1. When is distance a valid instrument?

Let's first look at a few examples of distance used as instruments

Oster (2012)

HIV prevalence $\uparrow$ $\Rightarrow$ Risky sexual behaviour $\downarrow$

Instrument: Distance to DR Congo

$\hat{\beta}_{IV} < 0$ while $\hat{\beta}_{OLS} > 0$

Woodruff & Zenteno (2007)

Migration rate to rich country (Mexico $\rightarrow$ USA) $\uparrow$ $\Rightarrow$ Investment in home country $\uparrow$

Instrument: Distance to early 20c railway stations

$\hat{\beta}_{IV} > 0$

Issues on distance as instruments #1

(cf. Gibson & McKenzie 2007, p. 227)

Exclusion restriction

Selection in space

• More affluent can live close to cities, etc.

Distance to other things in the same place

• e.g. Distance to cities: access to markets, schools, clinics...

Oster (2012)

HIV prevalence $\uparrow$ $\Rightarrow$ Risky sexual behaviour $\downarrow$

Instrument: Distance to DR Congo

Closer to DR Congo

$\Rightarrow$ Higher mortality due to proximity to conflict?

$\Rightarrow$ People don't mind risking their survival (Oster et al. 2013)

i.e. Distance to other things in the same place

Woodruff & Zenteno (2007)

Migration rate to rich country (Mexico $\rightarrow$ USA) $\uparrow$ $\Rightarrow$ Investment in home country $\uparrow$

Instrument: Distance to early 20c railway stations

Closer to historical railway stations

$\Rightarrow$ More prosperous due to path dependence? (Bleakey and Lin 2012)

i.e. Selection in space

Issues on distance as instruments #2

(cf. Gibson & McKenzie 2007, p. 227)

LATE

Treatment can be induced by other factors than distance

Is LATE of interest? (cf. Imbens 2010)

2. Nunn (2008)

Perhaps the best example of using distance as instruments

Research Question

Did slave trades cause African underdevelopment?

Important?

• Many conjecture slave trades adversely affected Africa's living standards

Original?

• First systematic and convincing evidence of causality

Feasible?

Data

Treatment variable

# of slaves exported from each country: constructed from

(1) # of slaves exported from each port of Africa

(2) Ethnicity of 100,000+ slaves shipped from Africa

(3) Murdock's (1959) map of ethnic homelands in Africa

We will learn how to allocate (1) across countries
by intersecting (3) with country polygons

Data (cont.)

Instruments

Distance to nearest slave trade centers

• Trans-Atlantic
• Indian Ocean
• Trans-Saharan
• Red Sea

Data (cont.)

Instruments

Distance to nearest slave trade centers

• Trans-Atlantic
• Indian Ocean
• Trans-Saharan
• Red Sea

We will learn how to obtain distance to Trans-Atlantic trade centers

Exclusion restrictions

Selection in space?

• Location of slave trade centers:
• Determined by climate suitability of plantation crops / location of mines (p. 160)
• Not affected by distance to slave export locations in Africa

Distance to other things in the same place?

• Slave markets $\neq$ other economic opportunities
• Reduced-form correlation is absent outside Africa (p. 163)

LATE

Maybe a smaller impact if countries voluntarily engaged in slave trades

But LATE may be of more interest in this context

Empirical specification (2nd stage)

\begin{align*} y_{i} = & \ \alpha + \beta \ln \Big(\frac{exports_i}{area_i}\Big) + \boldsymbol{X}'_{i}\boldsymbol{\gamma} + \varepsilon_{i} \end{align*}

Empirical specification (1st stage)

\begin{align*} \ln \Big(\frac{exports_i}{area_i}\Big) = & \ \ \delta + \boldsymbol{D}'_i\boldsymbol{\Omega} + \boldsymbol{X}'_{i}\boldsymbol{\eta} + \mu_{i} \\ \end{align*}

We will learn how to obtain some of controls with ArcGIS

• Distance from equator (i.e. latitude of centroid)
• Longitude of country $i$'s centroid

1st stage results

(Table IV of Nunn 2008)

Weak instruments

F-stat on excluded instruments: very low

$\Rightarrow$ Moreira's (2003) CLR confidence intervals

• Stata ado: condivreg
• Works only for single endogenous regressor
• For multiple endogenous regressors, use LIML with Bekker's (1994) s.e. correction (cf. Imbens 2007)

2nd stage results

(Table IV of Nunn 2008)

Mechanisms

Ethnic fractionalization

Weaker state

Low interpersonal trust (Nunn & Wantchekon 2011)

3. Distance calculation

Distance calculation: overview

Depends on input feature types

1. Point to point
2. Point to polyline
3. From polygon
1. From the edge of a polygon
2. From the centroid of a polygon
1. To point
2. To polyline/polygon

For more advanced distance calculation, see pp. 18-25 of Dell (2009) "GIS Analysis for Applied Economists"

Distance calculation #1

Point to point

1. Obtain geographic coordinates

2. Use the Great Circle Distance formula

\begin{align*} d_{ij} =& \ 111.12 \times \cos^{-1}\big[\sin(La_i)\sin(La_j) \\ & + \cos(La_i)\cos(La_j)\cos(Lo_i-Lo_j)\big] \end{align*}

• $d_{ij}$: distance in km from $i$ to $j$
• Proof: see Wolfram MathWorld
• Can be implemented by Stata ado globdist

Globdist

1. In Stata, type: findit globdist, to install

2. Prepare the data so that

• lat / lon: coordinates of each observation
• lat_i / lon_i: coordinates of location $i$

3. Type: globdist newvar, lat0(lat_i) lon0(lon_i)

• newvar: distance to location $i$
• use latvar(), lonvar(), to specify coordinate variables if not named lat / lon

Alternative method for small areas

UTM projection (cf. Lec 3) + Pythagorean theorem

• For study area spanning < 6° in longitude

Distance calculation #2

Point to polyline

Examples: distance to roads, railway lines, rivers...

Need the coordinate of nearest point on the polyline

Use ArcGIS's Near tool

• It also calculates the distance to nearest point

Application: Redding & Sturm (2008)

West German cities near the border with East Germany:

Population growth $\downarrow$ after 1945

Distance to border: can be obtained by Near tool

Distance calculation #3

From polygon

We have two cases

1. From the edge of a polygon
2. From the centroid of a polygon

Distance calculation #3.1

From the edge of a polygon

We can just use the Near tool

Distance calculation #3.2

From the centroid of a polygon

More appropriate when mean distance from any point within a polygon matters

To calculate the distance to a point:

• Obtain the coordinate of a polygon centroid by:
• Stata ado shp2dta (cf. Lec 2)
• Add Geometry Attributes in ArcGIS (cf. Lec 2 Ex 1 Step 3)
• Then use the Great Circle Distance formula
• Stata ado globdist

Application: Campante & Do (2014)

Population concentration around US state capital city

• Measured by the distance-weighted sum of county population
• Distance: btw capital and county centroids

$\Rightarrow$ US state govt quality $\uparrow$

• Newspaper coverage of state politics $\uparrow$
• Money politics $\downarrow$
• Public good provision $\uparrow$

Distance calculation #3.2 (cont.)

From the centroid of a polygon

To calculate the distance to a polyline/polygon:

1. Create centroid point features in ArcGIS
• Feature To Point
• Add XY Coordinates
2. Use the Near tool

Application: Nunn (2008)

Exercise #1: Overview

Replicate instruments in Nunn (2008): Distance to Slave trade centers

Exercise #1: Overview (cont.)

We proceed in three steps:

1. Create country centroid point features

• Used as control variables as well

2. Identify closest point on the coast from country centroid

3. Calculate distance to closest slave trade centers

• Trade center coordinates: use online gazetteer (cf. Lecture 1)

Exercise #1: Step 1

Obtain country centroids

Input: Country polygons for Africa

• Created by the lecturer from GADM (cf. Lec 1 Ex 1)

Geo-processing tools:

• Feature To Point
• Add XY Coordinates

Exercise #1: Step 1

Feature To Point

Input Features: ...\Lecture4\input\gadm36_africa.shp

• Country polygons

Output Feature Class: ...\Lecture4\temporary\centroids.shp

Uncheck "Inside"

• How this option works: "[F]ind a location in a relatively wide or open area inside the polygon and to avoid a location being too close to the polygon boundary" (personal correspondence with ESRI)

Exercise #1: Step 1 (cont.)

Now save and run the Model.

Overlay the output over gadm36_africa.shp.

You should see something like this:

Exercise #1: Step 1 (cont.)

Also browse the attritube table.

Notice that Feature To Point doesn't add coordinates to the attribute table of the output.

So...

Exercise #1: Step 1 (cont.)

Add XY Coordinates (Data Management)

Input Features: centroids.shp

• The output from Feature To Point

NOTE: This tool overwrites the input data.

You might wonder if we can use Add Geometry Attribute, but it works only for polygons.

Exercise #1: Step 1 (cont.)

Now save and run the Model.

Browse the attribute table. Now you should see two new fields POINT_X and POINT_Y.

Exercise #1: Step 2

Closest point on the coast

Inputs: Coastline polylines

• Natural Earth 1:10m Physical Vector "Coastline"
• If you need more detailed coastline data, try GSHHG (used by Henderson et al. 2018)

Geo-processing tool: Near (Analysis)

• Generate Near Table tool does the same job
• But it will drop country names...

What Near tool does

(source: ArcGIS Help on Near)

Exercise #1: Step 2

Near (Analysis)

Input Features: country_centroids.shp (2)

• Output from Add XY Coordinates

Near Features: ...\Lecture4\input\10m_coastline.shp

• Coastline polyline features

Exercise #1: Step 2 (cont.)

Check "Location"

• Otherwise the coordinate of the nearest point on coast won't be attached to attribute table

Method: GEODESIC

• Calculates distance by Great Circle Distance Formula
• If we use data in UTM, choose PLANAR.

NOTE: This tool overwrites the input data.

Exercise #1: Step 2 (cont.)

Now save and run the Model. Browse the attribute table. Now you should see four new fields:

• NEAR_FID: FID of coastline segment
• Useful for spatial RD (Lecture 7)
• NEAR_DIST: Distance to coast in meters
• NEAR_X: Longitude of the nearest point on coast
• NEAR_Y: Latitude of the nearest point on coast

Exercise #1: Step3

Distance to slave trade centers

Approach 1: use globdist

1. Table to Excel, to export the output from Near tool
2. In Stata, use globdist to calculate distance between nearest point on the coast (NEAR_X, NEAR_Y) and all slave trade centers.
3. Pick the shortest distance

Exercise #1: Step3 (cont.)

Distance to slave trade centers

Approach 2: use the Near tool in ArcGIS

1. Create slave trade center point features
2. Create nearest coast point features (use NEAR_X, NEAR_Y)
3. Use Near (near features: slave trade centers)
4. Table to Excel

"Model" models for Exercise 1

In the Lecture4\solutions4exercises folder, you can find models.tbx\exercise1

Extra exercise #1

Centroids outside polygons

Nunn (2008, p. 170): "For five countries where the centroid falls outside the land borders of the country (Gambia, Somalia, Cape Verde, Mauritius, and Seychelles) the point within the country closest to the centroid is used."

This can be done by the Near tool

• Near features: country polygons
• (NEAR_X, NEAR_Y) will be different for those centroids outside polygons

Extra exercise #2

Shortest distance route polylines

To make a map that indicates the shortest distance:

Use the XY To Line tool

• Input Table: the output from Near tool
• Start X Field / Y Field: POINT_X / POINT_Y
• End X Field / Y Field: NEAR_X / NEAR_Y

Model Python Script for Exercise 1

Due to time constraint, we skip Python for Exercise 1

Model Python scripts: see Lecture4/solutions4exercises/exercise1.py

4. Intersect + Surface Area Calculation

Data we want to construct

# of slaves exported from each country in Africa

Input datasets:

• # of slaves shipped from each coastal country
• Each ethnic group's share in the total # of slaves exported from Africa
• Ethnic homeland map (cf. Lecture 2)

Data we want to construct (cont.)

Input data (hypothetical)

Data we want to construct (cont.)

Assign slaves from coast to inland

Data we want to construct (cont.)

Superimpose country boundaries

Surface area of ethnic C: 50% for X / 50% for Y

Data we want to construct (cont.)

Deal with split ethnic homelands

$\Rightarrow$ Assign slaves by surface area (Nunn 2008, fn. 4)

Data we want to construct (cont.)

# of slaves exported by country

Data we want to construct (cont.)

Use ArcGIS to create:

Ethnic homeland by country intersection polygons

Attribute table:

• Country ID
• Ethnic group ID
• Surfare area

Then export to Stata to do the other calculations...

Exercise #2: Overview

Surface area of intersection polygons

Input data:

1. Ethnic homeland polygons (borders_tribes.shp)

• Downloaded from Nathan Nunn's website

2. Country polygons (gadm36_africa.shp)

Exercise #2: Overview (cont.)

Geo-processing tools:

1. Intersect (Analysis)

• Match ethnic homelands with countries

2. Project (Data Management)

• Choose coordinate system for surface area calculation

3. Add Geometry Attributes

• Calculate surfare area as a new field of attribute table

Exercise #2: Step 1

Intersect (Analysis)

Input Features (Lecture4/input folder)

borders_tribes.shp

african_countries.shp

• Use shift+click to select more than one file

Output Feature Class: ...\Lecture4\temporary\intersect.shp

Join Attributes: ALL

Output Type: INPUT

Exercise #2: Step 1 (cont.)

Now save and run the Model.

Browse the output.

Browse the attribute table of the output

Intersect vs Spatial Join

You might wonder why we don't use Spatial Join...

If only to know which ethnic group lives in which country

$\Rightarrow$ Spatial Join (with JOIN_ONE_TO_MANY option)

• Output features: target features

To obtain data at the intersection level

$\Rightarrow$ Intersect

• Output features: intersection polygons

Application: Bleakey & Lin (2012)

Intersect fall lines + rivers to identify potential portage sites

Exercise #2 Steps 2-3

Surface area calculation

Use equal area projections (cf. Lecture 1)

• Study area: whole Africa
• UTM cannot handle such large area (cf. Lec 3)

Sinusoidal (Lec 1 Ex 8): often used for the entire world or continents

Sinusoidal projection

Assume the Earth is a sphere. Then:

Length of 360° in latitude: same across all longitudes

Length of 360° in longitude:

$\leftarrow$ Earth cross-section cut through North and South Poles

Sinusoidal projection (cont.)

Projected coordinate $(x',y')$ is given by:

\begin{align*} y' & = M_y * y \\ x' & = M_x * (x - x_0) * \cos(y) \end{align*}

Central meridian: affect how map looks, not surface area calculation

Sinusoidal projection (cont.)

Central meridian & all the parallels: straight lines

Other meridians: sinusoidal curves

(image source)

Exercise #2: Step 2

Project (Data Management)

Input Dataset or Feature Class: intersect.shp

• Output from Intersect

Output Dataset or Feature Class: ...\temporary\intersect_sinusoidal.shp

Output Coordinate System: Africa_Sinusoidal

• Projected Coordinate System > Continental > Africa
• Notice: central meridian is set at 15°E (middle of Africa)

Exercise #2: Step 3

Add Geometry Attributes

This tool can be used for surface area calculation, too

Input Features: intersect_sinusoidal.shp

• The output from Project

Geometry Properties: check AREA

Area Unit: SQUARE_KILOMETERS

• If not specified, it'll be square meters

Note: this tool overwrites the input file

Exercise #2: Step 3 (cont.)

If Add Geometry Attributes doesn't work in Model Builder...

Add Field + Calculate Field

• Create a blank field (Add Field)
• Enter the values to the field (Calculate Field)

Exercise #2: Step 3 (cont.)

Add Field

Input Table: intersect_sinusoidal.shp

• Output from Project

Field Name: area

• Or whatever you prefer (not exceeding 10 characters)

Field Type: FLOAT

• Surface area: takes decimal values

NOTE: This tool overwrites the input data.

Exercise #2: Step 3 (cont.)

Now save and run the Model.

Browse the output attribute table.

You should see a field whose value is all zero

Don't ask me why we cannot enter values to a new field directly...

Exercise #2: Step 3 (cont.)

Calculate Field

Input Table: intersect_sinusoidal.shp (2)

• Output from Add Field

Field Name: area

• Or the same as what you specified in Add Field

Calculate Field (cont.)

Expression: float(!SHAPE.AREA!)

• SHAPE.AREA: (hidden) field name for surface area
• ! ! tells Python what's enclosed is a field name
• float(): avoid rounding-off to integer

cf. ArcGIS Help on Calculate Field examples

Expression Type: PYTHON_9.3

NOTE: This tool overwrites the input data.

Exercise #2: Step 3 (cont.)

Now save and run the Model.

Browse the output and its attribute table.

Is everything as expected?

Exercise #2 Step 4

Export Attribute Table

Which geo-processing tool(s) should we use?

Exercise #2 Step 4 (cont.)

Table To Excel

• Input Table: intersect_sinusoidal.shp (2)
• The output from Add Geometry Attributes
• Output Excel File: ...\output\intersect_sinusoidal.xls

This time we go with Excel only.

• Advantage of Export Feature Attribute to ASCII: choose which fields to keep
• There are both country codes and names
• Which one works best with your country data is unknown
• Better to drop unnecessary variables in Stata

"Model" model for Exercise 2

Look at solutions4exercises\models.tbx\exercise2

5. List in Python

Specify multiple input files in Python

Now export a Python script

Look at the command line for Intersect

						
# Local variables:
borders_tribes_shp = "C:\\Users\\Masayuki Kudamatsu\\Desktop\\Lecture4\\input\\borders_tribes.shp"
gadm36_africa_shp = "C:\\Users\\Masayuki Kudamatsu\\Desktop\\Lecture4\\input\\gadm36_africa.shp"

# Process: Intersect
arcpy.Intersect_analysis("'C:\\Users\\Masayuki Kudamatsu\\Desktop\\Lecture4\\input\\borders_tribes.shp' #;'C:\\Users\\Masayuki Kudamatsu\\Desktop\\Lecture4\\input\\gadm36_africa.shp' #", intersect_shp, "ALL", "", "INPUT")
						
					

For geo-processing tools that take multiple inputs,
Model Builder fails to use local variables for input file names

We ourselves need to use local variables

Specify multiple input files in Python (cont.)

If you write the script as follows:

data1 = "data1.shp"

data2 = "data2.shp"

input_list = [data1, data2]

arcpy.Intersect_analysis(input_list, intersect_shp, "ALL", "", "INPUT")

$\Rightarrow$ Python recognises 1st argument as

["data1.shp","data2.shp"]

Python 101

Data type

In Python, a variable can take several data types

• number = 4
• string = "python"
• list = [4,"python"]
• dictionary = {"number": 4, "string": "python"} (cf. Lec 8)

See TutorialsPoint for more on data type

Python 101 (cont.)

List

list = [4,"python"]

To define a list, use [ ]

Each item is separated by ,

Items can either be numbers or strings

See TutorialsPoint for more on list

Which geo-processing tools take a list as input?

• Intersect
• Near (for near features)
• Extract Multi Values To Points (Lecture 5)
• Mosaic To New Raster (Lecture 6)
• And several others

See ArcGIS Online Help to tell whether list can be used

ArcGIS Online Help for Intersect

ArcGIS Online Help for Near

Exercise #2 (cont.)

Edit the exported Python script

1. Use the template (code/template4L4.py)

• Try-Except statement (Lec 2 Ex 6)
• String variables for file names (Lec 2 Ex 7)
• Print commands (Lec 2 Ex 8)

2. Replace Intersect's input file names w/ a list

3. Close outputs in ArcMap

4. Run the script

Exercise #2 (cont.)

The Python script relevant for using the Intersect tool should now look like:

						
# Local variables:
borders_tribes_shp = "input\\borders_tribes.shp"
gadm36_africa_shp = "input\\gadm36_africa.shp"
intersect_shp = "temporary\\intersect.shp"

# Process: Intersect
inFeatures = [borders_tribes_shp, gadm36_africa_shp]
arcpy.Intersect_analysis(inFeatures, intersect_shp, "ALL", "", "INPUT")
						
					

Model Python Script for Lecture 4 Exercise 2

Look at solutions4exercises/exercise2.py