Update of Multimarket Contact Paper (4/20/19)
Jung Hwan Koh
April 20, 2019
Update
- New Market Definition(k Nearest Neighbors algorithm) is addeed.
- Estimation of the effect of MMC on price with kNN and DBSCAN is added (2.2 and 2.3).
Summary
Market Definition
- Distance band approach: 2.5 miles from a hotel
- k Nearest Neighbor (kNN) algorithm: 4 nearest hotels from a hotels
- Density Based Clustering Analysis with Noices (DBSCAN): clusters formed by density.
Estimation
Reduced form models are used:
\[ adr_{im} = \alpha AVMMC_{im} + \beta X_{im} + \epsilon_{im} \] where \(adr\) is the average daily rates (prices), \(AVMMC\) is a measure of the multimarket contacts, and \(x\) is a vector of product characteristics, and \(\epsilon\) is a random shock.
- AVMMC: Average multimarket contact of firm \(i\) in market \(m=1, \cdots, M\) with rival \(j = 1, \cdots, J_m, j\neq i\):
\[ AVMMC_{im} = \frac{\sum_{j \neq i}I_{im} \cdot I_{jm} \sum_{n\neq m} I_{in} \cdot I_{jn}} {N_m - 1} \]
where \(I_{im}\) is equal to 1 if firm \(i\) is in market \(m\). Otherwise, this is zero. \(N_m\) is the total number of firms in market \(m\). A set of markets is all distance bands in which firm \(i\) presents.
- When calculating \(AVMMC\), independents firms (hotels) are not included since it is rare that independent owners who are not associated with franchising have multiple units in the same geographci markets.
Potental Endogeneity of \(AVMMC\)
- No. of the same brand hotels in the distance band and within a city
- No. of the hotels under the same hotel chain in the distance band and within a city
Estimation Results
- In general, the OLS and IV models show similar results: the higher level multimarket contacts, the higher prices.
- However, the estimation results of the kNN algorthimn within the same rating did not support this view. Even though futher investigation is needed, the kNN with the same rating may form markets bigger than othe approaches, such as the simple kNN. In addtion, hotels in the same geographic would be not much different from each other.
1 Data and Sample
I use hotels in Houston, TX from 2014 Q1 to 2014 Q4. The data set (from Source Strategic Inc) is quartely based so there are four time points. Due to entry and exit in the market, the data set is an unbalanced-panel one.
1.1 Descriptive Statistics
- adr: average daily rates
- room_sold: No. of rooms sold per quarter
- room: No. of rooms in the hotel
- rating: hotel rating from STR classification
- AVMMC: Average of multimarket Contacts across rivals in other markets (all markets included)when considering all markets
- AVMMC: Average of multimarket Contacts across rivals when considers
##
## ================================================================================
## Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
## --------------------------------------------------------------------------------
## adr 1,880 85.849 52.001 16.990 44.512 118.453 400.750
## room_sold 1,880 9,459.916 10,004.500 299.520 3,031.440 11,238.840 114,480.000
## room 1,880 111.690 117.694 6 37 131 1,200
## rating 1,880 1.763 1.659 0 0 3 6
## nhotel 1,880 20.755 10.918 1 13 29 46
## avmmc 1,880 26.689 29.279 0 0 46.1 132
## avmmc2 1,880 1.192 1.334 0 0 2 9
## hi.sales 1,880 0.138 0.119 0.038 0.081 0.148 1.000
## n.same.brand 1,880 0.070 0.294 0 0 0 3
## n.same.chain 1,880 0.853 1.412 0 0 1 7
## n.brand.city 1,880 5.166 5.154 0 0 9 20
## n.chain.city 1,880 18.226 18.375 0 0 34 55
## --------------------------------------------------------------------------------1.2 Hotel Brand and Chains
2 Market Definition and Estimation
2.1 Distance band approach
As mentioned earlier, I create a market for each hotel in Houston, TX. Using a radius of 2.5 mile from a focal hotel, I define a set of rivals in its market for the focal hotel. The average number of hotels for each market defined wit this approach (nhotel) is 20.75. This shows a large number of hotels locate in a small geogrpahic area in Houston, TX.
Using this approach to create other markets would be two possible problems, especially if the other markets are too close to the focal market: the first one is an issue of double counting of the same rivals, and the second one is the potential indirect effect on the forcal market. First, figure 1 illustrates potential double counting. The left circel represents the market of firm 1, while the right circle is for the market for firm 4. Texts in the figure represents the location for each firm. In the figure, firm 2 belongs to both firm 1’s market (the left circle) and firm 4’s market(the right circle). Thus, since firm 1 exists in the right circle, firm 2 can be a rival for firm 1 in the left circle. At the same time, firm 2 can be a rival for firm 1 in the right circle.
Figure 2 illustrates possible issues of the indirect effect of rivals that do not have direct contacts. If the market of firm 4 is included, it is not negligible the indirect effect from the rivals (firm 5) through the nearest rival (firm 2) on the focal firm (firm 1).
Due to these reasons, I exclude markets that are ovrelapped with the focal markets when calculating multimarket contants.
AVMMC
Since I use two different measures of the average multimarket contacts. Both measures use the same formals to calculate the average MMC, while they are different in recongizing other markets given a focal market. Figure 3 shows how to calculate AVMMC. Assume that we calculate the multimarket contacts of firm 1 in the left circle. In this approach of AVMMC, I assume distance bands of all hotels as independent markets. This means firm 1 appears in three right circles (Marekts B(Firm 4’s market) and C(Firm 1’s second market), market D (Firm 3’s market)). Thus, there are three other markets. At market B, firm 1 has a contact with firm 2, while firm 1 has a contact with firm 3 in markets C and D. Thus, the average multimarket contacts for firm 1 in market A is \(3/2 =1.5\) (total number of contants of rivals in other markets (B,C,D) / No. of rivals in the focal market (A), AVMMC=1.5).
AVMMC2
The second measure of MMC only considers markets where a focal firm is in its forcal markets. Figure 4 explains this. Assume one is intersted in the average MMC of firm 1 at market A. Rather than considering two markets B and C, market C ( firm 1’s second focal market) is only treated as other markets for firm 1. Thus, the average MMC of firm 1 at market A is 0.5 since firm 1 only has a contact with firm 3 in market C (AVMMC2 =0.5).
2.1.1 Estimation Results
##
## ======================================================================
## Dependent variable:
## --------------------------------------
## adr
## OLS instrumental
## variable
## (1) (2)
## ----------------------------------------------------------------------
## avmmc 0.160*** 0.239***
## (0.028) (0.037)
##
## rating 26.246*** 25.954***
## (0.669) (0.677)
##
## room 0.006 0.011
## (0.007) (0.007)
##
## hi.sales -27.548*** -27.286***
## (6.194) (6.215)
##
## cbd 47.500*** 48.975***
## (3.379) (3.421)
##
## air -13.078*** -13.458***
## (3.723) (3.737)
##
## factor(qtr)2 5.152** 5.264**
## (2.078) (2.085)
##
## factor(qtr)3 -1.106 -0.987
## (2.073) (2.080)
##
## factor(qtr)4 1.374 1.374
## (2.068) (2.075)
##
## Constant 24.337*** 21.120***
## (2.504) (2.707)
##
## ----------------------------------------------------------------------
## Observations 1,274 1,274
## R2 0.715 0.714
## Adjusted R2 0.713 0.712
## Residual Std. Error (df = 1264) 26.134 26.219
## F Statistic 353.101*** (df = 9; 1264)
## ======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## ======================================================================
## Dependent variable:
## --------------------------------------
## adr
## OLS instrumental
## variable
## (1) (2)
## ----------------------------------------------------------------------
## avmmc2 4.048*** 5.197***
## (0.597) (0.777)
##
## rating 26.320*** 26.174***
## (0.662) (0.666)
##
## room 0.008 0.012
## (0.007) (0.007)
##
## hi.sales -30.632*** -31.358***
## (6.175) (6.192)
##
## cbd 47.200*** 47.959***
## (3.346) (3.367)
##
## air -12.561*** -12.631***
## (3.703) (3.709)
##
## factor(qtr)2 5.258** 5.352***
## (2.068) (2.072)
##
## factor(qtr)3 -0.916 -0.795
## (2.064) (2.067)
##
## factor(qtr)4 1.491 1.524
## (2.058) (2.061)
##
## Constant 23.336*** 21.212***
## (2.487) (2.654)
##
## ----------------------------------------------------------------------
## Observations 1,274 1,274
## R2 0.718 0.717
## Adjusted R2 0.716 0.715
## Residual Std. Error (df = 1264) 26.009 26.047
## F Statistic 357.878*** (df = 9; 1264)
## ======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.012.2 k-Nearest Neighbors (kNN) algorithm
k Nearest Neighbors (kNN) clustering methods is a method of defining k nearest neigbors given a point. This is useful for this analysis because prior papers and industry practitioners argues that hotel managers, or professionals suggest a hotel considers four nearest hotels in its geographic market as primimary rivals.
Utilizing this fact, I create a market for a hotel with a focal hotel and its four nearest neighbors. This approach is not free from the issues mentioned in the distance band approach: doublue counting and indirect effects. To minize these effects, I excludes 4 nearest rivals of each rival given a hotel. An example is in the following table:
| ID | 1st | 2nd | 3rd | 4th |
|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 |
| 2 | 1 | 6 | 7 | 8 |
| 3 | 1 | 9 | 10 | 11 |
| 4 | 1 | 12 | 13 | 14 |
| 5 | 1 | 15 | 16 | 17 |
Firm 1 faces four NN (the 1st NN). Each NN in the 1st NN faces its 4 NN (the 2nd NN). Each NN in the 2nd NN face another NN (the 3rd NN). I exclude hotels in the 1st to the 3rd NNs to avoid these issues of the overlapping when calculating the level of multimarket contacts.
AVMMC and AVMMC2 are defined in the same way in the distance band approach.
##
## ==============================================================
## Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
## --------------------------------------------------------------
## avmmc.knn 1,880 4.165 7.279 0.000 0.000 5.000 51.000
## avmmc.knn2 1,880 0.917 1.725 0 0 1 12
## n.brand 1,880 0.011 0.105 0 0 0 1
## n.chain 1,880 0.183 0.387 0 0 0 1
## --------------------------------------------------------------##
## ======================================================================
## Dependent variable:
## --------------------------------------
## adr
## OLS instrumental
## variable
## (1) (2)
## ----------------------------------------------------------------------
## avmmc.knn -0.026 1.179***
## (0.098) (0.200)
##
## rating 26.963*** 28.543***
## (0.688) (0.762)
##
## room -0.004 0.008
## (0.007) (0.008)
##
## hi.sales -1.428 -10.881
## (10.193) (10.869)
##
## cbd 45.051*** 46.731***
## (3.420) (3.627)
##
## air -10.980*** -10.112**
## (3.792) (4.014)
##
## factor(qtr)2 4.909** 5.217**
## (2.122) (2.246)
##
## factor(qtr)3 -1.274 -1.150
## (2.118) (2.241)
##
## factor(qtr)4 1.461 1.289
## (2.113) (2.236)
##
## Constant 27.308*** 16.750***
## (3.627) (4.121)
##
## ----------------------------------------------------------------------
## Observations 1,274 1,274
## R2 0.703 0.668
## Adjusted R2 0.701 0.665
## Residual Std. Error (df = 1264) 26.685 28.237
## F Statistic 332.926*** (df = 9; 1264)
## ======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## ======================================================================
## Dependent variable:
## --------------------------------------
## adr
## OLS instrumental
## variable
## (1) (2)
## ----------------------------------------------------------------------
## avmmc.knn2 -0.130 4.993***
## (0.406) (0.838)
##
## rating 26.959*** 28.467***
## (0.686) (0.758)
##
## room -0.004 0.007
## (0.007) (0.008)
##
## hi.sales -1.329 -13.214
## (10.208) (10.958)
##
## cbd 45.036*** 47.051***
## (3.421) (3.641)
##
## air -10.987*** -9.988**
## (3.792) (4.026)
##
## factor(qtr)2 4.909** 5.164**
## (2.122) (2.252)
##
## factor(qtr)3 -1.274 -1.207
## (2.118) (2.247)
##
## factor(qtr)4 1.465 1.170
## (2.113) (2.242)
##
## Constant 27.314*** 18.175***
## (3.598) (4.027)
##
## ----------------------------------------------------------------------
## Observations 1,274 1,274
## R2 0.703 0.666
## Adjusted R2 0.701 0.664
## Residual Std. Error (df = 1264) 26.685 28.314
## F Statistic 332.938*** (df = 9; 1264)
## ======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.012.2.1 Extension of kNN
I assume that the competition is more valid among hotels in the same star rating. Hotels are divided into two quality groups: low (rating 1 to 3) and high(rating 4 to 6).
##
## =========================================================
## Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
## ---------------------------------------------------------
## avmmc.knn 1,880 3.401 4.209 0 0 5.2 34
## avmmc.knn2 1,880 0.756 0.909 0 0 1.2 5
## n.brand 1,880 0.030 0.170 0 0 0 1
## n.chain 1,880 0.243 0.429 0 0 0 1
## ---------------------------------------------------------##
## ====================================================================
## Dependent variable:
## -------------------------------------
## adr
## OLS instrumental
## variable
## (1) (2)
## --------------------------------------------------------------------
## avmmc.knn -0.413*** 0.012
## (0.113) (0.189)
##
## rating 21.690*** 21.106***
## (0.712) (0.747)
##
## room -0.034*** -0.025*
## (0.012) (0.013)
##
## hi.sales 10.866 11.537
## (11.614) (11.709)
##
## cbd 48.909*** 49.322***
## (6.075) (6.125)
##
## air -8.538*** -8.826***
## (3.208) (3.235)
##
## factor(qtr)2 4.279* 4.336*
## (2.311) (2.329)
##
## factor(qtr)3 -0.459 -0.495
## (2.306) (2.325)
##
## factor(qtr)4 1.544 1.459
## (2.301) (2.320)
##
## Constant 39.758*** 37.880***
## (3.810) (3.898)
##
## --------------------------------------------------------------------
## Observations 901 901
## R2 0.678 0.673
## Adjusted R2 0.675 0.670
## Residual Std. Error (df = 891) 24.428 24.622
## F Statistic 208.814*** (df = 9; 891)
## ====================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## ======================================================================
## Dependent variable:
## --------------------------------------
## adr
## OLS instrumental
## variable
## (1) (2)
## ----------------------------------------------------------------------
## avmmc.knn2 -1.710*** 0.156
## (0.384) (0.647)
##
## rating 23.333*** 22.923***
## (0.531) (0.548)
##
## room -0.064*** -0.056***
## (0.010) (0.010)
##
## hi.sales 13.494 13.475
## (9.789) (9.880)
##
## cbd 51.383*** 51.974***
## (5.611) (5.665)
##
## air -8.704*** -8.991***
## (2.952) (2.981)
##
## factor(qtr)2 3.923** 4.000**
## (1.814) (1.831)
##
## factor(qtr)3 -0.435 -0.424
## (1.812) (1.829)
##
## factor(qtr)4 1.533 1.466
## (1.807) (1.824)
##
## Constant 38.946*** 37.234***
## (3.053) (3.118)
##
## ----------------------------------------------------------------------
## Observations 1,274 1,274
## R2 0.709 0.703
## Adjusted R2 0.707 0.701
## Residual Std. Error (df = 1264) 22.808 23.020
## F Statistic 341.600*** (df = 9; 1264)
## ======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.012.3 Clustering Analysis
2.4 Density based spatial clustering and application with noise(DBSCAN)
This approach aims to define dense regions which is measured by the number of points close to the given point.
DBSCAN requires two parameters: distance (\(\epsilon\), or eps) and the minimum number of points (minPts). Given a point i, a radius neighbood is defined with \(\epsilon\). With this neighbood, if there are more than minPts, the point is considered as a core point and then form a cluster. Other points in the cluster will be considered as board points. If any border points within their own neighbors have more points than minPts, they are considered as core points and form their clusters. Since these clusters are closed enogh, the clusters are combined into one. Any other points (neither core nor border) will be considered as noise.
Figure 4. Core(X), Border(Y), and Noise(Z) points in DBSCAN
2.4.1 DBSCAN for the Houston Hotel Market (2014)
2.4.1.1 Parameter determination for DBSCAN
Since DBSCAN requires two pre-determined parameters (eps and minPts), I explain how these two parameters are determined.
minPts: Hotels, in general, consider 4 ~ 5 hotels as major competitors in the local market (cite needed). Based on this, I choose four for minPts. In addition, if minPts is greater than 4, there would be much difference in clustering results(cite needed)
eps: Given minPts = 4, I create four plots of the distributions of distances to four nearest hotels(points) for each hotel by using the data set of hotels in Houston, TX in 2014. These plots are called k-NN distance plots, each representing a quarter in 2014. Since there are about 470 hotels per quarter, the number of distances calculated in these plots is about 1,880. Based on the observations on these four plots, most of the distances are included between distance = 0 and distance =0.02. Thus, setting eps for this analysis as 0.02 is reasonable since with this eps, I includes most hotels (points) as core or border points.
In sum, I set minPts = 4 as well as eps = 0.02.
2.4.1.2 DBSCAN clustering
Based on the parameter values determined earlier(eps= 0.02, minPts = 4), I conduct clustering using DBSCAN.
The results of the clustering are summarized in the following figure and table. In sum, for each quarter, 21 clusters are created with 58 or 59 noise points (the ones that do not belong to any clusters)
2.4.1.3 Estimation with Clusters (Markets) defined by DBSCAN
2.4.1.3.1 Measure of AVMMC
Since the market definition is changed, the measure of MMC should be changed. The basic intutiion of AVMMC is the same as the previous measures, but this AVMMC allows the contact to be more greater than 1 if a firm meets more than one rivals in other markets than the focal markets. Figure 6 illustrates this cases. Assume one is interested in the AVMMC of firm 1 in cluster A. In cluster B, firm 1 meets firm 2 twice and firm 3 once since firm 2 has two units while firm 3 only has an unit. The AVMMC of firm 1 in clustter 1 is 1.5 ((contact of firms 1 and 2 in cluster B + contacts of firms 1 and 3)/ No. of rivals in cluster A = (2+1)/2 =1.5). 
##
## ===========================================================
## Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
## -----------------------------------------------------------
## avmmc 1,880 0.616 0.736 0 0 1.0 4
## n.same.brand 1,880 1.055 1.160 0 0 1 5
## n.same.chain 1,880 2.555 3.482 0 0 4 16
## -----------------------------------------------------------##
## ======================================================================
## Dependent variable:
## --------------------------------------
## adr
## OLS instrumental
## variable
## (1) (2)
## ----------------------------------------------------------------------
## avmmc 7.789*** 0.742
## (1.119) (14.832)
##
## rating 26.852*** 26.925***
## (0.699) (0.727)
##
## room -0.001 -0.005
## (0.007) (0.012)
##
## hi.sales -37.201** -38.331**
## (15.929) (16.377)
##
## cbd 48.535*** 47.891***
## (3.554) (3.860)
##
## air -10.222*** -11.055***
## (3.758) (4.204)
##
## factor(qtr)2 5.255** 5.207**
## (2.210) (2.251)
##
## factor(qtr)3 0.258 0.197
## (2.334) (2.378)
##
## factor(qtr)4 4.581* 4.842*
## (2.699) (2.800)
##
## Constant 21.341*** 29.046*
## (2.655) (16.392)
##
## ----------------------------------------------------------------------
## Observations 1,148 1,148
## R2 0.717 0.707
## Adjusted R2 0.715 0.705
## Residual Std. Error (df = 1138) 26.349 26.804
## F Statistic 320.526*** (df = 9; 1138)
## ======================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01