EMPIRICAL METHODOLOGY

To quantify the agglomeration benefits of transport investment, Venables (2007)

suggested that researchers should consider two major factors: 1) the change in access to

economic benefits that will result from improved transport service through transport

investment; 2) the change in productivity as a way of reflecting an increase in

agglomeration. Consequently, this study incorporates these two factors into two selected

empirical methods to estimate the casual effects of HSR investment and agglomeration

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 Method 1: Multivariate OLS Regression Model 𝒀𝒊𝒋 = 𝜶 + 𝑿𝒊𝒋𝜷 + 𝒆𝒊𝒋,

where 𝒀_𝒊𝒋 is the change in the agglomeration economies indicator. Let X denote a

vector of explanatory variables, including the change in access to economic benefits as a

result of introducing HSR service; 𝒆_𝒊𝒋 is the error term and subscripts i, j are index city and

time period between 1982 and 2009, respectively.

In this case, the OLS model can be written as follows:

∆∆_𝑡−1𝑡 _{𝐴𝑔𝑔𝐸𝑐𝑜 = 𝛼 + ∑ 𝛽}

𝑖(𝐻𝑆𝑅 𝐹𝑒𝑎𝑡𝑢𝑟𝑒)𝑡,𝑡−1𝑖

𝑖 +

∑ 𝛾𝑗 𝑗(∆∆𝑡−1𝑡 𝐸𝑐𝑜𝑛𝐶𝑜𝑛𝑡𝑟𝑜𝑙)𝑗 + ∑ 𝛿𝑘 𝑘(𝐶𝑖𝑡𝑦𝐶𝑜𝑛𝑡𝑟𝑜𝑙)𝑘 + ∑ 𝜃𝑚 𝑚(𝐺𝑒𝑜𝐶𝑜𝑛𝑡𝑟𝑜𝑙)𝑚+ 𝜀 ,

where ∆∆_𝑡−1𝑡 𝐴𝑔𝑔𝐸𝑐𝑜 is the growth of agglomeration economies in commune i

between the time periods t and t–1. The explanatory variables are as follows:  HSR Feature:

o Train frequencies of HSR service to/from Paris

o Travel time savings to/from Paris

o Train frequencies of all rail services to/from Paris

o Level of overall accessibility(calculated in an earlier chapter)

o Location of the HSR station

 EconControl(Economic performance indicators):

o Human capital

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o Population density

 CityControl(City size and city type indicators):

o Categories of city size, including major, big-medium, small-medium and

small city

o Seaside city

o Regional capital city

 GeoControl:

o Proximity to neighboring countries, including Belgium (BEL), Italy (ITA),

Switzerland (CHE), Germany (DEU), Luxembourg (LUX), and Spain (ESP)

The major caution in using the OLS model is that the model neglects the cross-

sectional and time series nature of the data. In this case, each city as the study subject is

observed for three time periods between 1982 and 2009. The economic performance of

each city is highly correlated among the three time periods. However, the OLS model treats

these three observations independently. Moreover, for most economic datasets, the error

terms are not randomly distributed. Unobserved individual heterogeneity may also be

correlated with listed independent variables. Eventually, these existing unobserved

correlations will lead to omitted variable bias. To consider this major limitation of the OLS

model, this study adopts the linear mixed effects model.

 Method 2: Linear Mixed Effects Model

With the panel data, the linear mixed effects model, and including both fixed and

random effects, it is possible to estimate the parameters that describe how the mean

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in the future. Moreover, it allows the analysis of between-subject and within-subject

sources of variation in the longitudinal responses. In this case, the linear mixed model

provides good control of the variation between French HSR cities and the variation of each

city among different time periods.

The linear mixed effects model can be expressed as

𝒀𝒊 = 𝑿𝒊𝜷 + 𝒁𝒊𝒃𝒊+ 𝒆𝒊,

where 𝑋𝑖 is a matrix of covariates by using the same variables listed in the OLS

model, 𝑍_𝑖 is an 𝑛_𝑖× 𝑞 matrix of covariates with 𝑞 ≤ 𝑝, 𝛽 is a 𝑝 × 1 vector of fixed effects,

𝑏_𝑖 is a 𝑞 × 1 vector of random effects and 𝑏_𝑖~𝑁(0, 𝐷) and 𝑒_𝑖 is an 𝑛_𝑖 × 1 vector of errors

and 𝑒𝑖~𝑁(0, 𝑅𝑖) 𝑖 = 1, … 𝑛.

 Model Hypothesis

Table 2 lists the hypothesis of each variable in the methods. The analysis assumes

each variable in the category of the HSR feature is positively related to the increase of

agglomeration economies, with the exception of the train frequencies because train

frequencies to/from Paris not only include HSR frequencies but also all other types of rail

services, such as overnight train services. Thus, with the control of HSR train frequencies,

more overnight train services indicate a lower level of accessibility and further indicate a

lower increase in agglomeration.

As the economic control variables, human capital, occupied housing rate and

population density are assumed to have a positive relationship with an increase of

agglomeration economies. In addition, a city located in close proximity to the ocean and

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in job density. Similarly, a city proximal to nearby countries is assumed to obtain more

economic benefits from HSR investment.

Table 6-2: Model Hypothesis

HSR Feature: Hypothesis

Train frequencies of HSR service to/from Paris +

Travel time savings to/from Paris +

Train frequencies of all rail services to/from Paris -

Level of overall accessibility +

Location of HSR station from edge to center +

EconControl

Human capital +

Occupied housing rate +

Population density +

CityControl

Seaside city +

Regional capital city +

GeoControl:

Proximity to Belgium (BEL) +

Proximity to Italy (ITA) +

Proximity to Switzerland (CHE) +

Proximity to Germany (DEU) +

Proximity to Spain (ESP) +