Spatial Econometricsweb.sgh.waw.pl/~atoroj/ekonometria_przestrzenna/1... · Source of information about the spatial order In spatial econometrics, the order is described by a spatial

Why spatial modelling Spatial data structure Software and data

Spatial EconometricsLecture 1 The notion of spatial modelling Visualisation of

spatial data in R

Andrzej Toroacutej

Institute of Econometrics Department of Applied Econometrics

Andrzej Toroacutej Institute of Econometrics Department of Applied Econometrics

(1) Spatial Econometrics 1 30

Contents

1 Why spatial modelling

Space vs ties between units

Applications of spatial modelling

2 Spatial data structure

Spatial order vs temporal order

Types of spatial inuences

3 Software and data

Software

Sources of spatial data and literature

Plan prezentacji

3 Software and data

Paradigms

Toblers law (1970) Everything is related to everything else

but near things are more related than distant things

Toblers second law (2004) The word near may have a lot

of meanings

In other words Beck (2006) There is more to space than

geography

Paradigms

of meanings

geography

Paradigms

of meanings

geography

Case 1 neighbourhood ties between counties in USA

Case 2 following tweets among French members ofparliament

How are spatial ties generated

Units impact on one anothereg spatial diusion cases of u in a given district

But also

Level of measurement not suitable for the investigatedphenomenon (np regional aggregates instead of micro-data)Common measurement errors (eg community-level dataprepared under dierent guidelines of regional statisticaloces)Spatial aggregation level

Spatial aggregation level (1)

On average 0 neighbours of the same colourAndrzej Toroacutej Institute of Econometrics Department of Applied Econometrics

Applications of spatial modelling (1)

Applications

traditional maps of ties between states or regions eg intrade or foreign investmentregional analyses ties between relatively small units (poviatscommunities) observable via eg unemployment rates or localgovernment nancebusiness analyses big data from GIS systems (eg modellingthe attractiveness of business locations optimisation of salesnetwork managing logistics)

Applications

security policy (alliances wars military interventions)

protection of environment (air pollution water contagion)

international interdependence of policies (copying legislation

patterns)

political science (constituencies and electoral systems)

epidemiology (spreading of epidemics)

economic diusion (local labour markets)

More Haegerstrand (1967) Manski (2000) Simmons et al(2005)

Plan prezentacji

3 Software and data

Temporal order

For time series we use the notion of serial correlation It

makes sense when

observations are aligned in a linear order (1-D)the frequency of the series is set ie identically long reportingperiods (or intervals between measurement moments)

Source of information about the order the records are

sorted or there is an explicit timestamp

Spatial order

The temporal 1-D order is not the only possible one for our

observations may be attributed to areas or points on a surfaceor sphere (2-D)implications of such an order are more dicult to manage (2-Drather than 1-D) but ignoring this may lead to the sameproblems as temporal serial correlation

Source of information about the spatial order

In spatial econometrics the order is described by a spatial weight

matrix (see next lecture) It might be based on

manual imputation of neighbourhood relationships (tedious)

eg USA linked to Mexico Canada linked to USA Mexico notlinked to Canada

distance matrix between units in space

how to generate ithow exactly to measure the distance

graphical 2-D representation of space ie a map from which

neighbourhood relationships or distances can be derived

Econometric implications of spatial linkages

Observations are not independent

In this model yi = β0 + β1xi + εi it is not any more true thatεi sim i i d (independent identically distributed)The consequence is at best ineciency of OLS estimation(like in the case of temporal autocorrelation)

The big dierence while the temporal impact runs in onedirection only (past rarr present) spatial autocorrelation canrun in both directions (our region larrrarr neighbourhoodregion larrrarr other regions larrrarr our region)

Here the implications can be more serious and involveinconsistency and bias in OLS estimation (like in simultaneousequations models)

Main types of spatial inuences

will be presented by world-class experts in neighbourhood topics

Main types of spatial inuences (1)

Types of spatial inuences additional remarks

Hasty conclusions of spatial interdependence should be avoided

(situation 3) unless other cases have reasonably been

excluded

Spatial interdepencence (situation 3) is relatively unlikely when

modelling spatial aggregates Situations 1 and 2 more likely in

that case

Plan prezentacji

3 Software and data

Software

A small number of econometric packages oers tools for spatial

modelling The leading ones Matlab Stata R The materials

accompanying this lecture use R (via RStudio)

Installing package spdep

installpackages(spdep)

library(spdep)

Another useful package is rgdal and for visualising data on map

additionally maptools RColorBrewer i classInt

Lista wszystkich pakietoacutew R do analizy danych przestrzennych na

Example

Our task is to plot a map illustrating the unemployment rate from

the le BDL_danexls for poviats This sample covers Poland in

2014 and comes from Local Data Bank by GUS (Central

Statistical Oce in Poland)

To do this we must merge the unemployment data with

cartographic data

This is how we impose a spatial structure on the data

Will also be useful in modelling in the following lectures

Solution with comments in the accompanying R code

Example nal eect of the code

Sources of cartographic data

GADM administrative divisions in almost all countries of the world

CODGiK more accurate maps by Polish Centralny Oplusmnrodek Dokumentacji

Geodezyjnej i Kartogracznej (surveyor authority)

Eurostat maps of EU states in NUTS nomenclature from NUTS0 toNUTS3 (in Poland NUTS2 voivodships NUTS4 poviats)

package cshapes in R ready-made world map (current and historicalafter 1945) with additional functions for international spatial analyses

and many more

Optimization of map size

Map les are usually ver precise taking many MB of disc space

One can decrease this size - often without any detriment to the

illustration quality - using converters (eg mapshaperorg)

Functions in use

readOGR imports the map and uses the following les

shp shapes of the regionsadditionally shx (auxiliary indexing le) and dbf

(accompanying database)prj technical details related to the projection of geosphere onthe plane

spTransform allows to transform all the geocoding

information into longitude and latitude in degrees (required by

a number of R packages)

colorRampPalette useful to transform the visualised

(continuous) variable into colours

Homework 1Using the Eurostat database and R please illustrate the regional variation in a selected variable in aEuropean country of Your choice and a chosen time period (this should not be the unemployment ratenor Poland but still a relatively large country)

One can use an own alternative data source The map should consist of 25-30 regions Theillustrated variable will be the dependend variable in the model prepared in subsequenthomeworks so one should be able to nd further variables for the same set of regions (to beused as sensible regressors)

The uploaded PDF le should contain a short descritption of the analysed variable data sourceand map source indication and the illustration (map) itself max 1 page

The uploaded ZIP le should contain the whole replication package data le R code andpossibly map les (if these are the same les as the ones used in the class this can be skipped ifthese are dierent les but prohibitively big ie making the upload size exceed the 5 MB limitplease put only a txt le with URL codes of every of the map les (or a ZIP package) on theuploaded archive This remark is related to all future homeworks

Literature

Compulsory

Arbia G A Primer for Spatial Econometrics with Applications inR 2014 Palgrave Macmillan

Anselin L Spatial Econometrics ch 29 in TC Mills and KPatterson (Eds) Palgrave Handbook of Econometrics Volume 1Econometric Theory Basingstoke Palgrave Macmillan 2006 pp901-969

Le Sage J and Pace RK Introduction to Spatial Econometrics2009 Chapman and HallCRC

Why spatial modelling

Spatial data structure

Software and data

Contents

3 Software and data

Software

Plan prezentacji

3 Software and data

Paradigms

of meanings

geography

Paradigms

of meanings

geography

Paradigms

of meanings

geography

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Plan prezentacji

3 Software and data

Paradigms

of meanings

geography

Paradigms

of meanings

geography

Paradigms

of meanings

geography

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Paradigms

of meanings

geography

Paradigms

of meanings

geography

Paradigms

of meanings

geography

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Paradigms

of meanings

geography

Paradigms

of meanings

geography

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Paradigms

of meanings

geography

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

But also

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Applications

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

patterns)

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Plan prezentacji

3 Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Temporal order

makes sense when

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Spatial order

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

excluded

that case

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Plan prezentacji

3 Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Software

library(spdep)

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

Example

cartographic data

and many more

Functions in use

Literature

Compulsory

Software and data

and many more

Functions in use

Literature

Compulsory

Software and data

and many more

Functions in use

Literature

Compulsory

Software and data

Functions in use

Literature

Compulsory

Software and data

Literature

Compulsory

Software and data

Literature

Compulsory

Software and data

Documents

Spatial Econometricsweb.sgh.waw.pl/~atoroj/ekonometria_przestrzenna/1... · Source of information about the spatial order In spatial econometrics, the order is described by a spatial