Quantification of Harm -advanced techniques- Mihail Busu, PhD Romanian Competition Council mihail.busu@competition.ro
Summary: I. Comparison Methods 1. Interpolation Method 2. Seasonal Interpolation Method 3. Linear Extrapolation Method II. Methods based on Financial Analysis 4. Cost and Finance Method 5. Financial Multiples Method III. Regression Analysis 6. Simple Linear Regression 7. Multiple Linear Regression 8. Difference-in-Differences Method 9. Stationarity analysis 10. Linear Regression Hypothesis 1/21
8. Difference in Differences Method This method was described in the first mission on a merger case example. It compares for the same market pre- and/or post cartel prices to the prices paid by purchasers during collusion. It is assumed that the competitive situation in the market during the cartel would have been similar to the situation before and/or after collusion. Regressing the price of the product in question on a binary variable for the cartel period and a number of control variables allows us to determine the average cartel induced price increase during collusion and, thus, the identification of a suitable benchmark price is necessary.
8. Difference in Differences Method The damage is then calculated as the difference between the observed cartel price and the corresponding but-for price, multiplied by the quantity of the product sold in the cartel period. Formally, difference-in-differences method (DID) is making a benchmark analysis on two groups: the treatment group and the control group and the difference between the two groups is measured. The basic assumption is that the control group is only affected by the general factors, the evolution of normal, while the treatment group is affected by the general factors plus the treatment effect. The difference isolates the effect of the analysed treatment.
8. Difference in Differences Method There are some necessary conditions in order to apply DID method: The two groups have parallel trends (although levels may vary); The control group captures the normal evolution (affected by general factors affecting everyone and treated group); The price evolution of the companies involved in the cartel is affected by all the common factors affecting the control group, plus the cartel effect (treatment). If the inflation rates are different from control group that it is from treatment group, then the prices must be deflated.
8. Difference in Differences Method Taking all these factors into consideration, we could build an econometric model as follows: Y T D T D X i, t 1 i, t 2 i, t 3 i, t i, t 4 i, t i, t where Ti,t =1, if observation i comes from the treatment group, 0 otherwise; Di,t=1, if moment t is after treatment, 0 otherwise; Ti,t Di,t - interaction between the two variables, 1 if interaction i is from the treatment group and moment t is after the treatment, 0 otherwise; X = average weekly cost of undertaking i per product sold
8. Difference in Differences Method Y T D T D X i, t 1 i, t 2 i, t 3 i, t i, t 4 i, t i, t Period Before Infringement Period After Infringement Damages Estimate Infringement Market α + β 1 +β 4 α + β 1 + β 2 + β 3 +β 4 ΔY T = β 2 + β 3 Non-infringement Market α +β 4 α + β 2 +β 4 ΔY C = β 2 ΔΔY = ΔY C ΔY T = β 3
8.1. Implementing DID Method in cartel cases The analysis depends on the particularity of each case. We will do the set up as follows: Control group similar competitors, which offer similar products from other geographical market; Data daily or weekly prices (minimum). Quantities and a measure of quality would be a plus; Time periods choosing periods involve certain assumptions. In general, symmetric period, avoiding 3-3,6-6 or more months.
8.1. Implementing DID Method in cartel cases
8.1. Implementing DID Method in cartel cases Possible problems are related to finding an adequate control group and the availability of the data, since, generally, parties and other competitors have no obligation to provide information. Likewise, the validity of the assumptions we have made affect the representativeness of the results. An example of using Difference in Differences method to quantity the harm could be found in the attached EXCEL file (Quantifying Harm using DiD method).
8.1. Implementing DID Method in cartel cases - Example On Market I there is found to be a cartel on the 3 undertakings: A, B and C which are active on the market. The cartel was active during the period of time: Week 31-Week 50 of Year 2015. In order to apply Difference in Difference method, we will consider A, B and C as the Treatment Group and other 3 undertakings X, Y and Z, from another Geographical Market, we call it Market II, similar to Market I. X, Y and Z will make the Controled Group. Now we are able to set up the DiD method as follows: Treatment Group: Market I: Undertakings A, B and C. Control Group: Market II: Undertakings X,Y and Z. Non-Cartel Period: Week 1- Week 30 Cartel Period: Week 31- Week 50
8.1.1. Implementing DID Method in cartel cases - EXCEL To compute the harm, we need to compute the weighted price during cartel period and the counterfactual price for the cartel undertakings A, B and C. The formula we use to compute the weighted averages for weekly prices and quantities of the cartel- undertakings are: P C q p q p q p q q q A A A A A A A B C Q C q p q p q p p p p A A A A A A A B C We also calculate the weighted averages for weekly prices and quantities of the non-cartel undertakings: P Non C q p q p q p q q q X X Y Y Z Z X Y Z Q Non C q p q p q p p p p X X Y Y Z Z X Y Z
8.1.1. Implementing DID Method in cartel cases - EXCEL The Cartel Revenue is: The Non-Cartel Revenue is: Revenue PC Q C Revenue P Non C Q Non C C Non C The Harm is: Harm RevenueC RevenueNon C See EXCEL file 4. (Quantifying Harm using DiD method).
8.1.2. Implementing DID Method in cartel cases - Eviews The regression equation use was: Y T D T D X i, t 1 i, t 2 i, t 3 i, t i, t 4 i, t i, t Where the parameters were defined before. Now we will run a Multilinear Regression Analysis in Eviews to estimate the parameters. (View Eviews File) The coefficient of interest is β3.
8.1.2. Implementing DID Method in cartel cases - Eviews Eviews commands 1. Unstructured data: 50 2. Right click: New object/pool 3. Choose: _01 _06 (six companies) 4. Spreadsheet/Stacked Data 5. Proc/ Estimate
8.1. Implementing DID Method in cartel cases - Example We import the output from Eviews and get Dependent Variable: PRICE? Method: Pooled Least Squares Date: 09/02/16 Time: 13:21 Sample: 1 50 Included observations: 50 Cross-sections included: 6 Total pool (unbalanced) observations: 284 Variable Coefficient Std. Error t-statistic Prob. TREATMENT? 2.119351 0.276972 7.651872 0.000 DUMMY? 2.040674 0.309046 6.603141 0.000 INTERACTION? -2.058729 0.482749-4.264591 0.000 COST? 0.881202 0.081046 10.87284 0.000 R-squared 0.933235 Mean dependent var 3.897887 Adjusted R-squared 0.966041 S.D. dependent var 1.191902 S.E. of regression 2.056176 Akaike info criterion 4.293557 Sum squared resid 1183.8 Schwarz criterion 4.344951 Log likelihood 605.6851 Hannan-Quinn criter. 4.314162 Durbin-Watson stat 1.417036
8.1.2. Implementing DID Method in cartel cases - Example Since all the p_values (Prob.) from the above table are less than 0.05, we could conclude that all the independent variables introduced in the model are significant. Also, we could conclude that the coefficient of the interaction β 3 is statistically significant as its p_value is less than 0.05. That means the cartel has a significant impact on prices. Now, that we proved that the existence of the cartel has a statistically significant impact on prices, we will quantify the harm by using the regression equation formula:
Y 2.12 T 2.04 D 2.06 TD 0.88 X Y 2.12 (1) 2.04 (1) 2.06 (1 1) 0.88 X Y 2.12 2.04 2.06 0.88 X Y 2.1 0.88 X So the above formula will be used to compute the counterfactual price in EXCEL (see EXCEL file 5. Quantifying Harm using EViews). Harm will be computed as (Real Price Counterfactual Price)* (Weighted Quantities)
9. Analysis of the Stationarity of the data A Time Series is Stationary if the trend is not changing in time. In other words, the properties are constant in time (mean, variance, autocorrelation). From the economic point of view, a series is stationary if any shock on the series is temporary and not permanent. Examples of stationary time series: Real GDP, inflation rate etc. Examples of non- stationary time series: exchange rates, CPI etc. If a series is not stationary, by taking the first or second differentiation, we obtain a stationary series. This represents the integration number.
Question: Why is important to have a stationary time series data? Answer: Time series data are easy to be analyzed. Examples of two time series data 19
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Stationarity analysis: Graphical Method: Visualization of the price evolution 21
Stationarity analysis: Graphical method: graphical view of the price evolution Statistical testing: cannot be done in MS Excel, but we could do it in Eviews and Stata 22
10. Multilinear regression Hypothesis A multilinear regression is valid if the following hypothesis are validated: Hypothesis 1. Residual variables have 0 mean. Hypothesis 2. Residual variables are not autocorrelated This could be done by the Durbin Watson Test. If the value of the test is close to value 2, then we conclude that the residuals are not autocorrelated and this hypothesis is accepted. 23
10. Multilinear regression Hypothesis A multilinear regression is valid if the following hypothesis are validated: Hypothesis 3. The variance of the residual variables is constant (homoskedadicity) Hypothesis 4. Independent variables are not correlated with the residual variable (multicollinearity) This could be tested with VIF (Variance Inflection Factor) test. If the value of VIF <3, then we do not have multicollinearity and the hypothesis is valideted. 24
10. Multilinear regression Hypothesis A multilinear regression is valid if the following hypothesis are validated: Hypothesis 5. There are no measurement errors Hypothesis 6. The independent variables are linearly independent Hypothesis 7. Residual variable is Normally Distributed. Draw the graph of the Residuals and compare it to Normal Distribution: Plot: Regression standardized residuals vs. Predicted Draw the Graph which have the Predicted Errors on Oy axis and Observed values on Ox axis. 25
10. Multilinear regression Hypothesis Plot: Quantile Quantile graph / Normal Distribution If the first graph shows normal distribution output (Bell shape curve) and the second line have the points close to the regression line, then we conclude that Hypothesis 3 and 7 are validated. The Hypothesis 1, 5 and 6 are validated through the way the data was collected. Example Eviews 2 (EXCEL file 3. Quantifying Harm using Multiple Linear regression) 26
10. Eviews Output Residual Diagnostics Dependent Variable: PRICE Method: Least Squares Date: 10/12/16 Time: 15:19 Sample: 1 40 Included observations: 40 Variable Coefficient Std. Error t-statistic Prob. C 16.21692 2.872433 5.645709 0 COST 0.775056 0.075693 10.23947 0 EMPLOYEES 0.036519 0.020349 1.794626 0.0811 DUMMY 19.83809 0.844408 23.4935 0 R-squared 0.962705 Mean dependent var 46.85 Adjusted R-squared 0.959597 S.D. dependent var 11.24221 S.E. of regression 2.259744 Akaike info criterion 4.56302 Sum squared resid 183.832 Schwarz criterion 4.731908 Log likelihood -87.26039 Hannan-Quinn criter. 4.624084 F-statistic 309.7569 Durbin-Watson stat 1.883577 Prob(F-statistic) 0 27
Reference Peter Davis Eliana Garces Quantitative Techniques for Competition and Antitrust Analysis Princeton University Press, 2010 28
Lexecon An Introduction to Quantitative Techniques in Competition Analysis 2005 29
OFT Quantitative Techniques in Competition Analysis 1999 30
Thank you for your attention!