Transportation Infrastructure Facilities
and the Total Factor Productivity of “the New Silk Road”- Spatial Econometrics Analysis on Panel Data
Li zhong-min, Liu Yu-hong(International Business School，Shaanxi Normal University，Xi'an 710062，China)
Abstract：This thesis used panel data to establish empirical model approach to analyze therelationship between transportation infrastructure facilities and the total factor productivity growthwhich based on the 17 important cities which covered by the East and West traffic artery ofLong-Hai and Lan-Xin railways along the New Silk Road. The empirical result proved that:transportation infrastructure facilities have a significant positive impact on the total factor
productivity growth; also, railway and highways of higher class have a spatial spillover effect on
the total factor productivity growth to the extent of 74.59%, the contribution share of all kinds oftransportation is 59.0872%. In addition, the railway and freeway have a significant positive effecton the total factor productivity growth.
Key words: the New Silk Road; transportation infrastructure; the total factor productivity;
spatial spillover effect

1. The Issues Rose and the Review of Related Scientific Literatures
1.1 The Issues Rose
The Silk Road, a historical international route, made an important contribution tohumans’ economical and cultural exchanges. It is the artery that associates China with
the Asia and Europe. The Silk Road occupies an important position in the history
development of the world. The New Silk Road refers to the Eurasian Continental
Bridge, which is a conception raised in the new era. From the East to the West, it
includes Long-Hai line and Lan-Xin line. The new Silk Road links a prosperous
economic zone in East Asia in the east and the developed European economic zone in
the west. In 21st century, compared with other channels, this section has been ignored
for a long time, which had been very brilliant in the history. Many inland cities arelocated in western area of less developed economy in China. There is a big gap of
GDP per capita in these cities compared with other cities in China, although thesecities boast prosperous history, and they are rich in mineral resources, energy
resources, land resources and human resources and also valuable tourism resourcesthat consist of many historical heritages, magnificent natural sceneries of1multinational culture. Thus, an economical depression belt appeared between China
and central-Asia. In order to solve these problems, the Chinese Party Central
Committee proposed economical strategies in a timely manner, for example, “theWestern development”, “the rise of central China”, “Guanzhong-Tianshui economicarea” and so on. [1]In recent years, the infrastructure of “the new Silk Road” transportation along the
China-Central Asia has be improved a lot, thanks to efforts of China, Central Asian
countries and relevant international organizations. Emergence of new cities andchanges in conditions of modern land transportation has created an opportunity for thedevelopment of the new Silk Road. The research on transportation infrastructure
investment around “the New Silk Road” economic zone and total factor productivity
growth can help us to know the contribution rate of total factor productivity growth bydifferent types of transportation infrastructure investment, also the spatial spillover
effect. Meanwhile, it will provide certain practical significance and reference on
decision-making of the Western development, revitalization of the Silk Road,
formation of the great international passage by connecting Eurasia Bridge.
1.2 Review of Related Literature
In the 1940s, the positive impact of infrastructure on economic growth caused general
concern from development economists, represented by Rosenstein Rodan, Ragnar
Nurkse, Walt Rostow and Albert Hirschman, they analyzed the impact of transport
infrastructure on economic growth from the perspective of different theories. Under
the impetus of the World Bank, Aschauer (1989) [2] started to study the relationshipbetween economic growth and infrastructure for econometric studies. Later on,
Holta-Eakin (1994) [3], Barro (1995) [4], also separate the infrastructure from the total
investment; estimate the impact of infrastructure capital to economic growth
separately by using the method of production function. Scholars represented by
Aschauer（1989）[2]、Munnell（1990）[5]、Hulten，Schwab（1991）[6]、Merriman（1990）[7]、Christodoulakis（1993）[8]、Wylie（1995）[9]、Denny，Kevin（1997）[10]、Everaert，Heylen（2001）[11]use the part of the production function method, towork out the considerable flexibility by using time series data. For a more accurate
analysis of relationship between infrastructure capital investment and output, Munnell(1990) [5], Moonaw,Williams (1991) [12], Garlino,Voith (1992) [13], Evans,Karras(1994), [14]Nourzad,Vrieze (1995) [15], Picci (1995) [16], Prud,Homme (1996)[17],Garcia-Mila,McGuire,Porter(1996)[18],Kelejian,Robinson(1997)[19],Bonaglia,Ferrara(2000)[20] Panel sample data, such as empirical research that Infrastructure using panel
data at the State level of output elasticity than the general use of infrastructure at thenational level time series data output flexibility is much smaller, the reason for this2

may be the infrastructure in the counties between the positive spillover effects in themodel are ignored. Holtz-Eakin[3] and Schwartz (1995) the first spatial weight matrix,
joining in the traditional production function the adjoining infrastructure variables,
study the spillover effects on infrastructure, Boarnet (1998)[21]and Schwartz (1995) on
the basis of the Holtz-Eakin and Schwartz (1995) modeling, found the roadinfrastructure for economic growth there was a negative spillover effect of theevidence. Foundation facilities of Agent variable selection is divided into two class:one was follow new classical of capital concept, to currency forms of page to said, isnow was most related literature by used; the other was on new classical of“technology relationship” be restore, to real form to said, this method of research
since in the late 1990 of the 20th century began constantly mature, to Sanchz-Robles(1998) [22], Fernald (1999) [23], Canning& Pedroni (1999) [24] and Li Ching, a family
tracing peak (2006) [25], Wang Ren-fei and Wang Jin-jie (2007) [26], Zhang Xue-liang(2009) [27], Liu Bing-lian, Wu Peng, Liu Yu-hai (2010) [28], and so on.
At present, looking from the domestic and foreign literature which may consult,very little the relations which grows using the spatial kneading board gauging device
research transportation infrastructure and the entire essential factor productivity,
nobody is more right the relations which “the new Silk Road” the economical belt'stransportation infrastructure and the entire essential factor productivity grow. In viewof this, this article uses the establishment kneading board data model the real
diagnosis method, takes east China, west transportation aorta Long-hai, theLanzhou-Xinjiang line to cover the new Silk Road most important 17 cities to take thesamples along the route, between analyzes this economy to take to bring with thetransportation infrastructure and the entire essential factor productivity grows therelations.
2. An Empirical Model
2.1Calculation of Total Factor Productivity
1) Data Select
There are 17 cities of great importance which was selected from Ri-zhao city
Shandong Province in the east, till to Urumqi city in Xin-jiang in the East, (from Westto East they are: Urumqi, Zhang-ye, Wu-wei, Xi-ning, Yin-chuan, Lan-zhou, Tian-shui,
Bao-ji, Xian-yang, Xian, Wei-nan, Sanmen-xia, Luo-yang, Zheng-zhou, Shang-qiu,
Ji-nan, and sunshine), all of them were covered by two major railways covered by the
new Silk Road, the time span from 2001-2008, Output variables is presented by GDP,
Input variables including material capital and practitioners. Zhang June (2004) [29]3

calculation will be used in the Physical capital, and shrink swell will be done on GDP
and material capital follows constant prices in 2000 years.

2) Model and Calculation Results
To set the function of national production of “the New Silk Road” traffic
economic belt as stochastic frontier production function form of Douglas production
function model:

ln GDPit   0   1 ln Kit   2 ln Lit   3t  ( it   it )

 it  i exp (t  T )  ~ iidN  ( ， 2 )（1）

The left side of the equation was explained variable for GDP, the right one
including explained variable substances capital K and labor number L,  0 — 3 areassessment parameter; i is sample mark, t is sample observation period, T is sample
base period annual,  i is random interference item, which obeys normal distribution,

 i is technology without efficiency item, which obey zero points truncated of half
normal distribution,  is expectations under non-truncated normal distribution
conditions.  is time-varying parameter technology efficiency Shi. Using the
Frontier 4.0 software, the results are shown in table 1.
Table 1: function model to estimate of “the New Silk Road” economic production
Variables

Coefficient

0
1
2
3

The intercept

ln K
ln L
t


t Statistics

Estimated value
1.1234＊＊＊7.0716

0.5074＊＊＊22.2150.3898＊＊＊19.2031＊＊＊7.53240.0544＊＊＊15.65540.9627＊＊＊181.0061

0.4568＊＊＊6.169

0.0008＊＊＊2.89860.02112


Log Likelihood function value

341.4651

technical inefficiency of non-exist values

445.02312

of testing value of LR
Note: *** indicates1% the significance level.

From the testing results, the estimated parameters are passed test of 1%
significance level. Also,  values of is 0.9627, it means that there is an obvious
representation model of composite structure, technical inefficiency of non-exist values
4

of testing value of LR shows using stochastic frontier model reflect “the New Silk
Road” of the production function of the national economy more effectively.
According to the estimated results of Table 1, the factor productivity ( TFP ) of traffic
economic belt along “the new Silk Road” should be as follows by calculation (2)TFPit  exp( 0   3t )TEit（2）

exp( 0   3t ) In the equation (2) stands for frontier skills of technical levels of tperiod. TEit Is the number i city’s efficiency in the period of t . According tocalculations, during 2001-2008, an annual increase of “the New Silk Road” transporteconomic total factor productivity is 3.193%, relative to its average annual economic
growth rate of 12.19%, a contribution rate is 26.19%.
2.2 Spatial Econometric Model
1) Spatial Econometric Model
Considering the correlation of model errors in space, the establishment of spatial
error model ( SEM ) may lead to spatial correlation When spatial dependence is very
important for models. Thus, model ( SLM ) should be established:
SEM Model:
GDPit   0    jXitj  itnj 1

 it  W  it   it it ~ N（0， 2 I）

（3）

SLM Model：
GDPit   0  WYit    jXitj  itnj 1

 it ~ N（0， 2 I）

（4）

In the equation (3) and the equation (4), GDP is the dependent variables, Xj isarguments,  it and  it are normal distribution of the random error term,  0 isintercept,  j 、  、  are coefficients, W is the spatial weight matrix, adjacent tofirst-order function of the distance matrix representation of the adjacent city assigned
the value 1, otherwise, the value 0. Due to space model, Xj has the partial effect on
GDP which reflected in the space on the exterior, which will fade as the circles
spreading, i in the equation (5) and the equation (6) indicate that an external on a
district Center in scale out circles of ordinal numbers, to build space external effects
models are:

5



i

 j  
i 1

 j
1 

（5）

Xj Variables for the GDP on the overall effect model are:i j  
i 0

j
1 

（6）

2) Spatial Correlation Test

Moran indices of Spatial autocorrelation is generally used for inspection of
spatial correlation of economic variables, from the calculated of Stata10.0 software, in
2001-2008, for “the New Silk Road” total factor productivity of traffic economic area,
Moran Spatial autocorrelation test results (table 2) shows: in years of 2001-2008
Moran I had passed 1% significance level test, all are positive ones, and the value
increasing year by year, which indicating that there is a clear positive correlation in
space for “the new Silk Road” Traffic economic belt of total factor productivity, thatis spatial agglomeration phenomena.[28]Table 2: total factor productivity Moran I spatial autocorrelation test of “the New Silk Road” traffic economic belt
Year

The value of I
＊＊＊

Year

The value of I

2001

0.3421（3.1872）

2005

0.3541＊＊＊（3.2122）

2002

0.3454＊＊＊（3.2010）2006

0.3551＊＊＊（3.2234）

＊＊＊

2003

0.3457（3.2018）2007

0.3554＊＊＊（3.2312）

2004

0.3519＊＊＊（3.2114）

2008

0.3556＊＊＊（3.2325）

Note: *** indicates 1% significance level.

2.3 Model Check of Transportation Infrastructure and Total Factor Productivity
Growth1) Variables Select and Model
Two indexes were selected for the transportation infrastructure: take every
square kilometer of operating railway mileage as the density of railway ( X 1 ), andevery square kilometer of highway traffic mileage as a highway density of ( X 2 ). And
according to the road classification, Roads can be divided into Expressway ( X 2  0 ),highway ( X 2  1 ), the secondary road ( X 2  2 ), three-level Highway ( X 2  3 ), thefour-class road ( X 2  4 ) and substandard Highway ( X 2  5 ). Take the right 17 cities
as samples, the time span for the 2001-2008. Take two control variables of
non-agricultural production ( Non  agr ) and per capita levels of education indicatorvariable（ Edu ）descriptive statistics as shown in table 3. to build the model(1) toanalyze the relationship between two indexes on density of railway and highway andtotal factor productivity, the model (2) of the relationship between roads and totalfactor productivity.

6

Table 3: the variable statistics of “the New Silk Road” traffic economic belt

Variables

Sample number

Average

Std

Min

Max

TFP
X1
X2
X20
X 2 1
X22
X23
X24
X25

136

1.89870.61430.87018.8245136

17.5741

15.1368

1.515470.6589136

420.5641

309.8945

19.4687

1759.4261

136

9.012413.27530.0000100.1275

136

9.8967

15.12150.000073.5982136

53.124357.97841.4785423.2595

136

73.288173.58416.6059418.6580

136

208.9435

172.9845

8.2948948.7893

136

66.568384.89240.0000515.9041

2) Model estimation
According to test results from the model (table 4), SLM data models of area
point double stationary panel should be selected. Also, from the view ofvalue Log  Likelihood , SLM area point double fixed of panel data model obviously
better than traditional panel data and other spatial space Panel model, what’s more,
R 2 value is very high in area point double fixed of panel SLM data model (1), and (2),therefore, either from statistics inspection or from economic significance view, area
point double fixed of panel data model is the priority.
In the double fixed point panel SLM data model (1), the explanatory variables
pass the 1% of the significant level test, estimation of coefficient of railway density,
road density is positive, the transportation infrastructure for growth has a catalyticrole in highway density coefficient is smaller. In double fixed point panel SLM data
model (2), effects on four-level highways, substandard highway on TFP growtheffect are not obvious, and other explanatory variables estimation coefficient surpass
10% significance level test, its value is positive, railway and highway facilities on the
TFP growth effect of higher level significantly.
Table 4: the spatial statistical results and total factor productivity growth of “the New Silk Road” transportation
infrastructure
panel SEM data models
The area is
The time is
Double
fixed
fixed
fixed
Model（1）panel SLM data models
The area is
The time is
Double
fixed
fixed
fixed

variables

Traditional
individual
fixed effectln X 10.05785＊＊＊0.0012-0.0172（2.2014）（1.2457）（-5.6981）（4.0521）（3.5511）

＊＊＊

＊＊＊

＊＊＊

＊＊＊

＊＊＊

ln X 2
Non  agr

0.051210.00010.0000＊＊＊0.01380.0001＊＊＊0.00650.0001＊＊＊（5.3845）（3.5015）（4.7892）（6.2685）（4.6112）

＊＊＊

＊＊＊

＊＊＊

＊＊＊

＊＊＊

0.0201-0.00810.041870.03680.0117-0.0148＊＊＊（-5.6347）
0.0004＊＊＊0.0075＊＊＊(4.2029)0.0001＊＊＊（6.07921） （4.8568）
0.0373＊＊＊0.0125＊＊＊（10.2547）

Edu

0.0620＊＊＊（6.5548）W  it（-6.3641）-0.0063（-1.0932）
0.9578＊＊＊（123.3654）（11.1094）
0.3658＊＊＊（11.4431） （5.3791）
0.1357＊＊＊（9.5012）（7.8624）＊＊＊＊＊＊0.5192（7.9441）0.42870.0551＊＊＊（9.024）0.3810＊＊＊（5.0491）（9.4021）0.6157＊＊＊0.1327＊＊＊（14.3498） （2.1046）

R

Log  Likelihood

0.0509＊＊＊（5.8057）（5.9130）

W ln TFP
2（7.9594）

0.6438＊＊＊（79.9754）

0.99340.99930.76850.98980.99760.72900.9975461.07497.89-52.73287.71420.79-58.84-679.61＊-0.0764

Model（2）ln X 10.0358＊（1.7219）ln X 2 - 0

0.0175＊＊＊（3.5894）ln X 2  1

0.0111＊（1.7913）ln X 2  20.1309＊＊＊（7.0614）ln X 2  3
ln X 2  4
ln X 2  5
Non  agr

Edu

＊＊＊

0.0073＊＊（2.0781）-0.0009（-1.0892）-0.0029＊＊＊（-2.6671）-0.0071＊（-1.8002）-0.0735＊＊（-2.491）-0.0630＊＊＊（-3.4321）
0.0945＊＊＊（4.6638）
0.0112＊＊0.0046＊＊＊（3.3864）0.0014-0.0635＊＊＊（-3.453）0.0897＊＊＊（7.0124）＊＊＊＊＊＊

0.1621

0.1131（5.6514）（6.7124）＊＊＊＊＊（-2.5081）-0.0003-0.0112（1.2407）（-0.0861）（-0.3721）

0.00020.0204（1.9359）（0.3019）

＊＊＊

＊＊＊

＊＊

0.6375（3.5748）0.0241＊＊＊（3.2914）0.0261（4.3615）0.0094＊（1.6682）0.0004（0.2116）＊＊0.1568（5.3912）-0.0753＊＊-0.0084＊＊（2.3089）（0.8504）（2.2087）（2.2256）

＊＊＊

＊＊＊

＊＊＊

＊＊＊

0.00370.01960.0094（5.5612）（7.0925）（4.5815）（5.6512）（7.0624）（4.6915）

＊＊＊

＊＊＊

＊＊＊

＊＊＊

＊＊＊

＊＊＊

0.0281（3.5739）W  it0.0036（2.6864）0.9876＊＊＊（328.1213）

0.1306（7.9782）-0.0491（-0.5043）

0.0280（4.3118）0.28760.00860.0058＊＊＊（4.2918）0.0030＊（1.7375）
0.0221＊＊＊（4.0257）
0.0106＊0.0027（-0.3052） （1.2458）

0.00140.0086＊＊（-2.4471） （1.9098）

0.00160.00920.0129（-2.5771） （2.1146）（0.8372）（-0.2383）

0.00230.0197＊＊＊＊＊＊0.00970.0100（20.9041） （1.8914）＊＊（2.1167）（2.7089）0.00450.0115＊＊＊-0.0778＊＊＊（7.3054）-0.0008

0.05350.03830.1282（3.7136）（7.8143）0.7446＊＊＊0.07580.0009（1.4501）
0.0035＊＊＊（7.0695）
0.0091＊＊＊（4.3291）＊＊＊（3.5354）

W ln TFP（33.4321） （1.1776）

0.7428＊＊＊(79.9781)

R2

0.99540.99970.75850.99520.9996

0.76530.9996

Log  Likelihood518.29786.68104.82519.04733.15106.76-6522.69

Note: *** indicates 1% significance level, ** indicates 5% significance level, * indicates 10% significance level.

Through type (5), and (6) the calculation of area point double fixed of panel
SLM data model (2), in the coefficient more significantly of various traffic
Foundation facilities partial effect and proportion (table 5), the results are shown:railway, and grade higher of traffic Foundation facilities on growth of space external
partial effect accounted for TFP overall partial effect of 74.59%, among which, thespace external partial effect of the second-level highway is the biggest, when its
investment increased 1% each , the TFP growth will be 0.0866%; following by
8respectively is railway, and three level Highway, and Expressway and the level
Highway, external effects and overall effects of highway space on TFP growth isleast obvious.
Table 5: All kinds of transport infrastructure in total factor productivity growth effect of “the New Silk Road”
Overallleaning
effectflexibleln X 1ln X 2 - 0

0.05020.01280.03740.02310.00590.0172ln X 2  1
ln X 2  2
ln X 2  3

0.01190.00300.08660.0221

0.06450.04230.01070.0316variables

Direct leaning effectOutside space leaning effectProportion %25.41

flexible

0.0089Proportion %74.59

Due to various stock of transportation infrastructure, there will be inevitabledeviation that judge contribution size of all variables to the growth of TFP withelasticity. Therefore, specific calculation is needed to judge the contribution rate ofvarious traffic foundation facilities of “the New Silk Road” on full elements
productivity growth. The increase of various traffic foundation facilities stock of “theNew Silk Road” boasts a contribution share of 59.0872%on growth of TFP (table 6).
Among them, secondary roads boasts the highest rate of TFP growth, accounting for23.9859%, followed the highway, railway, and roads of lower levels do thecontribution to TFP growth rate is very low. [28]Table 6: the transport infrastructure contribution to total factor productivity growth rate of “the New Silk Road”
transportation
infrastructure
railway

10.47

The growth rateof TFP %0.5293

The Contribution rate
to TFP growth %2.8281highway177.334.132722.0587

Arterial road

98.62

1.19046.3658

Secondary road

51.76

4.489623.9859

Tertiary highway

17.01

0.71983.8487Total-

11.061859.0872

The growth rate%

According to the statistical data of 2001-2008, estimated results of the Panel
SLM model, of which “the New Silk Road” traffic Foundation facilities and fullelements productivity growth relationship, table 7 shows that: in model (1)and (2), in
the year of 2001-2008 railway density has a continuous and significant effect on thefull elements productivity growth; in the year of 2001-2004 of Highway density ofmodel (1), the effect is continuous and significant, but that not so obvious in the yearof 2005-2008. In model (2), highway density in two periods affects the total factor
productivity growth obviously, while others are not.
9

Table7: Transport infrastructure and norm estimates of total factor productivity growth results of “the New Silk
Road”

variables

ln X 1Years of 2001-2004
model（1）model（2）＊＊＊＊＊＊0.0126（3.6476）ln X 2Years of 2005-2008

0.0090（2.6389）0.0109＊＊＊（3.3067）（6.2012）＊＊＊-0.0008（-0.7653）＊＊＊-0.0044（3.4275）
0.0079ln X 2  5（-1.1483）＊＊＊

0.0004（1.6237）（0.1656）0.0100＊＊＊-0.0013（2.6079）（-1.3527）

0.0015＊＊＊0.0004（2.6013）

Non  agrEdu
W ln TFPR

2

Log  Likelihood

0.0009＊＊＊0.0007＊＊＊（1.5026）0.00060.0006（1.5754）（3.5759）（3.1756）（1.2054）

＊＊＊

＊＊＊

＊＊＊

0.0081（4.3632）（2.8793）0.0112ln X 2  4＊＊＊

0.0151＊＊＊（3.3756）

ln X 2  3

0.0130（0.5849）0.0489ln X 2  2model（2）＊＊＊0.0017ln X 2  1

0.0113＊＊＊0.0006（4.4281）ln X 2 - 0

model（1）0.00590.00580.0048＊＊＊（7.8970）（5.5872）（3.4297）（2.5963）

＊＊＊

＊＊＊

＊＊＊

0.8968＊＊＊0.92380.87370.9288（115.5856）（105.7654）(80.7689)(92.9890)

0.99980.99980.99980.9998-14681.32-14484.79-10266.48-12410.16

Note: ***indicates 1% significance level, ** indicates 5% significance level, * indicates 10% significance level.

3. The Conclusions
1) During the years of 2001-2008, the transportation infrastructure of “the New
Silk Road” has significant positive effects on total factor productivity growth, among
which promoting effect of Highway, secondary Highway are particularly notable.
2) The effects of four-level Highway and substandard highway on total factor
productivity growth is not obvious; while effects of railway, Expressway, highway,
secondary highways and tertiary roads on total factor productivity growth issignificant, space external effects on total factor productivity growth is larger,
accounting for the whole effect of 74.59%. the space external partial effect of thesecond-level highway is the biggest, when its investment increased 1% each, the TFP

10growth will be 0.0866%; railway investment increased every 1%, the total factor
productivity growth will be 0.0502%, respectively, followed by railway, three level
Highway, Expressway and the level Highway, the external effects and overall effects
of highway space on growth are least obvious.
3) The contribution share of “the New Silk Road” of transport infrastructure tototal factor productivity growth of the stock is 59.0872%. Among them, secondary
roads boasts the highest rate of growth in total factor productivity, accounting for23.9859%, followed by the highway, railway and the tertiary highway’s contribution
share.
4) During the years of 2001-2008, “the new Silk Road” traffic economic belt
railway, highway has the significant positive effect on total factor productivity growth,
while effects of the other classes of highway are no longer notable since 2005,
without continuity. This indicates that transportation is the top priority in China's“Western development”, “the rise of central China”, to increasing investment oftransportation infrastructure investment has led to significant growth of the “New Silk
Road” economic zone.
In order to promote the new round of “the Western development”, revive “theSilk Road”, and build “the new Eurasia Bridge”, it is urgent and realistic thatincentives should be given to the traffic Foundation facilities investment of “the New
Silk Road” economic with of Central and western area. Especially that to increase
policy tilt intensity of Western area, to promote economic development of railway,
and expressway construction along “ the New Silk Road”, [31]for coordination
economic development in western area, promoting the implementation of the strategy“Central rise” and “the Western development” , finally, to achieve the development ofWestern areas.

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