The assignment deals with Econometrics in a fairly limited scope, but the main issue I am having is with the python programming. I use Jupyter (a notebook program using Anaconda) to open the .ipynb file, but I attached a PDF printout of the assignment in case you can't open it. I have also attached the additional files needed to complete the assignment.
Problem_Set_2 Horizontal Mergers Horizontal merger: Two firms that compete against each other in the same market merge with each other. Examples: Ford and Volvo, MCI and Worldcom, AT&T and Cingular. Anheuser Busch InBev & SABMiller Page 1 Lecture Outline I. Data: Mergers are a common occurrence. II. Theory: Why do firms merge? • Differentiated goods markets. III. Department of Justice (DOJ) Merger Guidelines. • Market definition. • Herfindahl–Hirschman Index (HHI). • Diversion ratios. • Challenge criteria. Page 2 I. Data Facts Page 3 I. Data Fact 1 Figure: Mergers & Acquisitions in the United States I Mergers are increasingly common (bars, left y-axis) and the overall value of M&A activity is also increasing (red line, right y-axis). I US M&A looks pro-cyclical: When times are bad (i.e., 90-91, 01, & 08-09 recessions), M&A activity (number, value) seems to decrease. Why? Page 4 I. Data Fact 2 Figure: Value of Announced Mergers & Acquisitions (2017) ValueofglobalM&AdealsinbillionU.S.dollars 871.8871.8 713.3713.3 359.8359.8 358.7358.7 339339 308.4308.4 200.2200.2 149149 98.598.5 17.517.5 Valueofglobalmergersandacquisitionsin2017,byindustry(inbillionU.S. dollars) AdditionalInformation: Worldwide;Bloomberg;2017 Financial ConsumerNon-cyclical Communications Industrial ConsumerCyclical Energy Technology Utilities BasicMaterials Diversified Source Bloomberg ©Statista2018 0 100 200 300 400 500 600 700 800 900 1… I Mergers are common across a variety of industries. I In some of these industries firms produce homogeneous goods (e.g., energy, utilities) while in other industries firms produce differentiated goods (e.g., consumer goods). Page 5 II. Theory Page 6 II. Theory: Why do competing firms choose to merge? 1. Reduce competition, raising prices and profits. 2. Coordination of prices or quantities. 3. Production efficiencies: lower fixed and/or marginal costs (greater economies of scale or scope), leads to higher profits. 4. Other efficiencies: Eliminate inefficient competitors. Takeovers, or the threat of takeovers, may discipline bad management. Let’s start by focusing on the effects of mergers on competition. Page 7 Horizontal Mergers in Differentiated Good Markets Most markets are differentiated good markets. What are the gains to merging in these kinds of markets? Example: Three firms, three goods, marginal costs are zero and demands are given by y1 = 1− p1 + s(p2 + p3) y2 = 1− p2 + s(p1 + p3) y3 = 1− p3 + s(p1 + p2) Assume substitutes so 1 > s > 0. Firms compete in prices. Page 8 Benchmark Nash Equilibrium Firm 1 chooses price to solve max p1 p1 × ( 1− p1 + s(p2 + p3) ) Differentiating and solving for best reply, p1 = 1 2 [1 + s(p2 + p3)] Imposing symmetry, p? = 1 2(1− s) , y? = 1 2(1− s) , π? = 1 4(1− s)2 Page 9 Merger Nash Equilibrium Suppose Firms 1 and 2 merge. In contrast to homogenous good case, the new firm continues to produce both types of goods. Firm 12 chooses p1 and p2 to maximize profits from both products: max p1,p2 { p1 ( 1− p1 + s(p2 + p3) ) ︸ ︷︷ ︸ π1(p1,p2,p3) + p2 ( 1− p2 + s(p1 + p3) ) ︸ ︷︷ ︸ π2(p1,p2,p3) } Differentiating, ∂π12 ∂p1 = 0⇒ 1− 2p1 + s(p2 + p3)︸ ︷︷ ︸ ∂π1 ∂p1 +sp2 = 0 ∂π12 ∂p2 = 0⇒ 1− 2p2 + s(p1 + p3)︸ ︷︷ ︸ ∂π2 ∂p2 +sp1 = 0 Page 10 What Effect Does the Merger Have on NE Prices and Profits? One Strategy: Solve the new NE and compare equilibrium prices and profits to the benchmark case. Alt. Strategy: Evaluate ∂π12∂p1 , ∂π12 ∂p2 at (p?1 , p ? 2 , p ? 3 ). This tells us whether the new firm will increase prices at the old NE, ceteris paribus. Note that ∂π1(p ?) ∂p? = 0, ∂π2(p ?) ∂p? = 0, and sp ? > 0 so the derivatives for firm 12 at the old equilibrium prices are strictly greater than zero. To lower the value of the derivatives, I Firm 12 increases the prices of its goods (p1 ↑, p2 ↑) and I Firm 3 responds by also raising its price (p3 ↑) because best replies are strategic complements (look at the BRs). Results: 1. Merger leads to higher prices. 2. Merger is profitable since profits for the merged firm are π1 + π2 and it can generate the old equilibrium profits by choosing p?. Page 11 A More General Model I For simplicity, assume one market. If there are more than one, loop over the markets to solve for prices. I J products. Product r ∈ J produced with constant marginal cost cr . I F multi-product firms. Firm f ∈ F has portfolio F . Denote the portfolio of a firm f which produces product j as F j I Each firm f chooses the vector of prices (p) in its portfolio to solve πf (p ?) = max p { ∑ r∈F j (pr − cr )× yr (p) } . I Profit maximization implies the following FOC for firm f ’s product j : yj(p) + ∑ r∈F j ( pr − cr ) × ∂yr ∂pj = 0 . I In Bertrand-Nash equilibrium, J firm prices simultaneously satisfy all J FOCs. Page 12 A More General Model I For simplicity, assume one market. If there are more than one, loop over the markets to solve for prices. I J products. Product r ∈ J produced with constant marginal cost cr . I F multi-product firms. Firm f ∈ F has portfolio F . Denote the portfolio of a firm f which produces product j as F j I Each firm f chooses the vector of prices (p) in its portfolio to solve πf (p ?) = max p { ∑ r∈F j (pr − cr )× yr (p) } . I Profit maximization implies the following FOC for firm f ’s product j : yj(p) + ∑ r∈F j ( pr − cr ) × ∂yr ∂pj = 0 . I In Bertrand-Nash equilibrium, J firm prices simultaneously satisfy all J FOCs. Page 12 III. Mergers and Acquisitions in Practice: Government Guidelines Page 13 III. DOJ Merger Guidelines: How is a merger evaluated? I The Department of Justice (DOJ) is tasked with approving potential mergers and acquisitions in order to ensure that such changes of ownership meet the standards of antitrust law (e.g., Sherman, Clayton, Robinson-Patman). I Usually, the DOJ has only a matter of months to understand the implications of a merger and we’ve already established that each year there are thousands of mergers across disparate industries. I To increase efficiency, the DOJ simplifies things in two important ways: 1. It uses several “sufficient statistics” to simplify the analysis. Conducting a merger analysis properly requires computing pre and post equilibria which requires a lot of time and data to do properly. Instead, the hope that is with a handful of simple statistics (and perhaps a simple model), we can capture 80% of the truth. 2. It publishes guidelines for how it evaluates mergers. This is useful for prospective firms since a merger between two firms can be costly and time-consuming. These costs multiply when the government challenges the merger. For example, both companies are required to submit detailed (and proprietary) information about their business. Making the guidelines public enables firms to make better decisions about the future costs of a merger. Page 14 Market Definition I Economic definition typically based on price correlations and cross price elasticities. Products that are close substitutes are in the same market. I Antitrust definition is based on the Hypothetical Monopolist test: “A market is defined as a product or group of products and a geographic area in which it is sold that a hypothetical, profit-maximizing firm, not subject to price regulation, that was the only present and future seller of those products in that area would impose a small but significant and non-transitory increase in price (SSNIP) above prevailing or likely future levels.” Idea: A “market” should contain products which compete with each other and be small enough such that consumers can choose not to participate. But how to define what a market is? Big Question: Is there a simple, yet effective way (i.e., a “sufficient statistic”) of to identify a market as well as use the current equilibrium to forecast a future one? Page 15 The Herfindahl-Hirschman Index (HHI) I Herfindahl-Hirschman Index (HHI) is given by HHI = N∑ i=1 (100si ) 2 Range of the index is from 10,000/N (equal- sharing) to 10,000. Page 16 Properties of HHI a. HHI decreases with number of firms. b. HHI increases with the variance of the distribution of firm sizes. c. Recall from the Cournot model that in equilibrium, each firm i’s output satisfies the first order condition (P? − ci )/P? = si/η(Y ?) Multiplying by 10000si and summing over all i yields N∑ i=1 10000si ((P ? − ci )/P? = (HHI )/η(Y ?) In other words, HHI is proportional to a weighted average of the firms’ percentage markups of price over cost. It is a summary statistic of market power. I A market with a higher HHI has a higher average markup. I Useful, since markups are not observable. Page 17 Challenge Criteria - HHI The DOJ says it will not challenge a merger if post-merger HHI is I Less than 1000 I Between 1000 and 1800, and ∆HHI < 100;="" i=""> 1800 and ∆HHI < 50. remark: post-merger hhi is calculated on the basis of pre-merger shares. theory suggests that this is not a reasonable assumption. page 18 an example i the soft drink industry consists of firms with the following market shares. company si coca-cola 26% pepsi 24% sprite 14% seven-up 13% snapple 10% others 13% i suppose seven-up makes an offer to acquire snapple. i calculate the pre-merger hhi of industry concentration, the post-merger hhi, and the change in the hhi. for simplicity, let’s treat “others” as one firm. the pre-merger hhi is 262 + 242 + 142 + 132 + 102 + 132 = 1, 886 the post-merger hhi is 262 + 242 + 142 + (13 + 10)2 + 132 = 2, 146 i the ∆hhi is 260. i the doj would look into the merger. they may still approve it but the investigation will be expensive and time-consuming. page 19 another sufficient statistic - diversion ratios i relevant to industries where firms produce horizontally-differentiated goods. i consider the discrete choice framework we discussed earlier (i.e., multinomial logit) where a consumer buys one of j + 1 products. i a diversion ratio, which measures the fraction of consumers that switch from one product to an alternative after a price increase, is a central calculation of interest to antitrust authorities for analyzing horizontal mergers. i mathematically, define (qj , qk) as demand for products j and k 50.="" remark:="" post-merger="" hhi="" is="" calculated="" on="" the="" basis="" of="" pre-merger="" shares.="" theory="" suggests="" that="" this="" is="" not="" a="" reasonable="" assumption.="" page="" 18="" an="" example="" i="" the="" soft="" drink="" industry="" consists="" of="" firms="" with="" the="" following="" market="" shares.="" company="" si="" coca-cola="" 26%="" pepsi="" 24%="" sprite="" 14%="" seven-up="" 13%="" snapple="" 10%="" others="" 13%="" i="" suppose="" seven-up="" makes="" an="" offer="" to="" acquire="" snapple.="" i="" calculate="" the="" pre-merger="" hhi="" of="" industry="" concentration,="" the="" post-merger="" hhi,="" and="" the="" change="" in="" the="" hhi.="" for="" simplicity,="" let’s="" treat="" “others”="" as="" one="" firm.="" the="" pre-merger="" hhi="" is="" 262="" +="" 242="" +="" 142="" +="" 132="" +="" 102="" +="" 132="1," 886="" the="" post-merger="" hhi="" is="" 262="" +="" 242="" +="" 142="" +="" (13="" +="" 10)2="" +="" 132="2," 146="" i="" the="" ∆hhi="" is="" 260.="" i="" the="" doj="" would="" look="" into="" the="" merger.="" they="" may="" still="" approve="" it="" but="" the="" investigation="" will="" be="" expensive="" and="" time-consuming.="" page="" 19="" another="" sufficient="" statistic="" -="" diversion="" ratios="" i="" relevant="" to="" industries="" where="" firms="" produce="" horizontally-differentiated="" goods.="" i="" consider="" the="" discrete="" choice="" framework="" we="" discussed="" earlier="" (i.e.,="" multinomial="" logit)="" where="" a="" consumer="" buys="" one="" of="" j="" +="" 1="" products.="" i="" a="" diversion="" ratio,="" which="" measures="" the="" fraction="" of="" consumers="" that="" switch="" from="" one="" product="" to="" an="" alternative="" after="" a="" price="" increase,="" is="" a="" central="" calculation="" of="" interest="" to="" antitrust="" authorities="" for="" analyzing="" horizontal="" mergers.="" i="" mathematically,="" define="" (qj="" ,="" qk)="" as="" demand="" for="" products="" j="" and="">