Estimating Multiple-Discrete Choice Models: An Application to Computerization Returns

1. Estimating Multiple-Discrete Choice Models: An Application to Computerization Returns Presentation by Le Chen, Zhen Huo, Bernabe Lopez-Martin, Shihui Ma, Naoki Takayama, and Andrew Triece

2. Motivation • The PC market is interesting from an IO perspective because it is characterized by rapid technological change and this technology can impact productivity in other markets • Firms purchase PCs from multiple brands, and they purchase multiple PCs from each brand (multiple-discreteness)‏ • “Computerization Puzzle”: empirical finding that computerization has had no effect on firm productivity • Hendel's paper aims to incorporate the multiple-discreteness of the PC market into a model and estimate welfare gains from computerization

3. Basics • In Hendel's model, each firm has a number of potential tasks that can be performed by PCs and these tasks relate to the brands and quantities of PCs they demand • The model predicts that some firms will buy multiple brands of PCs and/or multiple units per brand depending on the tasks they need to perform • Based on the estimates of demand, return on investment on PCs in the banking industry is 92%, and an increase of 10% in the performance-to-price ratio of microprocessors is estimated to add 2.2% to end-user surplus

4. Multiple-Discreteness in the PC Market Let F denote the number of firms, I denote the number of PC types.

5. Firms’ Tastes for Various Computer Attributes • Each PC is a bundle of N built-in attributes (ex: MHz, RAM, etc.). • One of the N attributes is considered to be an unobservable measure of “quality” of the type of PC. • Firm’s tastes over attributes are unobservable, hence can be treated as random variables. • These are denoted by: • Where there are N-1 built-in attributes and I dummies for PC type. • This vector Af is assumed to be multivariate normal.

6. Characteristics of the Firm • Let Df denote all the characteristics of firm f (size, sector, etc.) • Each firm can do up to Jf =Γ(Df) different tasks, where the number of tasks is a stochastic function of the firm’s characteristics. • Γ(Df) is assumed to be a Poisson distribution with parameter Λ(Df). • Firm seeks to maximize profit: • Key assumption: No inter-task externalities (profit in one task does not affect profit in another).

7. The Firm’s Problem • At the task level, the firm’s profit function is assumed to be of the following form: • Here, S(Df) is a return shifter and m(Df) is a taste shifter. • Assumption: PC types are perfect substitutes at the task level. • A firm will only use one PC type for each task.

8. What do we know? Firm characteristics: D(f) Firm PC purchases: Xf What don’t we know? The distribution of A and J, which is determined by the parameters θ Note: We assume the distribution form, but need to estimate the parameters

9. From the model, we know that the optimal purchases are • So we expect the firm to purchase: • The error term is given by the difference:

10. Suppose the assumed purchase process is true, then given the true parameter values: • Wecan generate the moment conditions • GMM method then can be implemented:

11. How to calculate the expected purchases: Simulation • Idea: • Suppose the parameters are given. • Given J, the number of tasks, draw many random variables from the distribution of A, and calculate the average. • Draw different numbers of tasks from Poisson process, repeat the procedure above, and calculate the average. • According to the existing work, when the number of random draws are large enough, the average from the simulation will equal to the true expected value.

12. Summary • 1. Write down the observable numbers. • 2. Given parameters, using simulation method, find the expected purchase. • 3. Using moments condition, calculate G(θ). • 4. Repeat 2 and 3 until minimize G(θ), which implies we find the true parameters.

13. Flow of Data Simulation r.v. Prediction GMM Pi e Xf Parameters Ci Df Xf Actual Data

14. Data Sets • Prices and PC attributes - from advertisements - MHz, RAM and expandable RAM etc. • Actual behavior and characteristics of the establishments - representative survey with questionnaire - # of PC for each model and software etc. - # of employees and white collars etc.

15. Explanatory Variables • empf = # of employees • whf = # of white colors • softf = # of different types of software • dinsf = 1 if establishment f belongs to the insurance sector • dpif = 1 if firm f held in stock PCs i in the previous year

17. Results • Distributional and functional forms. • Dummies control for unobserved quality differences (full set of brand dummies).

18. Asymptotic Chi-square test rejects the model; functional forms may not be sufficiently flexible.

19. Welfare gains from computerization: estimates of the profits of each establishment by using PCs represent 4.2% of total profits. • Return on investment is 92% (should be taken as an upper bound). • Some caveats.

20. Price aggregate demand elasticities (validity check if they imply reasonable substitution patterns). • Matrix of price elasticities: (1) all elements in the diagonal are negative, (2) larger substitution toward similar machines.

21. Potential biases. • Inter-task externalities (estimates would over-estimate per-task benefits). • Nonlinear pricing of PCs (large establishments get lower prices): they are actually willing to pay less for the PCs than the prices used in estimation.