# Drivers of changes in Spanish accessibility for the 1960–2010 period

**Part of the following topical collections:**

## Abstract

### Purpose

The accessibility of a certain place can evolve either as the direct result of transport changes or as a consequence of the spatial redistribution of economic activities. These two factors are often indistinguishable—especially at regional level—since improved infrastructure stimulates relocation of activities. Moreover, infrastructure investment choices tend to follow population and economic activity patterns, distorting the cause and effect relationship between infrastructure and accessibility even further. The methodology and results presented here decompose the impact of both factors in terms of accessibility using Spanish data between 1960 and 2010. During this period, Spain experienced profound changes in transport infrastructure and economic activity.

### Methods

We use the potential accessibility indicator and resort to index number theory to disentangle the contribution of transport infrastructure from that of land-use changes. Detailed historical data on road infrastructure and population is used to represent the transport and land-use components of accessibility.

### Results

Our results show that changes in transport infrastructure had a relevant impact on accessibility, as expected, but changes in the spatial distribution of population had an even greater effect. This outcome may be used as an argument for sustainable accessibility, a concept that advocates integration of transport and land use planning.

### Keywords

Historical accessibility Transport infrastructure assessment Population change Productivity index## 1 Introduction

There is a growing trend in the literature on transport planning that advocates a change of paradigm from mobility to accessibility planning ([1, 2, 3, 4, 5]). Mobility-based measures that have dominated many transport policies include delay per capita, monetary cost of congestion, and highway level of service. Behind the mobility approach, travel speed is considered to be a fundamental key to transport policy success. However, many of those arguing for a paradigm change recall that mobility is rarely an end in itself, but rather a means to increase accessibility [6]. People move towards opportunities and thus the ultimate objective of transport policies should be maximising accessibility instead of speed.

The accessibility concept may be defined as ease of access to markets and it is usually related with lower transport costs, higher levels of competitiveness and better quality of life. This concept has the advantage of simultaneously showing the quality of transport systems (infrastructure) and the location of activities (land-use). An improvement in transport infrastructure, such as constructing a new highway, will reduce travel time and increase accessibility. While, (re)location of economic activities, will change job opportunities for residents in the surrounding areas.

However, in the long run, the effects of transport infrastructure and land uses on accessibility may merge. New economic geography literature suggests that the relationship between transport investments and changes in activity patterns does not always favour economic cohesion but may result in core-periphery distributions [7]. Decreasing returns of transport investments have been measured by several authors ([8, 9]). This is also true for accessibility, since accessibility impacts decrease with network density.

In addition, increased transport capacity may induce spatial dispersion of economic activities, resulting in longer and costlier trips. Spence and Linneker [10] studied the relationship between regional employment and accessibility changes due to new motorways. Their results showed that employment growth was higher in areas with low accessibility, suggesting a decentralization process of economic activities.

Conversely, the agglomeration of economic activities usually entails higher congestion levels which negatively affect accessibility, through increasing transport costs. Nonetheless, most of the more accessible regions also have the highest congestion levels.

It is clear that accessibility is a function of transport infrastructure and the location of economic activities, but which of the two conjoint effects will have a higher impact on accessibility changes? And how does the weight of these two factors evolve over time?

The present study attempts to answer these questions by proposing a new methodology and analysing accessibility change in Spain at the NUTS-3 level, over a 50 year period between 1960 and 2010. During this period a significant transformation of transport infrastructure and economic activity took place. We do so by applying index number theory, which allows us to aggregate (i.e. summarize into a single scalar) the bilateral relation between a given location (origin) and its surrounding destinations (e.g. commercial partners), considering infrastructure as the main input yielding accessibility to economic opportunities. Infrastructure, in the form of travel time, is considered as the input producing accessibility to markets as output, resulting in a productivity index that is defined as the ratio of potential economic opportunities to infrastructure. Furthermore, resorting to the product rule of index numbers, we can consistently decompose accessibility change across locations and over time, enabling us to disentangle the contribution of transport infrastructure from the land-use dimension.

The next section reviews previous studies devoted to the effects of transport infrastructure and land-use on accessibility change, and discusses the advantages of index number theory when pursuing this objective. The following sections present the data and statistical sources used for this analysis (section 3) and the methodology employed to measure accessibility change and decompose it into suitable infrastructure and land use components (section 4). Section 5 reports the results for the Spanish case, while section 6 draws the main conclusions.

## 2 Accessibility dimensions and their decomposition

Land-use: represents the amount and spatial distribution of opportunities at destinations. Opportunities can be measured as population, jobs or other socio-economic variables that may characterize the economic importance of places;

Transport: describes the transport system as a facilitator of movements (both passenger and freight flows) between an origin and destination. This is commonly represented by time or cost variables reflecting the quality of the transport system;

Time: captures the potential to access a certain location, depending on factors such as time budgets or opening hours of available opportunities;

Individual: accessibility is a characteristic of individuals and varies according to their socio-economic status (i.e. income, age, education level).

Given the aggregate national scope of our analysis we will focus on the contribution of the first two dimensions, while time and individual aspects of accessibility are better looked at using micro-level approaches.

Selected accessibility studies looking at different accessibility components

Studies | Network | Scale | Accessibility indicator | Accessibility component | Analysed period |
---|---|---|---|---|---|

Gutiérrez, J., and G. Gómez [12] | Road network | Metropolitan (Madrid) | Average distance to nearest highway; potential accessibility | Infrastructure | 1990–1996 |

Holl, A. [13] | Road network | National (Spain) | Average distance to nearest highway; potential accessibility | Infrastructure | 1980/2000 |

López, E., J. Gutiérrez, and G. Gómez [14] | Road and rail network | National (Spain) | Weighted average of travel time; Potential indicator; Efficiency Indicator | Infrastructure | 1992/2004 |

Kotavaara O., H. Antikainen, J. Rusanen [16] | Road and rail network | National (Finland) | Distance to the nearest station; potential accessibility | Infrastructure | 1970/2007 |

Monzón, A., E. Ortega, and E. López [15] | High speed rail | National (Spain) | Potential accessibility | Infrastructure | 2005/2020 |

Condeço-Melhorado, A., J. Gutiérrez and J.C.García-Palomares [17] | Road | National (Spain) with spatial spillovers | Potential accessibility | Infrastructure (road charging) | 2005 |

Gutiérrez, J., A. Condeço-Melhorado, and J. C. Martín [19] | Road | National (Spain) with spatial spillovers | Potential accessibility | Infrastructure | 2005/2020 |

López, E., A. Monzón, E. Ortega, and S. Mancebo [20] | Road and rail network | National (Spain) with spatial spillovers | Efficiency Indicator | Infrastructure | 2005–2020 |

Geurs, K. and, J. R., Ritsema van Eck [18] | Road | National (Netherlands) | Potential accessibility | Infrastructure, land-use and combined effect | 1995/2020 |

Spence, N., and B. Linneker [10] | Road | National (UK) | Potential accessibility | Infrastructure, land-use and combined effect | 1971/1976/1989 |

Koopmans, C., P. Rietveld, and A. Huijg [21] | Rail | National (Netherlands) | Potential accessibility | Combined effect | 1840–1930 |

Axhausen, K. W., P. Froelich, M. Tschopp [22] | Road/Rail | National (Switzerland) | Potential accessibility | combined effect of Infrastructure and land-use | 1850–2000 |

Only a few studies evaluate both the contribution of transport and land use dimensions to accessibility levels. Spence and Linneker provide one of the first attempts to analyse the evolution of motorways and changing levels of employment on accessibility in Great Britain [10]. Using a standard market potential indicator, these authors show a positive effect of motorways on accessibility levels and some negative impacts due to decentralization of employment, mainly in London and the cities surrounding it.

For the Netherlands, Geurs and Ritsema van Eck, study the effect of transport infrastructure (further subdivided into changes in infrastructure and changes in congestion) and the land use component (measured as the number of jobs), as well as impacts from the interaction of both components [18]. Authors found a higher overall accessibility increase due to changes in employment levels, a lower positive contribution of infrastructure expansion and a negative contribution of the congestion and interaction components.

At a metropolitan level, an interesting study decomposes accessibility into speed and proximity effects for several pairs of US metropolitan regions, [6]. In overall terms, authors show a positive relationship between area density and accessibility, given the greater weight of origin-destination proximity. They have also shown that increasing urban density improves the number of jobs and services 10 times more than a proportional change in travel speed.

Some studies look at longer periods of time, individualizing the contribution of population and/or transport infrastructure change to accessibility ([21, 22]). However, depending on the study’s objective, the separate contribution from accessibility components is omitted.

Despite attempts in the literature to draw conclusions on the contribution of different accessibility dimensions to the overall variation of accessibility levels, the use of different methodologies and case studies make them difficult to compare. In this study we use index number theory to define and decompose accessibility variation into mutually exclusive transport infrastructure and land-use components ([23, 24]). Specifically, we define a productivity index that relates the infrastructure component to land-use, where the latter can be consistently used to recover the former by means of the product rule (and vice versa).

One of the main advantages of analysing accessibility levels and its determinants using index number theory is that this type of approach allows comparability with other studies that may use the same methodology in other places and times. In addition, we improve the methodology to accurately measure the change in accessibility and provide a consistent decomposition of these changes, which allows us to draw conclusions on the precise effects of transport infrastructure and population determinants.

Zofío, J. L. et al. have applied this methodology to study the drivers of generalized transport cost evolution, basically economic costs and infrastructure [25] although as far as we know, this is the first time basic index number theory has been used to estimate the relative contribution of different accessibility components, namely, transport infrastructure and land use dimensions.

Another contribution from this study is the use of historical data to measure the contribution from these two components to accessibility change, covering a long time period (50 years) and providing outcomes for every decade within this period.

## 3 Data

To calculate accessibility changes in Spain, we use Eurostat population data for the 47 Spanish NUTS 3 regions (islands are excluded), representing 1960, 1970, 1980, 1990, 2000 and 2010. NUTS 3 regions are represented by their centroids (the regional central point) for distance matrix calculations, while NUTS 3 boundaries are used to represent accessibility changes in maps. NUTS 3 regions seemed the most appropriate level of analysis given the relatively low spatial detail of the road network (presented below), while the use of more disaggregated units (i.e., NUTS 5) would require a set of assumptions on how those regional units connect with road links.

The road network is the most extensive transport infrastructure and also the most used transport mode (90% modal share for passenger transport in 2012 and 84% of freight transport, [26]).

Change of road length, by road class

Road class | Travel speed (Km/h) | 1960 | 1970–1960 | 1980–1970 | 1990–1980 | 2000–1990 | 2010–2000 | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Km | ΔKm | Δ% | ΔKm | Δ% | ΔKm | Δ% | ΔKm | Δ% | ΔKm | Δ% | ||

Highway | 120 | 0 | 200 | 20,000 | 2049 | 1024 | 2259 | 100 | 3815 | 84 | 5745 | 69.03 |

Main roads | 90 | 20,545 | -68 | -0.33 | -248 | -1.21 | -1928 | -9.53 | -2588 | -14 | -3382 | -21.52 |

Second. roads | 70 | 19,919 | -5 | -0.03 | -665 | -3.34 | -211 | -1.10 | -501 | -2.63 | -1446 | -7.80 |

Despite the potential drawbacks of the aforementioned networks, including the low level of detail mentioned at the beginning of this section, this is the only dataset that covers such a long period of time. The Spanish highways started during the 60s around Madrid, Barcelona and Galicia. In the following decade, the corridors linking Catalonia with the Basque Country and the Mediterranean corridor, connecting Catalonia with Valencia were built. In 1990, many radial highways linking Madrid with the remaining provincial capitals were already in place, and this radial system of highways was fully completed by 2000. In the following decade, there was an attempt to connect provincial capitals, resulting in a more meshed configuration of high capacity roads.

Table 2 shows the evolution of the Spanish road network between 1960 and 2010, according to our set of digital networks. Highways evolved from 0 km in 1960 to almost 5700 km in 2010, while main and secondary roads have declined in terms of length. The decrease in length of these types of roads is mainly due to a common assumption considering that they are upgraded to highways when new lanes run parallel to existing roads.

## 4 Methods

### 4.1 Measuring accessibility

*j*= 1,...,

*i*, …,

*n*, locations, the potential accessibility indicator of a particular location

*i*has the following general form:

where:

- \( {M}_j^t \)
represents the economic opportunity (mass) of each

*j*= 1,...*n*locations in period*t*;- \( f\left({t}_{ij}^t\right) \)
is a function reflecting the distance decay (travel time) between locations in period

*t*; and finally,- \( {A}_i^{t, t} \)
is the indicator of accessibility of location

*i*to all its*n*counterparts—including itself, defined as the sum of the ratios of the two previous expressions, and where time superscripts refer to the reference periods of the economic opportunities and access costs.^{1}

The accessibility indicator measures access to opportunities at destinations in which smaller and more distant (costly) opportunities provide diminishing influence. In this sense, it correctly replicates some aspects of accessibility valued by individuals such as distance and the socio-economic importance of destinations.

This ratio can be understood as an efficiency or productivity index where infrastructure (in this case through travel time) yields access to markets, defined in terms of socio-economic potential. Indeed, according to Eq. 1, for a population living in location *i*, the importance of access to each destination *j* is represented by a function that is directly related to *j*’s economic weight (mass, *M*) and is inversely related to the access time through *f*(*t*) between *i* and *j*. In this study the economic weight (*M*) is represented by population, and the origin and destination locations are represented by the centroids of the NUTS 3 regions.

*i*and

*j*is formulated as:

and *D*^{t}_{ii} is the internal distance of NUTS 3 region, in squared kilometres, X is a transformation of the regional radius equal to 0.33. Internal tavel time is obtained, assuming an internal travel speed of 50 km/h. Internal travel distances are important in accessibility analysis that use the potential indicator, since they determine the contribution of self-potential that is the weight of internal market in the overall accessibility level. Equation 3 has the advantage of requiring very little data and it is easy to calculate. This explains why it is used throughout the accessibility analysis, especially when there is a lack of data on mobility patterns or in the level of network detail [30] as in our case. This measurement estimates internal travel time comparing the region to a circle of equivalent area and assuming that population is concentrated towards the regional centre.

### 4.2 Decomposing the accessibility variation: productivity indices

*A*

_{i}

^{t,t+1}) between a base period

*t*= 0 and the current period

*t*+ 1 = 1 (see also [24, 31, 33] for general references). Specifically:

where Δ*A*_{i}^{0,1} measures the variation in accessibility as the ratio of the indicators corresponding to the reference period\( \kern0.5em {A}_i^{1,1} \)\( ={\sum}_{j=1}^n{M}_j^1/{t}_{ij}^1 \) to that of the base period \( {\ A}_i^{0,0} \)=\( {\sum}_{j=1}^n{M}_j^0/{t}_{ij}^0 \) . This index contains information relating to the change in both accessibility components: land-use (population) and infrastructure (time), referred to alternative time periods *t* according to the superscripts. In order to disentangle the individual contribution of these components to the overall accessibility change, we make use of a productivity index that consider the change in population *M*^{t}_{j}, and its counterpart index representing the change in optimal travel time *t*^{t}_{ij}.

*t*= 0 as the benchmark yielding market accessibility:

where the denominator corresponds to Eq. 4, but the numerator reflects a *hypothetical* accessibility value \( {A}_i^{1,0} \) that considers current period population and the base year road network—with the superscript 0 in \( {PA}_i^0 \) referring to the constant base (time) benchmark. If \( {PA}_i^0 \) > 1 it means increasing accessibility change due to population variation, while the opposite is true for \( {PA}_i^0 \) < 1.

^{2}In particular, it can be solved for in the following way:

Equation 7 renders the infrastructure index explicit but on this occasion considering the current period population as the reference constant:\( {A}_i^{1,1} \) and \( {A}_i^{1,0} \)—hence the superscript in \( {IA}_i^1 \), and updating the road network for consecutive periods. \( {IA}_i^{1\ } \) reflects the aggregate increase of accessibility brought about by changes in transport infrastructure, and therefore it is normally expected that \( {IA}_i^1 \) > 1, showing that improvements in transport networks will lead to an increase of accessibility levels by reducing travelling times.^{3}

We now define analogous indices to Eqs. 5 and 7 reversing the reference current and base periods for the network infrastructure and population levels, respectively. In this case, we define \( {PA}_i^1={A}_i^{1,1}/{A}_i^{0,1}=\left({\sum}_{j=1}^n{M}_j^1/{t}_{i j}^1\right)/\left({\sum}_{j=1}^n{M}_j^0/{t}_{i j}^1\right) \), with the same interpretation as Eq. 5, but on this occasion the optimal (minimum time) itineraries remain constant in the current period. Similarly the counterpart decomposition to Eq. 6 is \( {\Delta A}_i^{0,1}={A}_i^{1,1}/{A}_i^{0,0}={PA}_i^1\bullet {IA}_i^0=\left({A}_i^{1,1}/{A}_i^{0,1}\right)\cdotp {IA}_i^0 \), allowing us to recover the corresponding implicit input infrastructure index that uses the population levels observed in the reference period, thereby obtaining \( {IA}_i^0={\Delta A}_i^{0,1}/{PA}_i^1=\left({A}_i^{1,1}/{A}_i^{0,0}\right)/\left({A}_i^{1,1}/{A}_i^{0,1}\right)={A}_i^{0,1}/{A}_i^{0,0}=\left({\sum}_{j=1}^n{M}_j^0/{t}_{i j}^1\right)/\left({\sum}_{j=1}^n{M}_j^0/{t}_{i j}^0\right) \).

*t*of the output population and input infrastructure indices: \( {PA}_i^t \) and \( {IA}_i^t \),

*t*= 0, 1. Indeed, depending on the selected reference period, we would generally obtain alternative values for the different accessibility terms of the population and infrastructure measures. This suggests the following geometric mean decomposition taking both periods into account symmetrically:

*t*= 0, 1, 2, it is verified that \( {\Delta A}_i^{0,2}={\Delta A}_i^{0,1}\cdotp \Delta {A}_i^{1,2} \). Focusing on the initial definition in Eq. 4 and the decomposition presented in Eq. 8, we see that for a general sequence of

*T*periods,

*t = 0,…T*, it is possible to decompose the variation in accessibility between the first and last periods into any subperiods using any of the available alternatives:

*t*and the final year

*T*by dividing the fixed base indices corresponding to those periods; i.e.

*t*and

*t + k*, whose particular definition is (

*k*= 1 would yield year by year variations):

## 5 Results

This section shows the variation of accessibility levels for the 1960–2010 period and it presents the results of decomposing the accessibility variation into population and infrastructure contributions.

*PA*

_{i}

^{0,t}) and infrastructure (Δ

*IA*

_{i}

^{0,t}). Values are expressed as the arithmetic mean of all provinces (47 NUTS-3). For the overall period between 1960 and 2010, about two thirds of the accessibility increase is due to population change (50.0% out of 78.1%).

^{4}The remainder is due to changes in transport infrastructure. Regarding the accumulated change in accessibility and its population and infrastructure components in ten year periods, we can see that the increase in accessibility driven by population and infrastructure is monotonic, as it increases constantly in a cumulative way.

Decomposition of the fixed base \( \Delta {A}_i^{0, t} \) into population \( \Delta {PA}_i^{0, t} \) and infrastructure \( \Delta {IA}_i^{0, t} \)components

Fixed based indices | Percentage variation (%) | |||||
---|---|---|---|---|---|---|

Δ | Δ | Δ | Δ | Δ | Δ | |

70/60 | 1.12 | 1.12 | 1.00 | 11.78 | 11.51 | 0.23 |

80/60 | 1.29 | 1.23 | 1.05 | 29.42 | 23.14 | 4.98 |

90/60 | 1.38 | 1.27 | 1.09 | 37.91 | 26.71 | 8.73 |

00/60 | 1.50 | 1.31 | 1.14 | 49.88 | 30.85 | 14.50 |

10/60 | 1.78 | 1.50 | 1.19 | 78.10 | 50.08 | 18.72 |

It is worth noting that some regions register a positive contribution of population in their accessibility levels, despite the decline of their population. This happens because regional accessibility levels take into account not only the population within the regional boundaries but also the population of all other regions. Thus, a region that experiences population decline in a specific period can still benefit from positive population changes occurring elsewhere, especially if these changes are registered in nearby places (given the gravity formulation of Eq. 1).

Decomposition of interannual Δ*A*_{i}^{t,t+k} into population and infrastructure components

Interannual indices | Percentage variation (%) | |||||
---|---|---|---|---|---|---|

Δ | Δ | Δ | Δ | Δ | Δ | |

70/60 | 1.12 | 1.12 | 1.00 | 11.78 | 11.51 | 0.23 |

80/70 | 1.16 | 1.10 | 1.05 | 15.79 | 10.43 | 4.73 |

90/80 | 1.07 | 1.03 | 1.04 | 6.56 | 2.90 | 3.57 |

00/90 | 1.09 | 1.03 | 1.05 | 8.68 | 3.27 | 5.31 |

10/00 | 1.19 | 1.15 | 1.04 | 18.83 | 14.69 | 3.68 |

For the period between 1980 and 1990 and 1990–2000, accessibility changes were lower due to a modest population increase, especially in most accessible Spanish provinces. On the other hand, during this period the contribution from transport infrastructure outweighs the contribution from population and partly compensates the negative population growth in provinces such as Orense and Vizcaya. If we compare the interannual infrastructure contribution with the number of kilometres constructed in every decade (Table 2), we can conclude that the highest contributions do not fully correspond with the highest investment periods. Instead, transport infrastructure has had the highest impacts in years of network structural changes, such as 1970–1980 when the radial system of highways started to emerge, and during 1990–2000 when this radial structure led to a denser configuration of highways.

## 6 Conclusions

Historical data on population and transport infrastructure enables the analysis of accessibility change over time, while the computation of its separate infrastructure and land use components offers a much richer explanation concerning the drivers of accessibility improvements. Index number theory has proven very useful to consistently disentangle these components of accessibility change at a regional level.

When applying this methodology for Spain, our results show that changes in transport infrastructure have helped to increase accessibility, although to a lesser degree than demographic changes. In practical terms, this is the result of transport infrastructure developments following the actual needs of land use and economic activity during most of the period being analysed, as opposed to being used as an instrument to stimulate growth in less developed zones. The findings for Spain are generally consistent with the results reported in the literature, summarized in section 2.

The results suggest that while transport infrastructure can have a long term regional development dimension, policy makers give priority to short-term maximisation of the positive impacts of increasing accessibility. Transport networks linking the main centres of population and economic activity—mainly Madrid and Barcelona in the case of Spain—usually follow radial patterns, which are normally the most efficient solutions in terms of return on investment. The alternative strategy of improving access for areas that lack opportunities would lead to a more equitable evolution of accessibility, but would be far less efficient in economic terms, at least in the short term. For most countries that are in an important spatial redistribution phase (like Spain during the period), the temptation to concentrate on the short term effects is difficult to avoid. Such investment decisions, however, also lead to a vicious circle: improving the accessibility of the central zones draws new activities to these zones, reinforcing their central role, their attractiveness for additional future investments, and resulting in core-periphery patterns.

It is also clear that priorities, choices and impacts change over time, depending on the level of development already achieved. The returns on improving transport infrastructure in the most accessible regions begin to diminish after reaching a certain point of development. For Spain, given the already high connectivity of Madrid and Barcelona with other locations, increasing their accessibility even more would come at a high cost. The political pressure to invest in less developed regions also increases over time, changing the balance between economic and equity considerations in investment decisions.

Our results show that the highest impact of transport infrastructure on accessibility changes does not correspond to the years of greatest network extension, but with years when the network changes structurally. This is particularly due to the development of a radial system of highways, with Madrid as the central point and subsequently, due to the construction of a denser, better connected highway system.

As a general conclusion, the approach and results presented here add to the discussion on the need to integrate transport and land use planning. Our results suggest that the goal to improve accessibility can be better achieved by combining social-economic policies with transport investment decisions.

They also provide evidence on the impacts of improving transport networks and their relative weight compared to the impacts of population change for a 50 year period. This allows an ex-post evaluation of the impact of transport infrastructure policies and the quantification of the role of infrastructure and land-use changes in the evolution of accessibility. While the approach can certainly be useful for transport policy in different contexts, it should be kept in mind that the results refer to a specific country (Spain) and a single mode of transport (road). Second order effects, such as congestion, have not been taken into account but may be relevant for other geographic areas.

## Footnotes

- 1.
As distance is actually measured in terms of network travel time, we have decided to adopt

*t*to denote distance, which should not be confused with the time superscripts referring to the year in which variables are referred. - 2.
While the proposed decomposition of accessibility change is multiplicative in nature and only differentiates between the land-use and infrastructure components, other studies adopt an additive decomposition that results in a third term capturing the interaction or combination effect between the two [18]. This latter component represents the change in accessibility that cannot be solely ascribed to the land use or infrastructure components. This interaction does not emerge in our approach as it allocates accessibility change into the land use (population) and travel time change (infrastructure) components; i.e., the index number methodology results in an exact decomposition that fully exhausts accessibility change into these two mutually exclusive terms.

- 3.
Indeed, \( {IA}_i^1 \) corresponds to the inverse of the change in time access, thereby contributing to productivity increases with values greater than 1. This can be shown by resorting to the single bilateral relationship between origin

*i*and a specific destination*j*(hence the*ij*subscript notation). In this case\( {IA}_i^1={\varDelta A}_i^{0,1}/{PA}_i^0=\frac{A_i^{1,1}}{A_i^{0,0}}/\frac{A_i^{1,0}}{A_i^{0,0}} = \frac{M_j^1/{t}_{i j}^1}{M_j^0/{t}_{i j}^0}/\frac{M_j^1/{t}_{i j}^0}{M_j^0/{t}_{i j}^0}=\frac{A_i^{1,1}}{A_i^{1,0}} = \frac{M_j^1/{t}_{i j}^1}{M_j^1/{t}_{i j}^0}=\frac{1}{{t_{i j}^1/ t}_{i j}^0} \),*i*= 1,…,*n*,*j*= 1,…,*n*. - 4.
A similar outcome is achieved using municipalities (LAU regions instead of NUTS3), where for the overall period between 1960 and 2010 we have registered \( \varDelta {A}_i \)

^{60,t}= 86.3%; \( \varDelta {PA}_i \)^{60,t}= 52.4%; \( \varDelta {IA}_i \)^{60,t}= 22.2. Additionally, we have performed a sensitivity analysis on the role of distance decay parameter and internal distances definition. It was found that accessibility variations slightly decrease with higher distance decay parameters and smaller internal travel distance specifications. However, differences are small and similar patterns are observed regarding the contribution of transport infrastructure and population change. Summary results of this sensitivity analysis can be seen in the Appendix.

### References

- 1.Levine J, Garb Y (2002) Congestion pricing’s conditional promise: promotion of accessibility or mobility? Transp Policy 9:179–188CrossRefGoogle Scholar
- 2.Department for Transport (2004) Guidance on accessibility planning in local transport plans. DfT, LondonGoogle Scholar
- 3.Litman T (2016) Evaluating accessibility for transportation planning. Victoria Transport Policy Institute, VictoriaGoogle Scholar
- 4.Litman T (2013) The new transportation planning paradigm. ITE J 83(6):20–28Google Scholar
- 5.Bertolini L, le Clercq F, Kapoen L (2005/5) Sustainable accessibility: a conceptual framework to integrate transport and land use plan-making. Two test-applications in the Netherlands and a reflection on the way forward. Transp Policy 12:207–220. doi: 10.1016/j.tranpol.2005.01.006
- 6.Levine J, Grengs J, Shen Q, Shen Q (2012) Does accessibility require density or speed? J Am Plan Assoc 78(2):157–172CrossRefGoogle Scholar
- 7.Fujita M, Krugman P, Venables AJ (1999) The spatial economy. Cities, regions and international trade. MIT Press, CambridgeMATHGoogle Scholar
- 8.Fernald JG (1999) “Roads to prosperity” assessing the link between public capital and productivity. Am Econ Rev 89:619–638CrossRefGoogle Scholar
- 9.Moreno R, Artís M, López-Baso E, Suriñach J (1997) Evidence on the complex link between infrastructure and regional growth. Int J Dev Plan Lit 12(1&2):81–108Google Scholar
- 10.Spence N, Linneker B (1994) Evolution of the motorway network and changing levels of accessibility in Great Britain. J Transp Geogr 2:247–264. doi:10.1016/0966-6923(94)90049-3 CrossRefGoogle Scholar
- 11.Geurs KT, van Wee B (2004) Accessibility evaluation of land-use and transport strategies: review and research directions. J Transp Geogr 12:127–140. doi:10.1016/j.jtrangeo.2003.10.005 CrossRefGoogle Scholar
- 12.Gutiérrez J, Gómez G (1999) The impact of orbital motorways on intra-metropolitan accessibility: the case of Madrid's M-40. J Transp Geogr 30:1–15CrossRefGoogle Scholar
- 13.Holl A (2007) Twenty years of accessibility improvements. The case of the Spanish motorway building programme. J Transp Geogr 15(4):286–297CrossRefGoogle Scholar
- 14.López E, Gutiérrez J, Gómez G (2008) Measuring regional cohesion effects of large-scale transport infrastructure investments: an accessibility approach. Eur Plan Stud 16:277–301CrossRefGoogle Scholar
- 15.Monzón A, Ortega E, López E (2013) Efficiency and spatial equity impacts of high-speed rail extensions in urban areas. Cities 30:18–30. doi:10.1016/j.cities.2011.11.002 CrossRefGoogle Scholar
- 16.Kotavaara O, Antikainen H, Rusanen J (2011) Population change and accessibility by road and rail networks: GIS and statistical approach to Finland 1970-2007. J Transp Geogr 19:926–935CrossRefGoogle Scholar
- 17.Condeço-Melhorado A, Gutiérrez J, García-Palomares JC (2011) Spatial impacts of road pricing: accessibility, regional spillovers and territorial cohesion. Transp Res A Policy Pract 45:185–203. doi:10.1016/j.tra.2010.12.003 CrossRefGoogle Scholar
- 18.Geurs K, van Ritsema Eck JR (2003) Evaluation of accessibility impacts of land-use scenarios: the implications of job competition, land-use, and infrastructure developments for the Netherlands. Environ Plann B Plann Des 30:69–87. doi:10.1068/b12940 CrossRefGoogle Scholar
- 19.Gutiérrez J, Condeço-Melhorado A, Martín JC (2010) Using accessibility indicators and GIS to assess spatial spillovers of transport infrastructure investment. J Transp Geogr 18:141–152. doi:10.1016/j.jtrangeo.2008.12.003 CrossRefGoogle Scholar
- 20.López E, Monzón A, Ortega E, Mancebo S (2009) Assessment of cross-border spillover effects of national transport infrastructure plans: an accessibility approach. Transp Rev 29:515–536CrossRefGoogle Scholar
- 21.Koopmans C, Rietveld P, Huijg A (2012) An accessibility approach to railways and municipal population growth, 1840–1930. J Transp Geogr 25:98–104. doi:10.1016/j.jtrangeo.2012.01.031 CrossRefGoogle Scholar
- 22.Axhausen KW, Froelich P, Tschopp M (2011) Changes in Swiss accessibility since 1850. Res Transp Econ 31(1):72–80CrossRefGoogle Scholar
- 23.Fisher I (1922) The making of index numbers. Houghton-Mifflin, BostonGoogle Scholar
- 24.Diewert EW (1992) Fisher ideal output, input, and productivity indices revisited. J Prod Anal 3:211–248. doi:10.1007/bf00158354 CrossRefGoogle Scholar
- 25.Zofío JL, Condeço-Melhorado A, Maroto-Sánchez A, Gutiérrez J (2014) Generalized transport costs and index numbers: a geographical analysis of economic and infrastructure fundamentals. Transp Res A Policy Pract 67:141–157. doi:10.1016/j.tra.2014.06.009 CrossRefGoogle Scholar
- 26.MFOM (2014) Los transportes, las infraestructuras y los servicios postales en España: Informe Anual 2013. Ministerio de Fomento, MadridGoogle Scholar
- 27.Stelder D, Groote P, de Bakker M (2013) Changes in road infrastructure and accessibility in Europe since 1960. Tender reference nr 20112 CE.16.BAT.040. Final ReportGoogle Scholar
- 28.Hansen WG (1959) How accessibility shapes land-use. J Am Inst Plann 25:73–76. doi:10.1080/01944365908978307 CrossRefGoogle Scholar
- 29.Rich D (1980) Potential models in human geography. Norwich, Report Number, 26Google Scholar
- 30.Condeço-Melhorado AM, Demirel H, Kompil M, Navajas E, Christidis P (2016) The impact of measuring internal travel distances on self-potentials and accessibility. Eur J Transp Infrastruct Res 16(2):300–318Google Scholar
- 31.Konüs AA (1924) The problem of the true index of the cost of living. Transp Econ 7(1939):10–29Google Scholar
- 32.Maroto A, Zofío JL (2016) Accessibility gains and transport infrastructure in Spain: a productivity approach based on the Malmquist index. J Transp Geogr 52:43–152. doi:10.1016/j.jtrangeo.2016.03.008 CrossRefGoogle Scholar
- 33.Balk B (1998) Industrial price, quantity, and productivity indices. Springer, New YorkCrossRefGoogle Scholar

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