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

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

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

Multiple-Discreteness in the PC Market

Let F denote the number of firms, I denote the number of PC types.

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 A f is assumed to be multivariate normal.

Characteristics of the Firm     Let D f denote all the characteristics of firm f (size, sector, etc.) Each firm can do up to J f =Γ(D f ) different tasks, where the number of tasks is a stochastic function of the firm ’s characteristics.

Γ(D f ) is assumed to be a Poisson distribution with parameter Λ(D f ).

Firm seeks to maximize profit:  Key assumption: No inter-task externalities (profit in one task does not affect profit in another).

The Firm’s Problem  At the task level, the firm’s profit function is assumed to be of the following form:  Here, S(D f ) is a return shifter and m(D f ) 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.

What do we know? Firm characteristics: D(f) Firm PC purchases: X f 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

 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:

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

 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.

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.

P

i

C

i

D

f

X

f

r.v.

Flow of Data

Simulation

X

f

e Prediction GMM

Parameters

Actual Data

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.

Explanatory Variables

 emp

f

= # of employees  wh

f

= # of white colors  soft

f

= # of different types of software  dins

f

= 1 if establishment

f

insurance sector belongs to the  dp

if

= 1 if firm

f

previous year held in stock PCs

i

in the

Results

 Distributional and functional forms.

 (

D f

) 

g

1 

emp f



g

2 

soft f S

(

D f m

(

D f

) ) 

s

0  1  

s

0

ins m

1  

wh dins f f



s

1 

emp f



m

1

ins



dins f

 Dummies control for unobserved quality differences (full set of brand dummies).

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

 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.

 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.

 Potential biases.

1.

Inter-task externalities

(estimates would over estimate per-task benefits).

2.

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.