Estimating Durable Goods Adoption Decisions From ...

Estimating Durable Goods Adoption Decisions From Stated Preference Data∗ Jean-Pierre Dubé

Günter J. Hitsch

Pranav Jindal

Booth School of Business University of Chicago

October 2009 Preliminary and Incomplete—Please Do Not Distribute or Quote Without Authors’ Permission

Abstract —

∗

We acknowledge the Kilts Center for Marketing at the Booth School of Business, University of Chicago for providing research funds. The first author was also supported by the Neubauer Family Faculty Fund, and the second author was also supported by the Beatrice Foods Co. Faculty Research Fund at the Booth School of Business. All correspondence may be addressed to the authors at the Booth School of Business, University of Chicago, 5807 South Woodlawn Avenue, Chicago, IL 60637; or via e-mail at [email protected] or [email protected].

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1

Introduction

Durable goods adoption decisions are complicated to model because of the inherent intertemporal substitution between buying in the present versus buying at a future date. Therefore, consumers’ adoption decisions depend not only on their preferences among alternative products, but also on the extent to which they discount future utility flows and on their subjective expectations about future market conditions, such as future prices. The marketing literature has developed two different methodologies, conjoint analysis and new product diffusion models, that can be used to predict durable goods adoption decisions. Conjoint analysis (originating with Green and Rao 1971) has often been applied to durable goods purchases (see Green and Srinivasan 1990, Green, Krieger, and Wind 2001, and Huber 1997 for recent surveys). The advantage of the approach is that it can be used to infer how consumers trade off the price of a new product for other product attributes. However, the conjoint literature typically disregards the question of how consumers trade off buying a product now versus buying it in future. Effectively, the literature assumes that consumers are myopic and that they fully discount the future (i.e. have a discount factor of zero). Adoption is therefore reduced to a classic discrete choice problem. Since this assumption of myopia is unlikely to hold in many consumer goods markets, we expect it would lead to biased preference estimates. For example, assuming myopia for a subject who chooses not to purchase today in anticipation of a price cut in the future would lead to a downward bias in the predicted utility for the good in question. New product diffusion models, which originated with the seminal work of Bass (1969), address the question of when consumers will adopt a new product. New product diffusion models typically fit the historical sales evolution of a new product well. However, traditional diffusion models are not derived from individual consumer decisions. Hence, an analysis of how individual preferences, expectations, and discount factors affect the adoption of a new product is not directly possible. In contrast, the recent diffusion literature, beginning with Horsky (1990), derives the aggregate sales evolution from individual decisions. During the last decade, this literature has adopted the dynamic discrete choice approach of Rust (1987) to model and estimate durable goods demand (Melnikov 2000, Song and Chintagunta 2003, Nair 2007). While theoretically attractive, dynamic discrete choice models suffer from a fundamental under-identification problem. Consumers’ utility functions are only identified given knowledge of the discount factors and the subjective beliefs about future market conditions (Magnac and Thesmar 2002). In practice, researchers using field data on consumer choices assume a value

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for the discount factor and assume that consumers have rational (self-fulfilling) expectations. We expect that the assumptions of rational expectations and a known discount factor are unlikely to be correct in many empirical contexts. The discount factor is typically assumed to reflect the current interest rate. From other work, we know that the rate at which consumers discount the future can vary tremendously across individuals and can differ substantially from the current market rate of interest (Frederick, Loewenstein, and O’Donoghue 2002). It is also unlikely that consumers form mutually-consistent, self-fulfilling beliefs about future market outcomes such as prices. We develop a new approach to estimating a durable goods adoption model, which combines elements of the dynamic discrete choice approach with the experimental advantages of a conjoint survey design. Our approach overcomes the inherent identification problem in dynamic discrete choice models that are calibrated from field data, and extends the conjoint literature to account for forward-looking consumer behavior. The critical advantage of the conjoint setting is the researcher’s ability to manipulate (i.e. create independent variation) in the subjects’ expectations about the future. Our approach also has the advantage that it can be implemented before actual sales data from a new product are available. In contrast, the parameters of a new-product diffusion model are typically calibrated using a “guessing by analogy” approach. We run two studies in which subjects are asked to choose when they would adopt a BluRay player. In both studies, subjects are provided with expert forecasts of future prices and the number of available movie titles. In the second study, we also allow subjects to choose between the two leading brands, Sony and Samsung, to allow for a more realistic choice context. In both studies, our findings strongly support forward-looking consumer behavior. The raw data provide striking evidence of rational, forward-looking choices. Focusing on the observed choices within a subject, we routinely observe delayed adoption in response to future price reductions and accelerated adoption in response to current price reductions. These responses are too systematic to be the outcome of chance alone (i.e. random error). We also assess forward-looking behavior by fitting a structural discrete choice demand model to the choice data in which subjects are allowed to discount future utility flows. This model is found to fit the choice data considerably better than models that restrict the discount factor to be zero (i.e. myopia) or that restrict the discount factor to be one (i.e. subjects do not perceive a trade-off between current and future consumption). Several interesting insights emerge from the estimated distribution of discount factors. 3

First, subjects’ typically discount the future at a much higher rate than is typically assumed by the empirical research using field data. In both studies, the average discount factor is roughly 0.7, as opposed to assumptions ranging from 0.9 to 0.99 in the field data literature. That is, we find subjects to be much more impatient in their adoption decisions than is typically assumed. However, probing deeper into the role of impatience, we fail to detect strong support for hyperbolic discounting. This finding is consistent with Chevalier and Goolsbee (2005) who also measure discount factors for a durable good (textbooks). To the best of our knowledge, empirical evidence for hyperbolic discounting (c.f. the survey by Angeletos, Laibson, Repetto, Tobacman, and Weinberg (2001)) has not been documented in the context of purchase decisions for durable goods. The remainder of the document is organized as follows. In section 2, we discuss the dynamic discrete choice and the inherent identification problems associated with its estimation using field data. In section 3 we derive the adoption model used for our conjoint setting. We discuss the design of our survey and the resulting data in sections 4 and 5, respectively. Evidence of forward-looking and actual model estimates are presented in sections 6 and 7, respectively. We conclude in section 8.

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Dynamic Discrete Choice Adoption Models

As discussed in the introduction, the recent literature on durable goods demand estimation has adopted the dynamic discrete choice model approach of Rust (1987). Consider a consumer who decides to adopt one of J products in each period t = 0, 1, . . . The consumer’s choice in period t is denoted by j ∈ {0, . . . , J}, where j = 0 denotes the decision of postponing the adoption of a product until some future period. In each period, the consumer observes a state vector xt , which may include the prices of all products or the availability of complementary goods, such as Blu-ray movies for a Bluray player. The consumer believes that the state evolves according to the Markov process p(xt+1 |xt , j). We denote the flow utility from action j in period t by uj (xt ). As is standard in discrete choice models, we normalize the utility from one choice, j = 0, such that u0 (xt ) ≡ 0. In addition to uj (xt ), the consumer receives a random utility component, jt , which we assume is i.i.d. across products and periods with pdf p(), where  = (0 , . . . , J ). The value of choosing action j, net of the random utility component, jt , is given by the

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choice-specific value function of j, Z vj (xt ) = uj (xt ) + β

max {vk (x0 ) + k }p()p(x0 |xt , j)ddx0 .

k∈{0,...,J}

β ∈ [0, 1) is the consumer’s discount factor. This equation says that the value from adopting j is given by the current flow value, and the expected present value of the best choice that the consumer can make tomorrow, after the consumer observes the realized values of xt+1 and t+1 . Define the expected value function: Z v(x) ≡

max {vk (x) + k }p()d.

(1)

k∈{0,...,J}

v(xt ) is the value that the consumer expects in period t after observing xt but before observing t . Using the definition of the expected value function, the choice-specific value functions can be written in simpler form as Z vj (xt ) = uj (xt ) + β

v(x0 )p(x0 |xt , j)dx0 .

(2)

Furthermore, the expected value function satisfies the recursive relationship Z v(xt ) =

Z max {uk (xt ) + k + β

k∈{0,...,J}

v(x0 )p(x0 |xt , k)dx0 }p()d.

(3)

It can be shown that under mild conditions, the right-hand side of the Bellman equation (3) defines a contraction mapping; thus there exists a unique value function satisfying equation (3). Let us summarize the discussion so far. The primitives of our model are the utility functions, uj (xt ), the distribution of latent utility components, p(), the consumer’s belief about the evolution of the state vector, p(xt+1 |xt , j), and the consumer’s discount factor, β. Given these model primitives, the expected value function is defined by equation (3), and the choice-specific value functions are defined by equation (2). The consumer will then choose action j, given xt and t , if and only if vj (xt ) + jt ≥ vk (xt ) + kt for all k 6= j. In the econometric analysis of dynamic discrete choice models, we assume that the researcher observes all or part of the state vector xt , but not the random utility components jt . We thus define the probability of choosing action j, given the state xt , as σj (xt ). σj (xt ) is called the conditional choice probability (CCP) of j. If jt has the Type I Extreme Value

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distribution, the conditional choice probabilities are given by the logit formula exp(vj (xt )) . σj (xt ) = PJ k=0 exp(vk (xt )) Along many dimensions, dynamic discrete choice models are very similar to standard, static discrete choice models, with the choice-specific value functions, vj (xt ), taking the place of the utility functions in a static choice model. However, static and dynamic discrete choice models differ fundamentally in terms of the conditions under which the model primitives are econometrically identified. We will discuss these differences next. Identification of Dynamic Discrete Choice Models In this section we explore the conditions under which the dynamic discrete choice model is identified. Our discussion follows Bajari, Chernozhukov, Hong, and Nekipelov (2008). We assume that all components of the state vector, xt , are observed. Given an infinitely large data set, we thus observe the conditional choice probabilities, σj (xt ), hereafter CCPs. Given the CCPs, and the assumption that the random utility components are type I extreme value distributed, we can infer the choice-specific value function differences directly from the data: vj (xt ) − v0 (xt ) = log(σj (xt )) − log(σ0 (xt )).

(4)

As shown by Hotz and Miller (1993), a similar inversion exists for more general distributions of the random utility components, p(), although the inversion will typically not have a convenient closed form. Proposition. Suppose we know the distribution of the random utility components, p(), the consumers beliefs about the evolution of the state vector, p(x0 |x, j), and the discount factor, β. Let the CCPs, σj (x), be given for all x and j = 0, . . . , J. Then: (i) We can infer the unique choice-specific value functions, vj (x), consistent with the consumer decision model. (ii) The utilities, uj (x), are identified for all states, x, and choices, j. To see why the proposition holds, first re-write the expected value function: Z max {vk (x) + k }p()d

v(xt ) =

k∈{0,...,J}

Z =

max {vk (x) − v0 (x) + k }p()d + v0 (x).

k∈{0,...,J}

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(5)

Using equation (5) and the inversion (4), we can express v0 (xt ), as given by (2), in the following form (remember that u0 (xt ) ≡ 0): Z

v0 (xt ) = u0 (xt ) + β v(x0 )p(x0 |xt , 0)dx0 Z Z 0 0 0 0 = β max {vk (x ) − v0 (x ) + k }p()p(x |xt , 0)ddx + β v0 (x0 )p(x0 |xt , 0)dx0 k∈{0,...,J} Z = β max {log(σk (x0 )) − log(σ0 (x0 )) + k }p()p(x0 |xt , 0)ddx0 k∈{0,...,J} Z +β v0 (x0 )p(x0 |xt , 0)dx0 (6) Note that the first term on the right-hand side of the equation above can be calculated given the CCPs and the distributions of  and xt+1 . Under some weak assumptions (see Bajari et al. 2008), equation (6) defines a contraction mapping with a unique solution v0 (x). Hence, we can infer v0 (xt ) from the data. We can then calculate all choice-specific value functions from the inversion (4): vj (xt ) = log(σj (xt )) − log(σ0 (xt )) + v0 (xt ). Given the choice-specific value functions, we can also calculate the the expected value function (1), and then infer the utility functions from the equation defining the choice-specific value functions: Z uj (xt ) = vj (xt ) − β

v(x0 )p(x0 |xt , j)dx.

The proposition says that if we are willing to treat p(), p(x0 |x, j) and β as known, the consumer’s utility function is non-parametrically identified. Assuming knowledge of p(), the distribution of the latent utility terms, is standard in the discrete choice literature and— especially if we allow for heterogeneity across consumer preferences—not a strong assumption. However, the solution to the contraction mapping (6) depends on β and p(x0 |x, j). If we assume a different discount factor, β 0 , or a different transition density, p(x0 |x, j), we would infer a different set of choice-specific value functions, vj0 (x), and utilities, u0j (x). Hence, for any assumption about the consumer’s discount factor, β, and the consumer’s beliefs about the evolution of the state vector, p (x0 |x, j) , there exist utility functions, uj (x), that entirely rationalize the observed choices! Without further assumptions, the model primitives uj (x), 7

β, and p(x0 |x, j), are not non-parametrically identified. To overcome the identification problem partially, the recent dynamic discrete choice literature assumes rational expectations. Rational expectations mean that the consumer’s subjective beliefs, p(x0 |x, j), coincide with the actual evolution of the state vector. Thus, p(x0 |x, j) can be directly inferred from the data. However, we showed above that knowing p(x0 |x, j) is insufficient to identify jointly the utility functions, uj (x), and the discount factor, β. In practice, the identification problem is sufficiently strong such that researchers are typically unable to estimate β even if a specific parametric form of uj (x) is assumed. Hence, the extant literature typically assumes the discount factor is known to reflect some economy-wide interest rate, r, such that β = 1/(1 + r). We consider the non-identification results discussed above to be grave problems for applied research. First, countless studies in psychology and behavioral economics cast doubt on the assumption of a uniform discount factor that corresponds to long-run asset returns (Frederick, Loewenstein, and O’Donoghue 2002). Second, the rational expectations assumption is hard to justify, particularly in the case of a new product where consumers do not have access to past data from which to learn the process that governs prices and other components of xt . The identification problem described above does not apply to static discrete choice models. In static discrete choice models, we can directly infer the utility differences from equation (4). Given the normalization u0 (x) ≡ 0, the utility functions uj (x) are non-parametrically identified.

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Adoption Model

We discuss two models of the consumer’s adoption decisions for high-definition video technology specifically. Both of these models are special cases of the general dynamic discrete choice model of Section 2. As in the general model, time is discrete, and indexed by t = 0, 1, . . . We denote the last survey period by T. The state variable, xt = (Pt , Nt ), includes the prices of all products considered, Pt , and the number of available movie titles, Nt . A key feature of our survey simplifies the consumer’s decision process: while the consumers forms beliefs about the evolution of the state in the general model, they are presented with the future evolution of the states in our survey. Hence, the evolution of the state vector, x0 , x1 , . . . , is given to the consumers. To develop a specific form of the per-period utility function, uj (xt ), we first define the present value of watching movies

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ωt =

∞ X

β t−k ψ(Nk ).

k=t

ωt is the flow utility derived from watching some (or all) of the available movies, discounted to period t. In our empirical application, we assume that ψ(N ) = λN. We then define the choice-specific value of adopting product j in period t : vjt = β t (δj − αPjt + ωt ) . δj is the product intercept of product or brand j, which includes the consumer’s valuation of all tangible and intangible product attributes. α is the marginal utility of income. vjt is the present value of using a Blu-ray player and watching movies in all periods k ≥ t. vjt includes all current and future utilities from buying j; hence, no future expected value needs to be added. Model 1 Assume that consumers observe all random utility components, jt , for the survey periods t = 0, . . . , T. Also, consumers observe a random utility term for the outside option, 0 , which includes both the possibility that the consumer never adopts a product or that the consumer adopts after period T. The consumer then adopts product j in period t if and only if vjt +jt ≥ vlτ +lτ for all l = 1, . . . , J and τ ≤ T and vjt +jt ≥ 0 . If vjt +jt < 0 for all j and t ≤ T the consumer will not adopt the product by period T . We assume that the random utility terms are type I extreme value distributed. Consumer choices are then given by a multinomial logit model with T · J + 1 options. Because future prices and software titles are given, and because we assume that consumers observe the random utility terms, we have a model of perfect foresight. Hence, the model can be solved without having to use dynamic programming techniques. Model 2 In model 2 we assume that consumers do not evaluate all T · J + 1 options simultaneously, but instead evaluate the purchase decisions sequentially beginning in period t = 0. That is, they draw their latent utility terms, , sequentially. To derive the option value of waiting, assume that consumers expect that prices and the number of movie titles will remain at the value in the last survey period T, such that Pt = PT and Nt = NT for all t > T (this assumption can 9

be relaxed). The value of waiting in period T is then given by Z v0T =

max {vkT + k }p()d,

k∈{0,...,J}

and the value of waiting in periods t < T can be recursively defined as Z v0t =

max {vk,t+1 + k }p()d.

k∈{0,...,J}

If the consumer decides to wait in period t − 1, he or she then evaluates vkt + tk for all k = 0, . . . , J. If option j yields the largest value, the consumer reports the choice of adoption j in period t in the survey. Otherwise, the consumer moves on to period t + 1 and again evaluates the choice-specific values. A disadvantage of model 1 is that the outside option lumps together the value of never buying, and the option value of adopting one of the products after period T. Hence, the estimated intercepts need to be interpreted relative to this “compound” outside option. In model 2, on the other hand, the value of waiting is defined exactly to include both the probability of waiting again next period and the probability of adopting one of the J products. Hence, the estimated product intercepts can be interpreted relative to the option of never adopting one of the products. Model 2 is slightly more difficult to solve than model 1, however. The models differ in the assumption of how the consumers solve the choice process in the adoption survey. A priori, it is not clear which of the two assumptions is more “realistic.”

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Survey Design

We designed two online surveys which differ in the complexity of the choice tasks faced by the subjects. In several introductory screens, we first give the subjects an overview of the Blu-ray technology and compare the benefits of Blu-ray over regular DVD movies. We then present the subjects with the choice tasks. Figure 1 shows a screen in the first survey. The screen provides the subjects with information about the evolution of prices for a medium quality Blu-ray player from March 2009 (referred to as “Now”) to December 2011. We ask the subjects if and when they would adopt the Blu-ray player. Subjects can choose the “Will not buy” option which indicates that either they will never buy the Blu-ray player or that they might buy the Blu-ray player after December 2011. On each screen, we remind the subjects of the number of Blu-ray movie titles

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available in each period. In the first survey, the number of titles remains the same across choice tasks. In the second survey, the subjects choose among two Blu-ray player brands (Sony and Samsung). The left-hand side of the screen (Figure 3) provides the subjects with information about the evolution of prices for the two brands from December 2008 to December 2012. The right-hand side of the screen provides corresponding information on the number of available Blu-ray movie titles. We ask the subjects if and when they would adopt one of the available players. The subjects in these conjoint experiments face a complex task and need to process a large amount of information. For this reason, we do not vary all product attributes (current and future prices and movie titles) simultaneously across choice tasks. Instead, we vary one factor at a time. The survey consists of two or more blocks. Subjects and blocks are randomly matched. The first screen in each block presents a particular base scenario (Figure 3), defined by a sequence of prices and the number of movie titles. In the subsequent screens, we randomly vary current or future product prices in one time period only. For example, Figure 2 shows a screen where the price of a medium quality Blu-ray player in December 2009 is lower relative to the base scenario in Figure 1, while all other prices remain constant. In the second survey, we also vary the number of movie titles (in at most two time periods) across screens. Across different blocks, we vary the sequence of prices in all time periods, and, in survey two, we also vary the sequence of movie titles. Note that these particular designs of our survey are also useful to capture how the subjects change their adoption timing decisions in response to future price or title changes within a given choice scenario. This allows us to conduct simple tests of forward-looking behavior, which are discussed in Section 6.

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Data Description

The data were collected using the online panel of Market Tools, Inc, a national market research company. The panel is meant to represent the US population and is used by many large consumer goods firms such as General Mills. Tables 1 and 2 summarize the survey. The data from the first study consist of choices from 1,000 respondents; a fraction was randomly sampled from the Market Tools panel, while the remaining fraction was obtained using oversampling based on expressed interest in high definition products. Each respondent was exposed to 2 blocks and answered 4 questions in each block, resulting in 8,000 choices. The data from

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the second conjoint experiment consists of 505 respondents. Again, we selected a fraction of these randomly from the U.S. population and oversampled the remaining based on expressed interest in high definition products. Each respondent was exposed to either 2 or 3 blocks and answered 6 questions in each block, resulting in a data set of 6,576 choices. To avoid any bias, we ensured that the subjects were drawn from different samples for the two experiments. Table 4 shows the distribution of demographics and other attributes across the subjects in both studies. Due to the oversampling scheme employed, 77% of respondents in the first survey and 82% of respondents in the second survey expressed interest in high definition products. Tables 1 and 3 report the distribution of the modal choices across subjects. The data reveal a generally high purchase intent for a Blu-ray player—only 18% of subjects in survey 1 and 17% of subjects in survey 2 most frequently choose “Will not buy.” We observe subjects with modes in all survey periods, but overall the modal choices are concentrated in the last two periods in survey 1 and the middle two periods in survey 2. Within-subject variation in choices is important to document dynamic adoption timing patterns in the data (see Section 6) and to estimate consumer heterogeneity. Tables 1 and 3 show the distributions of the number of distinct choices made by the subjects. For example, if a subject chooses Sony in December 2009 once, Sony in December 2010 three times, and “Will not buy” in all other choice tasks, the number of distinct choices made by that subject is three. The highest possible number of distinct choices in the first experiment is 5 (4 periods and the “Will not buy” option) and in the second experiment it is 13 (a combination of 2 brands, 6 periods and the “Will not buy” option). We find that about one third of the subjects never vary their choice across tasks. In survey 1, 48% of the subjects make two distinct choices and 14% make three distinct choices. In survey 2, we observe 51% of the subjects making two or three distinct choices and 12% making four or five distinct choices. While 73% of the subjects always choose the same brand (or the “Will not buy” option), 63% make choices in at least two different time periods.

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Direct Evidence of Forward-Looking Behavior

In this section, we provide evidence for forward-looking consumer behavior and dynamic adoption timing without resorting to a statistical model. Our survey design allows us to detect within-subject changes in the adoption time which directly reveal whether the subjects respond to price changes in a rational manner.

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We focus on survey 1, where the subjects can only substitute across time, but not across products (although they can choose the outside option of not buying). Suppose a subject is exposed to the price sequence P0 , . . . , PT in the base screen, and chooses to adopt the product in period t. In each subsequent task, exactly one of the T + 1 prices increases or decreases. If the subject is exposed to a price decrease or increase in period t, then we classify the observation as exhibiting a current price increase or decrease. If the subject is exposed to a price increase or decrease in any period τ < t, then we speak of a past price increase or decrease, and we define future price increases or decreases in the same manner. Suppose the subject’s indirect utility function is additively separable across time periods and that the per-period utility function is decreasing in the current price. Rationality then implies that the subject should not change her adoption choice if the current price decreases. On the other hand, a current price increase is consistent with any choice, including a change of the adoption time to another period or a switch to the “will not buy” option. If a past price decreases, rationality implies that the subject should not change her choice or adopt the product earlier, in period s < t. Vice versa, if a future price decreases, the subject should not change her choice or delay the adoption of the product to period s > t. However, for both past and future price increases, the subject should not change her choice. These predictions only hold if the subject’s preferences do not vary across choice tasks, i.e. if the random utility terms jt remain constant. Suppose these terms do vary across tasks, for example because they represent mistakes that the subjects make. If the mistakes are random, then the changes in adoption times across periods should still be systematically related to the predictions of rational behavior as discussed above. Table 5 shows how the subjects respond to current, past, and future price increases. Overall, 90% of all observations are consistent with rational behavior as discussed above. For a past price decrease, 30% of the subjects buy the product earlier than indicated in the base screen, while 7% buy the product later and 2% switch to “no buy.” Vice versa, for a past price increase, 5% buy earlier, 5% buy later, and 3% switch to “no buy.” If there is a future price decrease, 42% of subjects delay their original purchase, while 5% buy earlier and 1% switch to “no buy.” If there is a future price increase, on the other hand, 16% buy later, while 4% buy earlier and 2% switch to “no buy.” Overall, therefore, we see that the subjects change their adoption times in a manner that is remarkably consistent with the predictions of rational choice, although we also observe choices that might be mistakes. Overall, 90% of all observations are “correctly classified,” i.e. can be explained by rationality without having to resort to change in the error terms jt across tasks. 13

7

Estimation and Results

We now discuss the empirical results for the two adoption studies. For each survey, we compare results for four model specifications. For each model, we report results for both homogeneous and heterogeneous (normally distributed random coefficients) specifications. In each case, we report quantiles of the posterior distribution of the population hyperparameters to assess the parameter magnitudes and precisions. We also report the log marginal density as well as a trimmed log marginal density where we trim the upper and lower 2 percentile posterior draws to correct for outlier effects. We use the Newton and Raftery (1994) approach to compute the log marginal density of each model. Comparing log marginal densities across models is roughly equivalent to computing a Bayes’ Factor to assess relative posterior model fit. We begin with our baseline dynamic MNL model which accounts for forward-looking behavior and dynamic adoption timing. Recall (Section 3) that the choice-specific value from adopting product j in period t is given by vjt = β t (δj − αPjt + ωt ) , where ωt denotes the present value of software, ωt =

P∞

k=t β

t−k ψ(N ). k

We assume that the

flow-value derived from watching Blu-ray movies is ψ(N ) = λN. For each subject h, we observe the adoption choice yjth . yjth = 1 if subject h chooses product j in period t, and yjth = 0 otherwise. Assuming that the total utility from choosing j in period t is given by vjth + jth , where the random utility term jth has the type I extreme value distribution, the choice probabilities are given by: Pr{yhjt = 1} =

1+

exp(vhjt ) . PJ exp(v ) hlk l=1 k=0

PT

(7)

This model is a dynamic analog of the multinomial logit model, and we call it the “Dynamic MNL Model.” We estimate the discount factor subject to the restriction that 0 ≤ β ≤ 1. We impose this restriction by expressing the discount factor using a logistic transformation based on the unrestricted parameter γ, such that β = exp(γ)/(1 + exp(γ)). To simplify the notation, we use the vector θh to denote the subjects’ taste parameters, (δ1h , ..., δJh , αh , λh , γ h ). We then allow for heterogeneity by assuming that the subjects’ parameters are drawn from a common population normal distribution: θh ∼ N (θ, Vθ ). Priors on the

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population hyper-parameters, θ and Vθ , are specified as follows: θ|Vθ ∼ N (0, a−1 Vθ ) Vθ ∼ IW (ν, νI)

(8)

where a = 1/16 and ν = dim(θh ) + 3, which are proper but very diffuse prior settings. The model is estimated using a hybrid MCMC approach with a customized Metropolis step as discussed in Rossi, Allenby, and McCulloch (2005) (Chapter 5) and applied in Dubé, Hitsch, and Rossi (2009). To assess the role of discounting in the model, we also estimate two benchmark specifications. The first benchmark model, Current Adoption MNL, considers only the current adoption decision, effectively imposing zero expected flow utility in any future period. Thus, vjth = δjh − αh Pjt + λh Njth for period t = 0, and vjth = 0 for all t > 0. This model is equivalent to assuming that a consumer is myopic, restricting the discount factor to be zero (β = 0) as in much of the extant literature. The second benchmark model, MNL, is a generic multinomial logit model in which each brand/period combination is treated like a separate choice alternative. Thus, vjth = δjh − αh Pjt + λh Njth for all periods t = 0, 1, . . . , T. This model is equivalent to a model where the consumer has a discount factor of 1 on future indirect utility and a separate discount factor of 0 on the future utility from watching movies. We also estimate a fourth specification, Dynamic MNL with Hyperbolic Discounting, to test whether consumers exhibit an inherent preference for immediacy. The discount function for the case of geometric discounting corresponds to the sequence (1, β, β 2 , . . . ). For the hyperbolic discounting case, following one specification which is widely used in the literature, we parametrize the discount function using the specification of Phelps and Pollak (1968). The corresponding sequence of discount factors is (1, ρβ, ρβ 2 , ρβ 3 , . . . ). The parameter ρ reflects an inherent preference for immediacy, which is a priori plausible for consumer electronics. Note that this specification nests the baseline Dynamic MNL model with geometric discounting when ρ = 1.

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Survey 1 In survey 1, we focus on a simple choice context in which subjects choose if and when to adopt a single Blu-ray player of medium or average quality. Our goal is to test whether subjects are forward-looking and the extent to which they discount future consumption. To keep the survey simple, we do not vary the number of Blu-ray movies across tasks (although the number of movies as reported to the subjects varies across periods). Hence, we do not attempt to estimate the value of watching movies. Instead, we estimate a period-specific intercept to control for the effect of movie titles on choices. Below, in survey 2, we will explicitly consider the effect of movie availability on adoption choices. Results for the four model specifications are reported in Tables 6, 7, 8, and 9. Focusing on the log-marginal density of each of the four models, it is not surprising to see that controlling for between-subject heterogeneity increases fit substantially as seen by the large increases in the log-marginal-density. We also observe that the dynamic MNL specification fits better than the two benchmark models. Given our model-free evidence for forward-looking adoption behavior (Section 6), it is not surprising that the Current Adoption model has a considerably worse relative fit than the other specifications. Since the Dynamic MNL model nests the Current Adoption model, we can interpret our comparison of log marginal densities as strong evidence against the restriction that β = 0. Substantively, we can see the importance of freeing up the discount factor parameters. Besides improving model fit, we also see substantive changes in the estimated preferences. The Dynamic MNL model exhibits much more heterogeneity, as seen by comparing the population standard deviation of tastes across models. The Dynamic MNL model also generates a posterior distribution on the price coefficient that is centered around a larger magnitude than the benchmark MNL specification. The Dynamic MNL model also has a marginally better relative fit than the Dynamic MNL models that allows for hyperbolic discounting, in spite of the fact that the latter includes one additional free parameter. The distribution of parameters determining the hyperbolic discount factor ρ = exp(γρ )/(1+exp(γρ )) in Table 9 implies that most of the mass of the distribution of ρ is concentrated close to 1, which can be directly seen in Figure 6. Given the scant evidence for hyperbolic discounting, we will therefore focus on the Dynamic MNL specification for the remainder of this Section. Given the strong relative fit of the Dynamic MNL model, we conclude that discounting plays an important role in the subjects’ decision-making. In Figure 4, we report the dis-

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tribution of subjects’ posterior mean discount factors. In practice, researchers estimating dynamic discrete choice problems routinely assume that consumers discount the future with a common discount factor predicated by the current interest rate. For annual decision-making, this assumption would imply a discount factor of approximately 0.95 if the interest rate is 5%. Looking at the estimates, subjects’ clearly exhibit considerably more discounting than is typically assumed. The average subject has a discount factor of roughly 0.7, which corresponds to an interest rate of 43%. Moreover, there is striking heterogeneity in the degree of discounting across subjects. While the axioms of rationality do not per se imply how subjects should discount the future, our findings indicate considerably more impatience than would be implied by historic long-term asset returns.

Survey 2 We conducted survey 2 to verify that our findings regarding discounting and forward-looking are robust to a more complex and possibly more realistic environment. Survey 2 considers a choice between the two leading brands, Sony and Samsung, and we also vary the number of available movie titles across choice tasks. Results for the four model specifications are reported in Tables 10, 11, 12, and 13. Our basic findings are highly consistent with those from survey 1. The Dynamic MNL model fits much better than the two benchmark models. As before, the Dynamic MNL model with hyperbolic discounting has a comparable fit to the Dynamic MNL model. Substantively, we see the importance of allowing for an unrestricted discount factor much more strongly in survey 2. The posterior distribution of the coefficient on titles in both benchmark models (Tables 10 and 11) is centered well below zero, which seems implausible for the technology in question.1 However, we obtain a positive sign on the Titles coefficient once we free up the discount factor parameter in the Dynamic MNL model, Table 12. The Dynamic MNL model also generates a posterior distribution on the price coefficient that is centered around a larger magnitude than the benchmark specifications. Finally, the Dynamic MNL model predicts more heterogeneity across subjects in their tastes. Interestingly, the Dynamic MNL model with hyperbolic discounting has a slightly better fit than the Dynamic MNL model. Technically speaking, this comparison of log marginal densities implies that we reject the parameter restriction ρ = 1. However, close inspection of the two models reveals that they lead to qualitatively and statistically indistinguishable 1 In fact, the magnitude of the standard deviation of the posterior distribution for the coefficient on titles implies that most of the mass is over negative utility.

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results. As shown in Figure 7, the distribution of the posterior means of the hyperbolic discount factors ρ has most of its mass very close to 1. For the remainder of this section, we will therefore focus on the Dynamic MNL specification. In Figure 5, we report the distribution of subjects’ posterior mean discount factors. As in survey 1, the average subject has a discount factor of roughly 0.7, which corresponds to an interest rate of 43%. We also observe considerable heterogeneity across subjects in their subjective discount rates, albeit less than in survey 1. In Table 14, we report the estimated correlation matrix for the population distribution of the taste parameters. Interestingly, we observe a very strong negative correlation between γ (recall thatβ = exp(γ)/(1 + exp(γ))) and the price coefficient. Roughly speaking, this implies that higher patience (i.e. a larger discount parameter) is associated with higher price sensitivity (i.e. a larger in magnitude price coefficient). To a lesser extent, we also observe a negative correlation between the discount parameter and the titles coefficient, implying that subjects with a relatively low utility from titles exhibit more patience. Both these correlations have interesting managerial implications. Suppose a monopolist was selling a BluRay player to this population of consumers. Coase argued that skimming (inter-temporal price discrimination) would unravel if high willingness-to-pay consumers could anticipate future price discounts and wait for them. Nair (2007) qualified this argument by pointing out that consumer discounting of future utility might nevertheless permit some skimming, albeit as a considerably lower rate than in a world with myopic consumers. Our findings indicate that high willingness-to-pay consumers (i.e. those with a low sensitivity to prices and a high sensitivity to titles) are the most impatient, which works even more strongly against the Coasean view. This insight could not be estimated from an analysis of standard field data as one could not distinguish between early adoption due to high intrinsic utility versus impatience. This point illustrates the under-identification problem we discussed in section 6.

8

Conclusions (Very Preliminary)

We find strong evidence that subjects in our studies are forward-looking in their purchase decisions for a durable good. Direct examination of the within-subject variation in adoption timing reveals responses to price changes that are, overall, consistent with rational behavior. A Bayesian model selection test based on the demand estimates rejects a model with myopic decision making and a model where subjects do not perceive a trade-off between buying now and buying in future over a model with forward-looking.

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In both studies, we find an average discount factor in the population of roughly β = 0.7. This discount factor corresponds to an annual interest rate of 43% and implies much less patience than usually assumed in empirical applications of dynamic discrete choice models. There is also substantial heterogeneity in the discount factor across consumers. While most subjects are found to be more impatient than empirical applications with field data typically assume, we find little evidence for hyperbolic discounting. Namely, subjects do not appear to exhibit an inherent preference for immediate consumption. These findings have several substantive implications for managers. First, the findings suggest that conjoint surveys for durable goods should be augmented to allow for forwardlooking behavior. Second, such surveys should allow the discount factor to vary freely as our evidence suggests more impatience than is typically assumed. Finally, our demand estimates have interesting implications for the pricing of a new product launch. We find a segment of “early adopters,” i.e. subjects who are impatient but have a high value for the product. The existence of such consumers enables firms to implement a successful price-skimming strategy. We see several directions for future research based on the findings herein. Most importantly, our current survey design calibrates subjects’ beliefs to be deterministic. In practice, a consumer may not have access to expert forecasts or may have, at best, imperfect information. An interesting extension would be to study how consumers form beliefs about future market outcomes and to incorporate these beliefs into the choice forecasting exercise. In light of our findings about discount factors, we also believe that empirical applications of dynamic discrete choice models would benefit from combining field and survey data.

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References Angeletos, G.-M., D. Laibson, A. Repetto, J. Tobacman, and S. Weinberg (2001): “The Hyperbolic Consumption Model: Calibration, Simulation, and Empirical Evaluation,” Journal of Economic Perspectives, 15(3), 47–68. Bajari, P., V. Chernozhukov, H. Hong, and D. Nekipelov (2008): “Nonparametric and Semiparametric Analysis of a Dynamic Game Model,” manuscript. Bass, F. M. (1969): “A New Product Growth Model for Consumer Durables,” Management Science, 15(5), 215–227. Chevalier, J., and A. Goolsbee (2005): “Are Durable Goods Consumers Forward Looking? Evidence from College Textbooks,” NBER Working Paper 11421. Dubé, J.-P., G. J. Hitsch, and P. E. Rossi (2009): “State Dependence and Alternative Explanations for Consumer Inertia,” manuscript. Frederick, S., G. Loewenstein, and T. O’Donoghue (2002): “Time Discounting and Time Preference: A Critical Review,” Journal of Economic Literature, 40(2), 351–401. Green, P. E., A. M. Krieger, and Y. Wind (2001): “Thirty Years of Conjoint Analysis: Reflections and Prospects,” Interfaces, 31(3), S56–S73. Green, P. E., and V. R. Rao (1971): “Conjoint Measurement for Quantifying Judgmental Data,” Journal of Marketing Research, 8(3), 355–363. Green, P. E., and V. Srinivasan (1990): “Conjoint Analysis in Marketing: New Developments with Implications for Research and Practice,” Journal of Marketing, 54(4), 3–19. Horsky, D. (1990): “A Diffusion Model Incorporating Product Benefits, Price, Income and Information,” Marketing Science, 9(4), 342–365. Hotz, V. J., and R. A. Miller (1993): “Conditional Choice Probabilities and the Estimation of Dynamic Models,” Review of Economic Studies, 60(3), 497–529. Huber, J. (1997): “What We Have Learned from 20 Years of Conjoint Research: When o Use Self-Explicated, Graded Pairs, Full Profiles or Choice Experiments,” Sawtooth Software Research Paper Series.

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Magnac, T., and D. Thesmar (2002): “Identifying Dynamic Discrete Decision Processes,” Econometrica, 70(2), 801–816. Melnikov, O. (2000): “Demand for Differentiated Durable Products: The Case of the U.S. Computer Printer Market,” manuscript. Nair, H. S. (2007): “Intertemporal Price Discrimination with Forward-Looking Consumers: Application to the US Market for Console Video-Games,” Quantitative Marketing and Economics, 5, 239–292. Newton, M. A., and A. E. Raftery (1994): “Approximate Bayesian Inference with the Weighted Likelihood Bootstrap,” Journal of the Royal Statistical Society, Series B, 56(1), 3–48. Phelps, E. S., and R. A. Pollak (1968): “On Second-Best National Saving and GameEquilibrium Growth,” Review of Economic Studies, 35(2), 185–199. Rossi, P., G. Allenby, and R. McCulloch (2005): Bayesian Statistics and Marketing. John Wiley & Sons. Rust, J. (1987): “Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher,” Econometrica, 55(5), 999–1033. Song, I., and P. K. Chintagunta (2003): “A Micromodel of New Product Adoption with Heterogeneous and Forward-Looking Consumers: Application to the Digital Camera Category,” Quantitative Marketing and Economics, 1, 371–407.

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Appendix

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Table 1: Survey 1 Description Survey Overview Price variation over time Across subjects Within subjects Variation in no. of titles over time Across subjects Within subjects Adoption decision No. products (brands) No. of survey time periods Total no. of choices(*)

Yes Yes No Yes Only inter-temporal choice 1 4 5

Survey Summary No. subjects No. blocks per subject No. questions per block (including baseline) No. of price manipulations No. of title manipulations Total number of choices in data

1,000 2 4 3 0 8,000

Distribution of Choices Mar-09 Dec-09 Dec-10 Dec-11 Will not buy

3% 11% 27% 41% 19%

Modal Choices Mar-09 Dec-09 Dec-10 Dec-11 Will not buy

2% 11% 28% 41% 18%

Number of distinct choices 1 2 3 4 5

36.5% 48.3% 14.2% 0.7% 0.3%

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Table 2: Survey 2 Description Survey Overview Price variation over time Across subjects Within subjects Variation in no. of titles over time Across subjects Within subjects Adoption decision No. products (brands) No. of survey time periods Total no. of choices(*)

Yes Yes

Yes Yes Inter-temporal and brand choice 2 6 13

Survey Summary No. subjects No. blocks per subject No. questions per block (including baseline) No. of price manipulations No. of title manipulations Total number of choices in data

505 2 or 3 6 3 2 6,576

Distribution of Choices Dec-08 Jun-08 Dec-09 Dec-10 Dec-11 Dec-12 Will not buy

Sony 3% 4% 6% 8% 5% 5%

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Samsung 2% 5% 11% 15% 9% 10% 18%

Table 3: Survey 2 Summary of Choices Modal Choices Dec-08 Jun-08 Dec-09 Dec-10 Dec-11 Dec-12 Will not buy

Sony 3% 4% 9% 8% 4% 5%

Number of distinct choices 1 2 3 4 5 6 7 8 9

Samsung 1% 5% 11% 16% 7% 9% 17%

34.3% 32.5% 18.8% 6.9% 4.8% 1.6% 0.8% 0.2% 0.2%

Number of distinct brands chosen 1 73% 2 25% 3 2% Number of distinct time periods chosen 1 36.8% 2 33.9% 3 19.6% 4 7.7% 5 1.2% 6 0.8%

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Table 4: Survey Demographics Number of respondents % Males Interest in HD products? Age Distribution 20-25 26-30 31-35 36-40 41-45 45+ Ethnicity White/Caucasian African American Hispanic Asian Other Education Level Less than high school High school College Graduate degree Other Household Income Less than $25,000 $25,000 - $50,000 $50,000 - $75,000 $75,000 - $100,000 $100,000 - $150,000 More than $150,000 Future Income Expectation Decrease in near future No change Increase in near future Ownership TV Satellite/Cable TV DVD player Flat panel Other HD DVR

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Survey 1 1000 49% 77%

Survey 2 505 62% 82%

8% 12% 16% 11% 11% 43%

7% 13% 16% 11% 11% 41%

87% 5% 2% 4% 2%

84% 5% 4% 5% 2%

1% 28% 48% 21% 2%

0% 22% 50% 24% 3%

9% 28% 23% 17% 9% 5%

10% 28% 22% 16% 13% 4%

14% 70% 16%

13% 68% 19%

92% 78% 95% 47% 22% 40%

91% 78% 92% 41% 23% 37%

Table 5: Direct Evidence of Forward-Looking Behavior

No. obs. No change Buy earlier Buy later Switch to no buy Correctly classified Total correctly classified

Future Price Increase

954

Future Price Decrease 332

62% 30% 7% 2%

87% 5% 5% 3%

53% 5% 42% 1%

78% 4% 16% 2%

92%

87%

95%

78%

Past Price Increase

483

Past Price Decrease 960

89% 7% 3% 1%

18% 19% 36% 28%

89%

100%

Current Price Decrease 398

Current Price Increase

311

90%

Table 6: Survey 1: Current Adoption Model Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% δ1 -2.20 -1.93 -1.65 -7.35 -5.62 -4.38 2.99 3.71 4.62 Price (α) -36.59 -22.08 -10.99 -113.22 -81.01 -39.37 3.93 10.58 29.16 Log marginal density -12293.19 -11785.32 Trimmed log m.d. -12292.01 -11774.41

δ1 δ2 δ3 δ4 Price(α) Log marginal density Trimmed log m.d.

Table 7: Survey 1: MNL model Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% 6.56 7.04 7.49 14.77 16.99 19.55 12.27 13.89 15.71 6.29 6.64 6.97 17.70 19.10 20.67 11.50 12.87 14.36 5.78 6.06 6.33 18.11 19.37 20.89 9.51 10.54 11.77 4.48 4.67 4.86 14.09 15.03 16.14 6.17 6.94 7.80 -3.12 -2.97 -2.81 -9.75 -9.04 -8.38 4.46 5.06 5.76 -10333.08 -4291.01 -10331.39 -4216.51

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δ1 δ2 δ3 δ4 Price(α) Discount (γ) Log marginal density Trimmed log m.d.

Table 8: Survey 1: Dynamic MNL Model Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% 6.58 7.05 7.53 32.67 38.82 43.23 14.83 20.00 22.72 6.27 6.65 7.00 31.81 39.47 44.55 16.62 21.42 23.94 5.80 6.08 6.34 32.78 40.88 45.66 15.86 21.16 23.70 4.48 4.68 4.88 26.94 34.29 38.97 10.95 14.54 17.07 -3.14 -2.97 -2.81 -22.32 -19.96 -15.87 7.51 9.87 11.28 4.51 9.58 22.86 0.97 1.15 1.64 0.94 1.06 1.27 -10334.69 -4009.70 -10331.46 -3933.54

Table 9: Survey 1: Dynamic MNL with Hyperbolic Discounting Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% δ1 6.57 7.33 7.50 25.53 36.07 41.54 12.92 17.35 20.12 δ2 6.25 6.83 7.04 26.43 36.13 41.00 14.52 19.52 22.23 δ3 5.74 6.20 6.41 26.91 37.37 42.39 13.37 19.39 22.47 δ4 4.47 4.75 4.91 21.42 31.40 35.81 8.37 12.72 14.53 Price(α) -3.14 -3.06 -2.80 -20.65 -18.25 -13.02 6.12 8.92 10.19 Discount (γρ ) 3.24 7.93 20.56 5.54 7.49 8.78 1.56 4.02 5.02 Discount (γβ ) 4.39 7.89 14.18 1.02 1.31 2.19 0.90 1.04 1.52 Log marginal density -10334.02 -4065.00 Trimmed log m.d. -10331.36 -3998.43

Table 10: Survey 2: Current Adoption Model Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% δSony 0.80 2.08 3.37 -5.13 3.07 12.97 4.14 8.11 12.01 δSamsung 0.40 1.38 2.40 -4.05 1.79 8.62 4.21 7.02 9.77 Price (α) -1.17 -0.84 -0.48 -6.39 -3.10 -0.87 1.61 2.68 4.17 Titles (λ) -1.11 -0.60 -0.11 -2.50 -1.23 0.27 0.86 1.60 2.46 Log marginal density -10827.43 -10299.89 Trimmed log m.d. -10826.12 -10279.34

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δSony δSamsung Price (α) Titles (λ) Log marginal density Trimmed log m.d.

Table 11: Survey 2: MNL Model Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% 4.57 4.92 5.24 29.09 32.88 37.66 19.58 22.25 25.70 4.09 4.37 4.64 26.40 29.72 33.89 16.82 19.22 21.98 -1.78 -1.67 -1.56 -11.46 -10.27 -9.23 6.47 7.43 8.48 -0.17 -0.16 -0.15 -1.27 -1.13 -1.00 0.89 1.00 1.13 -10372.45 -4385.77 -10370.30 -4350.95

δSony δSamsung Price (α) Titles (λ) Discount (γ) Log marginal density Trimmed log m.d.

Table 12: Survey 2: Dynamic MNL Model Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% 3.50 4.51 5.59 30.66 37.26 45.27 40.32 45.96 52.06 2.77 3.60 4.47 26.24 31.85 38.40 34.78 39.55 44.61 -2.43 -2.18 -1.93 -22.98 -20.26 -18.22 13.71 15.46 17.79 0.12 0.18 0.25 1.10 1.30 1.52 1.05 1.24 1.46 0.03 0.16 0.29 0.72 0.88 1.04 0.93 1.05 1.19 -10443.79 -4109.48 -10441.87 -4049.63

Table 13: Survey 2: Dynamic MNL with Hyperbolic Discounting Homogeneous Tastes Heterogeneous Tastes Pop. mean Pop. SD 2.5% 50% 97.5% 2.5% 50% 97.5% 2.5% 50% 97.5% δSony 3.67 4.56 5.42 26.26 34.97 43.37 43.56 53.60 61.60 δSamsung 2.92 3.61 4.26 22.81 29.81 36.61 37.84 46.24 52.71 Price (α) -2.42 -2.18 -1.93 -23.36 -20.43 -17.97 14.54 17.19 19.59 Titles (λ) 0.11 0.19 0.25 1.10 1.32 1.61 1.01 1.24 1.52 Discount (γρ ) 4.05 11.03 24.90 5.39 7.02 9.84 3.61 4.80 7.23 Discount (γβ ) 0.06 0.16 0.30 0.89 1.05 1.22 0.94 1.06 1.20 Log marginal density -10444.61 -4022.80 Trimmed log m.d. -10441.77 -3995.47

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Table 14: Survey 2: Correlation Matrix for Population Distribution of Tastes (Dynamic MNL Model) δSony δSamsung Price (α) Titles (λ) Discount (γβ ) δSony 1 (1,1) δSamsung 0.93 1 (0.9,0.95) (1,1) Price (α) -0.90 -0.92 1 (-0.93,-0.86) (-0.94,-0.88) (1,1) Titles (λ) -0.14 -0.23 0.12 1 (-0.3,0.01) (-0.38,-0.08) (-0.02,0.29) (1,1) Discount (γ) 0.15 0.23 -0.40 -0.34 1 (-0.01,0.33) (0.06,0.39) (-0.54,-0.25) (-0.49,-0.18) (1,1)

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Figure 1: Survey screen: Base scenario

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Figure 2: Survey screen: Price decrease in December 2009 relative to base scenario

32

Figure 3: Base screen in second survey

33

100 0

50

Frequency

150

Posterior Means of Subjects’ Discount Factors

0.4

0.6

0.8

1.0

Discount Factor

Figure 4: Survey 1: Distribution of Subjects’ Posterior Means of the Discount Factor (Dynamic MNL Model)

34

40 0

20

Frequency

60

80

Posterior Means of Subjects’ Discount Factors

0.2

0.4

0.6

0.8

1.0

Discount Factor

Figure 5: Survey 2: Distribution of Subjects’ Posterior Means of the Discount Factor (Dynamic MNL Model)

35

400 0

200

Frequency

600

800

Posterior Means of Subjects’ Discount Factors

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Discount Factor

Figure 6: Survey 1: Distribution of Subjects’ Posterior Means of the Hypberbolic Discount Factor ρ

36

150 0

50

100

Frequency

200

250

Posterior Means of Subjects’ Discount Factors

0.2

0.4

0.6

0.8

1.0

Discount Factor

Figure 7: Survey 2: Distribution of Subjects’ Posterior Means of the Hypberbolic Discount Factor ρ

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