Quantitative Price Tests in Antitrust Market Definition with an Application to the Savory Snacks Markets

Yannis Katsoulacos; Ioanna Konstantakopoulou; Eleni Metsiou; Efthymios Tsionas

doi:10.1515/jafio-2013-0022

Published by De Gruyter February 4, 2014

Quantitative Price Tests in Antitrust Market Definition with an Application to the Savory Snacks Markets

Yannis Katsoulacos , Ioanna Konstantakopoulou , Eleni Metsiou and Efthymios Tsionas

From the journal Journal of Agricultural & Food Industrial Organization

https://doi.org/10.1515/jafio-2013-0022

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Abstract

In this paper, we utilize the complete set of quantitative tests at the disposal of economists for delineating antitrust markets. This includes the Small but Significant Increase in Price (SSNIP) test but also a large number of traditional and newer price co-movement tests. We apply these tests to the savory snacks market using Greek bi-monthly data. This market has been subject to many antitrust investigations because of its market structure and its important implications for consumer welfare. However, no dominant view has yet emerged regarding the appropriate definition of the relevant market. Our results indicate that a wide relevant market definition is appropriate.

Keywords: market definition; quantitative price-co-movement tests; savory snacks market

JEL Code: K21; L40; L66

Prof. Y. Katsoulacos and E. Metsiou acknowledge support from the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: Thalis – Athens University of Economics and Business – Thalis – Athens University of Economics and Business – NEW METHODS IN THE ANALYSIS OF MARKET COMPETITION: OLIGOPOLY, NETWORKS AND REGULATION.

Appendix A.1: Values of correlation coefficients

In Table A1 below, we consider the regression ΔlogP_ΟΤ= α + βΔlogP_DTS for Snacks and also for Nuts, for the different regions. The correlation coefficient R (or equivalently here, R²) is not significant for the total channels or for channels OT and DTS with very few exceptions.

In Table A2 we consider the regression ΔlogP_SNACKS= α + βΔlogP_NUTS for the whole market and the different regions. Here we see that for the market as a whole and certain regional markets (three out of ten), the differences of log prices are statistically significantly correlated with a negative relationship.

All p-values are derived from the p-value of regression coefficient β. In Table A2 we also examine autocorrelation – robust standard errors (and thus p-values) according to the well-known methodology of Newey and West (1994). The same has been performed for Table A1 but we did not reach different results.

Table A1

R² coefficients from a regression of ΔlogP across channels

	SNACKS	NUTS
Region
Total	0.007 (–)	0.00002
Attica	0.010	0.049
Thessaloniki	0.0005	0.014 (–)
Macedonia/Thrace	0.004	0.017 (–)
East Macedonia/Thrace	0.002 (–)	0.059 (–)
West Central Macedonia	0.020	0.081
Central Greece	0.006 (–)	0.012
East Central Greece	0.420 (**)	0.105 (*)
West Central Greece	0.005	0.022 (–)
Peloponnese	0.01 (–)	0.014 (–)
Crete	0.096 (*)	0.031

^[1]

Table A2

R² coefficients from a regression of ΔlogP for the whole market

Region	R²	p-Value	p-Value (AR)
Total	0.108 (–)	0.075	0.0017
Attica	0.111 (–)	0.072	0.0152
Thessaloniki	0.067	0.170	0.056
Macedonia/Thrace	0.021 (–)	0.440	0.282
East Macedonia/Thrace	0.102 (–)	0.085	0.001
West Central Macedonia	0.00 (–)	0.96	0.95
Central Greece	0.004 (–)	0.73	0.60
East Central Greece	0.01 (–)	0.60	0.302
West Central Greece	0.00	0.97	0.98
Peloponnese	0.00 (–)	0.85	0.783
Crete	0.036	0.31	0.129

^[2]

One important question in empirical Industrial Organization is what values of correlation coefficients are “small”. From the data on total market we get the following results.

Dependent variable: LD1P1
Method: Least squares
Sample (adjusted): 2000Q2 2007Q3
Included observations: 30 after adjustments
Variable	Coefficient	Std. error	t-Statistic
C	0.102893	0.115276	0.892582
LD1P1(–1)	0.959204	0.048430	19.80613
R-squared			0.933378
Adjusted R-squared			0.930999
Durbin−Watson stat			1.698816
Mean dependent var			2.385368
S.D. dependent var			0.058937
Prob (F-statistic)			0.000000

The constant term is not statistically significant while the value of ρ is close to 1. According to the ADF test the series is I(1). Suppose we construct a series X as Xt=Xt−1+0,015et, where et∼IIDN0,1. Let us also construct the second price (logP2, or Υ) as Yt=Xt+0,03vt, and vt∼IIDN0,1, as our estimates show. The question is then what kinds of correlation coefficients we should expect. Given our sample size, n = 30, 100,000 Monte Carlo simulations provide the results shown in the figures below.

Clearly we should expect correlations as low as 0.40. The 99% confidence interval is from 0.048 to 0.961 so correlations can be practically anything. On the contrary if we had Xt,Yt∼IIDN0, 0.062 then the 99% confidence interval is –0.537 to 0.544 so correlation coefficients above 0.60 are highly improbable as shown in the next sampling distribution.

Therefore, the correlation coefficient behaves differently when the underlying time series are I(0) or I(1).

Even if a comparable basket of goods is available, simple correlations in levels or differences will be misleading since they depend crucially on the time series properties of the data. Now, the authors of a study on the Greek Savory Snacks market by LECG (2011) obtained a correlation coefficient of 0.49 “which is the average of correlations between sweet biscuits and bars, wafers and bites” as opposed to “correlations of 0.31 and 0.29 for salty snacks vs. salty biscuits and crackers, respectively”. The authors of LECG claim that correlations like 0.30 are “substantially lower” than 0.50.

Why are they substantially lower? How different can be a correlation coefficient of 0.30 say, compared to 0.49 in sample sizes N = 36? No statistical test is provided here so we have to return to statistical principles and wonder whether in samples of size N = 36 correlations like 0.30 and 0.50 are compatible. From Kendall and Stuart^[40](1977, 261) the standard error of the correlation coefficient is 1−ρ2N. Given that ρ = 0.5 the standard error is (1 – 0.5²)/6 = 0.125, so the 95% confidence interval would be 0.5±1.96×0.125, that is [0.255, 0.745]. Therefore, the “basket estimate” of a correlation coefficient about 0.50 cannot reject the hypothesis that, in fact, this correlation coefficient is as low as 0.255. Therefore, it can be 0.30.

To put it in another way, if ρ = 0, then the standard error would be 1/N=0.17, approximately so the estimate r = 0.50 would come with a standard error se = 0.17 and a 95% confidence interval 0.50±1.96×0.17=[0.17, 0.833]. This asymptotic 95% confidence interval, apparently rationalizes values of the correlation coefficient like 0.30 or as low as 0.17.

The normal approximation in small samples is known to be inaccurate and Kendall and Stuart mention that. They provide a closer approximation in pages 417–418 of their classical book. Suppose z=12log1+r1−r which in our case, with r = 0.5, becomes z = 0.5493. If the true value of ρ = 0.3, then ζ=12log1+ρ1−ρ = 0.3095. The question then is whether z and ζ are statistically close. As Kendall and Stuart mention (p. 419) one can take as standard error of z –ζ the expression 1n−1+4−ρ22n−12 = 0.1737, much like as before. The z-transformation tends to normality fast, so we can use the 95% confidence interval 0.5±1.96×0.1737 which gives us a wider estimate: [0.159, 0.840].

This means that to the estimate of the correlation coefficient r = 0.5 one must attach a standard error, se = 0.1737, and thus given the estimate a good approximation to a 95% confidence interval is simply 0.5±1.96×se (see Kendall and Stuart 1977, 419).

Of course, the correct way would be to use the Toda and Yamamoto (1995) in the context of I(1) processes. The difference in terms of the sampling distributions is shown in the next figure.

Distributions of r from Toda and Yamamoto (1995) (_____) and first differences (---)

Appendix A.2: Results of Granger causality tests

Table A3

Granger causality tests

TOTAL			TTL GR F + T + D		ATTICA		THES/NIKI		MACEDONIA/THRACE		EAST MACED/THRACE		WEST CENTRAL MACEDONIA
Price of nuts
			F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.
Price of snacks	lags = 1	Ho1	9.451	0.0048	4.1590	0.0513	5.7522	0.0236	4.4334	0.0447	1.4955	0.2319	9.5683	0.0046
		Ho2	2.123	0.1566	5.8950	0.0221	0.0005	0.9822	1.9567	0.1732	3.0854	0.0903	0.0027	0.9585
	lags = 2	Ho1	15.929	0.000	20.386	0.000	3.3018	0.0541	2.0582	0.1496	1.1863	0.3226	3.8966	0.0342
		Ho2	2.883	0.0755	5.5140	0.0107	0.0951	0.9096	2.8944	0.0748	1.8690	0.1760	1.5297	0.2370
	lags = 3	Ho1	6.625	0.0025	8.9365	0.0005	2.2776	0.1092	1.1683	0.3454	1.2552	0.3152	2.0637	0.1357
		Ho2	9.515	0.0004	17.275	0.00006	0.0621	0.9792	2.3755	0.0989	1.8667	0.1662	1.5552	0.2299
			CENTRAL GREECE		EAST CENTRAL GREECE		WEST CENTRAL GREECE		PELOPONNESE		CRETE
Price of nuts
			F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.
Price of snacks	lags = 1	Ho1	12.083	0.0017	8.0277	0.0086	2.8389	0.1035	6.8902	0.0141	13.573	0.0010
		Ho2	0.5028	0.4843	0.0621	0.8050	1.0058	0.3248	2.3317	0.1384	0.8531	0.3638
	lags = 2	Ho1	7.5647	0.0028	4.2758	0.0258	0.9305	0.4081	3.4610	0.0478	8.8415	0.0013
		Ho2	0.2229	0.8018	0.6667	0.5226	0.6307	0.5408	0.6652	0.5234	0.2674	0.7676
	lags = 3	Ho1	2.7274	0.0698	1.6180	0.2153	0.5007	0.6858	1.6087	0.2173	3.8200	0.0250
		Ho2	3.8525	0.0243	3.5211	0.0328	2.2800	0.1089	4.5516	0.0131	0.7681	0.5247

Channel DTS			Total DTS		ATTICA		THES/NIKI		MACEDONIA/THRACE		EAST MACED/THRACE		WEST CENTRAL MACEDONIA
Price of nuts
			F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.
Price of snacks	lags = 1	*Ho1*	2.8787	0.1013	2.2810	0.1426	6.3826	0.0177	1.8940	0.1801	1.1166	0.3000	5.8208	0.0229
		*Ho2*	1.6911	0.2044	4.6742	0.0396	0.4932	0.4885	1.9049	0.1789	3.4607	0.0738	0.0309	0.8616
	lags = 2	*Ho1*	2.1323	0.1405	3.6649	0.0408	4.4675	0.0224	1.0474	0.3663	0.8091	0.4570	3.2239	0.0575
		*Ho2*	3.3354	0.0527	6.9695	0.0041	0.0989	0.9062	2.9817	0.0697	3.5131	0.0459	1.0621	0.3614
	lags = 3	*Ho1*	2.4709	0.0899	2.7495	0.0683	3.6684	0.0287	2.0578	0.1365	0.4027	0.7525	3.7803	0.0259
		*Ho2*	1.1464	0.3535	2.4328	0.0934	0.0961	0.9613	1.2236	0.3259	1.7694	0.1838	0.3620	0.7810
			CENTRAL GREECE		EAST CENTRAL GREECE		WEST CENTRAL GREECE		PELOPONNESE		CRETE
Price of nuts
			F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.
Price of snacks	lags = 1	*Ho1*	14.248	0.0008	13.995	0.0009	8.1182	0.0083	2.1890	0.1506	0.7658	0.3892
		*Ho2*	2.2344	0.1466	1.6665	0.2077	0.1819	0.6731	3.5821	0.0692	0.5809	0.4525
	lags = 2	*Ho1*	5.0875	0.0144	4.6565	0.0195	3.4146	0.0495	1.6031	0.2221	2.8709	0.0762
		*Ho2*	0.2281	0.7977	0.1318	0.8771	0.0236	0.9767	3.5019	0.0463	0.8413	0.4435
	lags = 3	*Ho1*	2.3797	0.0985	3.0766	0.0498	1.8809	0.1638	0.9645	0.4279	3.7923	0.0256
		*Ho2*	3.1225	0.0477	1.8924	0.1618	0.9401	0.4389	1.3795	0.2765	0.7891	0.5135

Channel OT			Total OT		ATTICA		THES/NIKI		MACEDONIA/THRACE		EAST MACED/THRACE		WEST CENTRAL MACEDONIA
Price of nuts
			F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.
Price of snacks	lags = 1	Ho1	3.8872	0.0590	2.8197	0.1046	3.0372	0.0928	5.8905	0.0222	0.9502	0.3383	6.4181	0.0174
		Ho2	12.086	0.0017	13.152	0.0012	8.2043	0.0080	10.000	0.0038	2.3181	0.1395	1.9060	0.1787
	lags = 2	Ho1	6.3245	0.0062	5.7198	0.0093	3.6718	0.0406	4.4954	0.0220	0.7338	0.4905	7.4835	0.0030
		Ho2	10.341	0.0006	11.332	0.0003	5.2801	0.0126	5.1927	0.0134	1.1006	0.3489	1.1156	0.3441
	lags = 3	Ho1	3.1953	0.0445	3.3191	0.0396	2.9060	0.0587	4.6152	0.0124	0.7050	0.5597	3.9382	0.0225
		Ho2	11.448	0.0001	9.9522	0.0003	4.3111	0.0162	2.6740	0.0736	0.7127	0.5553	1.4947	0.2449
			CENTRAL GREECE		EAST CENTRAL GREECE		WEST CENTRAL GREECE		PELOPONNESE		CRETE
Price of nuts
			F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.	F	*Prob*.
Price of snacks	lags = 1	Ho1	6.0080	0.0210	3.5161	0.0716	1.4119	0.2451	9.3044	0.0051	12.202	0.0017
		*Ho2*	11.381	0.0023	8.7628	0.0063	8.3913	0.0074	2.7352	0.1097	0.6980	0.4108
	lags = 2	Ho1	4.7804	0.0179	4.8581	0.0169	0.5350	0.5925	7.1046	0.0038	7.1710	0.0036
		Ho2	6.9787	0.0041	5.0541	0.0147	5.5933	0.0101	4.4276	0.0231	1.5190	0.2392
	lags = 3	Ho1	4.2216	0.0175	5.7863	0.0048	0.0768	0.9718	5.1976	0.0077	4.4753	0.0140
		Ho2	9.4265	0.0004	4.8186	0.0105	6.7703	0.0023	3.4455	0.0352	1.5488	0.2314

^[4]

Appendix B: Individual unit root tests

Table B1

ADF and KPSS unit root tests

P1	ADF		KPSS
	Levels	Differences	Levels	Differences
Total
TTL GR F+T+D	–3.07	–4.50*	0.842	0.068***
Attica	–3.51**	–4.36*	0.845	0.103***
Thessaloniki	2.60	–4.91*	0.812	0.102***
Macedonia/Thrace	–2.71	–4.26**	0.8	0.073***
East Macedonia/Thrace	–2.03	–4.48*	0.684	0.096***
West Central Macedonia	–2.85	–4.45*	0.82	0.09***
Central Greece	–3.06	–4.35*	0.849	0.121***
East Central Greece	–2.92	–5.38*	0.844	0.084***
West Central Greece	–3.43***	–7.44*	0.847	0.164***
Peloponnese	–2.57	–6.26*	0.824	0.072***
Crete	–1.59	–4.72*	0.81	0.079***
Channel ΟΤ
Total OT	–4.84*	–5.80*	0.858	0.112***
Attica	–5.22*	–5.75*	0.855	0.113***
Thessaloniki	–3.64**	–4.43*	0.835	0.097***
Macedonia/Thrace	–4.87*	–6.41*	0.85	0.089***
East Macedonia/Thrace	–2.56	–5.59*	0.75	0.086***
West Central Macedonia	–4.94*	–6.05*	0.837	0.096***
Central Greece	–3.92**	–5.88*	0.853	0.122***
East Central Greece	–3.51***	–5.88*	0.839	0.21***
West Central Greece	–2.67	–5.40*	0.81	0.212***
Peloponnese	–4.27*	–5.42*	0.865	0.138***
Crete	–3.83**	–5.20*	0.867	0.09***
Channel DTS
Total DTS	–3.23***	–4.50*	0.829	0.061***
Attica	–2.05	–4.94*	0.817	0.059***
Thessaloniki	–3.30***	–4.65*	0.829	0.061***
Macedonia/Thrace	–1.92	–4.38*	0.812	0.066***
East Macedonia/Thrace	–2.68	–3.80**	0.757	0.07***
West Central Macedonia	–1.77	–4.42*	0.827	0.075***
Central Greece	–2.57	–3.68**	0.853	0.072***
East Central Greece	–2.61	–4.26**	0.851	0.069***
West Central Greece	–2.47	–3.68**	0.857	0.073***
Peloponnese	–3.27**	–4.10**	0.827	0.059***
Crete	–2.75	–3.91**	0.807	0.07***

P2	ADF		KPSS
	Levels	Differences	Levels	Differences
Total
TTL GR F+T+D	–4.87*	–5.45*	0.834	0.052***
Attica	–4.54*	–5.30*	0.766	0.067***
Thessaloniki	–3.37***	–3.90**	0.714	0.118***
Macedonia/Thrace	–5.32*	–7.16*	0.849	0.129***
East Macedonia/Thrace	–5.26*	–4.89*	0.826	0.13***
West Central Macedonia	–3.41***	–6.12*	0.829	0.083***
Central Greece	–3.51***	–5.39*	0.839	0.209***
East Central Greece	–2.20	–5.10*	0.796	0.343**
West Central Greece	–0.60	–2.65	0.691*	0.152***
Peloponnese	–3.70**	–6.89*	0.868	0.182***
Crete	–3.18	–4.78*	0.768	0.073***
Channel ΟΤ
Total OT	–4.74*	–5.21*	0.763	0.066***
Attica	–4.58*	–5.26*	0.727	0.071***
Thessaloniki	–4.28**	–5.26*	0.753	0.128***
Macedonia/Thrace	–4.57*	–5.00*	0.821	0.06***
East Macedonia/Thrace	–4.78*	–5.54*	0.507	0.057***
West Central Macedonia	–4.11**	–5.19*	0.869	0.076***
Central Greece	–4.23**	–4.94*	0.82	0.059***
East Central Greece	–5.53*	–5.46*	0.846	0.108***
West Central Greece	–3.33***	–5.48*	0.564	0.172***
Peloponnese	–4.70*	–5.22*	0.83	0.076***
Crete	–4.75*	–9.52*	0.794	0.094***
Channel DTS
Total DTS	–2.44	–3.73**	0.836	0.23***
Attica	–3.42***	–3.80**	0.779	0.068***
Thessaloniki	–4.46*	–5.41*	0.71	0.066***
Macedonia/Thrace	2.73	–5.29*	0.812	0.139***
East Macedonia/Thrace	–3.60**	–4.58*	0.821	0.18***
West Central Macedonia	–3.09	–5.90*	0.724	0.086***
Central Greece	–2.35	–5.93*	0.655*	0.353**
East Central Greece	–2.25	–6.01*	0.453**	0.434**
West Central Greece	–3.60**	–6.11*	0.812	0.057***
Peloponnese	–2.90	–5.81*	0.814	0.14***
Crete	–2.72	–6.74*	0.573**	0.296***

Q1	ADF		KPSS
	Levels	Differences	Levels	Differences
Total
TTL GR F+T+D	–4.88*	–5.61*	0.161***	0.057***
Attica	–4.27**	–4.57*	0.097***	0.064***
Thessaloniki	–4.56*	–4.76*	0.146***	0.061***
Macedonia/Thrace	–4.82*	–6.50*	0.537*	0.082***
East Macedonia/Thrace	–4.57*	–6.07*	0.591*	0.081***
West Central Macedonia	–4.62*	–6.45*	0.437**	0.081***
Central Greece	–4.16*	–5.96*	0.394***	0.07***
East Central Greece	–3.77**	–5.99*	0.495*	0.076***
West Central Greece	–4.70*	–4.73*	0.096***	0.062***
Peloponnese	–4.11**	–6.41*	0.161***	0.07***
CRETE	–3.89**	–7.96*	0.145***	0.067***
Channel ΟΤ
TOTAL OΤ	–4.66*	–6.20*	0.348**	0.058***
Attica	–4.44*	–5.78*	0.191***	0.057***
Thessaloniki	–1.53	–2.53	0.44**	0.311***
Macedonia/Thrace	–5.14*	–7.24*	0.705	0.061***
East Macedonia/Thrace	–4.96*	–6.88*	0.788	0.066***
West Central Macedonia	–4.39*	–7.07*	0.373**	0.069***
Central Greece	–4.57*	–6.37*	0.554*	0.063***
East Central Greece	–4.99*	–6.24*	0.393**	0.06***
West Central Greece	–4.51*	–6.29*	0.683*	0.071***
Peloponnese	–6.02*	–7.00*	0.585*	0.07***
Crete	–4.75*	–6.40*	0.409**	0.05***
Channel DTS
Total DTS	–4.11**	–4.62*	0.101***	0.07***
Attica	–4.42*	–5.32*	0.112***	0.089***
Thessaloniki	–4.04**	–4.67*	0.285***	0.071***
Macedonia/Thrace	–4.59*	–5.74*	0.327***	0.083***
East Macedonia/Thrace	–4.26**	–8.61*	0.319***	0.092***
West Central Macedonia	–4.45*	–5.63*	0.32***	0.078***
Central Greece	–3.97**	–4.57*	0.26***	0.084***
East Central Greece	–3.31***	–6.59*	0.433*	0.087***
West Central Greece	–4.81*	–5.10*	0.365**	0.068***
Peloponnese	–3.57**	–7.93*	0.323	0.083***
Crete	–3.32***	–7.49*	0.109	0.077***
Total

Q2	ADF		KPSS
	Levels	Differences	Levels	Differences
TTL GR F+T+D	–5.51*	–5.13*	0.253***	0.074***
Attica	–5.36*	–4.77*	0.158***	0.067***
Thessaloniki	–4.86*	–4.71*	0.333***	0.057***
Macedonia/Thrace	–4.43**	–5.38*	0.424**	0.097***
East Macedonia/Thrace	–3.08	–4.90*	0.501*	0.144***
West Central Macedonia	–5.68*	–5.78*	0.123***	0.061***
Central Greece	–5.82*	–6.10*	0.379**	0.105***
East Central Greece	–5.61*	–6.17*	0.272***	0.109***
West Central Greece	–6.00*	–5.87*	0.597*	0.094***
Peloponnese	–6.26*	–7.40*	0.448**	0.124***
Crete	–4.74*	–5.08*	0.451**	0.072***
Channel ΟΤ
Total OT	–5.58*	–5.15*	0.277***	0.07***
Attica	–5.45*	–4.81*	0.17***	0.064***
Thessaloniki	–4.88*	–4.67*	0.435***	0.05***
Macedonia/Thrace	–5.43*	–5.70*	0.575*	0.075***
East Macedonia/Thrace	–4.28**	–5.34*	0.662*	0.09***
West Central Macedonia	–5.89*	–5.96*	0.149***	0.066***
Central Greece	–5.96*	–6.05*	0.401**	0.106***
East Central Greece	–5.73*	–6.09*	0.259***	0.11***
West Central Greece	–5.77*	–5.80*	0.664*	0.108***
Peloponnese	–5.60*	–7.20*	0.378**	0.148***
Crete	–3.88**	–4.98*	0.233***	0.095***
Channel DTS
Total DTS	–4.03**	–4.63*	0.104***	0.14***
Attica	–2.98	–5.58*	0.292***	0.09***
Thessaloniki	–3.77**	–6.25*	0.195***	0.135***
Macedonia/Thrace	–3.19*	–5.29*	0.151***	0.181***
East Macedonia/Thrace	2.22	–5.19*	0.15***	0.248***
West Central Macedonia	–3.92**	–4.62*	0.058***	0.093***
Central Greece	–3.74**	–4.90*	0.462*	0.191***
East Central Greece	–3.27***	–5.95*	0.394***	0.104***
West Central Greece	–3.32***	–3.61**	0.088***	0.135***
Peloponnese	–3.26***	–4.55*	0.592*	0.075***
Crete	–1.76	–5.03*	0.475*	0.221***
Total

Log(P1)	ADF		KPSS
	Levels	Differences	Levels	Differences
TTL GR F+T+D	–3.02	–4.38*	0.84	0.50***
Attica	–3.43***	–4.61*	0.84	0.112***
Thessaloniki	–2.55	–4.82*	0.81	0.104***
Macedonia/Thrace	–2.66	–4.21**	0.801	0.073***
East Macedonia/Thrace	–1.98	–4.56*	0.678	0.093***
West Central Macedonia	–2.79	4.47*	0.822	0.093***
Central Greece	–3.13	–7.31*	0.851	0.106***
East Central Greece	–2.99	–6.3*	0.845	0.075***
West Central Greece	–3.47***	–7.35*	0.848	0.149***
Peloponnese	–2.62	–6.29*	0.824	0.072***
Crete	–1.71	–4.76*	0.81	0.079***
Channel ΟΤ
Total OT	–4.85*	–5.81*	0.858	0.112***
Attica	–5.06*	–5.67*	0.855	0.113***
Thessaloniki	–3.66**	–5.4*	0.835	0.097***
Macedonia/Thrace	–5.05*	–6.55*	0.85	0.089***
East Macedonia/Thrace	–2.56	–5.58*	0.75	0.086***
West Central Macedonia	–4.64*	–6.19*	0.837	0.096***
Central Greece	–3.87**	–5.88*	0.853	0.122***
East Central Greece	–3.3***	–5.84*	0.839	0.210***
West Central Greece	–2.77	–5.47*	0.81	0.212***
Peloponnese	–4.32*	–5.5*	0.865	0.138***
Crete	–3.81*	–5.32*	0.867	0.092***
Channel DTS
Total DTS	–3.22	–4.45*	0.829	0.0617***
Attica	–3.44***	–4.87*	0.817	0.59*
Thessaloniki	–3.3***	–4.58*	0.829	0.0617***
Macedonia/Thrace	–1.93	–4.32*	0.812	0.066***
East Macedonia/Thrace	–2.65	–3.83**	0.757	0.708
West Central Macedonia	–1.77	–4.39*	0.827	0.0756***
Central Greece	–2.62	–3.72**	0.853	0.0726***
East Central Greece	–2.67	–4.34*	0.851	0.0693***
West Central Greece	–2.51	–3.62**	0.857	0.731
Peloponnese	–3.27***	–4.13**	0.827	0.0592***
Crete	–2.76	–3.91**	0.807	0.0705***
Total

Log(P2)	ADF		KPSS
	Levels	Differences	Levels	Differences
TTL GR F + T + D	–4.81*	–5.48*	0.83	0.054***
Attica	–4.48*	–5.34*	0.768	0.070***
Thessaloniki	–3.00	–5.24*	0.72*	0.130***
Macedonia/Thrace	–5.47*	–7.14*	0.848	0.117***
East Macedonia/Thrace	–5.01*	–4.87*	0.821	0.121***
West Central Macedonia	–3.50***	–6.18*	0.832	0.077***
Central Greece	–3.32***	–5.66*	0.8406	0.197***
East Central Greece	–2.41	–5.42*	0.804	0.334***
West Central Greece	–0.62	–2.69*	0.695*	0.153***
Peloponnese	–3.85**	–7.19*	0.868	0.182***
Crete	–3.29***	–4.73*	0.768	0.073***
Channel ΟΤ
Total OT	–4.68*	–5.24*	0.763	0.066***
Attica	–4.54*	–5.29*	0.727**	0.071***
Thessaloniki	–4.29**	–5.30*	0.753	0.128***
Macedonia/Thrace	–4.35*	–4.96*	0.821	0.0607***
East Macedonia/Thrace	–4.91*	–5.65*	0.5071*	0.057***
West Central Macedonia	–4.45*	–5.11*	0.869	0.076***
Central Greece	–4.14*	–4.90*	0.82	0.059***
East Central Greece	–5.53*	–5.48*	0.846	0.108***
West Central Greece	–3.47***	–5.56*	0.564*	0.172***
Peloponnese	–4.47*	–5.18*	0.83	0.076***
Crete	–5.04*	–9.89*	0.794	0.094***
Channel DTS
Total DTS	–2.51	3.70*	0.836	0.2309***
Attica	–2.64	–5.97*	0.779	0.0682***
Thessaloniki	–3.51***	–5.06*	0.71*	0.0669***
Macedonia/Thrace	–2.74	–5.22*	0.812	0.139***
East Macedonia/Thrace	–3.71**	–4.48*	0.821	0.1803***
West Central Macedonia	–3.06	–5.87*	0.724*	0.0863***
Central Greece	–2.52	–6.06*	0.655*	0.0353***
East Central Greece	–2.36	–6.24*	0.4539**	0.434**
West Central Greece	–3.52***	–6.18*	0.812	0.057***
Peloponnese	–3.04	–4.78*	0.814	0.1402***
Crete	–4.82*	–6.71*	0.573*	0.296***
Total

Log(q1)	ADF		KPSS
	Levels	Differences	Levels	Differences
TTL GR F+T+D	–4.71*	–5.82*	0.153***	0.056***
Attica	–4.55*	–7.41*	0.103***	0.065***
Thessaloniki	–4.78*	–5.59*	0.136***	0.065***
Macedonia/Thrace	–5.02*	–6.37*	0.46*	0.078***
East Macedonia/Thrace	–4.97*	–6.24*	0.536**	0.079***
West Central Macedonia	–4.84*	–6.29*	0.368**	0.076***
Central Greece	–4.48*	–6.07*	0.352**	0.073***
East Central Greece	–4.17*	–6.11*	0.449**	0.077***
West Central Greece	–4.48*	–5.74*	0.105***	0.065***
Peloponnese	–4.43*	–6.37*	0.161***	0.07***
Crete	–4.39*	–5.68*	0.145***	0.067***
Channel ΟΤ
Total OT	–4.88*	–6.49*	0.348**	0.058***
Attica	–4.68*	–5.94*	0.191***	0.057***
Thessaloniki	–2.85	–4.13*	0.44**	0.311***
Macedonia/Thrace	–5.34*	–7.33*	0.705*	0.061***
East Macedonia/Thrace	–4.81*	–6.92*	0.788	0.066***
West Central Macedonia	–4.58*	–7.26*	0.373**	0.069***
Central Greece	–5.15*	–6.79*	0.554*	0.063***
East Central Greece	–4.88*	–6.53*	0.393**	0.0608***
West Central Greece	–4.84*	–6.98*	0.683*	0.071***
Peloponnese	–5.85*	–7.51*	0.585*	0.07***
Crete	–5.34*	–6.46*	0.409**	0.0503***
Channel DTS
Total DTS	–4.44*	–4.75*	0.101***	0.07***
Attica	–4.04**	–5.20*	0.112***	0.089***
Thessaloniki	–4.31*	–4.78*	0.285***	0.071***
Macedonia/Thrace	–4.84*	–5.78*	0.327***	0.083***
East Macedonia/Thrace	–4.63*	–9.13*	0.319***	0.092***
West Central Macedonia	–4.73*	–4.66*	0.32***	0.078***
Central Greece	–4.33*	–4.82*	0.26***	0.084***
East Central Greece	–3.79**	–4.57*	0.433**	0.087***
West Central Greece	–4.64*	–5.14*	0.365**	0.068***
Peloponnese	–4.08**	–8.32*	0.323***	0.083***
Crete	–3.89**	–8.17*	0.109***	0.077***
Total

Log(q2)	ADF		KPSS
	Levels	Differences	Levels	Differences
TTL GR F+T+D	–4.32*	–4.64*	0.264***	0.073***
Attica	–5.44*	–5.00*	0.157***	0.064***
Thessaloniki	–4.65*	–5.90*	0.346***	0.054***
Macedonia/Thrace	–3.85**	–6.55*	0.434**	0.097***
East Macedonia/Thrace	–3.09	–5.78*	0.513**	0.152***
West Central Macedonia	–4.46*	–7.63*	0.132***	0.06***
Central Greece	–3.79*	–6.16*	0.408**	0.113***
East Central Greece	–3.82**	–5.94*	0.286***	0.115***
West Central Greece	–4.13*	–6.76*	0.64*	0.111***
Peloponnese	–3.61	–6.62*	0.448**	0.124***
Crete	–4.76*	–8.19*	0.451*	0.072***
Channel ΟΤ
Total OT	–4.98*	–4.56*	0.277***	0.07***
Attica	–5.39*	–4.58*	0.17***	0.064***
Thessaloniki	–4.89*	–4.62*	0.435***	0.05***
Macedonia/Thrace	–5.83*	–6.10*	0.575*	0.075***
East Macedonia/Thrace	–4.13**	–5.49*	0.662*	0.09***
West Central Macedonia	–6.15*	–6.49*	0.149***	0.066***
Central Greece	–6.46*	–6.74*	0.401**	0.106***
East Central Greece	–6.07*	–6.67*	0.259***	0.11***
West Central Greece	–6.50*	–6.58*	0.664*	0.108***
Peloponnese	–6.11*	–9.16*	0.378**	0.142***
Crete	–4.05**	–5.19*	0.233***	0.095***
Channel DTS
Total DTS	–4.04*	–4.56*	0.104***	0.14***
Attica	–3.00	–5.67*	0.295***	0.09***
Thessaloniki	–3.63**	–6.01*	0.195***	0.135***
Macedonia/Thrace	–3.17	–5.31*	0.151***	0.181***
East Macedonia/Thrace	–2.08	–5.02*	0.1505***	0.258***
West Central Macedonia	–3.97**	–4.59*	0.058***	0.093***
Central Greece	–3.86**	–4.83*	0.462**	0.191***
East Central Greece	–3.46**	–6.05*	0.394**	0.104***
West Central Greece	–3.33***	–3.69**	0.088***	0.135***
Peloponnese	–3.48***	–4.79*	0.592*	0.075***
Crete	–1.76	–5.03*	0.475*	0.221***

^[5]

Table B2

DF-GLS unit root test

P1	DF-GLS unit root test
	Levels		First differences
	Without trend	With trend	Without trend	With trend
Total
TTL GR F+T+D	–0.140	–2.474	–4.435*	–4.615*
Attica	–0.720	–3.617**	–4.744*	–4.744*
Thessaloniki	–0.829	–2.746	–3.620**	–3.765**
Macedonia/Thrace	–0.79	–2.784	–3.667**	–3.848*
East Macedonia/Thrace	–0.895	–2.053	–2.949***	–3.205**
West Central Macedonia	–0.706	–2.962	–4.074*	–4.208*
Central Greece	0.147	–3.030***	–5.622*	–6.744*
East Central Greece	–0.37	–2.719	–2.365	–4.325*
West Central Greece	0.269	–2.342	–4.027*	–4.182*
Peloponnese	0.004	–2.317	–3.534**	–3.896*
Crete	0.371	–1.805	–4.620*	–4.839*
Channel OT
Total OT	–0.344	–4.780*	–5.987*	–5.977*
Attica	–0.436	–4.961*	–5.831*	–5.86*
Thessaloniki	–0.494	–3.651**	–5.602*	–5.618*
Macedonia/Thrace	–0.506	–4.703*	–6.631*	–6.702*
East Macedonia/Thrace	–0.877	–2.803	–5.675*	–5.768*
West Central Macedonia	–0.609	–4.426*	–6.371*	–6.241*
Central Greece	–0.307	–3.931*	–5.941*	–6.125*
East Central Greece	–0.578	–3.327**	–5.313*	–6.034*
West Central Greece	–0.0192	–2.387	–5.385*	–5.520*
Peloponnese	–0.224	–4.335*	–5.408*	–5.427*
Crete	–0.08	–3.967*	–5.16*	–4.991*
Channel DTS
Total DTS	–0.511	–3.347**	–4.59*	–4.583*
Attica	–0.703	–3.581**	–5.004*	–4.999*
Thessaloniki	–0.594	–3.428**	–4.751*	–4.736*
Macedonia/Thrace	–0.724	–3.262**	–4.437*	–4.454*
East Macedonia/Thrace	–0.719	–2.756	–3.930*	–3.942*
West Central Macedonia	–0.675	–3.242**	–4.489*	–4.551*
Central Greece	–0.094	–2.716	–3.697*	–3.818*
East Central Greece	–0.174	–2.792	–4.094*	–4.375*
West Central Greece	–0.003	–2.560	–3.743*	–3.762*
Peloponnese	–0.473	–3.39**	–4.172*	–4.231*
Crete	–0.388	–2.895	–3.870*	–3.939*

P2	DF-GLS unit root test
	Levels		First differences
	Without trend	With trend	Without trend	With trend
Total
TTL	–0.644	–5.063*	–3.128*	–4.872*
Attica	–1.307	–4.682*	–3.119*	–4.904*
Thessaloniki	–1.023	–2.953***	–2.787*	–3.543**
Macedonia/Thrace	–0.039	–3.407**	–7.062*	–6.879*
East Macedonia/Thrace	–0.1507	–3.075***	–5.629*	–5.742*
West Central Macedonia	–0.817	–3.60**	–6.659*	–6.172*
Central Greece	–0.0604	–3.479**	–5.648*	–5.86*
East Central Greece	0.041	–2.549	–3.896*	–4.412*
West Central Greece	–1.104	–2.293	–5.042*	–6.985*
Peloponnese	0.107	–3.620**	–6.187*	–6.9*
Crete	–0.103	–2.96***	–2.099**	–3.442**
Channel OT
Total DTS	–2.009**	–4.913*	–3.92*	–4.715*
Attica	–2.083**	–4.739*	–3.893*	–4.861*
Thessaloniki	–1.826***	–4.219*	–3.103*	–4.574*
Macedonia/Thrace	–0.419	–3.891*	–3.07*	–4.096*
East Macedonia/Thrace	–2.588**	–3.084***	–3.817*	–4.548*
West Central Macedonia	0.293	–3.872*	–3.222*	–3.923*
Central Greece	–0.713	–4.17*	–4.812*	–3.96*
East Central Greece	–0.362	–4.349*	–2.826*	–3.573*
West Central Greece	–1.345	–2.468	–2.416**	–4.344*
Peloponnese	–0.382	–3.599**	–2.532	–3.49*
Crete	–0.387	–3.745*	–1.671	–3.06***
Channel DTS
Total DTS	0.858	–2.108	–5.539*	–5.906*
Attica	–0.601	–2.672	–5.510*	–6.08*
Thessaloniki	–1.408	–3.625**	–5.226*	–5.251*
Macedonia/Thrace	–0.072	–2.379	–5.315*	–5.328*
East Macedonia/Thrace	0.2211	–2.879	–4.33*	–4.602*
West Central Macedonia	–1.517	–3.111***	–5.277*	–5.846*
Central Greece	–0.323	–2.091	–2.338*	–5.77*
East Central Greece	–0.908	–1.927	–4.072*	–5.831*
West Central Greece	–0.833	–3.555***	–5.981*	–6.345*
Peloponnese	–0.098	–2.903***	–5.673*	–5.756*
Crete	–2.026**	–3.622***	–4.555*	–5.38*

^[6]

Table B3

ERS-point optimal unit root test

P1	ERS-point optimal unit root test
	Levels		First differences
	Without trend	With trend	Without trend	With trend
Total
TTL GR F + T + D	24.962	4.49**	1.766*	6.271***
Attica	35.665	3.513*	0.919*	3.018*
Thessaloniki	33.417	5.459**	1.872*	6.383***
Macedonia/Thrace	16.821	5.547**	1.834*	6.408***
East Macedonia/Thrace	18.038	16.605	1.868*	6.238***
West Central Macedonia	20.91	4.727**	0.961*	3.295*
Central Greece	26.163	4.498**	3.287***	1.775*
East Central Greece	20.654	1.801*	1.911**	0.303*
West Central Greece	34.116	8.905	2.340**	5.946***
Peloponnese	20.729	2.662*	0.309***	1.13*
Crete	21.987	3.815*	1.508*	4.08*
Channel OT
Total OT	48.427	2.221*	0.549*	1.963*
Attica	50.171	1.912*	0.531*	1.896*
Thessaloniki	31.98	3.676*	0.597*	2.189*
Macedonia/Thrace	20.292	2.955*	0.528*	1.869*
East Macedonia/Thrace	12.965	9.259	0.667*	2.432*
West Central Macedonia	19.257	3.175*	0.707*	2.405*
Central Greece	36.709	3.256*	0.585*	2.098*
East Central Greece	38.398	4.563	0.687*	2.068*
West Central Greece	30.373	13.886	0.773*	2.7*
Peloponnese	42.551	3.219*	0.948*	2.697*
Crete	42.878	3.56*	1.284*	3.214*
Channel DTS
Total DTS	16.646	3.743*	0.707*	2.579*
Attica	13.668	3.373*	0.622*	2.249*
Thessaloniki	16.571	3.693*	0.7138*	2.593*
Macedonia/Thrace	14.711	3.824*	0.774*	2.563*
East Macedonia/Thrace	12.467	5.616*	1.846*	6.517***
West Central Macedonia	16.896	3.706*	0.741*	2.383*
Central Greece	27.615	5.797***	2.045**	6.717***
East Central Greece	29.751	5.825***	2.146**	6.505***
West Central Greece	31.691	6.509***	1.811*	6.637***
Peloponnese	15.914	3.686*	0.881*	3.126*
Crete	16.914	5.000**	1.093*	3.664*

P2	DF-GLS unit root test
	Levels		First differences
	Without trend	With trend	Without trend	With trend
Total
TTL GR F+T+D	11.374	3.585	2.944*	5.201*
Attica	7.963	3.505***	2.971***	4.921**
Thessaloniki	16.994	7.392	3.28***	7.094
Macedonia/Thrace	33.445	9.065	2.381**	6.946
East Macedonia/Thrace	26.208	11.511	1.619*	5.953***
West Central Macedonia	14.33	6.817	3.426***	7.292
Central Greece	12.684	9.084	0.744*	2.605*
East Central Greece	14.231	6.933	1.914**	5.919**
West Central Greece	13.496	7.973	2.215**	2.572*
Peloponnese	21.983	7.929	1.995**	6.950
Crete	14.771	7.805		9.198
Channel OT
Total OT	7.212	3.541	3.169***	5.441**
Attica	6.707	3.424	3.060***	4.92**
Thessaloniki	11.696	5.791	5.041	3.381*
Macedonia/Thrace	18.802	5.848	4.839	1.559*
East Macedonia/Thrace	3.976	6.827	1.982**	6.830
West Central Macedonia	27.648	6.061	3.262***	3.324*
Central Greece	8.887	6.278	2.544**	7.041
East Central Greece	10.207	3.8708	2.208**	7.236
West Central Greece	6.513	8.611	3.478***	5.196**
Peloponnese	17.423	6.084	6.914	1.748*
Crete	27.133	6.855	17.684	3.605*
Channel DTS
Total DTS	58.113	17.625	2.604**	6.557**
Attica	24.167	8.476	3.115***	6.608***
Thessaloniki	8.148	3.695	1.596*	5.898***
Macedonia/Thrace	33.582	15.22	1.866*	6.312***
East Macedonia/Thrace	35.972	8.280	2.063*	6.105***
West Central Macedonia	6.943	7.93	1.55*	2.878*
Central Greece	12.138	20.65	5.419	6.927
East Central Greece	9.576	23.33	3.586***	7.039
West Central Greece	14.763	7.119	1.757*	6.331***
Peloponnese	23.785	10.158	1.676*	6.092***
Crete	19.276	16.607	2.546**	3.426*

^[7]

Appendix C: Johansen maximum likelihood cointegration tests at the regional level

Table C1

Maximum likelihood cointegration tests

H0: rank = r	Johansen
	P1 and P2
	Levels			Log
	Trace statistic	p-Value	Long-run coefficient	Trace statistic	p-Value	Long-run coefficient
	*r = 0 (15.494)*			*r = 0(15.494)*
Total
TTL GR F+T+D	27.82(1)*	0.0004	–1.73	27.39(1)	0.0005	–1.23
Attica	28.91(1)	0.0003	–1.61	28.66(1)	0.0003	–1.27
Thessaloniki	21.51(6)	0.005	–1.76	16.19(4)	0.0392	–2.44
Macedonia/Thrace	38.96(6)	0.000	–1.75	40.12(6)	0.0000	–1.067
East Macedonia/Thrace	40.03(6)	0.000	–1.73	45.96(6)	0.0000	–1.16
West Central Macedonia	21.86(5)	0.0004	–1.64	18.32(4)	0.0812	–0.97
Central Greece	31.25(6)	0.0001	–1.92	17.57(4)	0.024	–1.23
East Central Greece	17.36(4)	0.0258	–1.97	17.20(4)	0.027	–1.25
West Central Greece	19.61(6)	0.0113	–2.21	19.37(7)	0.0365	–0.24
Peloponnese	16.04(5)	0.0413	–1.55	40.82(6)	0.000	–0.95
Crete	26.20(3)	0.0009	–1.82	26.28(3)	0.0008	–1.16
Channel ΟΤ
TOTAL OΤ	27.24(1)	0.0006	–1.55	26.68(1)	0.0007	–1.36
Attica	28.92(1)	0.0003	–1.51	28.58(1)	0.0003	–1.41
Thessaloniki	23.16(1)	0.0029	–2.19	23.87(1)	0.0022	–1.82
Macedonia/Thrace	18.40(2)	0.0177	–1.11	18.09(2)	0.0198	–0.83
East Macedonia/Thrace	15.90(2)	0.0434	–2.63	17.03(2)	0.0291	–2.08
West Central Macedonia	33.87(6)	0.0000	–0.72	38.48(6)	0.000	–0.51
Central Greece	20.28(1)	0.0088	–1.19	19.49(1)	0.0118	–0.94
East Central Greece	18.18(1)	0.0192	–0.98	40.82(6)	0.000	–0.95
West Central Greece	19.74(2)	0.0108	–1.99	18.95(2)	0.0144	–1.63
Peloponnese	15.84(1)	0.0443	–1.55	15.67(1)	0.047	–1.29
Crete	16.59(2)	0.034	–1.56	15.51(1)	0.0496	–1.12
Channel DTS
Total DTS	16.80(5)	0.0316	–1.51	42.82(6)	0.000	–1.23
Attica	16.10(1)	0.0405	–1.20	16.17(1)	0.0395	–0.90
Thessaloniki	–	–	–	–	–	–
Macedonia/Thrace	26.03(6)	0.0009	–1.73	26.37(6)	0.0008	–1.02
East Macedonia/Thrace	18.43(6)	0.0175	–1.51	19.87(6)	0.0102	–0.92
West Central Macedonia	20.37(7)	0.0085	–2.04	16.19(5)	0.0392	–1.13
Central Greece	16.57(5)	0.0343	–0.99	16.10(5)	0.0403	–0.77
East Central Greece	16.68(5)	0.0469	–0.53	–	–	–
West Central Greece	31.84(7)	0.0001	–1.72	–	–	–
Peloponnese	15.74(4)	0.0459	–1.23	30.03(5)	0.0002	–0.82
Crete	–	–	–	–	–	–

^[8]

Explanation of symbols

Q1: Quantity of product 1
Q2: Quantity of product 2
q1: =log(Q1)
q2: =logQ2
P1: Price of product 1
P2: Price of product 2
M: Income
p1m: =logP1M
p2m: =logP2M
m: Percentage margin of a hypothetical monopolist
c: Unit variable cost
p: Original (pre-increase) price level of the product
τ: Percentage price increase
π: Reduction in output sales
π∗: Critical loss in sales
ε: Elasticity of demand
ε∗: Critical elasticity of demand

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Published Online: 2014-2-4

Published in Print: 2014-1-1

Quantitative Price Tests in Antitrust Market Definition with an Application to the Savory Snacks Markets

Abstract

Appendix A.1: Values of correlation coefficients

Appendix A.2: Results of Granger causality tests

Appendix B: Individual unit root tests

Appendix C: Johansen maximum likelihood cointegration tests at the regional level

Explanation of symbols

References

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