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关于PCAIDS模型的一点简介/A Brief Introduction to the PCAIDS Model


1 Introduction

Recently, I had to stop all the other works and have focused on the empirical test of a horizontal merge. Although, in fact, I'm not as interesting in this topic as some others, like the analysis of reputation and motivation and the empirical test of micro foundations for macroeconomics,  there is no better choice before finishing this project.

When calculating the price effect of the mergers, I was busying choosing an appropriate model for econometric use. Obviously, the easiest way was just using the "difference-in-differences" analysis, which was popular among many areas of economics. Thus, it was more effortless than doing with other complex models since so many relative resources were available.

However, the biggest problem for me was that the difficulty in collecting useful data. Because some data had  not been published, my research had to be laid on the table. An alternative way was to find another model which demands fewer data. Fortunately, I have find the PCAIDS model, which is developed by Dr. Epstein, Adjunct Professor of Finance at Boston College, and his coauthor Dan Rubinfeld at UC Berkeley.

As the author's description on its webpage(Link: http://www.royepstein.com/support.html),

The invention of PCAIDS (Proportionality Calibrated Almost Ideal Demand System) by Roy Epstein and Dan Rubinfeld stands at the forefront of current applications of merger simulation.

Meanwhile, the apparent advantage of PCAIDS is its lower requirement of data, just like the author's words:

The only data requirements for PCAIDS are market shares and two price elasticities: the elasticity for a single brand in the market and the industry price elasticity. Scanner data and econometric estimation, while useful, are not necessary. These features make it possible to perform simulation in nearly any transaction at relatively low cost.

Therefore, my estimation can be done more efficiently.

To better understand the application of PCAIDS, I'd love to read some relative papers first and translate the necessary knowledge on my blog for my readers who are also interested in using this PCAIDS model to simulate the potential effects of the merge. Thus, the following paragraphs are written in Chinese, compared with the original information in English. I'll try my best to avoid any possible mistakes especially misunderstanding, but anyway, the original words by the author is still the best way of understanding the model.

This blog-post will be updated continuously, and since the author wouldn't like to distributing the software program for PCAIDS right now, I'd like to write one (may work with Stata or Matlab) for my own use, and published here if I can get his permission.

After all, I could stop myself to show my gratitude for these two authors' talent work,  who developed this wonderful model for the analysis of merge effects, and also Dr. Epstein's kind help and support. Thank you very much!

1 序言












2 Overview of PCAIDS

(From: http://www.royepstein.com/mergersim.html)

Merger simulation is poised to become a standard economic tool to evaluate the potential unilateral price effects of mergers. A recent FTC working paper includes merger simulation among the past decade’s "remarkable developments in the quantitative analysis of horizontal mergers." (See Issues in Econometric Analysis of Scanner Data at www.ftc.gov). Despite its usefulness, however, simulation is probably still unfamiliar to many antitrust practitioners.

Unilateral effects are most relevant in markets with differentiated products. The competitive concern arises when a substantial number of customers who previously would have been lost after a price increase might be retained because the merged firm also offers the alternative brand preferred by these customers. In this case, the merged firm may find that it is profitable to increase prices because relatively few customers would be lost.

Merger simulation addresses the practical question of how to measure the size of potential unilateral effects. Using basic economic theory, it analyzes the post-merger market using key relationships involving market shares, price elasticities, and merger-related efficiencies. The economic model yields the unilateral effects as the price changes that are necessary for the market to be in equilibrium when the new firm (and its competitors) act to maximize profits without overt collusion.

The simulation can predict price increases or decreases from a transaction, depending on the configuration of inputs used to calibrate the model. Large shares for the merging parties or relatively large cross-price elasticities between them tend to result in large price effects. Small shares, small cross-price elasticities, and/or large efficiencies tend to produce small or even negative price effects.

This analysis is quite flexible and is able to integrate the traditional Merger Guidelines focus on factors such as market definition, efficiencies, and entry and product repositioning. It can also evaluate the impact of a divestiture, which might be especially useful in designing a "fix it first" strategy. Most importantly, simulation provides a coherent economic framework to analyze options for complex transactions that might otherwise be quite difficult to quantify reliably.

For details on technical issues of specifying and solving a merger simulation model, return to the PCAIDS Support main page and the links to articles given there.

Related Articles by Roy J. Epstein

2 PCAIDS模型概述

(From: http://www.royepstein.com/mergersim.html)

并购/兼并模拟渐渐成为一个标准的用于评估并购/兼并所带来的潜在的单边价格效应的经济学工具。最近的一篇FTC(联邦贸易委员会)工作论文包含了对于近十几年来在并 购/兼并模拟取得的“对于横向兼并的定量分析中的显著进步”(见扫描数据的计量分析,www.ftc.gov)。尽管它很有效,然而,并购模拟可能仍然对 于很多反垄断参与者来说所,是有所陌生的。






相关文章 by Roy J. Epstein

3 PCAIDS Technical Support Notes


Many readers of our PCAIDS article in the ALJ have asked about details of implementation. In terms of software, I have developed my version as an Excel add-in, which can handle all of the computations and is very convenient for many users. Others have told me they are using Mathlab, Mathematica, and even PERL. Any package with an optimization routine should be fine.

The most common issue so far is how to evaluate the FOC equation (A3). You must use post-merger values. The easiest way to do this is to update the shares using equation (1) to get s(new)=s(pre-merger)+ds. You can then generate new elasticity matrices E1...E* using equations (4) and (5). Remember that the E matrices are transposes in the appendix.

You should certainly explore the power of PCAIDS with nests. The Appendix discussion of nests has two minor typos--the last sentence in section 4.B. should read "the familiar si/sj." Also, the equation for bij at the top of page 918 should have a leading minus sign. There is also a minor typo in the derivation of (A5), the conclusion is correct but the line above it should replace the first two terms in the parentheses with the product bij/pj PQ/pi.

There was a slip in the example of entry on p. 909. The predicted price increase for B should be 4.5%. The corresponding value of alpha is .061, implying a threshold share for the entrant of 0.26%. I am indebted to Dave Schmidt at the FTC for pointing this out.

Table 3 (toilet paper shares) was scrambled in the ALJ version of the paper. Table 3 should read

Brand Share (%)
Scot Tissue 16.7
Cottonelle 6.7
Kleenex 7.5
Charmin 30.9
Northern 12.4
Angel 8.8
Private Label 7.6
Other 9.4
Total 100.00

The discussion and simulation results use the correct data.

[2009.7.26] Forthcoming: some parts quoted from these papers above.

3 PCAIDS技术支持笔记


很多我们PCAIDS论文(反垄断法期刊)的读者询问了完成的一些细节。关于软件,我已经开发了我自己的一个版本,作为一个Excel插件,可以掌控大多 数的计算并且对于很多人来说非常易用。一些其他的研究者告诉我他们使用matlab、Mathematica甚至PERL等软件。任何一个包含最优路径的软件包都很好。


你必须确定的使用nests挖掘PCAIDS的力量。附录中的关于nests的讨论有着两个微小的错误:4.B章的最后一句应该是“the familiar si/sj”。并且,918页上bij的方程式前面应该有一个-号。(A5)式的推导中也有一个小错误,结论是对的,但是它上面一行中最初两项应该用bij/pj PQ/pi替代。

909页的例子也有一些小失误。B的预期价格上升应该是4.5%。正确的alpha的估计值应该是0.061……我感激联邦委员会的Dave Schmidt指出该错误。


Brand Share (%)
Scot Tissue 16.7
Cottonelle 6.7
Kleenex 7.5
Charmin 30.9
Northern 12.4
Angel 8.8
Private Label 7.6
Other 9.4
Total 100.00

--------------------------------------To be contiuned (未完待续)-------------------------------

Dr. Epstein's

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