Silviase/jgov_v1.4_full_ann huggingface dataset:
$$ L n\left(\frac{P A X_{_{i}}}{\sum_{j=1}^{3}P A X_{_{j}}}\right)=\alpha_{3}+\sum_{k=89}^{91}\beta_{3k}A D_{_{k}}+\left(\gamma_{3}+\sum_{k=89}^{91}\delta_{3k}A D_{_{k}}\right)L n\left(\frac{F R Q_{_{i}}}{\sum_{j=1}^{3}F R Q_{_{j}}}\right)+\left(\phi_{3}+\sum_{k=89}^{91}\lambda_{3k}A D_{_{k}}\right)L n\left(\frac{E Q_{_{i}}}{\sum_{j=1}^{3}E Q_{_{j}}}\right)+\upmu $$

In equation (3) if the sum of $ \gamma_{3} $ and $ \phi_{3} $ are larger than unity, we suppose that airlines intend to increase its demand share by increasing its total seat supply share. And in case $ \gamma_{3} $ are larger than $ \phi_{3} $ with both of them statistically significant, we judge that the airline sheds more light on the strategy of increasing the number of departures.

The data in this section is obtained from Koku Yuso Tokei Nempo (this is an annual statistical report published by the MoT), issued between 1989-1992.

### 5.2 The Regression Results

The results are shown in Tables 3, 4 and 5.

In all cases, we say that the increase of flight share brings about that of passenger share, but each equation shows different results, judging from the result of the Chow test. Each firm might behave in a different manner in this period. In addition, in the case of JAL and JAS, a percent increase of frequency share leads to 1.3-1.4% increase of demand share, whereas with regard to ANA, which had already been in operation in the market of denser traffic and did not enter double or triple track routes during the period of 1989-1992, this phenomenon was no longer seen. From these results, JAL and JAS have the good reason to apply for the entry into the denser routes. And from the viewpoint of demand side, passengers tend to choose the flights of dominant airlines in the market.

Table 3. Regression results of demand share function (1) and the 95% confidence limit of parameter $ \gamma_{1} $ with regard to each firm.

$ \alpha 1 + \beta 1k $	$ \gamma 1 + \delta 1k $	adjR²	SE	Pr( $ \gamma 1 \leq x $ )=0.95
JAL N=76 (2)	1.616 (12.31a)	1.343 (46.27a)	0.966	0.121	1.285 $ \leq \gamma 1 \leq 1.401 $
-1.845+1.099AD89+0.793AD90 (12.30a)(2.96a) (2.67a)	1.426-0.253AD89-0.190AD90 (39.55a)(3.00a) (2.78a)	0.970	0.114	1.353 $ \leq \gamma 1 \leq 1.498 $
ANA N=122	0.019 (0.15)	0.995 (36.71a)	0.918	0.096	0.942 $ \leq \gamma 1 \leq 1.048 $
JAS N=68	-1.291 (7.65a)	1.266 (33.56a)	0.944	0.186	1.191 $ \leq \gamma 1 \leq 1.341 $

Note: (1) t-statistics are in parentheses ; Level of Significance: $ a=1\% $

(2) estimated by OLS.

(3) The confidence limit of JAL(2) is the value of '92.

(4) The equations in the upper row of each firm's empirical results were estimated without any annual dummy variables.

(5) the results of the Chow test between firms are:

$$ JAL/ANA:F=13.92>F(2,194:0.01)=4.71 $$

$$ JAL/JAS:F=14.01>F\left(2,140:0.01\right)=4.76 $$

$$ ANA/JAS:F=28.00>F\left(2,186:0.01\right)=4.71 $$
Next, we can compare the estimated results of equation (2) with those of (1), in Table 4.

Table 4. Regression results of demand share function (2) and the 95% confidence limit of parameter $ \gamma_{2} $

$ \alpha 2 + \beta 2k $	$ \gamma 2 + \delta 2k $	adjR²	SE	Pr( $ \left\|\gamma 2\right\|\leq x $ )=0.95
JAL(1)(2)	-1.101(12.49a)	1.233(63.16a)	0.982	0.089	1.194 \leq $ \gamma 2 \leq 1.272 $
-1.200+0.684AD89+0.340AD90(11.77a)(2.56b)(1.59d)	1.266-0.152AD89-0.077AD90(51.92a)(2.52b)(1.58d)	0.983	0.087	1.217 \leq $ \gamma 2 \leq 1.315 $
ANA(1)(2)	-0.420(5.68a)	1.090(67.27a)	0.974	0.054	1.058 \leq $ \gamma 2 \leq 1.122 $
-0.600+0.253AD90(5.10a)(1.33d)	1.124-0.053AD89-0.054AD90(46.12a)(1.38d)(1.39d)	0.975	0.053	1.076 \leq $ \gamma 2 \leq 1.171 $
JAS	-0.404(4.29a)	1.082(50.85a)	0.975	0.125	1.039 \leq $ \gamma 2 \leq 1.125 $

Note: (1) t-statistics are in parentheses ; the level of significance : a=1%, b=5%, c=10%, d=20%

(2) estimated by OLS

(3) The confidence limit of JAL(2) & ANA(2) are the value of '92

(4) The equations in the upper row of each firm’s empirical results were estimated without any annual dummy variables.

(5) The results of the Chow test between firms are :

JAL/ANA : F =23.62 > F (2,194:0.01)=4.71

JAL/JAS : F = 23.68 > F (2,140:0.01) = 4.76

ANA/JAS : F = 4.57 > F (2,186:0.05) = 3.04

What is apparently different from the results in Table 3 is that all the regression coefficients are larger than unity in this case, whereas the results of the Chow test are almost the same as those in Table 3. So it can be said from this viewpoint that all the Japanese airlines have room for choosing the strategy of expanding the equipment size, but their behavior may be different from one another. Especially in the case of ANA, there may be no choice but competing through the expansion of equipment, because it already operates as an incumbent in almost all the domestic denser markets.

Let's then look into the regression results of equation (3). Judging by the results shown in Table 5, we can recognize three notable findings:

(1) In all the cases $ r = \gamma_{3} + \phi_{3} > 1 $ is recognized. This means that the more each airline increases the total seat supply share, the more it can increase demand share.

(2) The Japanese airlines except for ANA may have the incentive of choosing these two strategies: 1) increasing frequency in double or triple track routes, 2) expanding equipment size in these routes.

(3) However, JAL and JAS seem to choose not so much frequency competition as equipment competition.

The reasons for these results may be that the lack of airport capacity makes it difficult for the airlines to depend heavily on frequency competition. The values of ANA - which has the biggest fleet in the domestic air network - gives us the evidence.
Table 5. Regression results of demand share function 3

$ \alpha 3 + \beta 3k $	$ \gamma 3 + \delta 3k $	$ \phi 3 + \lambda 3k $	adjR²	SE
JAL(1)(2)	-1.252(12.21a)	0.319(2.63b)	0.947(8.58a)	0.983	0.086
-1.481+0.880AD89+0.563AD90(12.63a)(3.49a)(2.74a)	0.282+0.427AD91(2.16b)(2.04b)	1.053-0.200AD89(8.61a)(3.51a)-0.133AD90-0.427AD91(2.80a)(2.05b)	0.987	0.080
ANA(1)(2)	-0.435(5.85a)	-0.018(0.28)	1.112(16.31a)	0.974	0.054
-0.608+0.271AD89(5.16a)(1.43d)	-0.063+0.247AD89(0.89)(1.56d)	1.189-0.306AD89(15.47a)(1.84c)-0.133AD90(1.32a)	0.987	0.080
JAS(1)(2)	-0.778(7.60a)	0.410(5.62a)	0.751(12.24a)	0.983	0.103
-0.739(7.95a)	0.513-0.277AD89(6.50a)(2.73a)	0.646+0.284AD89(9.19a)(2.66a)	0.984	0.098

Note: (1) t-statistics are in parentheses; the level of significance: $ a=1\% $ , $ b=5\% $ , $ c=10\% $

(2) estimated by OLS

(3) The equations in the upper row of each firm's empirical results were estimated without any annual dummy variables.

(4) The results of the Chow test between firms are :

JAL/ANA : F = 20.15 > F(3,192:0.01) = 3.88

JAL/JAS : F = 6.66 > F(3,138:0.01) = 3.93

ANA/JAS : F = 8.29 > F(3,184:0.01) = 3.89

### 5.3 Summary of Findings

Here we will sum up the findings in this section and briefly comment on them. According to the empirical results, passengers seemed to choose the airlines that had high frequency and seat-per-flight share (equipment). On the other hand, from the viewpoint of airlines, JAL and JAS were able to increase their demand share by increasing the frequency and seat-per-flight share. In addition, the strategy of increasing equipment share was probably of comparative importance for these carriers because of the airport capacity constraints. However, in the case of ANA, the strategy of increasing equipment share - that is, employing wider bodied airplanes - was important.

If we take into account these results, the regulatory change that authorized the entry into double or triple track routes was favorable not to ANA but to JAL and JAS. However, as in the case that once the frequency competition led to the waste of profit in the U.S. airline industry under regulation, it is necessary for the regulator (MoT) to pay attention to whether or not the service competition including frequency and/or equipment competition in double or triple track routes causes the waste of scarce resources.

In the following section, it will be clarified whether this competition has brought about excess capacity or not.
## 6 Does the Demand Meet Supply in Double/Triple Track Routes? :The Models and Regression Results

### 6.1 The Models and Data

According to the empirical results in section 5.2, something like service competition in double and/or triple track routes may bring about excess capacity. On the other hand, the capacity constraints in Haneda (Tokyo) and Itami (Osaka) Airports may be a crucial factor to prevent airlines from increasing their supply. In this section, we will focus on the load factor of the routes where entry was newly authorized after the regulatory change in 1986 and investigate whether or not supply meets demand in these routes. To begin with, we will construct two kinds of load factor functions. The definitions of the variables used in the models are shown in Table 6.

The data in this section is the same as in section 5, i.e., the panel data of 31 routes between 1989-1992; the sample number is 124.

In treating the load factor we have to take into consideration that the average load factor changes according to boom and slump. So we restored to the analysis of variance (one-way layout) in order to make sure the existence of load factor's difference between 1989-92. The result goes as follows.

$$ \mathsf{F}=10.84>\mathsf{F}(4,120:0.01)=3.48 $$

From the result, the null hypothesis that the average load factor in each year is equal is rejected at 1 % level. So we introduced the annual dummy variable $ AD_{x} $ (see Table 6).

Both demand and supply factors are to influence the load factor directly; demand factors, e.g., the number of passengers (PAX), and supply factors, e.g., the number of departures (FRQ), the number of seats per flight (EQ), and the stage length (DIST), and the factor of the market structure, e.g., the concentration (HERF). On the other hand, among these variables, PAX and EQ are endogenous variables in demand and supply function, so the load factor function may compose the simultaneous equations together with demand and supply functions.

In addition, we have to pay attention to the multicollinearity between variables. The partial correlation coefficients between variables are shown in Table 7.
Table 6. Variables and their definitions

Variables	Definition and data sources
LF	the average annual load factor of each market, reported in “A”
PAX	the number of O&D passengers in each market that traveled in a year, reported in “A”
DIST	each route's nonstop distance between O&D, reported in “A”
HERF	the Herfindahl index, the sum of the squares of the shares of each firm in the market, calculated by us. The data source is “A”
EQ	the average annual number of seats per flight in the market, which was calculated by the authors. The data source is “A”
FARE	the round trip ticket price of the market, filed in “B”
INC	the product of the per capita incomes of the two main cities served by each market, i.e., $ \sqrt{(Income of Origin) \times (Income of Destination)} $ The data source is “C”
POP	the product of the population of the two areas served by each market, i.e., $ \sqrt{(Population of Origin Area) \times (Population of Destination Area)} $ , where “area” is both main city and its commuting zone. The data source is “C”
ADx	annual dummy variable (x=89,90,91)
DS	single track dummy variable (1 for single track route and 0 otherwise)
DT	triple track dummy variable (1 for triple track route and 0 otherwise)
DTR	trunk route dummy variable (1 for trunk route and 0 otherwise)

Note: Data Source “A” is Koku Yuso Tokei Nempo (issued between '89-'92), “B” is Jikokuhyou (the time table, published by JTB), and “C” is Chiiki-keizai-souran, issued between 1991-94 (which reports regional annual data of population, income, etc., annually published by Toyo Keizai Shimposha)

Table 7. The partial correlation coefficients between variables

LF	PAX	DIST	FRQ	EQ	HERF
LF	1
PAX	0.253	1
FRQ	0.240	0.880 $ ^{*} $	1
DIST	-0.355 $ ^{*} $	0.014	-0.238	1
EQ	-0.048	0.667 $ ^{*} $	0.244	0.457 $ ^{*} $	1
HERF	0.162	-0.581 $ ^{*} $	-0.514 $ ^{*} $	-0.251	-0.445 $ ^{*} $	1

Note: * significant at 0.1 % level

Among these coefficients the correlation between PAX and FRQ is strong (coefficient is 0.88). So in the construction of the load factor function, we chose not to include these two variables simultaneously but to build two types of load factor equations (Load factor function $ [1] $ and $ [2] $ ) each of which includes PAX or FRQ as independent variables. Each equation in log-linear form and its expected sign of coefficients are as follows;
(1) Load factor function(x=89, 90, 91)

$$ \begin{aligned}Ln\big(LF\big)&=a_{1}+\sum_{x=89}^{91}b_{1x}AD_{x}+\Bigg(c_{1}+\sum_{x=89}^{91}d_{1x}AD_{x}\Bigg)Ln\big(PAX\big)+\Bigg(e_{1}+\sum_{x=89}^{91}f_{1x}AD_{x}\Bigg)Ln\big(DIST\big)\\ &\\&+\Bigg(g_{1}+\sum_{x=89}^{91}h_{1x}AD_{x}\Bigg)Ln\big(HERF\big)+\Bigg(i_{1}+\sum_{x=89}^{91}j_{1x}AD_{x}\Bigg)Ln\big(EQ\big)+\upmu_{1}\\ \end{aligned} $$

The coefficient of $ \mathrm{Ln}(\mathrm{PAX}) $ is expected to be $ c_{1}>0 $ , because, other things being equal, the more the traffic increases, the higher the load factor becomes. In addition, the value of the coefficient is thought to be $ 00 $ and the null hypothesis that $ c_{1}=1 $ cannot be rejected, airlines are thought to have enough capacity for demand.

According to Douglas & Miller [1974b], the longer the stage length is, the lower the actual load factor. $ ^{15} $ We accept this hypothesis and expect $ -1 < e_{1} < 0 $ .

On the other hand, against our expectation, if $ e_{1}>0 $ , then airlines are expected to make a profit in routes of longer distance. However, according to Murakami [1994], airlines do not necessarily make profits in longer routes other than monopoly ones, so in this paper we expect the coefficient of stage length to be $ -10 $ , because the higher load
factor of the double or triple track routes means that the OD cities of these routes are attractive for business passengers because of many business opportunities. $ ^{[16]} $ With regard to the coefficients of $ \mathrm{Ln}(EQ) $ and $ \mathrm{Ln}(PP) $ , $ e_{2} > 0 $ and $ g_{2} > 0 $ will be expected because both the variables reflect market structure. The coefficient of $ \mathrm{Ln}(FARE) $ will be $ i_{2} < 0 $ according to the law of demand, and $ k_{2} $ of $ \mathrm{Ln}(INC) $ will be $ k_{2} > 0 $ , if we assume that the air transport service is normal goods.

(3) Equipment (Supply per flight) function $ (x=89, 90, 91) $

$$ \begin{aligned}Ln\big(EQ\big)&=a_{3}+\sum_{x=89}^{91}b_{3x}AD_{x}+\Bigg(c_{3}+\sum_{x=89}^{91}d_{3x}AD_{x}\Bigg)Ln\big(PAX\big)+\Bigg(e_{3}+\sum_{x=89}^{91}f_{3x}AD_{x}\Bigg)Ln\big(FARE\big)\\&\quad+\Bigg(g_{3}+\sum_{x=89}^{91}h_{3x}AD_{x}\Bigg)Ln\big(DIST\big)+\upmu_{4}\end{aligned} $$

Airlines are expected to employ wide-bodied airplanes to meet demand, so $ C_{3} > 0 $ . And according to the condition of the sign of the price in a supply function, $ e_{3} > 0 $ . In respect of the relation between the equipment and stage length, the longer the distance of a route is, the bigger the size of airplane employed, so $ g_{3} > 0 $ will be expected.

(4) Fare determination function(x=89, 90, 91)

$$ \begin{aligned}Ln\big(FARE\big)&=a_{4}+\sum_{x=89}^{91}b_{4x}AD_{x}+\Bigg(c_{4}+\sum_{x=89}^{91}d_{4x}AD_{x}\Bigg)Ln\big(DIST\big)+\Bigg(e_{4}+\sum_{x=89}^{91}f_{4x}AD_{x}\Bigg)Ln\big(LF\big)\\ &\\&+\Bigg(g_{4}+\sum_{x=89}^{91}h_{4x}AD_{x}\Bigg)Ln\big(HERF\big)+\Bigg(i_{4}+\sum_{x=89}^{91}j_{4x}AD_{x}\Bigg)Ln\big(INC\big)+\upmu_{4}\\ \end{aligned} $$

In the fare determination function, we are to verify the hypothesis that the domestic air fares are determined according to the full-cost principle. The determinants of fares are supposed to be (1) stage length which reflects the operating cost, (2) the load factor, (3) concentration measured by Herfindal Index, and (4) income of the OD area of the market. The factors (2), (3), and (4) are supposed to determine the mark-up ratio. As regards the parameter $ c_{4} $ , $ 0 < c_{4} < 1 $ will be expected, because the fares are set higher, but the extent to which they increase decreases as the distance grows. The sign of coefficient of $ \ln(\text{LF}) $ is expected to be $ e_{4} < 0 $ , because in a route where the load factor is lower, airlines are expected to set higher fares in order to compensate for the loss of
revenue. The higher the concentration, and the higher the income of the OD areas a market serves, the easier it may be for an airline to set more substantial margin on the operational cost, so $ g_{4}>0 $ and $ i_{4}>0 $ may be expected.

In addition, another Load factor function [2] will be shown, where we substituted $ \mathrm{Ln}(\mathrm{FRQ}) $ for $ \mathrm{Ln}(\mathrm{PAX}) $ in Load factor function [1].

(5) Load factor function [2] (x=89, 90, 91)

$$ L n\big(L F\big)=a_{5}+\sum_{x=89}^{91}b_{5x}A D_{x}+\left(c_{5}+\sum_{x=89}^{91}d_{5x}A D_{x}\right)L n\big(F R Q\big)+\left(e_{5}+\sum_{x=89}^{91}f_{5x}A D_{x}\right)L n\big(D I S T\big) $$

$$ +\Bigg(g_{5}+\sum_{x=89}^{91}h_{5x}AD_{x}\Bigg)Ln\Big(HERF\Big)+\Bigg(i_{5}+\sum_{x=89}^{91}j_{5x}AD_{x}\Bigg)Ln\Big(EQ\Big)+\upmu_{5} $$

If a unit of increase of frequency causes one or more unit of increase of demand (e.g., the increase of frequency newly cultivates demand), $ c_{5} < 0 $ will be expected (for the sign of the other coefficients, see Load factor function $ [1] $ ).

### 6.2 Regression Results

In this subsection both the regression results of simultaneous equations (see Table 8) and the Load factor function [2] (See Table 9) will be shown. The former equations were estimated by 2SLS, the latter by OLS.

Prior to the appreciation of both the load factor functions by which we will judge whether supply meets demand, we are to appreciate the results of the other equations. With respect to the demand and the supply per flight function, all the signs of estimated values meet the required conditions. The price elasticity of demand is about -0.7. In addition, as to the method of estimation, we substituted single track dummy variable DS and triple track dummy DT for $ \ln(\text{PP}) $ in demand function, and the dummy variable DT which can be regarded as the variable reflecting distance for $ \ln(\text{DIST}) $ in supply per flight function. All of them were introduced in the intercept of each equation, so that the values of adj $ R^{2} $ and standard error were improved with the sign of coefficients of the other variables meeting the conditions.
Table 8. Regression results of simultaneous equations

d.v	INTERCEPT	LnLF	LnPAX	LnEQ	LnFAR E	LnDIST	LnHER RF	LnINC	STATISTICS
LnLF	4.215+0.073AD89(20.63a)(4.31a)0.101AD90+0.068AD91(6.01a)(4.13a)	0.025(1.84c)	0.071(1.72c)	-0.097(3.91a)	0.075(2.71a)	adjR²=0.401SE=0.065F=12.76
Ln PAX	-6.960-0.331DS(2.22b)(2.25b)+0.540DT+0.483DTR(3.78a)(4.09a)	1.283(2.13b)	1.018(3.69a)	-0.731(3.73a)	0.817(2.35b)	adjR²=0.670SE=0.482F=36.65
LnEQ	2.062+0.198DT(4.27a)(2.26b)+0.279DTR-0.068AD89(4.12a)(1.09)	0.105(2.11b)	0.420(4.71a)	adjR²=0.491SE=0.294F=24.74
LnFARE	2.960-0.084DH+0.123AD89(2.32b)(3.04a)(4.65a)+0.077AD90+0.053AD91(2.20b)(2.02b)	-0.851(2.78a)	0.770(31.29a)	0.100(3.76a)	0.328(5.74a)	adjR²=0.960SE=0.065F=367.17

Note: t-statistics are in parentheses: the level of significance is $ a=1\% $ , $ b=5\% $ , $ c=10\% $ . d.v means “dependent variable.”

Judging from the results of the fare determination function, we may say that air fares are determined according to the full-cost principle, and that the ratio of the increase of fares decreases with distance. As regards the other variables, all the estimated signs meet the expected conditions.

According to the results of Load factor equation $ [1] $ , the value of the estimated parameter of $ \mathrm{Ln(PAX)} $ and $ \mathrm{Ln(EQ)} $ is considerably small, to the extent that the hypothesis of $ c_{1}=0 $ and $ d_{1}=0 $ are barely rejected at 10% level, although both signs are expected ones. So in the markets which we chose as samples, it may be pointed out that not so much excess capacity as the equilibrium of demand/supply or excess demand is brought about. In addition, the sign of estimated parameter of $ \mathrm{Ln(HERF)} $ meets the expected condition at 1% level. From this result, e.g., especially in those single track routes the tracking number of which was once increased, the excess demand might occur, $ ^{17} $ or it can be said that in the routes where the number of tracking is large it is less easy for airlines to control the load factor.

Then let us check up whether the same results were obtained from the Load factor equation [2].

The difference between equation [1] and [2] is that in the latter equation we canceled the variable of $ \mathrm{Ln}(\mathrm{EQ}) $ , which was relatively insignificant, and added the ‘Shinkansen Express’
dummy variable DH which may reflect the competition between airways and railways in the markets the stage length of which is about 500km. Then the values of statistics were improved.

The results show that an additional flight brings about a bit increase of average load factor. In addition, it is true the estimated parameter of $ \mathrm{Ln}(\mathrm{FRQ}) $ is more stable than that of $ \mathrm{Ln}(\mathrm{PAX}) $ in the Load factor function $ ^{[1]} $ . But we can draw from this result the same appreciation as the Load factor function $ ^{[1]} $ , i.e., in the sample markets the demand/supply equilibrium or the excess demand may exist. And judged by the result that the estimated coefficient of trunk dummy variable DTR completely cancels out that of $ \mathrm{Ln}(\mathrm{FRQ}) $ , the inclination of the excess demand may be strong. On the other hand, both the estimated parameters of $ \mathrm{Ln}(\mathrm{HERF}) $ are less stable than in the load factor function $ ^{[1]} $ . In order to investigate why this result was brought about, we looked up the annual round-trip average load factors of all the markets chosen as samples, and then verified the null hypothesis that all the average load factors of single, double and triple track routes were equal (See Table 10).

Table 9. Regression results of the load factor function $ ^{[2]} $

INTERCEPT	LnFRQ	LnDIST	LnEQ	LnHERF	Statistics
1	4.201+0.346DTR+0.074AD89(19.80a)(3.88a) (4.52a)+0.105AD90+0.070AD91(6.46a) (4.38a)	0.074(4.47a)-0.074DTR(3.70a)	-0.071(3.72a)	0.027(1.45d)	0.047(1.74c)	adjR²=0.437SE=0.063F=11.62
2	4.504+0.348DTR+0.073AD89(20.87a)(4.02a) (4.56a)+0.105AD90+0.069AD91-0.080DH(6.60a) (4.45a) (2.80a)	0.066(4.05a)-0.067DTR(3.43a)	-0.090(4.46a)	0.032(1.20)	adjR²=0.464SE=0.061F=12.83

Table 10. The two-tailed test of the null hypothesis that all the average load factors of single, double and triple track routes were equal

the kind of routes dealt with	the difference of sample mean	t-statistics
double track/triple track	2.04	2.06 (significant at 5% level)
double track/single track	1.70	2.34 (significant at 5% level)
single track/triple track	0.34	1.21

Note: The sample number of single track routes is 14 (the sample mean is 73.71, standard deviation is 4.97), double track 78 (70.35, 5.37), triple track 32 (72.39, 2.84). And the null hypothesis that the variance of each sample is equal cannot be rejected at 5% level (the result of Bartlett test is $ X^{2}=5.983

The results show that the average load factor of the double track routes are substantially lower than that of the triple track routes, and also lower than that of the single track routes, although the t-value is insignificant. The reason why both the estimated parameter of $ \mathrm{Ln}(\mathrm{HERF}) $ in the load factor function $ ^{[2]} $ were not stable may be that we can recognize the phenomenon that the higher concentration leads to the higher load factor with regard to single and double track routes, whereas the inverse situation exists with regard to double and triple track routes. So in the