MMC-Reduced Form Analysis
Jung Hwan Koh
9/23/2019
1 Summary
1.1 Define Markets
Using the distance matrix approach, I estimated the parameters (distance limit and the number of the neigbors in the markets) to define local markets for each hotel in the dataset.
Before doing these estimation, I create two data sets: high-quality hotels(their hotel ratings from TripAdvisor \(\geq\) 3.5) and low-quality hotels (their hotel ratings \(<\) 3.5). Thus, there are three datasets: all, high, and low.
For all hotels, the estimated distance limit is 2.5 miles and 10 neighbors (For the robustness check, 5 miles and 5 rivals are tested).
For low-quality hotels, I have found that similar results of all models.
For high-quality hotels, these estimations are not statistically significant. Even though the estimated coefficients in the models estimating the distance limit are not significant, the sign of the coefficients are negative, indicating that the presence of other hotels with similar ratings in their markets negatively affect the prices (not consistent with the assumption of the Bertrand-Nash competition with differentiated products.)
In sum, I used 2.5 and 5 miles as the distance limits to define the markets. In addition, 5 and 10 neighbors as the rivals in the markets are chosen.
1.2 Effect of MMC on Price
Based on the estimated parameters for the market definition, I calculated the average multimarket contacts over rivals in the same markets (avmmc is based on the distance band approach; avmmc.knn is based on the k th nearest neighbor approach).
To estimate the effect of MMC on prices, I used the IV approach in which the average multimarket contact variables are considered endogenous variables in the right-hand side in the regression equation.
For all hotels and the low-quality hotels, I have found that avmmc and avmmc.knn are positive and statically significant across all the models.
For the high-quality hotels, avmmc is only positively significant on the model in which the distance limit is 5 miles. Other models of the high-quality hotels present insignicants or someitive the opposite sign than expected (negative). This might result from exlcusion conditions that I used in calculating the average multimarket contacts or small sample sizes.
2 Define Market
- Distance Band Approach
- The k th Nearest Neighbor Approach
2.1 Distance Band Approach
2.1.1 Estimated Distance Limit from All Hotels
##
## Distance Matrix Estiatmion with All Hotels
## ===============================================
## Dependent variable:
## ---------------------------
## adr
## -----------------------------------------------
## wp.d 0.062***
## (0.011)
## s_rating 40.335***
## (1.349)
## hi.sales -60.046***
## (13.019)
## room -0.001
## (0.008)
## cbd 18.785***
## (3.735)
## air -17.266***
## (3.530)
## Constant -22.613***
## (3.618)
## -----------------------------------------------
## Observations 1,521
## R2 0.751
## Adjusted R2 0.746
## Residual Std. Error 26.778 (df = 1490)
## F Statistic 149.689*** (df = 30; 1490)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
2.1.2 Estimated Distance Limit from High-Quality Hotels
##
## Distance Matrix Estiatmion with High-Quality Hotels
## ===============================================
## Dependent variable:
## ---------------------------
## adr
## -----------------------------------------------
## wp.d -0.009
## (0.032)
## s_rating 82.935***
## (7.477)
## room -0.028**
## (0.013)
## hi.sales 56.928
## (60.391)
## cbd 11.478
## (7.614)
## air -43.101**
## (17.733)
## Constant -140.670***
## (31.637)
## -----------------------------------------------
## Observations 253
## R2 0.661
## Adjusted R2 0.633
## Residual Std. Error 33.792 (df = 233)
## F Statistic 23.905*** (df = 19; 233)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
2.1.3 Estimated Distance Limit from Low-Quality Hotels
##
## Distance Matrix Estiatmion with Low-Quality Hotels
## ===============================================
## Dependent variable:
## ---------------------------
## adr
## -----------------------------------------------
## wp.d 0.022***
## (0.006)
## s_rating 9.657***
## (1.305)
## room -0.071***
## (0.013)
## hi.sales -28.757***
## (8.638)
## cbd 36.268***
## (3.756)
## air -11.515***
## (2.300)
## Constant 32.648***
## (3.024)
## -----------------------------------------------
## Observations 1,268
## R2 0.821
## Adjusted R2 0.817
## Residual Std. Error 16.810 (df = 1241)
## F Statistic 218.612*** (df = 26; 1241)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01
2.2 Estimate the number of rival (k) for All, High-Quality, and Low-Quality Hotels
3 Results of the IV models (The Effect of MMC on Prices)
##
## Model 1: Distand Band Approach (2.5 miles)
## ==========================================================================
## Dependent variable:
## ------------------------------------------------------
## adr
## All High-Quality Low-Quality
## (1) (2) (3)
## --------------------------------------------------------------------------
## avmmc 0.138*** -0.687 0.493***
## (0.051) (0.604) (0.057)
## hi.sales -44.654*** -40.096*** -19.827*
## (13.223) (8.667) (10.450)
## s_rating 33.340*** 47.912*** 17.551***
## (1.445) (7.697) (2.138)
## cbd 31.234*** 3.335 39.756***
## (3.450) (6.278) (4.290)
## air -17.432*** -26.802 -10.659***
## (3.363) (20.249) (2.697)
## Constant 31.443*** -9.634 60.498***
## (5.578) (30.800) (6.430)
## --------------------------------------------------------------------------
## Observations 1,141 211 930
## R2 0.788 0.709 0.803
## Adjusted R2 0.783 0.683 0.798
## Residual Std. Error 22.986 (df = 1112) 28.835 (df = 193) 17.595 (df = 905)
## ==========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## Model 2: Distand Band Approach (5 miles)
## ==========================================================================
## Dependent variable:
## ------------------------------------------------------
## adr
## All High-Quality Low-Quality
## (1) (2) (3)
## --------------------------------------------------------------------------
## avmmc 0.063** 1.620* 0.209***
## (0.029) (0.835) (0.031)
## hi.sales -154.404*** -166.581*** -139.129***
## (24.590) (54.282) (19.219)
## s_rating 32.295*** 44.541*** 17.043***
## (1.436) (8.573) (2.133)
## cbd 29.474*** 14.172** 39.644***
## (3.342) (6.410) (4.295)
## air -13.987*** -24.760 -12.868***
## (3.377) (19.517) (2.687)
## Constant 40.843*** -8.496 75.455***
## (5.249) (34.182) (6.296)
## --------------------------------------------------------------------------
## Observations 1,141 211 930
## R2 0.793 0.663 0.805
## Adjusted R2 0.788 0.633 0.800
## Residual Std. Error 22.736 (df = 1112) 31.055 (df = 193) 17.500 (df = 905)
## ==========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## Model 3: KNN approach (k = 5 rivals)
## ==========================================================================
## Dependent variable:
## ------------------------------------------------------
## adr
## All High-Quality Low-Quality
## (1) (2) (3)
## --------------------------------------------------------------------------
## avmmc.knn 0.624* -1.245 1.854***
## (0.321) (1.079) (0.260)
## hi.sales -27.852** 71.274 -16.148
## (11.083) (75.021) (20.488)
## s_rating 34.455*** 57.578*** 23.399***
## (1.569) (8.843) (2.429)
## cbd 31.918*** 13.600** 37.063***
## (3.406) (6.143) (4.692)
## air -16.387*** -45.787*** -10.132***
## (3.401) (17.074) (2.920)
## Constant 33.312*** -73.941** 52.264***
## (6.348) (37.174) (8.700)
## --------------------------------------------------------------------------
## Observations 1,141 211 930
## R2 0.781 0.675 0.766
## Adjusted R2 0.776 0.647 0.760
## Residual Std. Error 23.367 (df = 1112) 30.466 (df = 193) 19.177 (df = 905)
## ==========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## Model 4: KNN approach (k = 10 rivals)
## ==========================================================================
## Dependent variable:
## ------------------------------------------------------
## adr
## All High-Quality Low-Quality
## (1) (2) (3)
## --------------------------------------------------------------------------
## avmmc.knn 0.438*** -1.394** 0.838***
## (0.118) (0.612) (0.102)
## hi.sales -78.408*** 492.831*** 9.409
## (14.077) (147.750) (35.793)
## s_rating 34.298*** 61.955*** 21.237***
## (1.462) (9.035) (2.285)
## cbd 32.551*** 18.977*** 40.628***
## (3.374) (5.845) (4.513)
## air -12.850*** -60.357*** -8.258***
## (3.383) (16.026) (2.868)
## Constant 34.660*** -128.352*** 50.941***
## (5.912) (38.684) (7.842)
## --------------------------------------------------------------------------
## Observations 1,141 211 930
## R2 0.788 0.693 0.781
## Adjusted R2 0.782 0.666 0.775
## Residual Std. Error 23.025 (df = 1112) 29.624 (df = 193) 18.553 (df = 905)
## ==========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01