Web Appendix for “Price, Quality, and Variety: Measuring the Gains from Trade in Differentiated Products” Gloria Sheu∗ US Department of Justice October 2013

A A.1

Appendix: Theory Details NRCL Demand Model

This section explains the theory underlying the NRCL model, with the NL as a special case. The utility for consumer i of type r buying good j in group g is r urijt = ln(arjt mrijt ) + ζigt + rijt .

(A.1)

Here arjt is a good-specific measure of quality similar to bjt . The mrijt is the quantity of good j that consumer i chooses to buy. r Meanwhile the ζigt is a random draw from a logit distribution with scale parameter µr1 , and the rijt is a random draw from a logit distribution with scale parameter µr2 .1 Thus, each consumer has a series of independently and identically r distributed (iid) random draws, one for each product j ∈ Jgt and one for each 2 group g ∈ {ink, las}. ∗

The views expressed here are not purported to reflect those of the US Department of Justice. Email: [email protected] 1 A random variable x is distributed logit if it has a cumulative distribution function of exp [− exp (−x/µ + %)] where µ is the scale parameter and % is Euler’s constant (≈ 0.577). This is often referred to as a “Type I Extreme Value” distribution. 2 Note that here the random component of utility is written as the sum of group- and product-level logit shocks, following Anderson et al. (1992). This facilitates a clear analogy with the two-step choice problem in the NCES. Berry (1994), among others, writes the random component as two terms that sum to a logit shock, governed by a single parameter σ (not to be confused with σ in this paper). The two formulations result in equivalent choice probabilities.

1

Those familiar with other applications of the logit model may note that the specification here is slightly different in two ways. These changes were documented by Anderson et al. (1992) as necessary in order the make the MNL align exactly with the CES. First, consumers can buy a continuous amount of their chosen good j, instead of only purchasing of one unit. Second, the non-random part of utility enters in logs rather than in levels. These modifications result in demand equations in terms of expenditure shares (not quantity shares), with price and quality entering multiplicatively (not addively), just as in the NCES. Each time period, consumer i’s problem is to maximize current period utility subject to a budget constraint.3 The budget constraint is given by pjt mrijt = y r where y r is the consumer’s income. Substituting this constraint into the utility function gives an indirect utility of r r vijt = ln(arjt ) − ln(pjt ) + ln(y r ) + ζigt + rijt .

The consumers’ problem can be tackled in steps, starting with the demand for goods conditional on being within a certain product group. When focusing on r one group, the ζigt term drops out. Integrating over the remaining logit random shocks gives, 1 r

−1 µr

arjt µ2 pjt2

probrjt|g =

−1 r

1

P

r j∈Jgt

,

µ r arjt µ2 pjt2

which is the conditional probability that any type r consumer will choose good j. Turning to the choice of which product group to buy from, the consumer chooses the group with the maximum expected indirect utility, which results in a group probability of  P probrgt = P

r j∈Jgt

g∈{ink,las}

arjt

 P

1 µr 2

−1 µr 2

 µµr2r 1

pjt

j∈Jtr

arjt

1 µr 2

−1 µr 2

 µµr2r

pjt

r

.

1

Following Anderson et al. (1992), let arjt 1/µ2 = brjt , −1/µr2 = 1 − σ r , and 1/µr1 = γ r − 1. Then convert probrjt|g and probrgt to (expected) expenditure shares by multiplying and dividing by the consumer’s income. The resulting expenditure shares are r brjt p1−σ jt r (A.2) sjt|g = P r 1−σ r r bjt pjt j∈Jgt 3

This is an entirely static problem, with no borrowing or saving.

2

and P srgt = P

r j∈Jgt

g∈{ink,las}

1−σ r brjt pjt

P

r j∈Jgt

1−γ r  1−σ r

1−σ r brjt pjt

1−γ r .  1−σ r

(A.3)

Multiplying these two shares gives srjt

= P

r j∈Jgt

r brjt p1−σ jt

r −σ r  γ1−σ r

1−σ brjt pjt P

r

g∈{ink,las}

P

r j∈Jgt

r brjt p1−σ jt

1−γ r .  1−σ r

(A.4)

If all types of consumers have identical preferences, meaning that brjt = bjt , σ r = σ, and γ r = γ for all r, these formulas collapse down to those in the NL model. If in turn σ = γ, the model reduces to the MNL. The market-level share is found by integrating srjt across the distribution of consumer types. For example, if the distribution is discrete the share is then X sjt = ftr srjt , (A.5) r∈{sm,lg}

where ftr is the fraction of expenditure accounted for by type r consumers in time t.

A.2

NCES Demand Model

This section shows how the NCES and NL are related. Assume there is a representative consumer that has a utility function given by γ  γ−1  γ−1 X Ut =  Mgtγ  , where γ > 1. (A.6) g∈{ink,las}

The consumption of each group is denoted by Mgt . Within each product group g the consumer has an inner nested utility function of the form σ   σ−1 X 1 σ−1 , where σ > 1. (A.7) Mgt =  bjtσ mjtσ  j∈Jgt

Each time period the consumer’s problem is to maximize current period utility subject to a budget constraint. The utility maximization problem can be solved in two stages. First, maximize Mgt conditional on the amount of money allocated to group g. Then decide on the allocation of expenditure across groups. This 3

exercise results in the expression for the share of expenditure allocated to product j within group g, bjt p1−σ jt sjt|g = P (A.8) 1−σ . j∈Jgt bjt pjt In turn, the share of expenditure devoted to group g out of total expenditure is P

j∈Jgt

sgt = P

g∈{ink,las}

1−σ bjt pjt

P

j∈Jgt

1−γ  1−σ

bjt p1−σ jt

1−γ .  1−σ

(A.9)

Multiplying these two expressions gives the share of expenditure allocated to product j out of the money spent on all product groups, sjt =  P

j∈Jgt

bjt p1−σ jt

 γ−σ 1−σ

bjt p1−σ jt P

g∈{ink,las}

P

j∈Jgt

1−σ bjt pjt

1−γ .  1−σ

(A.10)

These are the same expenditure share equations that appear in the NL model. In the special case where σ = γ, the NCES reduces to the CES model.

B

Appendix: Additional Data Details

Summary statistics for the printer data, including model characteristics, are in Table B.1. IDC categorizes each model into one of several groups based on the type of printer (multi-function or single function), technology (inkjet, laser), color versus monotone printing, and print speed. These categorizations provide the groupings used to construct the exchange rate instrument and are the basis for the aggregations used in the NCES results. The categories cross-referenced with the headquarters countries that appear in each are listed in Table B.2.

4

References Anderson, Simon P., Andr´ e de Palma, and Jacques-Fran¸cois Thisse, Discrete Choice Theory of Product Differentiation, MIT Press, 1992. [1, 2] Berry, Steven, “Estimating Discrete-Choice Models of Product Differentiation,” RAND Journal of Economics, 1994, 25 (2), 242–262. [1]

5

Table B.1: Summary Statistics Variable Price (USD) Units Sold Color Dummy BW PPM Speed RAM (MB) Resolution (DPI) A3 Capable Dummy Footprint (in2 ) Ethernet Interface Dummy MFP Dummy Laser Dummy Number of Model-Quarters Number of Unique Models

Mean 604.996 1059.538 0.468 20.806 49.764 1336.798 0.355 416.175 0.343 0.356 0.663 6413 1189

Standard Deviation 1084.060 4763.041 0.499 13.430 98.272 771.611 0.478 381.911 0.475 0.479 0.473

Notes: Data sources are in the main text of the paper, Section 3. Price is in real 2001 Indian Rs, then converted to USD at 1 Rs=47.12 USD. “BW PPM Speed” is the maximum number of pages per minute that can be printed in black and white.

6

Table B.2: Product Categories Product Type MFP Color Inkjet 1-10 PPM MFP Color Inkjet 11-20 PPM MFP Color Inkjet 21 PPM or more MFP Color Laser 1-10 PPM MFP Color Laser 11-20 PPM MFP Color Laser 21-30 PPM MFP Color Laser 31-44 PPM MFP Mono Inkjet All Speeds MFP Mono Laser 1-20 PPM MFP Mono Laser 21-30 PPM MFP Mono Laser 31-44 PPM MFP Mono Laser 45-69 PPM MFP Mono Laser 70-90 PPM Printer Color Inkjet 1-10 PPM Printer Color Inkjet 11-20 PPM Printer Color Inkjet 21 PPM or more Printer Color Laser 1-10 PPM Printer Color Laser 11-20 PPM Printer Color Laser 21-30 PPM Printer Color Laser 31-44 PPM Printer Mono Inkjet All Speeds Printer Mono Laser 1-20 PPM Printer Mono Laser 21-30 PPM Printer Mono Laser 31-44 PPM Printer Mono Laser 45-69 PPM Printer Mono Laser 70-90 PPM

Japan X X X X X X X X X X X X X X X X X X X X X X X

US X X X X X X X X X X X X X X X X X X X X X X X X X

Korea X X

EU

X X X X X

X

X X

Notes: Product types are from the IDC taxonomy. “PPM” stands for pages per minute.

7

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