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

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

## Web Appendix for âPrice, Quality, and Variety: Measuring the Gains ...

Measuring the Gains from Trade in Differentiated .... Ethernet Interface Dummy ... Speedâ is the maximum number of pages per minute that can be printed in.

#### Recommend Documents

Price, Quality, and Variety: Measuring the Gains from ... -
This paper explores the gains from trade in differentiated products from three channels: decreases in price, improvements in quality, and increases in variety. Using data on Indian imports of computer printers over 1996 to 2005, a period of trade lib

Online Appendix for: Competition and the welfare gains from ...
Jan 20, 2015 - A.4 Details on Data Preparation of the Difference-in-Difference Specification . .... national highway system into a graph, we used Network Analyst in ArcGIS. ..... that the lower Î¸ implies that firms with large market shares charge ..

GLOBALIZATION AND THE GAINS FROM VARIETY* It ...
using only the data available in a typical trade database. Unfor- tunately, his .... 124â129] note, preference systems based on the Hotelling and. Lancaster ...

Web Appendix
We again assume U(x)=x throughout, following Doyle. As in our paper and in. Bleichrodt, Rohde, and Wakker (2009; BRW henceforth), we write ln for the natural logarithm instead of Doyle's log. As in the main text, (T:F) denotes receiving \$F>0 at time

WEB APPENDIX FOR
For this level of Î¸ and above, the ruler centralizes the entire territory. .... are log area, major river, agricultural constraints, distance to coast, elevation, malaria, ...

The Variety and Quality of a Nation's Exports
Mar 4, 2008 - Data: UNCTAD's Trade Analysis and Information System CD-ROM. Exports from 126 countries to 59 importers in over 5000 6-digit product categories in 1995. Measurement: â» Measure of extensive margin: counting weighted categories of goods

Web Appendix
We again assume U(x)=x throughout, following Doyle. As in our paper and in. Bleichrodt, Rohde, and Wakker (2009; BRW henceforth), we write ln for the natural.

web appendix
This Web Appendix contains additional information and data analyses that could not be ... report a crime. Since we look at 40 years of crime data, it is impossible to correct reported crimes for the ..... Origin countries: Albania, Algeria, Banglades

Web Appendix for bCommuting, Migration and Local ...
employment locations within the economy. B.2 Computing Counterfactuals Using Changes. We now use the ... #U%'\$. QM using the current guesses and data. We start by computing: ?v#U\$. Q ...... We find pervasive two&way commuting, with the mean and media

The prize for best paper at GEP's recent Annual Postgraduate Conference went to Lisandra. Flach (University of ... how firms make their decisions regarding.

Price Competition in Product Variety Networks
(2017) who consider a competitive facility location problem on a network in which consumers located on vertices wish to connect to the nearest facility and each competitor locates a facility on a vertex trying to maximize her market share. This liter

Price Competition in Product Variety Networks
Email: [email protected]. ... At the same time, the marketing ... 1The approaches proposed in the marketing literature (e.g. Dikson and ...... This is exactly the result for the benchmark monopolistic competition model without network (see.

Appendix A - Keystone Home Loan Purchase Price and ... - PHFA
PENNSYLVANIA HOUSING FINANCE AGENCY. KEYSTONE HOME LOAN PROGRAM. MAXIMUM PURCHASE PRICE AND INCOME LIMITS *. By Region and ...

Price Competition in Product Variety Networks
Mar 19, 2018 - settings, where prices are typically strategic complements (Vives, 1999). Furthermore, we ... we provide examples obtained via simulations. 4 ...

pdf-1465\measuring-health-care-using-quality-data-for-operational ...
... one of the apps below to open or edit this item. pdf-1465\measuring-health-care-using-quality-data-for-operational-financial-and-clinical-improvement.pdf.

The price of variance risk - Online Appendix
Sep 21, 2016 - In this paper, we introduce two new data sets on variance swaps. Given that the ... is constructed in the same way and by the same company as the CDS data set from the same firm ..... of VS prices on top of the realized variance RVt. B

Idea Group Inc. gains exposure, increases web traffic and ...
After partnering with Google in both Google Scholar and Google Book Search, technology publisher Idea Group Inc. sees a fourfold increase in page views and ...

2004 measuring up quality standards.pdf
Quality Standards for Sewn Items/Projects. By: Kay Hendrickson, Jan Hiller, and Nancy Mordhorst. Introduction. An essential task for evaluating the quality of.

2004 measuring up quality standards.pdf
Characterized by secure stitching that is a. uniform distance from ... Have a shank (to allow room for the buttonhole ... 2004 measuring up quality standards.pdf.

Price Competition in Product Variety Networks
Jul 21, 2017 - Email: [email protected]. ... since, in our model, consumers purchase in volume and they may choose to purchase more than ... 1The approaches proposed in the marketing literature (e.g. Dikson and .... between product varieties is hi

Measuring the dimensions of quality in higher education - PDFKUL.COM
education. Stanley M. Widrick,1 Erhan Mergen1 & Delvin Grant2. 1College of Business, Rochester Institute of Technology, 108 Lomb Memorial Drive, .... Quality of performance deals with how well a service and/or product performs in the eyes of ..... wa

Measuring the dimensions of quality in higher education
1College of Business, Rochester Institute of Technology, 108 Lomb Memorial Drive, Rochester, NY. 14423, USA ... ISSN 0954-4127 print/ISSN 1360-0613 online/02/010123-09 ... This is relatively easy in .... developed speciÂ®c product ideas.

Measuring the dimensions of quality in higher education
of conformance and quality of performance) in higher education. ... examples are discussed of how Rochester Institute of Technology has used this approach to ...