DSC-T200/R

Cyber-shot Digital Still Camera
With slim vertical design in three fashion colors and a giant 3.51 Widescreen touch-panel LCD that fills the camera back, the DSC-T200 captures your attention before it even takes a shot. 8.1 MP imaging, Carl Zeiss 5X Optical zoom lens and special features like Face Detection and Smile Shutter Mode help you bring out the best in everyone -- and the Sony Double Anti-Blur Solution delivers sharp color images even in low light. With HD Output2 , you can also share images in high definition on your Sony Bravia HDTV or other compatible HDTV screen. Sleek, Slim-Line Vertical Design The ultra-compact DSC-T200 has an elegant look all its own -- in shining silver, matte black or deep red, with vertical styling and a huge 3.Widescreen touch-panel LCD that fills up the entire back of the camera and replaces function buttons with elegant on-screen icons. 8.1 MP Super HAD CCD More megapixels give you more detail and definition when you make big prints or crop in tight on your subject. The advanced Sony Super HAD (Hole Accumulated Diode) CCD design allows more light to pass to each pixel, increasing sensitivity and reducing noise. Carl Zeiss 5X Optical Zoom Lens Design. 5X Optical zoom brings you even closer to the action, for great action shots, distant landscape views and dramatic portraits. An ingenious Carl Zeiss lens design uses internal zooming, so even at full zoom the lens doesnt project beyond the ultra-slim camera body. The Sony Double Anti-Blur Solution With Super SteadyShot optical image stabilization and high sensitivity (ISO 3200), the DSC-T200 compensates for shaky hands, minimizes blur and allows flash-free shooting to preserve the mood -- and Sony Clear RAW Noise Reduction reduces the picture noise that can ruin low-light shots. 3.51 Widescreen Clear Photo LCD Plus Display The DSC-T200 puts a huge 3.Widescreen LCD in the palm of your hand, with Clear Photo LCD Plus design that displays photos in superb clarity and natural color -- with AR (antireflective) coating for excellent visibility even in bright sunlight. Touch-Screen Operation The DSC-T200s Widescreen touch-panel LCD replaces small buttons with simple on-screen icons and a user-friendly interface that make camera operation faster and simpler. In shooting mode, you can touch any point on screen to focus on the person or object youve selected -- and touch and zoom in playback mode to concentrate on your subject. Simple Icon Setup Controls To the left and right of the image area on your widescreen display, simple icons allow quick touch-screen operation of essential camera functions. The icons can be switched off to provide a full 16:9 widescreen view of your photos -- and the on-screen Function Guide display helps you learn camera setup operations. Face Detection Because the face makes the photo, Sony has created Face Detection technology that recognizes up to 8 faces in a photo and automatically controls focus, exposure, color and flash to bring out the best in everyone. Unlike some competitive systems, Sony Face Detection makes skin tones look more natural and reduces red-eye with pre-strobe flash. Smile Shutter Mode In Smile Shutter Mode, the DSC-T200 helps you capture more smiles by shooting automatically when your subject laughs, smiles, even grins - only when focus is fixed. You select the person to watch and the expression to catch -- your Cyber-shot cameras Face Detection system and intelligent Smile Shutter algorithm do the rest! HD Slide Show with Music Its the high-definition viewing experience that makes photos more entertaining to watch, accompanied by your choice of visual effects and any of four preset musical selections stored in memory or your favorite music downloaded from PC to your camera for use as background music4. 9-Point Auto Focus Because an off-center subject can make your shot more interesting, the DSC-T200 can measure auto-focus precision at 9 points on your screen -- giving you greater creative freedom to compose your image. D-Range Optimization Powered by the exclusive Sony Bionz high-speed processing engine, D-Range Optimization preserves image data in bright highlights and reveals more detail in shadows or backlit areas -- for great results even in difficult lighting conditions. In-Camera Retouching The DSC-T200 lets you add 8 creative effects to photos after you shoot -including new radial blur effect, retro color tint and trimming function along with soft edge filter to soften backgrounds, cross filter to place starry dazzles at highlight points, partial color filter to

HD Output2 Direct HD output2 to your Sony Bravia HDVT or other compatible HDTV screen ADDITIONAL FEATURES lets you view DSC-T200 still photos in spectacular clarity and detail. Optional In-Camera Red-Eye Reduction HD solutions include a Cyber-shot Enhanced Paint Function cradle/charger with component cable output, or component cable directly to 31 MB Internal Memory your HDTV. Memory Stick Duo Media Multi-Resizing Function ConvenienceMemory Stick Duo The in-camera feature that resizes your Media Convenience photos for any purpose! Standard 4:3 Up to 25X Smart Zoom Feature5 can be resized to widescreen 16:9 and -MP for giant-screen HDTV display MPEG Movie VX Fine Mode and images at 16:9 and larger than Stamina Battery Power VGA resolution can be resized to 4:3 Software for Managing Your Memories VGA for sharing with friends and family via e-mail (internet connection required). A simple 4-direction touchscreen control also makes it easy to trim photos. Wide Zoom Display To use the entire image area of your DSC-T200 Widescreen LCD and compatible HDTV2 screens, Wide Zoom automatically expands standard 4:3 images to 16:9.

Specifications

General
Megapixel: 8.1 MP Imaging Device: 1/2.5" Super HAD CCD Recording Media: 31MB internal Flash Memory, optional Memory Stick DUO Media, optional Memory Stick DUO PRO Media

Operating Conditions

Flash Effective Range: ISO Auto: 4 to 12' (0.1-3.7m)(W), ISO 3200: 4" to 24' (0.1-7.4m)(T) Flash Mode(s): Auto, Forced On, Forced Off, Slow Synch

Optics/Lens

Focal Length: 5.8 - 29mm 35mm Equivalent: 35 - 175 mm Focus: 9 Area Multi-Point AF, Center AF Aperture Range: f3.5-10 (Auto/Program Auto) Shutter Speed: 1/4-1/1000 sec. (Auto), 1"-1/1000 sec. (Program Auto) Exposure Compensation: 2.0 EV, 1/3 EV Step Increments ISO: Auto, 80, 100, 200, 400, 800, 1600, 3200 Filter Diameter: N/A Smart Zoom Technology: Up to 6.3X (5MP), 8.0X (3MP), 8.5X (16:9 2MP) 25X (VGA Resolution)4 Digital Zoom: 2X (Precision) Optical Zoom: 5X Macro Mode: Yes Total Zoom: 10X Minimum Focus Distance: 1911/16" (50cm) Normal, 3-1/8" (8cm) Macro, 3/8" (1cm) Magnifying Glass Face Detection: Yes

Convenience

White Balance: Automatic, Cloudy, Daylight, Fluorescent 1, Fluorescent 2, Fluorescent 3, Incandescent, Flash Self Timer: Yes (10 seconds, 2 seconds, Off) Memory Stick PRO Media Compatibility: Tested to support up to 8GB Memory Stick DUO PRO TM media capacity1 ; does not support Access Control security function. Still Image Mode(s): Burst, JPEG (Fine), Exposure Bracketing Red-Eye Reduction: Yes (On/Off all modes) Burst Mode: 100 shots at 2.2 fps (all resolutions) Erase/Protect: Yes/Yes Date/Time Stamp: No/ No Media/Battery Indicator: Yes/Yes Color Mode(s): Black & White, Natural, Sepia, Vivid
Battery Type: Lithium-Ion NP-BD1 Battery Capacity: 3.6V, 680 mAh

Convenience Features

Real Imaging Processor Technology: Yes - Bionz AF Illuminator Light: Yes PictBridge Compatible: Yes Multi-Pattern Measuring: Yes SteadyShot Image Stabilization: Yes Scene Mode(s): Beach, Fireworks, High Speed Shutter, High Sensitivity, Landscape, Snow, Soft Snap, Twilight, Twilight Portrait, Smile Shutter Movie Mode(s): MPEG VX Fine with Audio (640x480 at 30fps) (MPEG VX Fine requires Memory Stick DUO PRO media), MPEG VX Standard with Audio (640x480 at 16.6fps), Presentation Mode (320 x 240 at 8.3fps). Power Save Mode: Yes (after approx. 3 min. of inactivity) In-Camera Editing: Red-eye correction, soft edge filter, cross filter, partial color filter, fish-eye filter, retro, radiation, trimming
Service and Warranty Information
Limited Warranty: 1 Year Parts & Labor

Software

Supplied Software: Windows: Picture Motion Browser Vers 2.1 + USB Driver Operating System Compatibility: Microsoft 2000 Professional, Me, XP Home and Professional, and Vista; Macintosh OS 9.1/9.2/OS X (10.110.4)

Processor

Bionz Engine: Yes (LSI with Dynamic Range Optimizer (DRO))

Dimensions

Weight: 5.6 oz (160 g) Body; 6.6 oz. (186 g) including Battery and optional Memory Stick DUO Media Measurements: 3 11/16" x 2 5/16" x 13/16" (93.5 x 59.3 x 20.4 mm)

Supplied Accessories

NP-BD1 rechargeable battery BC-CSD battery charger A/V and USB multi-connector cables Adaptor plate for cradle Wrist strap Paint Pen Software CD-ROM Note: No Memory Stick DUO media or adaptors are included.

Inputs and Outputs

Accessory Terminal: N/A Audio/Video Output(s): Yes via MutliUse Connector USB Port(s): Yes (Supports USB 2.08 ) HD Output: Yes (1080i)with optional accesory

Hardware

LCD: 3.5"1 (230K Pixels) Clear Photo LCDTM plus screen Viewfinder: N/A Lens Construction: 12 Elements in 10 Groups, 3 Aspheric Elements, 1 prism Microphone/Speaker: Yes/ Yes Lens Type: Carl Zeiss Vario-Tessar Docking Station: Yes, via optional HD cradle

Optional Accessories

Accessory Kit (ACC-CLGB) Color: Red UPC Code: 027242713345
1 : Viewable area, measured diagonally. 2 : HD Output requires an optional Sony HD component cable or cradle; HDTV sold separately. 3 : Actual results may vary based on product settings, usage patterns, battery and environmental conditions. 4 : Maximum playback length of each music file is 180 seconds. 5 : Smart Zoom feature will not work at highest resolution setting. 6 : Shooting at high frame rate of up to 30 frames per second requires Memory Stick PRO Duo media. 7 : The online map service is currently provided courtesy of Google, and is subject to change or termination without notice. 8 : Not all products with USB 2.0 connectorsmay communicate with each other. 9 : A portion of the memory is used for data management functions. 2007 Sony Electronics, Inc. All rights reserved. Reproduction in whole or in part without written permission is prohibited. Sony, Bionz, Bravia, Clear Photo LCD Plus, Clear RAW, Cyber-shot, Handycam, Memory Stick Duo, Memory Stick PRO Duo, Picture Station, Smart Zoom, Stamina, Super HAD, Super SteadyShot, and Walkman are trademarks of Sony. All other trademarks are trademarks of their respective owners.
Please visit the Dealer Network for more information at www.sony.com/dn Sony Electronics Inc. 16530 Via Esprillo San Diego, CA 92127 1.800.222.7669 www.sony.com Last Updated: 09/18/2007

STRUCTURAL ESTIMATION OF COMPETITIVE PRICE PROMOTION PATTERNS OF ONLINE STORES
Xiaoxun (Cathy) Gao+ First Draft: August, 2008 Current Version: April, 2010 Abstract We structurally estimate our proposed theoretical model with nonlinear least squares method using real price data collected from a leading price comparison website. Monte Carlo experiments show that nonlinear least squares method gives consistent parameter estimates. Our symmetric model explains the real world price data reasonably well. Factors that generate price dispersion are similar across the four digital cameras: the maximal profit margin ranges from 16 to 22 percent and the estimated proportion of consumers who visit the price comparison site is 16 to 26 percent. The cost of updating the prices is about two percent of the maximal profit margin. Finally, our estimates suggest that store managers believe to be competing with four to five stores. Keywords: clearinghouse models, price dispersion, structural estimation JEL Classification: C14, D43, D83, L13
I would like to thank my dissertation committee members: Michael Baye, Michael Rauh, Roy Gardner, Matthijs Wildenbeest and David Jacho-Ch for their guidance, encouragement, helpful comments and vez suggestions. I am very grateful to Chenguang Li for sharing his data with me. I also benefited from discussions with Lan Zhang and Chenguang Li, the industrial organization class on structural estimation taught by Matthijs Wildenbeest and the computational econometrics class that introduces me to nonparametric estimation taught by David Jacho-Ch vez. Any errors that remain are my responsibility alone. + Indiana University, Department of Economics, E-mail: gaox@indiana.edu.

1. Introduction

Price dispersion of an identical product is widely observed in nearly every online and offline brick-and-mortar stores. Empirical studies use data collected from online price comparison websites because they are relatively easy to obtain. Researchers have documented persistent price dispersion in a variety of industries such as electronics, books, and CDs.1 However, most of these papers investigate whether the observed pricing patterns are in line with the model equilibrium implications instead of attempting to estimate the parameters in the model as if it is the data generating process. One shortcoming of this approach is that different theoretical models may have the same equilibrium implications. For example, the consumer search model and the clearinghouse model both predict that firms use mixed strategy price. In the consumer search literature, it is typically assumed that each single price observation is costly to obtain. 2 Heterogeneity in search costs will result in some consumers searching once, while others search more often. On the other hand, in the literature on clearinghouse models (e.g. Varian, 1980; Baye and Morgan, 2001) the distinction between consumers is starker: some consumers have access to a clearinghouse and observe all prices, while others do not have access and observe the price of just a single firm. Because of the tradeoff between catering to consumers that do compare prices and consumers that do not, both types of models predict firms randomize their prices in equilibrium. So far very few studies have used the structure theoretical model on price dispersion directly to explain price dispersion. An exception is Hong and Shum (2006), which uses the equilibrium conditions of the consumer search model similar to Burdett and Judd (1983) to structurally estimate search frictions using price data alone. Moraga-Gonz lez and Wildenbeest (2008) extend their method to an oligopoly market and show how to estimate the model using maximum likelihood. Both papers focus on consumer search models. Clearinghouse models have received far less attention in the structural literature. In this paper we fill this gap by proposing a structural estimation method for a clearinghouse model with some modifications of Baye and Morgan (2001). Baye and Morgan (2001) is the first paper to explicitly model online price comparison websites. Based on their results, Gao (2010) proposes a more general model that allows for store differentiation and shows the model to be more consistent with the data collected from a leading price comparison website. In this paper, we add a hassle cost to Gao (2010) that reflects the trade-off of firms to change advertised prices online. It is an attempt to improve upon Villas-Boas (1995), the first paper to directly estimate

See papers by Brynjolfsson and Smith (2000), Pan, Ratchford and Shankar (2002) and Baye, Morgan, and Scholten (2004a, 2004b). 2 For example, see papers by Stahl (1989), Burdett and Judd (1983) and Reinganum (1979).
Varian (1980). He finds Varians model cannot be rejected for only 34 percent of the coffee brands and 50 percent of the saltine crackers brands. He argues the assumption that it is costless for the firms to change prices is not very realistic. The advantage of adding an updating cost (or a hassle cost) is that we allow more flexibility of fitting the price data on the theoretical model and the theoretical model yields a unique symmetric equilibrium when the gatekeeper charges a click fee. Nowadays, most of the major price comparison websites charge a click fee instead of a flat fee. Besides, the data we collected are also from such a click-fee website. In this paper, we explicitly investigate the impact of structural parameters like the number of shoppers, unit cost, and willingness to pay on price dispersion in online markets. A paper that also uses data from price comparison websites to structurally estimate a clearinghouse model is Yang (2008). The key insight of his paper is that not all firms that advertise on price comparison sites are actively competing. He proposes a two-step efficient GMM method. A major difference between that paper and ours is that firms draw prices from a common mixed strategy and he does not allow for store differentiation. In terms of methodology, we make two improvements upon his GMM method. First, we use a continuous nonparametric data distribution instead of the kinked empirical data distribution. We show the continuous nonparametric data distribution has better estimator properties through Monte Carlo simulations. In addition, we use bootstrap methods for standard errors. Since it is a two-step procedure, standard errors from the second step regression are well known to be smaller. Bootstrapping takes care of the additional variability from the first step estimation. The structure of the paper is as follows. In the next section, we introduce the theoretical model of Gao (2010) and solve the model with the addition of the hassle cost. Next, we describe the dataset and its empirical features. In Section 4, we present results from our structural estimation and explain the results. Section 5 concludes. Proofs of the propositions are delegated to the Appendix.
2. The Theoretical Model and the Equilibrium
Our model builds on the symmetric N-firm case of Gao (2010) and includes an updating cost if firms choose to change prices on the price comparison website which uses a click fee to collect advertising revenue. Gao (2010) is built on Baye and Morgan (2001) and Varian (1980). With some parameter configurations, her model can be written as the two influential papers mentioned above. 2.1 The Model We assume a continuum of consumers, each of whom has a unit inelastic demand. The total size of consumers is normalized to unity. N firms offer the product. Each firm chooses whether or not to advertise on the price comparison site and what price to charge.

The gatekeeper (owner of the price comparison website) decides on the optimal click fee ( ) that maximizes his advertising revenue from the firms. He offers the service for free to the consumers. There are two types of consumers: we call them loyal consumers and shoppers. Loyal consumers bypass the price comparing platform and purchase from their preferred stores. We assume each firm in the market has equal loyal shares. On the other hand, shoppers go to the platform and compare prices of those firms that choose to advertise. Because of the unity normalization, we have + = 1. We further assume firms have different service qualities and consumers care not just the product itself but also the store they purchase from. That is to say, they do not simply compare prices and purchase from the lowest-priced store. Instead, they look for the best deal a product-store bundle that gives them the highest utility. The service level of Firm i is denoted as . To provide better service, firms incur higher costs. The cost of a firm includes not only the cost of the product itself but also the service cost, denoted as . To restore the symmetry of the model, we restrict the maximal profit margin (denoted as X) to be the same across the N firms in the market. That is, = for all firms. In terms of decision making, if a consumer purchases from Firm i, he purchases the product-service bundle from the firm that yields utility , where is the service valuation (in dollars) and is the price. When all of the firms offer the same service (i.e. = ), the firm that has the best deal of the highest utility has the lowest price. As a result, this model is more general and allows for store service differentiation. As for firms, the margin per sale is . If we use a symbol to denote utility received by consumers, we can also say Firm i offers utility for the consumers to choose from. Because of the restriction imposed earlier, we claim that firms make decisions on picking a utility when they come to pick prices. There is a one-to-one mapping between utility and price: = = = = This is the key equation we use to transform the symmetric utility strategy to the asymmetric price strategy. We include an updating cost k if firms advertise prices on the price comparison website or post new prices. It can be best understood as opportunity cost. Firms need to maintain the catalogue and prepare conformable data feed files. Alternatively, firms pay companies like LinkShare and Commission Junction to manage their sales directed from the price comparison site. Adding this positive hassle cost k, we allow the concise theoretical model more flexibility and let the data tell us if the updating cost is really significant both statistically and significantly. Let us also define the terminologies here. The common utility strategy is denoted as G(m) and the symmetric advertising probability is denoted as. The price strategy for Firm i to be Fi (p). If Firm i advertises, its expected profit is denoted as EA p which is i A equivalent to setting a utility level or Ei m. If Firm i does not advertise, it sells only to

its loyal segment plus the fraction of 1/N shoppers if no firm advertises. To maximize profit, Firm i charges the reservation price Vi , i.e., zero utility offered to the consumers. We denote it as ENA Vi in terms of price and ENA (0) in terms of utility. The i i G expected revenue of the gatekeeper is R (t). The game is sequential. First, the gatekeeper announces a click fee. Second, firms decide whether or not to advertise and what prices to charge. Then, consumers make purchases. 2.2 The Equilibrium Our strategy here is to find the symmetric mixed strategy advertised utility and then to derive the asymmetric price strategies with the one-to-one mapping. To solve for the symmetric mixed strategy utility, we look at the two options of Firm i conditional on the N-1 firms behaviors. If Firm i does not advertise, it offers zero utility. That is, 0 = + 1
. If it advertises, Firm i wins the shoppers only
when it offers the highest utility among the advertised firms. Focusing on the symmetric strategy, it happens with a probability: 1 (1 ) 1. The expected profit hence is: = + 1 (1 ) 1 . Since the gatekeeper takes a click fee t from each transaction, we see per sale margin from the shoppers contains the subtraction. In addition, the hassle cost k is paid to some third party business. Because the gatekeeper has the final say on the click fee, he will extract as much surplus as possible from the firms. Hence, 0 0 = 0 given that every utility from the support of the mixed strategy yields the same expected profit. Equating the two expressions, we are able to solve for a unique advertising probability = 1

( 1 )

. It is straightforward to solve for the upper bound
of the utility strategy from 0 = 0 and its expression from 0 = 0 after pinning down the advertising probability. The following proposition summarizes our findings of the firms and those of the gatekeeper respectively. Proposition 1: When the gatekeeper charges a click fee t, the unique symmetric advertising probability is = 1

k S( 1N Xt)

. When the firm does not advertise, it

offers m = 0. If the firm advertises, it uses a mixed strategy G m = 1

k (X t ) +Lm X t N

S(Xmt)

where m 0, m and m =

Xt S+L

). The expected profit

of each firm is E m =

X Xt N

+ LX. The optimal flat fee of the gatekeeper is unique
and no explicit expression of t exists for a given hassle cost k > 0.3 Intuitively, if the hassle cost gets bigger, firms are less likely to advertise. The interesting feature of this equilibrium is that the expected profit of firms is positively related to the hassle cost. Firms compete less aggressively with the additional cost when they advertise. Furthermore, they advertise less frequently and hence charge the reservation prices more often. The overall effect is the higher value of the not-advertising option. The best the gatekeeper is able to do is to equalize the two options of the firms. Hence, the expected profit of firms increases when the hassle cost rises. Although we can view firms choose their advertised utilities from a common distribution, the observed data are prices. We recover a firms price from the above described one-to-one mapping. The transformation method is presented in the proposition below. Proposition 2: From the utility offering strategy G(m) in the previous two propositions, we can recover an individual firms pricing strategy: Fi p = 1 G(Vi p) where p Vi m, Vi. The model implication is that if firms do not different in service, they draw prices from a common mixed strategy price. If their service differs, we need to figure out a way to recover the service value for each firm or each type of firms Vi since = Vi . The reservation value of each firm can be parameterized in terms of the firms features. For example, if we assume consumers know nothing more than the listed features on the price comparison website, Vi = . A hedonic regression of prices on observable features will not only tell us the or the dollar value estimates consumers associate with each feature but also we can recover the residuals as the negative of utilities. However, we may run in to the omitted variable bias if the observable features are only a subset of what the consumers care about. Or, we can follow Wildenbeest (2008) and use a stores average price as a proxy for its service quality. That is, Vi = and hence, the deviation of a firms observed price
When k=0, there exists a continuum of advertising probabilities and the corresponding mixed strategy utility to every advertising probability. Optimally, the gatekeeper coordinates all firms to advertise. For details, read Gao (2010). We do not delve into the scenario because we observe the firms advertise on and off the price comparison website (see Table 1). For the model identification, we assume the unique symmetric equilibrium and see if the data tell us otherwise.

away from its mean is the negative of utility. In terms of method, it is essentially a fixed effects regression. Although the recovered utilities may be negative, we use the property that utilities are ordinal and the magnitude does not affect consumers purchasing decision. So, we rescale the lowest recovered utility to be zero to be consistent with the theoretical distribution. Furthermore, we can take away the time effects that impact all N firms. In other words, the store service levels are allowed to be different across time periods, it is Vi + Vt. To recover the utility, we use the following equation: = (Vi + Vt ) . Technically, we use to proxy Vt and for Firm i to proxy Vi , equivalent to running the two-way fixed effects regression. Since we follow the identical product markets over a period of time and pool the collected data for analysis, we make the assumption that firms play a stationary repeated game of finite horizon, whose equilibrium is the same as the one-shot game. The prices of every firm across periods are from an independent and identical distribution.
3. Data and Descriptive Statistics
The data is collected for digital cameras from a leading price comparison site: PriceGrabber.com. During the data collection period, there are fifty different digital cameras on sale from 132 retailers. Data is collected daily from October 2007 to May 2008 for a total of 27 weeks or 189 days. On a typical screen display of the search request of a particular model, we have the web page link, its advertised price, service rating, whether the retailer is featured, tax and shipping fee of a retailer, whether the product is in stock, an icon indicating whether the online retailer is hacker safe and if the product is on promotion. 4,5 Seller ratings are supplied by consumers who have bought products from the retailers. The scale is from 1 star (the worst) to 5 stars (the best) with the increment of star. Retailers that advertise under the digital camera category pay $0.75 for every click that leads a consumer to the store website. 6 They prepare updating data files to be uploaded to the price comparison site. 7 We assume that firms advertise with a positive probability and hence we observe the varying number of retailers (see Table 1 below). On
Retailers make additional payments to be featured but the amount is not specified on the comparison website. There are at most four featured retailers which have the first four positions of the initial screen display at the search request of a product. With a mouse click, the order can be easily sorted from the lowest price to the highest. 5 One example of promotion is to hand out free memory card with the purchase of the camera. 6 There are two types of retailers on PriceGrabber.com: online merchants which have their own websites and price comparison site storefronts which operate only under the comparison site. Storefronts are typically small-volume individual sellers. They pay commission which is a percentage of their sales value to the comparison site. See the FAQ page of PriceGrabber.com. We delete those storefronts from our analysis because they are sell to far fewer consumers than the online retailers. 7 A detailed five-step instruction webpage is in the FAQ of PriceGrabber.com.

a typical day, an average of 17 firms and the number varies from only two firms to a maximal thirty-six firms. For a typical firm, it advertises 65 out of 189 days. 8 Table 1: Price Change Frequency of a Typical Day and of a Typical Firm*
Mean (Std. Dev.) Number of Firms that Change Price in a Day Number of Firms in a Day Percent of Firms that Change Price in a Day Number of Days a Firm Changes Price Number of Days a Firm Advertises Price Percent of Days a Firm Changes Price 1.27 (0.75) 17.20 (8.61) 0.07 (0.0188) 4.77 (1.87) 65.26 (20.97) 0.07 (0.0146) Min, Max 0.07, 3.01 1.97, 35.76 0.02, 0.13 0.62, 8.19 12.65, 97 0.03, 0.09
* For each of the fifty digital camera markets, we have calculated 189 values of the above five price dispersion measures and obtain the averages. It is from the 50 average values we calculate the numbers in the above table.
In another paper Gao (2010), we use the same dataset and compare the model implications with the real price data. To avoid repetition, we borrow from her conclusions that store effects do play a part in explaining price dispersion. And, consumers care more than the observable features and hence, the residual from the hedonic regressions may subject to omitted variable bias. Furthermore, firms tend to price in an interval of three weeks. The results of the fixed effects regressions are presented below. Table 2: Store Fixed Effects and Store & Time Fixed Effects Regression
Canon PowerShot A560 Store Fixed Effects R2 F-test of Store Fixed Effects Store and Time Fixed Effects R2 0.87 Canon PowerShot SD800 0.88 Sony CyberShot DSC-T200 0.69 Pentax K10D SLR 0.85
We notice that firms keep their prices constant for some time. When they update prices, the change does not occur synchronously. About seven percent of the firms change prices in one day and a firm changes price five times on average when they advertise (See Table 1).
F-test of Time Fixed Effects F-test of Store and Time Fixed Effects

4. Structural Estimation

From the two-way fixed effects regression, we obtain the residuals which are the negative of the utilities. Since our theoretical model restricts the lower bound of the utility interval to be zero, we rescale them to start from zero. Based on the observation that firms keep prices constant roughly three weeks, we select the utilities every three weeks. The maximal possible observations for one firm are nine (the dataset consists of 27 weeks). The theoretical model implies that firms choose advertised utilities from one common distribution G(m). We aggregate the recovered utilities into a single distribution. 4.1 Model Implication Checks Adding a hassle cost, we obtain a unique positive probability of firms to advertise. Since the decision is random, we observe firms appear on and off the price comparison site. We pick several firms at random and present their advertised prices every three weeks in Figure 1 of Canon PowerShot A560.9 The missing dots mean the firm does not advertise. There seem not be a pattern of the advertising frequencies. In addition, when some firms raise prices, the other firms lower prices or keep prices constant. Price changes for a firm seem to be at random as well. Another noticeable feature is that although price variation for a firm exists but the variation seems to be bounded, which indicates the existence of the store service differences. Figure 1: Mixed Advertising and Pricing of Canon PowerShot A560
220 C r cui t i C ty i C puD r ect. com om i D l el H e om N egg. com ew O f i ceM f ax 210

D ay 148 169

Graphs of the other three products are available upon request.
Our assumption of repeated game with finite horizon implies the pricing decisions of firms across different periods should be independent. Following Moraga-Gonz and lez Wildenbeest (2008), we calculate the autocorrelation function of firms that advertise at least seven out of nine periods and use no less than two different prices. Results are in Table 3. We cannot reject the null that prices of the firm are not serial correlated at any significance level. Table 3: Autocorrelation Function of Firms in Four Product Markets

ACF Canon PowerShot A560 0.51(0.15) Canon PowerShot SD800 0.05(0.32) Sony CyberShot DSC-T200 0.35(0.21) Pentax K10D SLR Mean (Std. Dev.) Min. Max. # of Firms 0.31 0.-0.28 0.-0.05 0.-0.14 0.0.10(0.17)

4.2 Method

Our estimation strategy is to minimize =1 =1( | )2 where the theoretical distribution is from Proposition 1 and the parameters to be estimated consist of the hassle cost k, proportion of shoppers S, maximal profit margin X and the number of competing firms N.
In terms of identification, we first estimate the probability of advertising from the data and substitute in the theoretical distribution. Then, we estimate X-t together since the discriminating power of the theoretical distribution is not able to tell apart the two parameters. In our theoretical model, consumers who click through will buy from the retailer. In reality, it is usually not the case. To get around the difference, we calibrate the click fee and plug it in as a known value. For example we use the click fee at the time of data collection $0.75 and a proposed conversion rate of 30 percent. That is, 30 percent of consumers who click the retailers link will end up making a purchase. With symmetric conditions, we calculate the model click fee to be $0.75/0.30 = $2.5. Here, the estimated parameter X-t is the maximal profit margin minus the click fee assuming the conversion rate is 100 percent. Through a Monte Carlo study, we show that the other estimated parameters seem to be affected little and the effect of click-through fee is absorbed into the redefined net
maximal profit margin. We also compare the performance of using the non-continuous empirical distribution and using the continuous estimated nonparametric distribution as in the simulations. Both distributions converge to the true distribution at a rate of root n, the number of observations. Simulation result shows that the continuous nonparametric CDF outperforms the non-continuous empirical CDF in obtaining a lowered value of the mean squares errors. In addition, we check the validity of bootstrapped standard errors. That is because we estimate the advertising probability and plug it in the distribution as if it is observed. In order to obtain the valid standard errors, we also need to take into account the variability of the estimated advertising probability. Bootstrap provides us a conceptually and computationally easy fix. Simulations results are available upon requests. 4.3 Estimation Results We apply our nonlinear least squares method to estimate parameters that reflect the firms strategic interactions in the theoretical model. The data distribution is estimated non-parametrically and we use the smooth distribution function in the nonlinear least squares method. Results are presented in Table 4 below. The estimated updating cost and maximal profit margin are in dollars. To facilitate the product comparison with different average prices, we also calculate the hassle cost as a percentage of the maximal profit margin and the maximal profit margin as a percentage of the daily average maximal price. We find that factors that generate price dispersion are similar across the four digital cameras. During a three-week interval, firms pay roughly $2 in adjusting prices, or 2 percent of their maximal profit margin. The estimated hassle cost has a positive relationship with the average product prices. It may reflect the fact that firms are more careful in the pricing of high-priced products. The magnitude is very small, in part implying the efficiency of the online pricing practice. And, judging from the big standard deviations, the updating costs may not be very different from zero. The measure of special interest to store managers is the proportion of shoppers. It is estimated to range from 16 to 26 percent in the four digital cameras. To understand the predicted proportion of loyal consumers, let us discuss the number of competing firms now. The estimates of the number of firms are small as compared to what we observed in a typical day at the price comparison site. One reason for the discrepancy may be that store managers actually believe that they are competing with just a few other online stores when they set product prices. The share of loyal consumers in the market is estimated at about 18 percent.10 The estimated price variation within a firm comes from its tradeoff between selling to the price comparing consumers (about 21 percent) and the loyal consumers (about 18 percent). To those 21 percent of shoppers, a firm tries to set a low price to

It is calculated by (1-S)/N from the theoretical model. We use the average of proportion of shoppers in the four markets, 21 percent.
attract. To those 18 percent of loyal consumers, a firm reaps the highest possible profit by charging their reservation prices when it does not advertise. The maximal profit margin is about 20 percent of the maximal price which seems to be reasonable for electronics. Table 4: NLS Parameter Estimates Using Nonparametric CDF*
Canon PowerShot A560 Updating Cost Proportion of Shoppers Maximal Profit Margin Number of Competing Firms Observations Minimized Squared Value k/X X / avg max. daily price 1.30 (1.08) 0.16 (0.0424) Canon PowerShot SD800 2.36 (3.23) 0.21 (0.0534) Sony CyberShot DSC-T200 2.32 (3.06) 0.26 (0.0663) Pentax K10D SLR 3.00 (5.79) 0.21 (0.0529)

72.17 (5.99)

88.91 (13.06)

81.38 (13.00)

205.03 (28.32)

3.59 (0.38)

5.15 (0.83)

3.70 (0.56)

4.71 (0.76)

214 0.80

100 0.28

115 0.36

126 0.57

1.80% 21.87%

2.65% 21.17%

2.85% 16.31%

1.46% 19.11%
* Standard deviations in parentheses are obtained using 500 bootstrap samples.
From Table 4, we see the minimized squares value is small, implying a fine model fit. For visual interpretation, we also plot the smooth nonparametric distribution (the dotted lines are the 95 percent confidence interval of the estimated distribution line) and the theoretical distribution on the same graph for the four digital cameras in Figure 2 below.
Figure 2: Nonparametric CDF and Estimated Analytical CDF
Part I. Canon PowerShot A560

Nonparametric CDF

15 utility
Part II. Canon PowerShot SD800

20 utility

Part III. Sony CyberShot DSC-T200

Part IV. Pentax K10D SLR

60 utility
The theoretical distribution is contained inside the 95 percent confidence interval of the nonparametric distribution except for some high values of utility Canon PowerShot A560, which has the largest minimized square value in estimation. The kinks at zero and one occur because of the restriction imposed by the cumulative distribution function.
Overall, the theoretical model fits the data reasonably well considering the few parameters we use in estimation and strong symmetric conditions of the model.

5. Conclusion

In this paper, we empirically estimate a more general version of the clearinghouse model. Our estimates suggest that factors that generate price dispersion within a firm are similar across the four digital cameras. The maximal profit margin ranges from 16 to 22 percent and the estimated proportion of consumers who visit the price comparison site is 16 to 26 percent. When store managers believe to be competing with four to five stores, the estimated proportion of consumers who do not compare prices and buy from their local store is about 18 percent. The cost of adjusting prices at the comparison site is small across the four products. Although our theoretical model simplifies dramatically the observed real world price dispersion down to only four parameters, the theoretical model explains the data reasonably well.

6. Appendix

Proof of Proposition 1:
In Gao (2010)s proof of the click-fee scenario, the hassle cost k is not present. Her result is such that firms will have a continuum of advertising probabilities and hence the corresponding utility offering strategies. The key role of the hassle cost k is to establish a unique symmetric equilibrium, both in the advertising probability and the mixed strategy utility. When k is positive, we can pin down the unique from S EA 0 = ENA 0. That is, LX+ 1 N1 S X t k = LX + 1 N1 N X. So, = 1

k S( 1

1 Xt) N 1 N 1
. m is from EA m = ENA 0 and G m from EA m = ENA 0.
In terms of the optimal click fee, we look at the gatekeepers revenue maximization (or profit maximization so long as the cost structure of the gatekeeper does not depend on the flat fee instrument or the product prices which is usually the case). RG t = (1 (1 )N )St. By our model assumptions, if only one firm advertises on the price comparison website, the shoppers will click through the companys webpage link and purchase from it. Hence, the gatekeeper cares only the probability that no one firm advertises which is the term inside the parentheses before St. When at least one firm advertises, the gatekeeper earns the total of the market share of the shoppers (denoted as S) multiplied the per-click fee t. We follow the standard approach: plug in the expression of and take the first order condition of RG t. Furthermore, we check the second order condition and see if the first order condition indeed yields the maximum.

N N 1 N N 1 N N1

NS 2X t dR G t dt

k 1 X t N

+S(tX 1

k 1 Xt N

N 1 (N tX +X )
(2SX (N 1)2 +StN ) d2 RG t dt 2

(N 1)2 ( 1

1 X t)2 N
From the complex expression of the first order condition of the click fee, we can say there is no explicit expression for it. From the second order condition, we can tell there is unique click fee that optimizes the gatekeepers revenue.

Proof of Proposition 2:

It is the same as Gao (2010). The addition of the hassle cost does not affect the transformation from the utility offering strategy to the price strategy. By our assumption that the maximal profit margin X is the same across all firms that have different service qualities, we have = . Furthermore, the utility decision in fact is the price decision from = . As a result, an individual firms mixed strategy advertised can be recovered from the common mixed strategy utlity. = = + = = = 1 = 1 ( ). Accordingly, the support of an individual firms price follows from the transformation.

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