Student: Camilo Santa Cruz
E-mail:
Msc. Econometrics
Quantitative Regional Economics Seminar
Winter semester 2022/2023

1. Introduction

The main purpose of this paper is to verify whether the differences in wealth (measured as the GDP ar per capita and per worker level) between the German counties can be partially explained by both the provision of transport infrastructure and the accessibility to means of transport, controlling in turn for other variables that are associated with economic progress such as such as occupation levels, capital formation and human capital.

In the first instance, the theoretical elements that support the importance of transport infrastructure when it comes to understanding the asymmetries in wealth levels between different economies are exposed. In a second moment, some studies are mentioned that have proven the incidence that transport infrastructure has on economic growth, the methodological approaches addressed and the estimated coefficients. In a third place, the methodology is traced, which consists both in the application of an OLS with cross-sectional data and the application of different specifications that contain spatial coefficients. In a fourth instance, the different results that show a positive incidence between transport infrastructure and economic growth are exhibited.

This study closes with the main conclusions and recommendations, as well as the unknowns that arise from the findings.

2. Theoretical framework

At a theoretical level, there are vast academic contributions that expose an adequate framework that allows us to understand the mechanisms through which the transport infrastructure affects economic development. This section introduces at first what is meant by the provision of transport infrastructure and the measures that are counted for it. In a second instance, the mechanisms through which the transport infrastructure affects economic performance are exposed. A summary of it is provided below.

2.1 Transport infrastructure measures

According to Ferrari et al. (2018), transportation systems are the backbone of the global economy and its infrastructure, under certain conditions, contributes to the economy. In order to measure this impact, a series of measures are needed to allow accounting for the transport infrastructure endowments that a society has. These can be synthesized in physical and quantitative measures, qualitative measures and accessibility measures.

Quantitative measures considering the physical length of different routes (for example the length of highways). In the case of transport terminals, their quantity is counted in terms of capacity, for example passenger flow or merchandise movement. Likewise, in order to carry out comparative analyses, it is often transcendental to add coefficients that allow quality control of the transport infrastructure. For this, the most advanced part of the transport network is usually used (for example, the high-speed train network or the high-speed road network).

A third measure used to measure infrastructure endowment is accessibility measures. These allow interpreting the possibility offered to people and companies to access a certain type of infrastructure in a specific time, distance and/or cost.

2.2 Effect of transport infrastructure over economic growth

The literature that recognizes the importance of transport infrastructure in economic growth is of great diversity. For example, The Infrastructure Economics Center (IEC) (2020) emphasizes that it is difficult not to overestimate the impact that transport infrastructure has on economic growth and the well-being of the population, to the extent that transport makes it possible to move people and goods, creating an economic space unique. This translates into expansion of labor markets and goods markets, creating economic agglomeration and economies of scale. Along the same lines, the Center for Economic and Business Research (CEBR) (2016) affirms that transport infrastructure unites regions, making the workforce more mobile and flexible, increasing the probability of accessing education and jobs, reducing the costs of companies looking for employees. It also broadens the market for firms.

The OECD (2020), for its part, states that investment in transport infrastructure has an impact on economic growth through different channels. It facilitates the exchange of goods, reducing trade costs and enabling regions to specialize in their competitive advantages. Likewise, the positive aspects of the transport infrastructure in the economic agglomeration for both workers and firms, such as knowledge overflows and increases in factor productivity, are emphasized.

Hong et al. (2011) add that investment in road infrastructure puts pressure on the demand for goods and services at first, when carrying out the construction of the infrastructure. It also adds in a complementary way to the other theoretical contributions that a better transport infrastructure attracts FDI, which is a key engine for exporting economies.

3. Methodological framework

To measure the positive effects that transport infrastructure has on economic growth, there are different methodological approaches such as cost-benefit analysis (before and after), economic impact analysis, for example on the level of production, the creation of new works and multi-criteria analyzes that also incorporate qualitative measurements. (IEC) (2020). Likewise, there are different models with which the variation in conditions can be measured in response to changes in the quantity or quality of transport infrastructure, such as input-output models, LUTI models, Computable General Equilibrium models, and econometric approaches.

In this study we propose to carry out an econometric validation under the production function approach. This method, according to Gaus and Link (2020), despite being strongly criticized, continues to be the most widely used methodology for identifying the effects of public transport capital on economic performance. Below are some econometric studies and the approaches used to measure the effects of transport infrastructure on some indicator of economic performance.

Andreas (1997) elaborates a growth function for the manufacturing sector that incorporates road capital, focused on the 11 states of Germany. In such a Cobb-Douglas type specification: \[\begin{align}Q=A\left(t\right){\ G\ }^{\beta_G}{K\ }^{\beta_k}L^{\beta_L}\end{align}\] he determines an elasticity of 0.73 of road infrastructure on manufacturing production, of 12% of capital and 0.81% of labor: ln (Manufacturing GDP) = 0.012A + 0.734 ln (g) + 0.119 ln (K) +0.809 ln(L). This estimate breaks with the paradigm of constant returns to scale and solidifies his argument that road infrastructure acts as a catalyst for the economy in a similar way to technological variations.

Barzin et al. (2018) build a pseudo-panel to verify whether the development of road infrastructure in each Colombian region is associated with economic growth rates at the firm level. They use an extended Cobb-Douglas production function: \[\begin{align}{GDP}_{it} = K_{it}^{\beta_{kt}}L_{it}^{\beta_{lt}}E_{it}^{\beta_{Et}}M_{it}^{M_{Et}}H_{rt}^{H_t}e^{\varepsilon_{it}}\end{align}\] in which they add the use of energy E, the use of raw materials (M) and road capital (H), and use contemporary and lagged variables, contemplating that public infrastructure takes a period to affect private productive performance.

In this estimate, they obtain an elasticity of the road infrastructure generated in the previous period of 0.156, but not an instantaneous significant relationship. Likewise, they emphasize that the elasticity found is greater than others since the incidence of infrastructure on growth is assumed to be greater in developing countries, as mentioned by CEBR (2016).

Vlahinic et al. (2018), for their part, build a panel for the period 1995-2016, in which they evaluate the incidence of investment in transport infrastructure (train and road) on GDP for the member countries of the European Union. From said study, it stands out that they do not use a growth function as such, but rather control variables such as commercial openness, population, presented as follows:

\[\begin{align}GDP_{it} = \beta_0 + \beta_1N + \beta_2FBKF + \beta_3AC + \beta_4 Itrains + \beta_5IV+ \lambda_t + a_i + u_{it} \end{align}\]

With: N = population, FBKF = Capital investment, AC = commercial opening, Itrains = train infrastructure and IV: Road infrastructure and:\[\begin{align}\lambda_t\ =\ temporary\ unobservable\ effects; a_i=invariant\ individual\ effects; u_{it}=remanent.\end{align}\]. In said study, they do not estimate an elasticity but rather a magnitude at the level in which they find that a variation of 1 km of road corresponds to an increase of 14.5 thousand euros. They don´t detect a positive impact of rail infrastructure over the economic growth.

Gaus y Link (2020) for its part build a production function with spatial effects, in which they try to verify the incidence of the quantity and quality of road infrastructure on economic growth. The authors detect a significant contribution of the road infrastructure on economic growth within the regions as well as the neighboring regions. They do not find a positive effect of quality and add that for the latter, more research is needed to the extent that the negative effect detected is not theoretically justifiable.

\[\begin{align}ln(Y_{it}) + ln(A_{it})\beta_1\ + ln(K_{it})\beta_2\ + ln(L_{it})\beta_3\ + ln(H_{it})\beta_4\ \end{align}\]

\[\begin{align}+ 0.5ln(KL_{it})^2\beta_5\ + 0.4ln(L_{it})^2\beta_6\ + 0.5ln(H_{it})^2\beta_7\ + ln(K_{it})ln(L_{it})^2\beta_8\ \end{align}\]

\[\begin{align}+ ln(H_{it})ln(L_it)\beta_9\ + ln(K_{it})ln(H_it)\beta_10_{it} \end{align}\]

\[\begin{align}A = A\ (G,C) = (A_0\ast\ (G^\gamma_1)\ \ast\ (C^\gamma_2\ ))\end{align}\]

\[\begin{align}ln (A) = \gamma_1\ ln(G) + \gamma_2\ ln(C) \end{align}\]

And accounting for spatial effects: \[\begin{align}ln (A) = \gamma_1\ ln(WG) + \gamma_2\ ln(WC) \end{align}\]

4. Methodology

For the present investigation, we start from a methodological approach of the Cobb-Douglas type of production function, which incorporates, in addition to the traditional productive factors (capital and work), the stock of transportation capital, the human capital, accessibility to means of transport (airports, highways and train stations). In other words, the present work incorporates both length variables (transport infrastructure stock), as well as accessibility measures, in accordance with the framework provided by Ferrari et al. (2018). The variables are extracted from the INKAR.DE (2022) database. Below is a brief mention of the variables used and what exactly these indicators measure.

4.1. Description of the Variables

4.1.1. Bruttoinlandsprodukt in 1.000 € je Einwohner

As a measure of the economic performance of the districts, the Gross Domestic Product per inhabitant and per employed person is used. This is calculated by subtracting the inputs used in production (raw materials, auxiliary materials and supplies, rents and leases, costs for wage work carried out by other companies, etc.) from the value of all goods and services produced.

The GVA is valued at basic prices. This valuation concept means that the product subsidies granted on the goods and services produced or sold are included, but not the product taxes payable on the goods and services produced (VAT, import duties, mineral oil and tobacco tax, etc.). GDP is valued at market prices.

4.1.2 Unemployment rate

To measure the degree of employment or unemployment of each territorial unit, the unemployment rate and the employment rate are used. According to INKAR (2022), the unemployment rate shows the relative underutilization of the labor supply. It is a key measure of an unbalanced regional labor market. However, the development of the unemployment rate over time shows only limited structural problems in the regional labor market; this requires further information from the labor market.

The merging of unemployment and social assistance benefits as part of the labor market reforms in 2005 initially contributed to the increase in the unemployment rate. The subsequent decline is then more likely to be due to a slowdown in productivity development, the increase in atypical employment relationships, the distribution of the volume of work among more people and declining labor reserves. There are different variants for the reference variable (denominator); here, all civilian labor force is chosen as a reference value.

Mathematically, unemployment is expressed as the number of unemployed people out of the total labor force:

\[\begin{align}Unemployment\ rate\ =\ \frac{U_t}{L_t}\ast100 \end{align}\]

4.1.3 Human Capital

4.1.3.1 Students at technical institutions

To approximate the human capital and therefore, the stock of knowledge that each district has, the number of students at scientific universities and technical colleges per 1000 inhabitants is used. This measure approximates the accumulation of potentially qualified workers highly qualified workers trained in the region.

According to Inkar (2022), the Universities of applied sciences are also of particular importance here due to their practical relevance and their diverse relationships with regional economic actors. All universities recognized under state law, regardless of the sponsorship, are identified as universities.

Per student, it is considered people who are matriculated/enrolled in a subject, not including those on leave, guest auditors and preparatory college students. The number of students refers to the winter semester. With regard to the population, it should be noted that the figures before 2011 refer to the update based on the 1987 (FRG) and 1981 (GDR) census and from 2011 onwards to the update based on the 2011 census. The updating of the federal and state population figures are as of December 31st. of the year.

4.1.3.2 Employees with an academic professional qualification

Measured as the percentage of SV employees at the place of work with an academic degree (including bachelor’s, diploma, master’s, master’s, state examination, doctorate) according to the 2010 classification of occupations (KldB 2010). Employees subject to social security contributions are workers, employees and people in vocational training who are compulsorily insured in the statutory pension, health and/or unemployment insurance. Civil servants, the self-employed, helping family members or part-time employees are not taken into account here. Overall, only around 75% of all employees are recorded in this way. Despite this restriction, employees subject to social security contributions are used as a measure of the number of jobs available on the labor market. The employees are figures as of June 30th.

This indicator is expressed with the following formula: \[\begin{align}Students=\ \frac{S_t}{N_t}\ast100\end{align}\]

With N = Population.

4.1.4 Transport capital (Anteil der Siedlungs- und Verkehrsfläche an der Fläche in %)

To measure the stock of transportation infrastructure that each district has, the relative weight of transportation and settlement infrastructure over the total magnitude of the district area is used as a proxy measure. That is, the (Percentage of settlement and traffic areas in the area in %)

The indicator states the proportion of the area that is used for settlement purposes. Settlement and traffic areas are not to be equated with sealed areas. Settlement area includes the types of use residential building area, industrial and commercial area, public facilities as well as recreational area and cemeteries, minus the areas for mining operations and opencast mining (so-called mining land).

The traffic area is made up of the four subtypes of road and footpath traffic, rail traffic, air traffic and ship traffic. Accordingly, the indicator does not only refer to the sealed area, but also includes undeveloped and non-sealed areas such as house gardens, parks, green spaces, roadside greenery, etc. Percentage values of the area always depend on the (administrative) layout of the area unit. The areas are reported by the statistics in ha. From 2016, the survey is based on the official real estate cadastre information system (ALKIS), before 2016 on an evaluation of the real estate cadastre, most recently the automated real estate register (ALB). Due to the change in the basis for recording, the comparability of the data from 2016 with the previous years is significantly restricted for methodological reasons.

\[\begin{align}Transport Capital=\ \frac{Siedlungs\ und\ Verkehrsfläche}{Fläche}\ast100\end{align}\]

To measure the ease of the population with different means of transport, accessibility to:

highways, train stations and airports.

4.1.5 Accessibility to highways

’It is the area-weighted average value of car travel times to the next federal motorway junction. The accessibility calculations for motorized private transport are based on route searches in a road network model. The car speeds used as a basis for road types are determined depending on the development status as well as settlement structure and topographical conditions.

Car travel time to the next BAB junction in minutes

avg Driving time to the next BAB junction in minutes

4.1.6 Accessibility from airports

To measure accessibility to the airport, the average time required to reach the nearest commercial airport is used. The accessibility calculations for motorized private transport are based on route searches in a road network model. The car speeds used as a basis for road types are determined depending on the development status as well as settlement structure and topographical conditions.

4.1.7 Accessibility from IC/EC/ICE train stations

Similarly, accessibility to train stations is calculated using the average time required to reach a station for this type of means of transport. The selected stations are all DB AG IC, EC and ICE system stops, even those that are only served by individual trains. The accessibility calculations for motorized private transport are based on route searches in a road network model. The car speeds used as a basis for road types are determined depending on the development status as well as settlement structure and topographical conditions.

4.1.8 Stock of Capital

Lacking a measure of investment in infrastructure and machinery, the relative weight occupied by the secondary sector in the composition of GDP is used as a proxy measure of the capital stock.The secondary sector includes manufacturing, including construction and mining.

\[\begin{align}Capital=\ \frac{Gross\ value\-added\ secondary\ sector}{GAV}\ast100\end{align}\]

4.2 OLS econometric specification

The economic growth of each district is formulated based on the unemployment rate, the relative weight of the secondary sector in added value, transportation infrastructure, accessibility to the airport, highways, and train stations.

Likewise, two alternative variables of human capital are used. First, the number of university students as a proxy measure of the knowledge developed by each county. Second, the relative participation of workers with a university degree within the total employed as a proxy for how knowledge-intensive the county’s economy is and, therefore, how much it requires highly qualified human capital.

\[\begin{align}\ log(\frac{GDP}{L})\ =\ \beta_0+\beta_1\ log(\frac{O}{L})+\beta_2log(K)\ +\beta_3log(KT)\ +\beta_3log(AF)\ +\beta_4log(AAB)\ +\beta_4log(HK)\end{align}\]

\[\begin{align}\ log(\frac{GDP}{N})\ =\ \beta_0\ + \beta_1\ log(\frac{O}{L}) +\beta_2log(K)\ +\beta_3log(KT)\ +\beta_3log(AF)\ +\beta_4log(AAB)\ +\beta_4\log(HK) \end{align}\]

With:

\[\begin{align}\frac{GDP}{L} = Brutto\ Inlands\ Produkt\ in\ 1.000\ €\ je\ Einwohner\end{align}\]

\[\begin{align}\frac{GDP}{N}\ =\ Brutto\ Inlands\ Produkt\ in\ 1.000\ €\ je\ Einwohner\end{align}\]

\[\begin{align}\frac{O}{L}\ =\ Occupation\ rate = 100\ -\ \frac{U}{L}\end{align}\]

\[\begin{align}HK\ =\ Students\ at\ scientific\ universities\ and\ technical\ colleges\ per\ 1,000\ inhabitants\end{align}\]

\[\begin{align}HK1\ =\ Students\ at\ scientific\ universities\ and\ technical\ colleges\ per\ 1,000\ inhabitants\end{align}\]

\[\begin{align}AH:\ = Accessibility\ to\ highways\end{align}\]

\[\begin{align}KT:\ Settlement\ and\ traffic\ area\end{align}\]

\[\begin{align}AF:\ Accessibility\ to\ airports\end{align}\]

\[\begin{align}ATS:\ Accessibility\ to\ IC\ EC\ ICE\ train stations\end{align}\]

4.3 Spatial econometrics specification

4.3.1 Moran index

The Moran index, or Moran statistic, measures the linear relationship between the variable of interest and its spatially lagged values. Namely, \[\begin{align}corr(y, Wy)=\dfrac{Cov(y,Wy)}{\sqrt{Var(y)Var(Wy)}}\end{align}\]. According to this equation, we use the expression of the spatial lag. Also, we assume that under the assumption of stationarity (the same as stationary time series): \[\begin{align}Var(y)=Var(Wy)\end{align}\].

Therefore, this correlation coefficient is equal to: \[\begin{align}corr(y, Wy)= \dfrac{Cov(y, Wy)}{Var(y)}\end{align}\]. In empirical terms, the Moran index can be estimated as follows:

\[\begin{align}I= \dfrac{\sum_{i=1}^{n} \sum_{j=1}^n w_{ij}z_{i}z_{j}}{\sum_{i=1}^{n}z_{i}^{2}}\end{align}\].

Where n is the number of observations, z_i is the value of the variable for observation i, z_j is the value of the variable for observation j. so much z_i and z_j they are centered on the mean. Finally, w_ij is the ij element of the row-standardized spatial weight matrix.

In matrix terms, this formula can be expressed as follows: \[\begin{align}I=\dfrac{z^{T}W_z}{z^{T}z}\end{align}\].

where W is the row-standardized spatial weight matrix. As it can be seen, this index is the same as the estimates obtained through OLS. Therefore, the slope of the regression between the spatial lag of the variable under study (y) and the variable under study (x) is equal to the Moran index.

The Moran index is in the interval between [-1,1]. In this way, we can notice three situations: When the variable z is randomly distributed, the Moran index is close to 0. When the observed value of the Moran index is positive, it indicates the existence of positive autocorrelation. When the observed value of the Moran index is negative, it indicates the existence of negative autocorrelation.

\[\begin{align}H_{0}: \mbox{The observations are randomly distributed. There is no spatial autocorrelation}\end{align}\]

\[\begin{align}H_{1}: \mbox{There is spatial autocorrelation}\end{align}\]

4.3.2 Spatial specifications

\[\begin{align}y&=\beta_{0}+X_{1}\beta_{1}+\mu \\ \mu&=\lambda W \mu + \epsilon\end{align}\]

Where the dependent variable is a linear combination of the explanatory variables X and the spatial lag of the dependent variable. In this case, \(\rho\) measures the strength of the linear relationship between the dependent variable and its spatial lag.

\[\begin{align}y=\rho W y +X\beta+\epsilon\end{align}\]

5. Results

5.1 Summary statistics

The following table shows a summary of the main statistics of each variable.

As can be seen, the average vacancy rate per county amounts to 4.69% with a standard deviation of 2.1%. Likewise, it can be verified that 75% of the counties in the country have an unemployment rate less than or equal to 5.74%.

With regard to transportation infrastructure, it can be seen that the mean value of this variable is 21.65%, with a standard deviation of up to 15.47, thus representing great variability in transportation infrastructure endowments between counties. It can also be easily verified that 25% of the counties have only 11.24% transportation infrastructure or less and 75% of the counties have 29% transportation capital or less.

Regarding the accessibility measures to highways, train stations and airports, an average value of 12.41, 23.56 and 49.83 minutes is detected with variations around this of 8.35, 14.45 and 21.51 minutes.

Also in terms of economic performance measures, average labor productivity (ALP) amounts to a value of 70.91 thousand euros with a standard deviation of 12.46 thousand euros. 25% of the counties have a labor productivity of 63.43 thousand euros and only 25% have more than 74.65 thousand euros produced per worker.

Variable Median Mean SD SE Min Max q25 q75
U_rate 4.35 4.69 2.10 0.10 1.35 12.83 3.05 5.74
HK 13.58 34.52 51.10 2.55 0.10 379.57 4.84 42.52
TK 14.30 21.65 15.47 0.77 5.33 74.84 11.24 29.05
EH 10.13 12.41 8.35 0.42 0.43 53.59 6.68 15.93
ETS 22.37 23.63 14.32 0.71 0.44 75.09 14.22 32.63
EA 47.34 49.83 21.51 1.07 7.02 122.60 33.91 64.79
GDP_L 68.19 70.91 12.46 0.62 53.43 176.53 63.43 74.65
GDP_N 34.42 38.54 16.95 0.85 16.61 188.29 28.82 41.49
PSS 31.97 32.66 11.05 0.55 5.34 80.16 25.22 39.38
HK1 10.98 12.78 5.55 0.28 5.29 35.69 9.12 14.67

5.2 Spatial representations

Below are the spatial representations. As can be clearly seen, the levels of wealth between the states of the old eastern differ significantly.

This condition carries over to transport infrastructure, where there appears to be a correspondence between transport infrastructure endowments and wealth levels across counties in Germany. What intuits that there is a positive relationship between these two magnitudes. Likewise, it can be seen clearly how southern Germany, especially, is characterized by being an intensive sector in capital formation (measured as relative participation of the secondary sector).

As far as the human capital of each county is concerned, a pattern as illuminating as that of the Gross Domestic Product is not appreciated. More if there is a slight concentration of counties with a human capital of more than 16% in the south and south-west parts of the country. Likewise, with regard to accessibility to means of transport, it can be seen that those counties in which it takes more than 1 hour to access an airport and more than 16 minutes to access a highway are those corresponding to the Eastern parts. and South-Eastern Germany.

## Warning: sf layer has inconsistent datum (+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs).
## Need '+proj=longlat +datum=WGS84'
## Warning: sf layer has inconsistent datum (+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs).
## Need '+proj=longlat +datum=WGS84'

5.3 Correlations

Once these magnitudes are visually appreciated, a correlation analysis of these variables is carried out to verify their degree of association. At an exploratory level, by looking at the correlogram graph, it can be seen how all the variables follow the expected direction, both with the labor productivity indicator and with the per capita product indicator.

The measure of association between accessibility to the train station and labor productivity and economic growth is -0.28 and -0.37. Regarding access to highways it is -0.25 and -0.32 and to airports it is -0.26 and -0.18.

The level of human capital (measured as students enrolled in technical universities) of each county is associated with the product per worker in a 0.16 and with the per capita a 0.48. Regarding human capital, measured as the share of skilled workers in the economy, the associativity measure between these variables grows substantially to 0.54 and 0.62. Likewise, the unemployment rate is negatively associated with -0.17 and -0.02. The transportation capital that each county has is positively and strongly associated with both measures at 0.29 and 0.48 respectively.

5.4 Econometric specifications at GDP_L level

As can be seen in Table 1, a positive relationship between transport infrastructure and productivity labor is detected in all the functional specifications. The estimated elasticity fluctuates between 0.047 and 0.12, which indicates that those counties that have a 1% higher endowment in terms of transportation infrastructure have in avearge a higher wealth of between 0.084 and 0.106%. .

However, given the limitations in accounting for this variable, it is clearly intuited that the magnitude could be somewhat lower, to the extent that this variable is not only taking into account transportation infrastructure but also residential infrastructure.

Likewise, with regard to the accessibility to means of transport as a motor that explains the differences in the level of economic activity of the counties, significant values are also detected and in the expected direction.

Those counties where people take on average 1% longer to reach train stations have a lower level of labor productivity of 0.025% and 0.019% on average.

A similar value yields the estimated coefficient for accessibility to airports, in which a 1% shorter distance time to the airport is associated with -0.039% and -0.034% more labor productivity. In the case of highway access, this ratio fluctuates between -0.02 and -0.032-

Likewise, in the other control variables such as the stock of capital, the degree of employment of the labor force and human capital, values are estimated that go in the expected direction.

Those counties that have an occupancy rate that is 1% higher than others are associated with 0.11% and 0.137% more labor productivity. Likewise, those counties that are 1% more intensive in capital formation and machinery are associated with 0.12% higher labor productivity.

The explanatory capacity of both variables makes it possible to verify the importance that both physical capital and labor continue to acquire when explaining the level of production, as suggested by neoclassical postulates. It is also possible to clearly appreciate the relevance that human capital acquires when explaining labor productivity. Undoubtedly, the accumulation of skills in a knowledge-based economy is key today to explain economic differences at the regional level.

5.6 Comparison between models at per worker level

Dependent variable:
log(GDP_L)
(1) (2) (3) (4)
log(U_rate) -0.136*** -0.137*** -0.147*** -0.113***
(0.016) (0.015) (0.016) (0.014)
log(Transport_Infrastructure) 0.099*** 0.085*** 0.117*** 0.047***
(0.018) (0.018) (0.017) (0.016)
log(Secondary_Sector) 0.122*** 0.130*** 0.117*** 0.158***
(0.018) (0.018) (0.018) (0.016)
log(Erreichbar_AER) -0.030** -0.035**
(0.015) (0.015)
log(Erreichbar_TS) -0.032*** -0.026***
(0.009) (0.009)
log(Erreichbar_H) -0.018 -0.021 -0.029** -0.032***
(0.013) (0.013) (0.013) (0.011)
log(HK) 0.015*** 0.016***
(0.004) (0.004)
log(HK1) 0.223***
(0.018)
Constant 3.989*** 3.978*** 3.750*** 3.260***
(0.117) (0.116) (0.101) (0.097)
Observations 401 401 401 401
R2 0.385 0.404 0.376 0.527
Adjusted R2 0.376 0.393 0.368 0.521
Residual Std. Error 0.118 (df = 394) 0.117 (df = 393) 0.119 (df = 395) 0.104 (df = 395)
F Statistic 41.113*** (df = 6; 394) 38.042*** (df = 7; 393) 47.631*** (df = 5; 395) 88.080*** (df = 5; 395)
Note: p<0.1; p<0.05; p<0.01

5.5 Econometric specifications at GDP_N level

At the per capita product level, it stands out that most of the elasticities acquire a higher value, which indicates that each variable assumes a greater explanatory capacity when it comes to finding the sources of the difference in wealth at the regional level.

In the case of transport infrastructure, this magnitude rises to a value that is between 0.3 and 0.4, which indicates that those regions that have a 1% greater transport infrastructure, said differences are transferred to a difference of between 0.3 and 0.4 in the product per capita.

An even greater condition is that of human capital, in which a difference of 1% in the share of skilled workers translates into a difference of up to 0.43% in wealth per capita.

Regarding the accessibility to means of transport, only for the case of the train, a consistent relationship is presented that goes from -0.03 to -0.08. When incorporating the human capital variable as a percentage of skilled workers, the variables of access to transportation lose relative weight.

One possible explanation for this is that the transport infrastructure stock variable is already capturing accessibility at the same time, to the extent that by definition, greater transport infrastructure implies a greater amount of length of roads, train stations, ports and airports. .

Another possible explanation is also that in an economy based on knowledge and in which today’s possibility of working from home means that accessibility is not so decisive in explaining labor productivity and economic growth, once they are incorporated. many explanatory variables.

5.7 Comparison between models at per capita level

OLS regression at per capita level
Dependent variable:
log(GDP_N)
(1) (2) (3) (4)
log(U_rate) -0.261*** -0.262*** -0.267*** -0.219***
(0.032) (0.032) (0.030) (0.029)
log(Transport_Infrastructure) 0.390*** 0.399*** 0.328*** 0.310***
(0.037) (0.031) (0.035) (0.029)
log(Secondary_Sector) 0.174*** 0.175*** 0.207*** 0.247***
(0.038) (0.038) (0.035) (0.034)
log(Erreichbar_AER) 0.084*** 0.081*** 0.063** 0.128***
(0.031) (0.030) (0.029) (0.027)
log(HK) 0.063***
(0.008)
log(HK1) 0.421***
(0.041)
log(Erreichbar_TS) -0.083*** -0.083*** -0.058*** -0.031*
(0.018) (0.018) (0.017) (0.017)
log(Erreichbar_H) -0.012 -0.024
(0.027) (0.025)
Constant 2.199*** 2.154*** 2.149*** 0.730***
(0.241) (0.219) (0.224) (0.240)
Observations 401 401 401 401
R2 0.482 0.482 0.552 0.589
Adjusted R2 0.474 0.476 0.544 0.583
Residual Std. Error 0.243 (df = 394) 0.243 (df = 395) 0.226 (df = 393) 0.216 (df = 394)
F Statistic 61.185*** (df = 6; 394) 73.527*** (df = 5; 395) 69.053*** (df = 7; 393) 94.241*** (df = 6; 394)
Note: p<0.1; p<0.05; p<0.01

5.8 Variance inflactors at per capita level

Below are the inflation factors of the explanatory variables for the case of the models at the per capita level. As can be seen, all the explanatory variables take a value less than 5, which is positive to the extent that the problem of multicollinearity between variables is practically annulled.

However, those variables that have a higher inflationary factor are those corresponding to transport infrastructure and accessibility. This condition supports the aforementioned to the extent that there is a slight collinearity between the stock of transport infrastructure and the accessibility to said means.

Variable vif (reg5) vif (reg6) vif (reg7) vif (reg8)
log(Erreichbar_AER) 1.51 1.46 1.52 1.52
log(Erreichbar_H) 2.17 NA 2.18 2.18
log(Erreichbar_TS) 1.83 1.83 1.89 1.89
log(HK) NA NA 1.36 1.36
log(Secondary_Sector) 1.28 1.28 1.30 1.30
log(Transport_Infrastructure) 3.29 2.30 3.47 3.47
log(U_rate) 1.37 1.37 1.37 1.37

5.9 Spatial dependence

Next, the spatial matrices are incorporated that will allow us to appreciate if there is any degree of incidence of the transport infrastructure of each district on the other counties, as well as in the case of the other variables.

5.9.1 Moran Test

Since the Moran index is an open hypothesis test, it only indicates the presence of spatial autocorrelation but does not indicate that the spatial model best fits the structure of the data.

Therefore, the next step will be to estimate the hypothesis tests based on the lagrange multipliers (lagrange multiplier), to determine which spatial model best fits the data:

Moran P.value Variance
GDP/L 0.039345 0.96860 0.0011121
GDP/N -2.411000 0.01591 0.0011112

SAR

The direct impact refers to average total impact of a change of an independent variable on the dependent fore each observation, i.e., \[\begin{align} n^{-1}\sum_{i=1}^{n}\frac{\partial E(y_{i})}{\partial X_{i}} \end{align}\], the indirect impact which is the sum of the impact produced on one single observation by all other observations and the impact of one observation on all the other. The total is the summation of the two.

5.9.3 Spatial Simultaneous Autoregressive Lag Model

\[\begin{align} Y = \rho\ W y + X\beta\ + \varepsilon\ \end{align}\]

Dependent variable:
log(GDP_N)
log(U_rate) -0.220***
(0.028)
log(Transport_Infrastructure) 0.312***
(0.028)
log(Secondary_Sector) 0.249***
(0.034)
log(Erreichbar_TS) -0.032*
(0.017)
log(Erreichbar_AER) 0.126***
(0.027)
log(HK1) 0.416***
(0.041)
Constant 1.247***
(0.311)
Observations 401
Log Likelihood 51.371
sigma2 0.045
Akaike Inf. Crit. -84.742
Wald Test 6.282** (df = 1)
LR Test 5.593** (df = 1)
Note: p<0.1; p<0.05; p<0.01

5.9.3.1 Impacts

6. Conclusions and recommendations

The main purpose of this work has been to verify if the differences between transport infrastructure endowments and accessibility to transportation between counties translates into asymmetric levels of wealth, measured by Gross Domestic Product per Capita and Product Per Worker.

As it has been possible to verify, the transport infrastructure continues to represent a key element when it comes to explaining the sources of economic growth.

Likewise, another aspect that has been verified in the present investigation is the great importance that human capital acquires when explaining the differences in income between different counties.

This condition is typical of modern economies and is consistent with the statements that human capital is a key productive factor in knowledge-based economies.

7. References

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8. Appendix

8.1 Lag Transport infrastructure

## integer(0)

9. Other specifications

5.10 Comparison between models with spatial lag at labor level

By incorporating spatial lags in the initial specifications, it is detected that the portion of labor productivity that can be explained by differences in road infrastructure endowment is partly due to each county’s own endowment and another to transportation infrastructure endowment. which positively impacts neighboring counties.

A 1% increase in own transport infrastructure translates into 0.046% higher labor productivity. Likewise, a 1% increase in road infrastructure in neighboring counties translates into a 0.037% increase in labor productivity. In other words, the product per worker can also be explained by the installed capacity of road infrastructure in neighboring counties.

Likewise, by adding spatial lags, the significance of the level of employment and the levels of capital formation remain, with the elasticities obtained being 0.11 and 0.154 respectively. While the only means of transportation that remains significantly is access to highways with an elasticity value of -0.03.

Regarding human capital, this continues to be the productive factor in particular that assumes the greatest value with an elasticity that amounts to 0.22%.

Dependent variable:
log(GDP_L)
(1) (2) (3)
log(U_rate) -0.112*** -0.112*** -0.113***
(0.014) (0.014) (0.014)
log(Transport_Infrastructure) 0.044*** 0.044*** 0.048***
(0.017) (0.016) (0.016)
log(Secondary_Sector) 0.155*** 0.156*** 0.157***
(0.017) (0.016) (0.016)
log(Erreichbar_AER) -0.002
(0.013)
log(Erreichbar_TS) -0.002 -0.003
(0.008) (0.008)
log(Erreichbar_H) -0.032*** -0.033*** -0.031***
(0.012) (0.011) (0.011)
log(HK1) 0.222*** 0.222*** 0.224***
(0.020) (0.020) (0.019)
log(U_rate_L) 0.005
(0.027)
log(Transport_Infrastructure_L) 0.041 0.039 0.030
(0.028) (0.024) (0.019)
log(Secondary_Sector_L) 0.021
(0.034)
log(Erreichbar_AER_L) 0.027 0.026
(0.027) (0.026)
log(Erreichbar_TS_L) -0.022 -0.023
(0.018) (0.018)
log(Erreichbar_H_L) 0.038* 0.038* 0.041**
(0.021) (0.021) (0.020)
log(HK1_L) -0.040 -0.045
(0.038) (0.037)
Constant 3.063*** 3.156*** 3.068***
(0.269) (0.202) (0.135)
Observations 401 401 401
R2 0.538 0.537 0.532
Adjusted R2 0.521 0.524 0.524
Residual Std. Error 0.104 (df = 386) 0.103 (df = 389) 0.103 (df = 393)
F Statistic 32.045*** (df = 14; 386) 41.015*** (df = 11; 389) 63.931*** (df = 7; 393)
Note: p<0.1; p<0.05; p<0.01

5.11 Comparison between lag spatial models at per capita level

Dependent variable:
log(GDP_N)
(1) (2)
log(U_rate) -0.214*** -0.208***
(0.029) (0.030)
log(Transport_Infrastructure) 0.284*** 0.278***
(0.035) (0.028)
log(Secondary_Sector) 0.244*** 0.242***
(0.034) (0.035)
log(Erreichbar_AER) 0.132***
(0.028)
log(Erreichbar_TS) -0.026 -0.018
(0.017) (0.017)
log(Erreichbar_H) -0.041*
(0.024)
log(HK1) 0.424*** 0.390***
(0.042) (0.042)
log(Transport_Infrastructure_L) 0.047
(0.050)
log(Erreichbar_AER_L) -0.056
(0.055)
log(Erreichbar_TS_L) 0.007
(0.037)
log(Erreichbar_H_L) 0.018
(0.043)
log(HK1_L) -0.125 -0.067
(0.078) (0.055)
Constant 1.185*** 1.518***
(0.445) (0.239)
Observations 401 401
R2 0.595 0.568
Adjusted R2 0.583 0.561
Residual Std. Error 0.216 (df = 388) 0.222 (df = 394)
F Statistic 47.557*** (df = 12; 388) 86.325*** (df = 6; 394)
Note: p<0.1; p<0.05; p<0.01

9.1 Spatial Simultaneous Autoregressive Error Model

\[\begin{align}Y = X\beta + u, u = \lambda Wu + \varepsilon \end{align}\]

9.2 Spatial Simultaneous Autoregressive Error Model by Feasible Generalized Least Squares