introduction date is obtained from the internet; including firms’ own websites and other public ones, e.g. www.dpreview.com.
2. Only the top six brands of P&S cameras (4253 observations) are reported.
3. The reported sales are the total sales volume at each age averaged by the number of models within each age group.
4. The prices are the average prices of models within each age group.
Figure 4. Age elasticity of demand
0
-.3
-.6
-.9
-1.2
-1.5
-1.8
Elasticity
0 5 10 15 20 25
Age
Age elasticities of demand Median bands
The figure plots the percentage change in demand with respect to the percentage change in age for all observations included in the estimation. The age in the x-axis represents the number of months at the time of observation after a product is introduced into the market.
The age elasticity in the y-axis is in percentage terms.
Figure 5a. Price elasticity of demand excluding the age variable
-1 -2 -3 -4
-1 -2 -3 -4
0 200 400 600 800
0 200 400 600 800 0 200 400 600 800
6 12 18
24 30
Elasticities of demand Median bands
Price
Figure 5b. Price elasticity of demand including the age variable
-1 -2 -3 -4
-1 -2 -3 -4
0 200 400 600 800
0 200 400 600 800 0 200 400 600 800
6 12 18
24 30
Elasticities of demand Median bands
Price
Figures 5a and 5b plot the price elasticity of demand, where the former excludes the age variable but the latter includes it. All observations are organized into 5 groups according to their ages, i.e. age 1~6, age 7~12, age 13~18, age19~24 and age > 24. Each group is plotted in a separate panel. The scatters are associated with individual elasticities, while the belts show the median predictions.
Figure 6. Observed prices and estimated markups for six top selling models
$50
$150
$250
$350
$50
$150
$250
$350
Jul03 Jul04 Jul05 Jul06 Jul03 Jul04 Jul05 Jul06 Jul03 Jul04 Jul05 Jul06 CANON POWERSHOTA520 FUJIFILM FINEPIXA345 KODAK CX7430
NIKON COOLPIX3200 OLYMPUS D540 SONY DSCP72
Price Markups without Age
Markups with Age
Figure 7. Average prices and markup predictions for the top six brands
$50
$100
$150
$200
$250
$300
$350
$50
$100
$150
$200
$250
$300
$350
1 4 7 10 13 16 19 22 25 1 4 7 10 13 16 19 22 25 1 4 7 10 13 16 19 22 25
CANON FUJIFILM KODAK
NIKON OLYMPUS SONY
Markup without age Markup with age Price
age_a
Data plotted in the figure corresponds to average prices and markup predictions for each of the top six brands, grouped by the age of sales observations.
Appendix: Data on US digital camera market (for reviewing only)
In the original NPD data, there are a total of 1350 camera models. After checking for repetition of models, we find 1338 distinct models. Figure A1 below plots the sales volumes for the top 20 brands, showing a clear picture of steep declines in market shares. Listed characteristics of products include image resolution; weight and thickness of cameras;
dummy showing whether a camera features an optical zoom range or not; dummy showing whether a camera has an LCD screen or not; dummies for built-in-flash and the type of memory devices.
Total Sale of top 20 brands
0 2 4 6 8 10 12
1 3 5 7 9 11 13 15 17 19
Millions
Sales Ranks
Sales Volume
Figure A1
For attributes listed in the original dataset, there is a considerable amount of missing values, especially for the attribute measures for weight and thickness. Moreover, the data on characteristics of digital cameras are relatively raw. For example, with the key quality measure on cameras’ resolution, image quality is reported by ranges of resolution (e.g., 3-3.99 mega-pixel), not the exact value. Although dummies are reported for features like LCD and optical zoom range, in many cases, these dummies are not sufficient to indicate the quality of digital cameras. For instance, more than 90% of the cameras have the value of one for “built-in-flash” and “with optical zoom range”, making these cameras incomparable.
To derive accurate estimation, the original NPD data on camera features are supplemented by extensive searching through the website. To ensure the accuracy in definition of each model, observations derived from different sources are compared and matched. The features listed in the final dataset include the type of camera (Single-Lens-Reflex (SLR), SLR-alike, Point-and-Shoot cameras (P&S); the exact pixel number of image
resolution, the size of LCD screen, the number of optical zoom range, the size of built-in-memory, the size (three-dimension measures) of camera, the battery type (rechargeable or not); the number of digital zoom, etc. Our final sample has 1127 distinct models, with 22,527 observations, representing more than 96% of total sales of original 1338 models reported by NPD. To construct the age variable, we obtain the introduction date for all models included in the final sample. Most of the information comes from the website www.dpreview.com and the websites of the manufacturers. Hence, each observation in this study will be assigned a precise age value to indicate how long the product has been marketed since its introduction.
The study focuses on the standard point-and-shoot (P&S) digital cameras manufactured by top six brands. Other brands are not included in the analysis due to three empirical facts.
First, the output of the top six brands takes up about 83.79% of total sales of P&S cameras reported in the whole sample. The remaining 16.21% sales are shared by 40 smaller brands, with the aggregate market share of the 7th to 10th largest brands representing a total of less than 8% of market share. Second, we include observations belonging to the top six brands in part because of the lack of accurate price information of some smaller brands’ models. For instance, the seventh largest seller Hewlett Packard takes up about 3.62% of the P&S market but most HP products are sold in packages or bundles. Therefore, the observed prices are for the whole bundle including other items such as printers. Accurate prices for the digital camera within the bundle are not observed. Finally, functionality and quality measures for products provided by smaller firms/brands may not be comparable with popular brands. For example, some of the digital cameras in the original data are PC video camera (e.g. MICRO INNOVATIONS), while others feature special functions (e.g. Sealife DC250 and DC310 can be used under water). It is difficult to specify a cut-off on choosing comparable products from these manufacturers. Rather than making an ad hoc selection, the study uses only observations from the top six brands.