Measuring the Digital Divide:

1. Measuring the Digital Divide: Structural Estimation of the Demand for Personal Computers Jeff Prince Cornell University

2. The Digital Divide • What is it? • The separation between technology participants and non-participants • Why study it for PCs? • PCs have a wide range of household applications: • Education • Information searches • Digital photography • Interactive gaming

3. Household Heterogeneity Plays a Major Role in the Divide • The majority of new PC purchases are made by households already owning a PC • From a revealed preference perspective, the marginal utility of an upgrade for many households is greater than that of crossing the Divide

4. Separation Between Owners and Non-owners • The summary statistics above show that upgrades are faster than new purchases • This implies that the Technological gap is also widening • Upgraders can do even more with their PC while non-owners still can do nothing

5. NTIA Statistics Suggest Pertinent Areas of Heterogeneity • Ownership rates vary greatly across income, education, and age groups • Ownership rates are: • Strongly increasing with income • Strongly increasing with education • Strongly decreasing with age • Especially from 35-44 group onward

6. The Digital Divide and Diffusion Theory • The PC is a “new” product diffusing through the population • Non-owners are the late adopters • Generally attributed to heterogeneity – i.e., non-owners have a lower valuation for PCs • Adoption takes even longer if there’s a hurtle such as a set-up or learning cost

7. The Demand for Personal Computers This model has three main components: • Heterogeneity • Stock • Observed • Unobserved • Dynamics • Set-up (or learning) costs

8. Looking at the Divide in a New Way • The Divide is the result of the interaction of learning costs, persistent heterogeneity, and dynamic technological change

9. Literature/Contribution • Goolsbee & Klenow (’00) • Hendel (’99) • Departure from above papers: • Models the PC as a durable good • Accounts for dynamic nature of the problem • Considers replacement • Properly characterizes heterogeneity • Can address a wider array of questions…

10. Issues This Model Addresses • Short-term vs. long-term price elasticity • Price elasticity of owners vs. non-owners • “Technology elasticity” • I.e., the response of demand to changes in the rate of technological progress • The marginal value of quality improvements • Set-up costs for first-time buyers • Impacts of long-term and short-term subsidies for first-time buyers

11. Findings • Two demand curves (replacement and first-time) • Replacement price elasticity lower than that of first-time purchase • Owners more responsive to changes in the rate of quality improvement • Dynamics matter • Short-term price elasticity higher than long-term price elasticity • Fixed costs for first-time purchase are significant • Subsidizing first-time PC purchases can be effective

12. Three Main Components: Heterogeneity • Observed Heterogeneity • Variation in income, education, age, and family size • Unobserved Heterogeneity • Techies vs. Non-techies • Stock Heterogeneity • Variation in households’ current PC holdings

13. Three Main Components: Dynamics • The Classic “Buy or Wait” Decision • Since PCs are durable goods, purchase decisions today affect decisions tomorrow • Expectations about future available selection affect purchasing decisions today

14. Three Main Components:Set-up/Learning Costs • Buying a First PC Involves Learning about Hardware and Software, Suppliers, Set-up in the House, etc.

15. Outline of Talk • The Model • The Data • Results • Extensions • Conclusions

16. The Model • Dynamic Stochastic Discrete Choice (DSDC) Model • Good for modeling demand for durables • Accounts for discrete nature of the choice • Accounts for forward-looking consumers • Follows Rust’s 1987 DSDC Model

17. Model Details (Conceptual) • Households Observe the Current State of the World • They Form Expectations about the Future State of the World • Based on This Information, They Make the Choice that Maximizes Their Expected Present Value of Utility

18. What is a Relevant State of the World? • Household’s Observable Characteristics • Income, education, etc. • Unobservables (Techie or Non-techie) • Current PC Ownership • Does the household own a PC, and if so, how good is it? • Current Choice Set • PCs available at the time along with “no PC”

19. What are Relevant Expectations? • Households Today Form Expectations about PC Choices Available in Upcoming Years • Households Today Also Form Expectations about Their Future Purchasing Decisions

20. Model Details (Formal) • Consumers make PC purchasing decisions to maximize expected discounted lifetime utility: Expectation Discount UtilityChoiceInfo • Components: • X’s are vectors of PC characteristics (including price) • Z’s are vectors of household characteristics • θ is a vector of unknown parameters • η is a vector of utility shocks • s(t) is the state of the world at time t

21. Stochastically Evolving State Space? • For Many DSDC Models, the State Space Evolves Stochastically • For PCs, Only the Choice Set Could be Stochastic • Personal Characteristics and the PC Owned Won’t Change (in general) • The Choices Available Next Year Can be Considered Stochastic • But, Perfect Foresight is Plausible

22. The Choice Set • Accounting for All Specs (MHz, RAM, ROM, Brand, etc.) is Unfeasible for This Model • Choices Fit Nicely into Three Categories: • High-end – the “souped-up” PC • Median – the “standard” PC • Low-end – the “cheap” PC • The Choice Set for each household is: {H,M,L,Q} • Q is “status quo”, or “No New Purchase”

23. Key Assumptions • The Utility Function is Additively Separable • Markov Process • Knowing this year’s state is enough to optimally predict next year’s state • Conditional Independence • Given the observables this period, the error term this period is independent of the error term last period

24. The Recursive Problem • Households solve the same infinite-horizon problem every period • The value function can be written as: • Households make decisions to maximize current utility plus expected future utility • So, for given θ, we can solve for V or E[V] using Bellman’s equation

25. Specific Example • Consider the following formula for U • measures quality, is price, and z measures income • Unobserved heterogeneity is measured through • Random coefficient taking on two possible values • High with probability p • Zero with probability 1-p

26. Derivation of Probabilities • Error Term Assumed Type I Extreme Value • Probability of Choosing Option A: • P(H) = • P(L) = • P(A) = P(H) + P(L)

27. Identification • As Usual, Parameters for Factors Common to All Choices Aren’t Identified • Includes Coefficients on z’s and 1 • How Can We Identify Dynamic Preferences With Only Cross-Sectional Data? • Variation in Holdings Identifies This • Looking for Marginal Value of Quality • We Have Large Variation in Quality “Jumps”

28. Solving the Model • Maximum Likelihood • Likelihood function built from probabilities above • Maximization over the parameter space requires numerical methods • Outer Loop • Sequentially make guesses for the optimal θ • Amoeba method • Inner Loop • Each guess for θ requires a solution of Bellman’s equation

29. Data • Forrester Research • Surveys on technology purchases and preferences each year • Data includes: • Demographic information (Age, income, education) • Details on last PC purchased by the household • Questions include: • Please indicate in what year you or someone in your household purchased the computer that was bought most recently. • How much did you pay (in dollars) for your last computer, including the new monitor?

30. Acquiring PC Stock and Quality • The PC Stock entering an observation year • Not directly provided in the Forrester Data • Requires an overlap of two surveys for each household • Approx. 30,000 overlapping surveys for ’98 – ’99 and 20,000 for ’00 – ’01 • PC quality is inferred • Use price paid and year purchased along with yearly price lists from PC World Magazines

31. Summary Statistic:Demand Differences between Owners and Non-owners Persists across Income

32. Summary Statistic:Propensity to Replace by Quality of PC Owned

33. Results from DSDC Model

34. Heterogeneity in Marginal Values • Marginal Value (for an extra 200 MHz) varies greatly across demographic groups • Increasing in Income, Education, Family Size • Decreasing in Age • Highest marginal value is $392 for 1999 and $142 for 2001 • Household of 3 with head under 35 making $100,000 with college degree • Lowest marginal value is $34 for 1999 and $0 for 2001 • Household of 1 with head over 60 making less than $20,000 with less than a high school degree

35. Learning Costs • Estimated as $2938 in 1999 and $2234 in 2001 • If a Current Owner Requires an Increase in Value of K to make New Purchase, New Owner Requires K+LC • Estimates for learning costs are expected to increase over time • Estimates for the average non-owner • Increases in user friendliness and exposure to PCs in general may explain the decrease

36. Price Elasticity • Short-term vs. Long-term and Owners vs. Non-owners • Short-Term Price Elasticity • Measured by considering a one-year-only price decline • 1999: 3.6 for non-owners vs. 2.9 for owners • 2001: 2.6 for non-owners vs. 2.1 for owners • Long-Term Price Elasticity • Measured by considering a long-term price decline • 1999: 3.2 for non-owners vs. 2.1 for owners • 2001: 2.7 for non-owners vs. 1.7 for owners

37. Technology Elasticity • Demand’s Response to Expected Acceleration (Deceleration) in Quality Improvements • Consider Acceleration in Quality Improvements from Doubling Every 2 Years to Every 1.5 Starting in the Subsequent Year • 1999: Demand falls 4.2% for non-owners; falls 6.4% for owners • 2001: Demand falls .5% for non-owners; falls 3.9% for owners

38. Policy Issues

39. Model Comparisons • Dynamic vs. Static • Dynamic performs significantly better in both years (likelihood ratio test) • Static over-emphasizes observable differences in marginal value and under-emphasizes learning cost • Stock vs. No Stock • Can’t test directly • However, results for no stock are non-sensical • Expect this for a model inconsistent with the data

40. Robustness Analysis • Discount Rate • Technically can solve for it, but practically unlikely • Discount Rate of .9 was better fit than lower ones (.8, .7, etc.) • Horizon Length • Assumed 7 years • Results for cap at 6 and 8 years yielded trivial differences • Technological Evolution • Evolution assumed to continue roughly as it has for the last decade • Small fluctuations yielded trivial differences in the results

41. Results Recap • Two demand curves (replacement and first-time) • Replacement price elasticity lower than that of first-time purchase • Owners more responsive to changes in the rate of quality improvement • Dynamics matter • Short-term price elasticity higher than long-term price elasticity • Fixed costs for first-time purchase are significant • Subsidizing first-time PC purchases can be effective • Impact depends on time structure

42. Possible Extensions • Nested Logit • Random Coefficients? • Alternative considerations of unobserved heterogeneity • Time inconsistency

43. Conclusions • Heterogeneity is important • Variation in value of PC quality across demographic groups is large • Dynamics matter • For price elasticity • For technology elasticity • Stock effects matter • Overall, models like this one incorporate the major factors behind purchases of durable goods