1. Data Selection

# Load data
airline <- read.csv("/Users/pin.lyu/Desktop/BC_Class_Folder/Econometrics/Data_folder/PanelData.csv")
colnames(airline) <- c("Airline",
                       "Year",
                       "Total_cost",
                       "Output",
                       "Fuel_price",
                       "Load_factor"
                     )

Data summary

stargazer(airline, type = 'text', title = 'Airline Cost Data Summary Statistics')
## 
## Airline Cost Data Summary Statistics
## ============================================================
## Statistic   N      Mean        St. Dev.      Min      Max   
## ------------------------------------------------------------
## Airline     90     3.500         1.717        1        6    
## Year        90     8.000         4.345        1       15    
## Total_cost  90 1,122,524.000 1,192,075.000 68,978  4,748,320
## Output      90     0.545         0.534      0.038    1.936  
## Fuel_price  90  471,683.000   329,502.900  103,795 1,015,610
## Load_factor 90     0.560         0.053      0.432    0.676  
## ------------------------------------------------------------

Data Set contains Cost Data for U.S. Airlines, 90 Observations On 6 Firms For 15 Years, 1970-1984

Airline = Airline company name,
Year = Year,
Output = Output, in revenue passenger miles, index number,
Fuel_Price = Fuel price,
Load_Factor = Load factor, the average capacity utilization of the fleet

Total_cost = Total cost, in $1000

Comments: Based on the preliminary browsing and summary of the data, the data is balanced.

OLS Model

# Multi-linear regression model
linear_model <- lm(Total_cost ~      Fuel_price  +
                                     Output      +
                                     Load_factor,
                                     
   data = airline
     )

Interpretation:

  1. Each dollar increase in fuel price, the total cost of an airline increases by 1.225 dollars.
  2. Each unit increase in one airline’s total output, the total cost of that airline increases by 2,0026,114 dollars.
  3. Each unit increase in load factor, the total cost of that airline decreases by 3,065,753 dollars
  4. According to the data set, airlines’ annual fixed costs starts roughly around 1.2 billion dollars.

These coefficients do make sense to me. when fuel price is higher, the total cost of an airline will increases. As to why the increase in its total costs is disproportional to the increase in fuel price, I think, is because fuel distribution costs and fuel tax.

Fixed Effect Model

# Fixed effect model
fixed_effect <- plm(Total_cost ~      Fuel_price   +
                                      Output       +
                                      Load_factor,
   index = c("Airline","Year"),
   model = 'within',        
   data = airline
    )

stargazer(linear_model,fixed_effect, type = 'text', title = "Summary Of The Two Models")
## 
## Summary Of The Two Models
## ===================================================================
##                                   Dependent variable:              
##                     -----------------------------------------------
##                                       Total_cost                   
##                               OLS                    panel         
##                                                     linear         
##                               (1)                     (2)          
## -------------------------------------------------------------------
## Fuel_price                 1.225***                0.773***        
##                             (0.104)                 (0.097)        
##                                                                    
## Output                 2,026,114.000***        3,319,023.000***    
##                          (61,806.940)            (171,354.100)     
##                                                                    
## Load_factor            -3,065,753.000***       -3,797,368.000***   
##                          (696,327.300)           (613,773.100)     
##                                                                    
## Constant               1,158,559.000***                            
##                          (360,592.700)                             
##                                                                    
## -------------------------------------------------------------------
## Observations                  90                      90           
## R2                           0.946                   0.929         
## Adjusted R2                  0.944                   0.922         
## Residual Std. Error  281,559.500 (df = 86)                         
## F Statistic         503.118*** (df = 3; 86) 355.254*** (df = 3; 81)
## ===================================================================
## Note:                                   *p<0.1; **p<0.05; ***p<0.01

Comment: The control factor I introduced in the fixed effect model is “Airline” and “Year”. This enables us to capture the average effect of each company on the dependent variable “Cost”, and the coefficient associated with the other variables in the model will reflect their effects net for the individual-specific effects.

After introduction of the control, we can see that the magnitude of fuel price’s influence on total cost, though still positive, decreased by 36%. In the fixed effect model, it suggests that fuel cost is not as significant contributor of the total cost as what the linear model suggest.

the coefficient of “Output” increased by 63%. This means that the marginal cost for each increase in output is, in reality, greater than what we discovered from the linear model.

The utilization of load in each fleet matters more in reducing the costs in the fixed model, as we can see that airlines can save 23% more in their costs in the fixed effect model comparing to the OLS model.