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

[2009.7.25]

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

最近,我不得不停下手中其他的活儿,集中精力做一个关于横向并购的研究。虽然,事实上我并不是和对其他的那些问题,比如声誉和激励的分析、宏观经济学的微观基础的实证检验一样,对这个问题充满了兴趣。但是眼下我并没有更好的选择,直至做完这个项目。

在计算兼并的价格效应的时候,最忙碌的莫过于选择一个适合的计量模型了。显而易见,最简单的办法就是使用“双重差分法”(亦译作“倍差法”),其在经济学的很多领域得到了广泛应用。从而相比于其他复杂的模型而言,这是一种颇为节省时间的办法,因为可以很容易地查到太多的相关资料。

然而,对我而言最大的困难就是搜集相关数据。很多数据属于公司的私有信息,并没有被公开,所以我的研究不得不暂时搁置。另一种可行的办法就是找到一个所需数据量更少的模型。幸运的是,我找到了PCAIDS模型,是波士顿大学的Epstein博士和他的合作者加州大学伯克利分校的Dan开发的。

正如作者在它的网页上所述

PCAIDS(近乎完美的需求系统的比例校准)模型的发明站在了当今并购(兼并)模拟模型应用的最前沿

与此同时,PCAIDS模型最明显的优势就是其对于数据量的低需求,正如作者所言:

PCAIDS模型只需要市场份额和两种价格弹性的数据:对于市场中一个品牌的弹性和整个行业的价格弹性。扫描数据和计量估计虽然有用,但并不是必须。这些特点使得它可以低成本的模拟任何交易。

正因为此,我的估计研究将有希望更有效率的完成。

为了更好地理解PCAIDS模型的应用,我很乐意先阅读一些相关的论文,并且翻译一些必要的相关知识并放在我的博客上,希望那些同样对PCAIDS模型感兴趣、想用它来估计并购(横向兼并)潜在的单边价格效应的读者可以有所借鉴。因而,接下来的段落将主要用中文撰写,并且附有原始的英文信息以作对照。我会尽力避免可能的错误,尤其是理解上的偏差,但是无论如何,最好的办法依旧是阅读原创作者提供的介绍。

此外,这篇博文将会持续更新,而且由于作者暂时不希望分发PCAIDS的软件程序,我将试着自己写一个(应该会是针对stata或者matlab软件下运行的程序)作为自己研究所需,并且如经作者允许,我会把相关程序在此公开。

最后,我在此难以抑制心中对于这两位作者天才工作的感激之情,感谢他们开发了这么一个简单易行的计算并购效应的模型,还有Epstein博士的热情支持与帮助。非常感谢!

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。

单边效应在差异化产品的市场中尤其显著。出于竞争性的考虑会随着大量先期在价格上升中流失的消费者的保留而上升,因为兼并后的厂商依旧供应不同的品牌以供这些消费者选择。在这种情况下,兼并后的厂商会发现上升价格会带来更多的利润,因为很少的顾客会流失。

兼并的模拟强调一个实际问题:怎样衡量潜在的单边效应的规模?在基本经济学理论中,我们利用关键的因素,包括市场份额、价格弹性、兼并带来的规模效应等等,分析了兼并前市场状况。该经济学模型中产生了单边效应,由于新厂商和他的竞争者追求自身利润最大化(不包括公开的串谋),即恢复市场均衡所必须的价格变化。

这种模拟可以预测一个交易后的价格上升或者下降,依赖于投入资源的配置来校准这个模型。高份额的兼并双方,或者相对高交叉价格弹性的双方,倾向于产生高的价格效应。小份额、低交叉价格弹性、高效率则倾向于产生较小的甚至为负的价格效应。

这种分析方法是非常灵活的,并且可以整合传统的并购准则——关注市场界定、效率、进入和生产重新定位等等的诸多要素。它同时可以衡量“资产剥离”的影响,尤其是在设计一个“定资先行”的策略的时候。更为重要的,这种模拟提供了一个一致的经济学框架用来分析难以可靠估量的复杂交易的各种选择。

关于其他技术的细节和构造一个兼并模拟模型,请回到PCAIDS支持网页和其中所列的相关文章

相关文章 by Roy J. Epstein

3 PCAIDS Technical Support Notes

From:http://www.royepstein.com/support.html

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

From:http://www.royepstein.com/support.html

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。

最普遍的问题就是怎么估计一阶条件(A3)。你必须使用并购后的值。最简单的办法就是更新市场份额——使用(1)式来获取s(new)=s(pre=merger)+ds。你可以使用(4)和(5)式产生新的弹性矩阵E1...E*。谨记:E矩阵在附录中进行了转置。

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。

表3的格式和数据如下,该讨论和模拟结果使用了正确的数据。

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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