The city of Tianjin and the realization of the national development strategy put forward new requirements for air transport. This paper is based on Tianjin air transport and the interaction of regional economic development present situation, analy z ed problems of development, analyzed interactive development mechanism of the Tianjin aviation transport and economic, then, extracted the Tianjin aviation transportation and regional economy of main component, and established a principal component regression equation, for air transportation and Regional economy in Tianjin fitness trend prediction, gives countermeasures to promote the development of air transport and Tianjin economic interactions.
In recent years, various researchers in Western countries have published studies aimed at identifying the relationship between air transportation and local economy in different perspectives. Several studies analyze the linkage between investment of air traffic and growth rate of GDP [
Frédéric Dobruszkes, Moritz Lennert, Gilles Van Hamme [
Ye Zhou [
Jing Guang-lei, Li Ming, Jiang Liang, Pan Xiao-ling, Qin Yi, Chen Xuan-bing, Hu Jie [
However, we notice that most research is on general quantity, including GDP, investment of social fixed assets, passenger traffic, feight traffic, total throughput, passenger throughput, freight throughput and so on. So that there is a lack of research on relatively micro-region’s air transport and regional economic interaction research.
Moreover, the method applied most is establishing multiple linear regression model. When dealing with many variables, variables are always related, causing multicolinearity. In the presence of multicollinearity, the estimate of one variable’s impact on the dependent variable while controlling for the others tends to be less precise than if predictors were uncorrelated with one another. In some sense, the collinear variables contain the same information about the dependent variable. If nominally “different” measures actually quantify the same phenomenon, then they are redundant. Alternatively, if the variables are accorded different names and perhaps employ different numeric measurement scales but are highly correlated with each other, then they suffer from redundancy.
There are many variables for us to take into consideration to analyze interaction between local economy and air transport. We expect to use “comprehensive variables” instead of original variables so that we can use less variables to indicate information as much as possible. Based on this reduced-dimensional thinking, this paper applies principle component analysis and principal component regression to put forward policy recommendations to coordinate the development of air transport and local economy.
PCA is considered the oldest technique in multivariate analysis and was first generalized by Hotelling in 1933. PCA is a method that reduces the dimensionality of a dataset, by finding a new set of variables, smaller than the original set of variables. This efficient reduction of the number of variables is achieved by obtaining orthogonal linear combinations of the original variables―the so-called Principal Components (PCs). PCA is useful for the compression of data and to find patterns in high-dimensional data.
The mathematical equation for PCA are presented below.
We consider a set of n observations on a vector of p variables organized in a matrix X ( n × p ) :
{ x 1 , x 2 , ⋅ ⋅ ⋅ , x n } ∈ ℜ p . (1)
The PCA method finds p artificial variables (principal components). Each principal component is a “linear combination of X matrix columns, in which the weights are elements of an eigenvector to the data covariance matrix or to the correlation matrix, provided the data are centered and standardized”. The principal components are uncorrelated.
The first principal component of the set by the linear transformation is:
z 1 = a 1 T x j = ∑ i = 1 p a i 1 x i j , j = 1 , ... , n . (2)
In Equation (2), the vectors a1 and xj are:
a 1 = ( a 11 , a 21 , ... , a p 1 ) (3)
x j = ( x 1 j , x 2 j , ... , x p j ) . (4)
One chooses a1 and xj such as the variance of z1 is maximum. All principal components start at the origin of the ordinate axes. First PC is direction of maximum variance from origin, while subsequent PCs are orthogonal to first PC and describe maximum residual variance.
Economic variables are highly correlated. Multicollinearity is a statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated. In this situation the coefficient estimates may change erratically in response to small changes in the model or the data. It affects calculations regarding individual predictors. That is, a multiple regression model with correlated predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others. Principal component regression can be used as a remedy for multicollinearity.
In statistics, principal component regression (PCR) is a regression analysis that uses principal component analysis when estimating regression coefficients. It is a procedure used to overcome problems which arise when the exploratory variables are close to being colinear.
In PCR instead of regressing the independent variables (the regressors) on the dependent variable directly, the principal components of the independent variables are used. One typically only uses a subst of the principal components in the regression, making a kind of regularized estimation.
PCR (principal components regression) is a regression method that can be divided into three steps: the first step is to run a principal components analysis on the table of the explanatory variables. The second step is to run an ordinary least squares regression (linear regression) on the selected components: the factors that are most correlated with the dependent variable will be selected. Finally the parameters of the model are computed for the selected explanatory variables.
Air transportation services and economic development interact with each other through a series of mutualcausality feedback relationships. Reviewing the recent literature [
Air transportation provides employment in the aviation sector and creates wider socioeconomic benefits through its potential to enable certain types of activities in a local economy. As a result, the availability of air transportation services effectively increases the scope and cycle time of economic activity. The economic impacts of air transport include:
These cover employment and activity within the air transport industry including airline and airport operations, aircraft maintenance, air traffic control and regulation, and activities directly serving air passengers, such as check-in, baggage-handling, on-site retail and catering facilities. Not all of these activities necessarily take place at an airport, with some taking place at head office. Direct impacts also include the activities of the aerospace manufacturers selling aircraft and components to airlines and related businesses.
These include employment and activities of suppliers to the air transport industry, for example, jobs linked to aviation fuel suppliers; construction companies that build additional facilities; the manufacture of goods sold in airport retail outlets, and a wide variety of activities in the business services sector (call centres, IT, accountancy, etc.).
These include spending by those directly or indirectly employed in the air transport sector that supports jobs in industries such as retail outlets, companies producing consumer goods and a range of service industries (e.g. banks, restaurants, etc.).
The air transport industry’s most important economic contribution is through its impact on the performance of other industries and as a facilitator of their growth. It affects the performance of the world economy, improving the efficiency of other industries across the whole spectrum of economic activity―referred to as catalytic or “spin-off” benefits.
The region’s economic activity in turn generates the need for passenger travel and freight and drives the demand for air transportation services.
Practically, we will thus choose indicators of local economy in terms of the economic impacts of air transport (
With the Binhai New Area was included in the national development strategy, the Binhai New Area has played a leading role in the Bohai Sea region. A320 plane assembly line, being the first aircraft assembly line outside Europe and the first one in Asia, was established in Tianjin in 2006. With the help of Tianjin government, Hainan Airlines started Tianjin airlines, being local airlines of Tianjin. In these new circumstances, it is imperative to have a good knowledge of the interaction between air transport and regional economy. With the available data, qualitative analysis and scientific computing, we hope to make a better understanding of interaction between economic development and air transport in Tianjin. So that we could put forward policy recommendations to coordinate the development of Tianjin air transport and local economy. This paper presents a case study of Tianjin.
Reviewing the recent literature, we select the following variables on the basis
of available data and the purpose of this paper, yielding a sample that ranges from the year 2000 to 2010. They consist of (see
The software package used in this case is SPSS. We obtain the results as follows:
In
From the component matrices (
Z 1 = 0.996 1.986 X 1 * + 0.996 1.986 X 2 * (5)
and
V 1 = 0.998 8.529 Y 1 * + 0.885 8.529 Y 2 * + 0.996 8.529 Y 3 * + 0.995 8.529 Y 4 * + 0.999 8.529 Y 5 * + 0.943 8.529 Y 6 * + 0.974 8.529 Y 7 * + 0.997 8.529 Y 8 * + 0.969 8.529 Y 9 * (6)
Specifically, we can regard the variable Z 1 as standardized principal component of the air transportation variables selected. And we define X 1 * , X 2 * separately as standardized variables of X 1 , X 2 .
Furthermore, we regard the variable V 1 as standardized principal component of the local economy variables selected. And we define Y 1 * , Y 2 * , Y 3 * , Y 4 * , Y 5 * ,
Variables | |
---|---|
Air transportation | Passenger traffic (10 000 persons): x1 Freight traffic (10 000 tons): x2 |
Local economy | Gross domestic product of Tianjin (100 million yuan): y1 Total value of imports & exports in foreign trade (USD 100 million): y2 Total government revenue (100 million yuan): y3 Number of employment personnel (10,000 persons): y4 Foreign exchange earning from international tourists (USD 10,000): y5 Gross product of transportation storage and post services(100 million yuan):y6 Gross product of wholesale and retail trade (100 million yuan): y7 Per capita annual disposable income of urban households (yuan): y8 Foreign capital actually used (USD 10 000): y9 |
Air transportation | Local economy | |||
---|---|---|---|---|
Principal component | 1 | 2 | 1 | 2 |
Total | 1.986 | 0.014 | 8.592 | 0.345 |
% of Variance | 0.993 | 0.007 | 0.948 | 0.038 |
Cumulative % | 0.993 | 1.000 | 0.948 | 0.986 |
Variables of air transportation | Component matrix of Z 1 | Variables of local economy | Component matrix of V 1 |
---|---|---|---|
X1 | 0.996 | Y1 | 0.998 |
X2 | 0.996 | Y2 | 0.885 |
Y3 | 0.996 | ||
Y4 | 0.995 | ||
Y5 | 0.999 | ||
Y6 | 0.943 | ||
Y7 | 0.974 | ||
Y8 | 0.997 | ||
Y9 | 0.969 |
Y 6 * , Y 7 * , Y 8 * , Y 9 * separately as standardized variables of Y 1 , … , Y 9 .
We regress the component V 1 on the standardized variable X 1 * . Regression analysis yields the following results:
From the results given in
x 1 * = 0.998 V 1 (7)
We can now obtain the following relation from Equation (1):
x 1 = − 1315.17 + 0.030 y 1 + 0.266 y 2 + 0.117 y 3 + 0.899 y 4 + 0.002 y 5 + 0.560 y 6 + 0.264 y 7 + 0.014 y 8 (8)
Statistics | Results | |
---|---|---|
R Square | 0.997 | |
Adjusted R Square | 0.997 | |
Std. Error of the Estimate | 0.05509688 | |
F | Sig. | |
3284.170 | 0.000 | |
Standardized Coefficient | t | Sig. |
0.998 | 57.308 | 0.000 |
Furthermore, we get a series of principal component regression equations in the same methods as follows:
x 2 = − 32.189 + 0.001 y 1 + 0.007 y 2 + 0.003 y 3 + 0.024 y 4 + 0.015 y 6 + 0.007 y 7 (9)
y 1 = − 935.302 + 7.872 x 1 + 296.866 x 2 (10)
y 2 = 15.011 + 0.721 x 1 + 27.180 x 2 (11)
y 3 = − 447.736 + 2.045 x 1 + 77.103 x 2 (12)
y 4 = 392.406 + 0.266 x 1 + 10.046 x 2 (13)
y 5 = − 21047.9 + 128.295 x 1 + 4838.016 x 2 (14)
y 6 = 43.128 + 0.376 x 1 + 14.162 x 2 (15)
y 7 = − 107.882 + 0.854 x 1 + 32.216 x 2 (16)
y 8 = 2492.769 + 17.598 x 1 + 663.639 x 2 (17)
y 9 = − 104636 + 912.498 x 1 + 34410.513 x 2 (18)
It can been seen from Equation (8) and Equation (9) that for each additional 100 million yuan of GDP in Tianjin, passenger traffic increases on the average by 3410 persons and freight traffic increases on the average by 10 tons (assuming the other variables are held constant). So we can conclude that the local economy provides capital and generates demand for passenger and freight travel.
Together, Equations (10), (12), (13), (15) and (17) imply that for each additional 10,000 air passengers, GDP of Tianjin increase on the average by 787 million yuan, total government revenue increases on the average by 205 million yuan, number of employment personnel increases on the average by 2660 persons, per capita annual disposable income of urban households increases on the average by 18 yuan, Gross product of transportation storage and post services increases on the average by 38 million yuan (assuming freight traffic is held constant). Moreover, for each additional 10,000 tons of air cargo, GDP of Tianjin increases on the average by 30 billion yuan, total government revenue increases on the average by 8 billion yuan, number of employment personnel increases on the average by 100,460 persons, per capita annual disposable income of urban households increases on the average by 663.639 yuan, Gross product of transportation storage and post services increases on the average by 3 billion yuan (assuming passenger traffic is held constant). It is obvious to see that air transport is a significant tax payer and generates employment and wealth.
Furthermore, in Equation (16), for each additional 10,000 air passengers, Gross product of wholesale and retail trade increases on the average by 85 million yuan (assuming freight traffic is held constant). Moreover, for each additional 10,000 tons of air cargo, Gross product of wholesale and retail trade increases on the average by 66 billion yuan (assuming passenger traffic is held constant). Thus, air transport generates wide indirect and induced benefits.
Finally, it can be shown from Equations (11), (15) and (18) that for each additional 10,000 air passengers, total value of imports & exports in foreign trade increases on the average by USD 72 million, foreign exchange earning from international tourists increases on the average by 13 million, foreign capital actually used increases on the average by USD 91 million (assuming freight traffic is held constant). Moreover, for each additional 10,000 tons of air cargo, total value of imports & exports in foreign trade increase on the average by USD 3 billion, foreign exchange earning from international tourists increases on the average by USD 48 million, foreign capital increases on the average by USD 344 million (assuming passenger traffic is held constant). Hence, the air transport industry has a substantial catalytic impact.
Our research presents a principal component model establishing principal component regression equations. Then we apply this model to gaining insight into the relationship between air passenger travel in Tianjin and local economy. Future research should go into further detail by applying the principal component regression equations to forecast so that we shall find the mutual adaptation “gap” of air transport and local economy in the next five years. And thus we shall make relevant policy recommendations in terms of the current development situation and requirements of the new era. Consider the focus of this paper and space limitations, we shall not give relevant details here.
Possible differentiations to study include:
1) In order to better take into account the feedback-based interaction between air transportation and local economy, it could be interesting to use a measure of accessibility to population or to technology within a certain time range around the airport.
2) We illustrate the interaction taking Tianjin area as an example. It could be necessary to use both world-wide and country-level analysis to describe the relationship between air transportation and economic activity.
3) The criteria we take into account for indices selection are the availability of data and the frequency in relevant literature. But it is more scientific and reasonable to use other methods, such as cluster analysis and variance analysis to select variables. It is meaningful to get more comprehensive data to filter out the most suitable indices for evaluation of specific areas.
Li, Y.H., Zhang, Y. and Liu, T.Y. (2018) Analysis of Principal Component Regression Equations of Air Transportation and Local Economy: Taking Tianjin as an Example. Theoretical Economics Letters, 8, 1830-1839. https://doi.org/10.4236/tel.2018.810120