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

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