Urban Start-up Agglomeration and Venture Capital Investment
| Academic Paper | |
|---|---|
| Title | Urban Start-up Agglomeration and Venture Capital Investment |
| Author | Ed Egan |
| RAs | Peter Jalbert, Jake Silberman, Christy Warden, Jeemin Sim |
| Status | In development |
| © edegan.com, 2016 | |
Contents
- 1 New Work
- 2 Old Work Using Circles
New Work
Files
New files are in E:\projects\agglomeration
- agglomeration.sql -- new main sql file uses vcdb3
Contents of the Old Code subdirectory:
- Agglomeration.SQL -- This was the replacement code that was run when vcdb3 was made. We had to work through it to update the counts. Came from E:\projects\vcdb3\OriginalSQL\Agglomeration.SQL
- Agglomeration.sql -- Old version that makes colevel data for python script. Came from E:\mcnair\Projects\Agglomeration
- Analysis.sql -- Old version builds from HCL forward. Came from E:\mcnair\Projects\Agglomeration
See also:
CoLevelForCircles
Note: Make sure that the geocoding has been fixed first! See Restoring_vcdb3#Fix_the_Geocoding. Note that we are working with decimal degrees to six decimal places from Google Maps, which is equivalent to a staggering 11cm of accuracy at the equator. See http://wiki.gis.com/wiki/index.php/Decimal_degrees.
The build is as follows:
- portcomaster 48001 (where hadgrowth=1 34761) and portcogeo (47715 where latitude and longitude NOT NULL 47715) -> colevelsimple 33869
- colevelsimple 33869-> CoPoints (adds point geoms)
- tigerplaces 29322 (has place geoms) -> tiger2 (adds areas)
- tiger2,CoPoints ST_Intersects -> colevelbase 29442
- colevelbase,years -> colevelblowout 219060, CoLevelSummary 35344, PlacesWithGT10Active 200
- colevelblowout,PlacesWithGT10Active -> CoLevelForCircles 171170
HCA
Take CoLevelForCircles.txt and feed it into the HCA script in
E:\projects\hca\main.py
See also:
Take results.tsv and load it as the HCL table.
Layers and levels
See Agglomeration.sql for the following build:
- hcl loaded from results.tsv 29751998
- Determine if singleset, multiset or hullset (fully partitions data)
- Make hclsingletons, hclmultitons and hclhulls (which contains both hulls and lines)
- UNION them together to create hclmain (14875999), which contains geographies
- Make hcllayer 163887: Aggregate to the layer level calculating nosingleton, nomultiton, etc., as well as tothullarea etc.
Note that everything uses Geographies (except to find centroids), and pair lengths and hull areas are scaled so that they are in hm and hectares (hm2) [1], as this is close to being a city block length and square block [2] at least in Houston, TX (note that a block in Chicago is 2 Houston blocks and there is no standard block definition).
Then load up leveldefinitions.txt. Note that we are using more levels than before, with finer grained levels at the bottom end:
Level Label Target 1 100msq 0.01 2 1blfront 0.1 3 1blsq 1 4 5blsq 5 5 10blsq 10 6 25blsq 25 7 50sqbl 50 8 1kmsq 100 9 5kmsq 400 10 10kmsq 1000 11 20min rule 35000
Then build the nohulls as level 0 and the allhull as level 12. Note that we are going to have to throw out panels or observations with too few points per city-year later, as these can have singletons, multitons, or pairs as their allhulls. This can be done with nohull !=0. Also nohulls can be built using hcllayer then it will contain pairs, or from colevelforcircles. I opted for the later, so that it only contains singletons and multitons.
Finally in this part, build hcllevels and hcllayerwzero. For hcllevels we are going to compute mean distances between clusters. It is computational infeasible to do this for all layers. And then for all layers (inc zero) we are going to run our selection regression.
For the next steps on the data see Jeemin Sim (Work Log). This includes details of how to load the TIF data.
Approach
We want to choose some layers to work with. https://en.wikipedia.org/wiki/Hierarchical_clustering notes that "One can always decide to stop clustering when there is a sufficiently small number of clusters (number criterion). Some linkages may also guarantee that agglomeration occurs at a greater distance between clusters than the previous agglomeration, and then one can stop clustering when the clusters are too far apart to be merged (distance criterion)."
In a similar vein, https://en.wikipedia.org/wiki/Determining_the_number_of_clusters_in_a_data_set describes the elbow method, using AIC/BIC, etc., as well as an Information theoretic approach, the silhoette method, etc.
For us:
- Discarding outliers
- Elbow on fraction of locations in hulls
- Chosen by the researcher
- Maximum R-Squared
We also looked at:
- Elbow on fraction of maximum hull area in hulls
And finally, we need to think about:
- Reasonable exclusions
Discarding Outliers
We don't need to discard outliers, per se, just find a layer where outliers are singletons. A wrong approach is to take the highest layer with a single hull (or two hulls or three hulls, etc.). It is fair that if a layer never has a hull, then presumably it only has a single location or a line of locations (note that it is possible for a line to have more than 2 locations both because of multitons and because of perfect alignment, given our Google Maps accuracy), so we can discard it. However, this approach will find when there is just one hull left, rather than the last time that there is one hull in decomposition.
Possible options and issues:
- Find when there are first two hulls and then step back a layer -- but there might never be two hulls, so if there is only ever one hull then find the max layer.
- Form a chain from layer 1 on down that breaks when there is no longer just one hull. Perhaps count the number links, grouping where the chain has one hull or not, or require that the chain contain level 1... [3]
We went with the first option. The base table for this approach is hcllayer. The variables are highest1hulllayer, highest2hulllayer, and highest3hulllayer in the highesthulllayer table.
It is worth noting that the highest1hulllayer occurs on average at around 21.4% unclustered (with std dev. of 20.2%). These percentages go down alightly for highest2hulllayer and highest3hulllayer because cities that have 2 or 3 (or more) hulls have larger ecosystems and so more layers.
Elbow on fraction of locations in hulls
The elbowcalc and elbowdata queries provide the data. elbowdata takes layer/finallayer (i.e., fraction unclustered, as the layer 1 is the all encompassing hull and final layer is the raw locations), rounds it to two digits, and then calculates the average fraction of locations in hulls and the average hull area fraction of all encompassing hull area. The former gives a nice curve with an elbow (found by taking the second derivative and setting it equal to zero) at x=0.40237.
We then identify the layer that is closest to having a fraction of locations in hulls of 0.40237, taking the lower level (i.e., the more clustered level) whenever there is a tie. The resulting indicator variable is called elbowflhlayer and is made in table Elbowflh. This is analyzed in a sheet in "Images Review.xlsx" in E:\projects\agglomeration.
Fraction of Maximum Hull Area in Hulls
We also tried computing the fraction of the maximum hull area (MHA) in covered by hulls for each layer. The maximum hull area is on layer one, when every location is in an all-encompassing hull. We excluded data from layer one as well the final layer because they lead small data issues.
A cubic was a mediocre fit to this data, giving an R2 of 83% but with lots of deviation concentrated right around the local minimum ({-0.0224722, {x -> 0.446655}} [4], point of inflection and local maximum. A quartic had an R2 of 90% at around x=0.44 (6.408 x^4 - 15.176 x^3 + 12.592 x^2 - 4.3046 x + 0.517≈0.00825284 at x≈0.440275). I tried a quintic and it had inflection points are x=0.33, 0.55, and 0.82, as well as local maxima at 0.39 and 0.90. Visually there seems to be something going on in the 20% to 40% uncovered range too, perhaps a bifurcation of results, which might be due to rounding issues.
Reasonable Exclusions
We started by including all U.S. cities that received at least $10m of growth venture capital in a year between 1980 and 2017 (inclusive). This gave us a list of 200 cities. However, we still have a lot of city-years with low number of startups.
What is a reasonable number of startups to analyze agglomeration? Three locations (which is at least three startups) is the bare minimum required for one hull without excluding outliers. And we only made images for places with 4 or more startups. A visual inspection suggests that while there is greater (relative) dispersion when counts are low, it isn't hugely problematic. It is also worth noting that excluding 4 or less would get rid of Farmer's Branch, Fort Lauderdale, and Tempe (and Bloomington, MN) in 2017, and 6 or less in 2017 would eliminate Cary and Addison, all of which are slightly problematic. Burlington, VT has 7 years in the data with more than 6 startups, and one with 6.
But everywhere (i.e., all 200 places) have 10 or more layers at some point in time. And everywhere has at least 6 years with 6 or more observations. Detroit has just 7 obs that meet this criteria, half the number of Germantown, MD and a third of Greenwood Village, CO.! Requiring a year to have six observations would reduce us to 4916 observations from 6702 (i.e., down to 73% of the data). Requiring 9 would reduce the data down to 3889 obs (58%), and we'd lose more observations as places wouldn't have enough to form a time-series. The answer then appears to be to limit to observations with 6 or more layers. We'll code the number of layers, and the max and min number of layers for a place, into the data.
Maximum R-squared
Using a maximum R-squared approach to find the 'best layer' for a city is inherently problematic. A city might have 5 layers in 1980 and 80 layers in 2017, and so using layer 40, say, irrespective of year is somewhat meaningless. There are several alternative that make more sense. One is to use the fraction unclustered, much like with the elbow approach. The other is to find the layer with a certain hull count (or as close to it as possible). Hulls might tend to be somewhat stable over time, so three hulls in Portland in 2017 will be centered in more or less the same place as three hulls in Portland in 2003. This turns out to be somewhat true, as seen in the image on the right, which uses the last time (highest level) that there are three hulls, or two for 1998 and 1993 (one of which is out of frame). One issue with this approach is that the highest level with a certain hull count is that hulls almost always contain just three points.
An obvious alternative approach is to use the first time (lowest level) that there are three hulls. There is a big difference in the layer numbers for this. See the queries below. Essentially, the HCA algorithm often takes an original hull apart and then takes the resulting hulls apart, giving a quadratic for hull count again layer. But, as is apparent in the image, this leads to big areas that would only be good for overlap analysis and not for identifying individual clusters.
--Lowest,highest, and lowest-highest, and first-after-peak level where there are three hulls SELECT * FROM DisplayHullsFull WHERE place='Portland' and statecode='OR' AND year='2015' ORDER BY year,layer; --3, 41, 37, 33 (peak at 22,23,24,25) SELECT * FROM DisplayHullsFull WHERE place='Portland' and statecode='OR' AND year='2010' ORDER BY year,layer; --3, 24, 24, 24 (peak at 18) SELECT * FROM DisplayHullsFull WHERE place='Portland' and statecode='OR' AND year='2005' ORDER BY year,layer; --7, 23, 21, 21(peak at 18) SELECT * FROM DisplayHullsFull WHERE place='Portland' and statecode='OR' AND year='2000' ORDER BY year,layer; --3, 17, 17 , 17 (peak at 12,13,14) SELECT * FROM DisplayHullsFull WHERE place='Portland' and statecode='OR' AND year='1995' ORDER BY year,layer; --1(1), 8(1), 8(1), 8(1) (no peak-just flat but still take the highest layer with the nearest lower number of hulls) SELECT * FROM DisplayHullsFull WHERE place='Portland' and statecode='OR' AND year='1990' ORDER BY year,layer; --2(2), 5(2), 5(2), 5(2) (peak at 2,3,4,5 so 5 is first 'after' peak? but still take the highest layer with the nearest lower number of hulls) SELECT * FROM DisplayHullsFull WHERE place='Portland' and statecode='OR' AND year='1985' ORDER BY year,layer; --1(1), 1(1), 1(1), 1(1) (peak at 1 as that's the only layer with a hull but still take the highest layer with the nearest lower number of hulls)
right|300px Two further options are to find the lowest-highest and the first-after-peak. These often coincide. The lowest-highest finds the highest layer with x hulls and then works back down the layers taking the lowest in the continuous chain of x hulled layers. The first-after-peak finds the first layer with x hulls in or after the layers where there is the peak number of hulls. This last approach is a little problematic because sometimes there isn't a peak - its just flat - and it is inconceivable that there could be two or more peaks.
Image Analysis
Building Images
Use B&W:
- 50% grey at 75% transparent for city outline
- 50% grey at 50% transparent for hull
- Black + for singleton (size 10pt), 50% transparent when in pair or hull
- Black * for multiton (size 10pt), 50% transparent when in pair or hull
- Black line for pair
Informs colors:
- Orange: R240 G118 B34
- Blue: R31 G61 B124
- Green: R129 G190 B65
Town: Blue, 75% tranparent
Working with ArcPy
First version saved as E:\projects\agglomeration\Test.mxd
If the basemaps aren't available, connect to ERSI online using the icon in the system tray[5]
Basic set up is:
- displayhulls layer=1 grey50%,trans50%,noborder
- displaymultitons asterisk4,black,size10,trans50%
- displaysingletons cross1,black,size10,trans50%
- placetigerarea grey50%,trans75%,grey80%border
- Reference
- Basemap - World Light Grey Canvas
Change dataframe map to GCS 1984 and display to decimal degrees Saved as: FullHullReview2017.mxd
Open python window then:
#Load the map and create the dataframe
mxd = arcpy.mapping.MapDocument(r"E:\projects\agglomeration\FullHullReview2017Colored.mxd")
df = arcpy.mapping.ListDataFrames(mxd)[0]
df.credits="(c) Ed Egan, 2019"
#Now do the image generation!
myDict = {}
#myDict["Burlington_VT"] = [-73.27691399999999,-73.176383,44.445927999999995,44.539927]
#... See the entries in E:\projects\agglomeration\arcpydict.txt
for location in myDict:
newExtent = df.extent
newExtent.XMin = myDict[location][0]
newExtent.XMax = myDict[location][1]
newExtent.YMin = myDict[location][2]
newExtent.YMax = myDict[location][3]
df.extent = newExtent
df.panToExtent(df.extent)
filename="E:\\projects\\agglomeration\\Images\\"+location +".png"
arcpy.mapping.ExportToPNG(mxd, filename, resolution=144)
#arcpy.RefreshActiveView()
#mxd.save()
If you run into issues, it's useful to test things step by step:
#Test some exports, note that if the geocords are in a different system from the extent parameters, you'll be exporting blank images! arcpy.mapping.ExportToPNG(mxd, r"E:\projects\agglomeration\Images\BurlingtonAuto1.png", resolution=144) print df.extent #-73.5977988105381 44.1185146554607 -72.8022011894619 44.680787974202 NaN NaN NaN NaN #Test with Burlington, VT newExtent = df.extent newExtent.XMin =-73.219086 newExtent.XMax =-73.19356 newExtent.YMin = 44.460346 newExtent.YMax = 44.48325 df.extent = newExtent arcpy.mapping.ExportToPNG(mxd, r"E:\projects\agglomeration\Images\BurlingtonAuto2.png", resolution=144) df.panToExtent(df.extent) arcpy.mapping.ExportToPNG(mxd, r"E:\projects\agglomeration\Images\BurlingtonAuto3.png", resolution=144) #Test with Buffalo, NY (while looking at Burlington, VT) newExtent = df.extent newExtent.XMin =-78.95687699999999 newExtent.XMax =-78.795157 newExtent.YMin =42.826023 newExtent.YMax =42.966454999999996 df.extent = newExtent arcpy.mapping.ExportToPNG(mxd, r"E:\projects\agglomeration\Images\BuffaloAuto1.png", resolution=144) df.panToExtent(df.extent) arcpy.mapping.ExportToPNG(mxd, r"E:\projects\agglomeration\Images\BuffaloAuto2.png", resolution=144)
Remove basemap credits[6]:
- Click on World map layer
- Insert->Dynamic Text->Service Level Credits
- Set the symbol color to no color
Help pages:
- ArcPy Functions: https://desktop.arcgis.com/en/arcmap/10.3/analyze/arcpy-functions/alphabetical-list-of-arcpy-functions.htm
- Export to PNG: http://desktop.arcgis.com/en/arcmap/10.3/analyze/arcpy-mapping/exporttopng.htm
- Data Frames: http://desktop.arcgis.com/en/arcmap/10.3/analyze/arcpy-mapping/dataframe-class.htm
- Map Documents: http://desktop.arcgis.com/en/arcmap/10.3/analyze/arcpy-mapping/mapdocument-class.htm
- Text Elements: http://desktop.arcgis.com/en/arcmap/10.3/analyze/arcpy-mapping/textelement-class.htm
- Data access module: http://desktop.arcgis.com/en/arcmap/10.3/analyze/arcpy-data-access/what-is-the-data-access-module-.htm
Analyzing the results
The following issues became apparent (Counts out of 191 cities with 4 or more locations in 2017 and greater than $10m inv in a year over all time):
- Encapsulation - A small number of place boundaries are fully encapsulated inside of other geoplaces. We need to determine when this happens. The initial list includes Addison, Culver City, Santa Monica (might be extreme adjacency), and others. We need a query to work this out.
- Concavity (6 marked) - Some place boundaries are fairly extremely concave (for instance, Fort Lauderdale, FL, Birmingham, AL, Boulder, CO). This in itself isn't too much of an (addressable) issue. However, a small number of places have concavity and adjacency issues, which together lead to hull overlaps. This is ameriorated by removing outliers, but we should check them (e.g., Cary, NC, Morrisville, NC, the city next to Newark, CA, Roswell, GA)
- Adjacency (23 marked) - The entire of the valley has an adjacency issue (these weren't marked), as do a fairly large number of other cities. See Newport Beach, CA and others. Lexington, MA provides a nice example of containment despite adjacency. As does Cambridge, MA with the right outliers removed.
- Outliers (52 marked) - perhaps as many as 1 in 5 cities had one or two obvious outliers on a visual inspection.
Critical checks:
- Addison, TX: encapsulation
- Culver City, CA: encapsulation
- Oklahoma City, OK: scale issue (one outlier in State House?)
- Portland, ME: scale issue. Though Portland's place boundary contains an island and some sea area, making it very wonky, this isn't an issue.
- San Juan Capistrano, CA: Just 2 locations (1 singleton and 1 multiton) and no hull. Note that we might want to omit this place.
We might also want to check Twin Cities. Here's the results:
place statecode Issue Reason Champaign IL No Urbana isn't in the data Phoenix AZ No Mesa isn't in the data San Francisco CA No Twinned with Oakland! Oakland CA No Twinned with SF! Stamford CT Yes Norwalk Norwalk CT Yes Stamford New Haven CT No Bridgeport isn't in the data Tampa FL No St. Petersburg Portland ME No South Portland isn't in the data Minneapolis MN Yes St. Paul Bloomington MN No Normal isn't in the data Durham NC Yes? Raleigh Raleigh NC Yes? Durham Portland OR No Vancouver isn't in the data Bethlehem PA No Allentown isn't in the data Dallas TX Yes? Fort Worth Fort Worth TX Yes? Dallas Seattle WA No Tacoma isn't in the data
A visual inspection suggests that Stamford and Norwalk might be better combined but don't really matter. Minneapolis and St. Paul are pretty separate and really separate after removing outliers. Rarleigh and Durham are completely separate (Cary is more of an issue), as are Dallas and Fort Worth and SF and Oakland.
Encapsulation
The data suggests that there are 12 places that encapsulated by 7 other places:
SELECT A.place, A.statecode, B.place AS ContainedPlace, B.statecode AS ContainedStatecode
FROM placetigerarea AS A
JOIN placetigerarea AS B ON st_contains(ST_ConvexHull(A.placegeog::geometry),ST_ConvexHull(B.placegeog::geometry))
WHERE NOT (A.place=B.place AND A.statecode=B.statecode);
--12
place statecode containedplace containedstatecode Los Angeles CA Culver City CA Los Angeles CA Torrance CA Los Angeles CA El Segundo CA Los Angeles CA Santa Monica CA San Jose CA Santa Clara CA Fremont CA Newark CA Oakland CA Emeryville CA Cary NC Morrisville NC New York NY Jersey City NJ Dallas TX Richardson TX Dallas TX Addison TX Dallas TX Farmers Branch TX
We could ignore, flag or discard these cites. A visual inspection suggests that Culver City, Torrence, El Segundo, Jersey City, and probably Richardson, Newark, and maybe Cary don't have any issues. Santa Monica, Santa Clara, Emeryville, Farmer's Branch and Addison do look like they have issues, but with the exception of Farmer's Branch and Addison, these are big cites and with lots of locations, so the issue should be washed out by removing outliers or otherwise appropriately choosing the clustering layer.
Intersecting All Encompassing Hulls
52 places have all encompasing hulls intersect in our data (i.e., there are 26 intersections). This includes some of the places that suffer from encapsulation (especially Santa Monica, Santa Clara, Emeryville, Farmer's Branch and Addison). So beyond encapsulated places, there are an additional 20 intersections. These are:
place statecode intersectedplace intersectedstatecode Alpharetta GA Roswell GA Bellevue WA Redmond WA Boston MA Cambridge MA Boston MA Somerville MA Campbell CA San Jose CA Centennial CO Greenwood Village CO Cupertino CA San Jose CA Fremont CA Newark CA Greenwood Village CO Centennial CO Irvine CA Newport Beach CA Los Altos CA Mountain View CA Menlo Park CA Redwood City CA Milpitas CA San Jose CA Mountain View CA Palo Alto CA Mountain View CA Sunnyvale CA Newton MA Wellesley MA Phoenix AZ Tempe AZ Redwood City CA San Carlos CA San Jose CA Sunnyvale CA Santa Clara CA Sunnyvale CA
At a glance, most of these appear big or very big startup ecosystems. Accordingly, any process that deals with outliers (etc.) should address this issue.
First Estimation(s)
At this stage we have MasterLevels.txt and MasterLayers.txt as datafiles. MasterLevels.txt contains only layers corresponding to levels 0 through 12 and also has noothergeoms and avgdisthm as variables.
The questions we need to answer are: 1) Is there an agglomeration effect? 2) Which level or layer best describes a city (perhaps for a year, or perhaps over its life)?
We can just pick a level (say 25 hectares) and run a within-city regression:
. xtreg growthinv17l_f growthinv17l nosingletonl totmultitoncountl totpaircountl tothullcountl avgpairlengthl avghulldensi
> tyl avgdisthml i.year if level==6, fe cluster(placelevelid)
Fixed-effects (within) regression Number of obs = 5,027
Group variable: placelevelid Number of groups = 198
R-sq: Obs per group:
within = 0.4097 min = 3
between = 0.8310 avg = 25.4
overall = 0.5974 max = 37
F(44,197) = 78.20
corr(u_i, Xb) = 0.4087 Prob > F = 0.0000
(Std. Err. adjusted for 198 clusters in placelevelid)
-----------------------------------------------------------------------------------
| Robust
growthinv17l_f | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------+----------------------------------------------------------------
growthinv17l | .1388644 .0176074 7.89 0.000 .1041412 .1735877
nosingletonl | .1447935 .0402488 3.60 0.000 .0654197 .2241673
totmultitoncountl | .0909545 .0481349 1.89 0.060 -.0039714 .1858803
totpaircountl | .1724367 .0383185 4.50 0.000 .0968695 .2480039
tothullcountl | .7120504 .0467915 15.22 0.000 .6197739 .8043269
avgpairlengthl | -.0219417 .023633 -0.93 0.354 -.0685478 .0246645
avghulldensityl | .049566 .0202756 2.44 0.015 .0095808 .0895511
avgdisthml | .0933327 .076309 1.22 0.223 -.0571546 .2438201
Or:
. xtreg growthinv17l_f growthinv17l numstartups numstartupssq nosinglemulti nosinglemultisq nohull nohullsq nopair nopairs
> q i.year if level==6, fe cluster(placelevelid)
Fixed-effects (within) regression Number of obs = 5,773
Group variable: placelevelid Number of groups = 200
R-sq: Obs per group:
within = 0.4017 min = 4
between = 0.8425 avg = 28.9
overall = 0.5708 max = 37
F(45,199) = 72.39
corr(u_i, Xb) = 0.4222 Prob > F = 0.0000
(Std. Err. adjusted for 200 clusters in placelevelid)
---------------------------------------------------------------------------------
| Robust
growthinv17l_f | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------+----------------------------------------------------------------
growthinv17l | .220333 .018699 11.78 0.000 .1834595 .2572066
numstartups | .0062875 .0022944 2.74 0.007 .001763 .0108119
numstartupssq | -8.04e-07 1.14e-06 -0.70 0.483 -3.06e-06 1.45e-06
nosinglemulti | .0648575 .0168134 3.86 0.000 .0317023 .0980127
nosinglemultisq | -.0021614 .0006336 -3.41 0.001 -.0034108 -.000912
nohull | .1747691 .0255105 6.85 0.000 .1244636 .2250747
nohullsq | -.0057148 .0012164 -4.70 0.000 -.0081136 -.003316
nopair | .0896908 .0248207 3.61 0.000 .0407455 .1386361
nopairsq | -.0097196 .0024153 -4.02 0.000 -.0144825 -.0049567
Note that the following don't work, either alone or with other variables (including numstartups and numstartupsq), probably because they are third-order effects:
. xtreg growthinv17l_f growthinv17l avghulldensity avghulldensitysq avgpairlength avgpairlengthsq avgdisthm avgdisthmsq i.
> year if level==6, fe cluster(placelevelid)
Fixed-effects (within) regression Number of obs = 5,027
Group variable: placelevelid Number of groups = 198
R-sq: Obs per group:
within = 0.3579 min = 3
between = 0.5926 avg = 25.4
overall = 0.3753 max = 37
F(43,197) = 2152.49
corr(u_i, Xb) = 0.2529 Prob > F = 0.0000
(Std. Err. adjusted for 198 clusters in placelevelid)
----------------------------------------------------------------------------------
| Robust
growthinv17l_f | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
growthinv17l | .2668427 .0208574 12.79 0.000 .2257101 .3079752
avghulldensity | .0008076 .0003875 2.08 0.038 .0000433 .0015718
avghulldensitysq | -1.14e-07 8.80e-08 -1.29 0.197 -2.87e-07 5.97e-08
avgpairlength | -.0018724 .0036128 -0.52 0.605 -.0089972 .0052524
avgpairlengthsq | -.0000296 .0000596 -0.50 0.620 -.0001471 .0000879
avgdisthm | .001429 .0035371 0.40 0.687 -.0055465 .0084045
avgdisthmsq | -.000012 .0000157 -0.76 0.447 -.0000429 .000019
We can also do it with fractions and their squares (omit fracsinglemulti). However at level 6 (25 hectare), pairs seems more important than hulls:
. xtreg growthinv17l_f growthinv17l numstartups numstartupssq fracpair fracpairsq frachull frachullsq i.year if level==6,
> fe cluster(placelevelid)
Fixed-effects (within) regression Number of obs = 5,773
Group variable: placelevelid Number of groups = 200
R-sq: Obs per group:
within = 0.3919 min = 4
between = 0.8456 avg = 28.9
overall = 0.5274 max = 37
F(43,199) = 62.34
corr(u_i, Xb) = 0.4268 Prob > F = 0.0000
(Std. Err. adjusted for 200 clusters in placelevelid)
-------------------------------------------------------------------------------
| Robust
growthinv17~f | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
growthinv17l | .2481436 .0181447 13.68 0.000 .2123631 .283924
numstartups | .0100673 .0019792 5.09 0.000 .0061644 .0139702
numstartupssq | -6.92e-06 2.03e-06 -3.41 0.001 -.0000109 -2.92e-06
fracpair | .7540177 .3709212 2.03 0.043 .0225772 1.485458
fracpairsq | -1.936 .7030942 -2.75 0.006 -3.322472 -.5495289
frachull | .1969853 .562807 0.35 0.727 -.9128457 1.306816
frachullsq | -.1491389 .3878513 -0.38 0.701 -.9139649 .615687
Whereas across all levels:
. xtreg growthinv17l_f growthinv17l numstartups numstartupssq fracpair fracpairsq frachull frachullsq i.year, fe cluster(p
> lacelevelid)
Fixed-effects (within) regression Number of obs = 76,623
Group variable: placelevelid Number of groups = 2,600
R-sq: Obs per group:
within = 0.3956 min = 4
between = 0.8330 avg = 29.5
overall = 0.5279 max = 37
F(43,2599) = 827.33
corr(u_i, Xb) = 0.4143 Prob > F = 0.0000
(Std. Err. adjusted for 2,600 clusters in placelevelid)
-------------------------------------------------------------------------------
| Robust
growthinv17~f | Coef. Std. Err. t P>|t| [95% Conf. Interval]
--------------+----------------------------------------------------------------
growthinv17l | .2522524 .0049725 50.73 0.000 .2425019 .2620028
numstartups | .0100677 .0005323 18.91 0.000 .0090239 .0111114
numstartupssq | -6.95e-06 5.51e-07 -12.62 0.000 -8.03e-06 -5.87e-06
fracpair | .4152028 .0956859 4.34 0.000 .2275745 .6028311
fracpairsq | -.9753654 .1271631 -7.67 0.000 -1.224717 -.7260141
frachull | -.8606939 .1231519 -6.99 0.000 -1.10218 -.6192081
frachullsq | .495785 .0976557 5.08 0.000 .3042942 .6872758
This is probably because of the variation in hulls vs pairs at level 6, which has lots of cities with nothing in pairs and everything in hulls. We might want to 'control' for cityarea by restricting our within city analysis to large enough cities. A 25 hectare target area might be too encapsulating -- more than 10% of observations are 100% in hulls:
. su frachull if level==6, det
frachull
-------------------------------------------------------------
Percentiles Smallest
1% .2162162 .1153846
5% .3333333 .1153846
10% .4285714 .1428571 Obs 6,032
25% .6 .1428571 Sum of Wgt. 6,032
50% .8 Mean .7539126
Largest Std. Dev. .2209328
75% .9666666 1
90% 1 1 Variance .0488113
95% 1 1 Skewness -.6390206
99% 1 1 Kurtosis 2.400947
I tried using R2 to select levels, but only the second spec had an interior solution (at level 3):
forvalues i=1/12 {
quietly capture xtreg growthinv17l_f growthinv17l nosinglemulti nosinglemultisq nohull nohullsq nopair nopairsq avghulldensity avghulldensitysq avgpairlength avgpairlengthsq avgdisthm avgdisthmsq i.year if level==`i', fe cluster(placelevelid)
display "Reg: 1 level: " `i' " r2-within: " `e(r2_w)'
}
forvalues i=1/12 {
quietly capture xtreg growthinv17l_f growthinv17l nosinglemulti nosinglemultisq nohull nohullsq nopair nopairsq i.year if level==`i', fe cluster(placelevelid)
display "Reg: 2 level: " `i' " r2-within: " `e(r2_w)'
}
forvalues i=1/12 {
quietly capture xtreg growthinv17l_f growthinv17l numstartups numstartupssq fracsinglemulti fracsinglemultisq fracpair fracpairsq frachull frachullsq i.year if level==`i', fe cluster(placelevelid)
display "Reg: 3 level: " `i' " r2-within: " `e(r2_w)'
}
Reg: 2 level: 1 r2-within: .39552569 Reg: 2 level: 2 r2-within: .3998779 Reg: 2 level: 3 r2-within: .40348691 Reg: 2 level: 4 r2-within: .40130097 Reg: 2 level: 5 r2-within: .39931203 Reg: 2 level: 6 r2-within: .39707046 Reg: 2 level: 7 r2-within: .39366909 Reg: 2 level: 8 r2-within: .38957831 Reg: 2 level: 9 r2-within: .38398108 Reg: 2 level: 10 r2-within: .37662604 Reg: 2 level: 11 r2-within: .36999057 Reg: 2 level: 12 r2-within: .38393843
However, doing this by exgroup (0 t0 3), gives the same result - level 3 - for each exgroup.
Alternative approaches are to use AIC/BIC, or maybe entropy. For the same set of variables, in the same model, AIC/BIC are minimized when R2 is maximized, they are only useful when choosing the combination of the variables/estimation and the level. And it seems we can only do entropy one variable at a time:
entropyetc nohull if level==1
Other
See also:
Old Work Using Circles
Very Old Summary
Agglomeration is generally thought to be one of the most important determinants of growth for urban entrepreneurship ecosystems. However, there is essentially no empirical evidence to support this. This paper takes advantage of geocoding and introduces a novel measure of agglomeration. This measure is the smallest circle area that covers all startup offices, subject to having at least N startups in each circle. Using GIS data on cities, this paper controls for the density and socio-demographics of an area to identify the effect of just agglomeration.
Description
Clusters of economic activity plays a significant role in the firms performance and growth. An important driver of growth is the knowledge spillover between firms. This includes among others the facilitation of information flow and ideas between firms which could be a milestone especially in the growth of startup firms or small businesses. This project focuses on the effects of agglomeration on the performance and growth of startup firms. It introduces a novel measure of agglomeration which can be used to empirically test the effects of clustering. This measure the is smallest total circle area that covers all of the startups in the sample such that there are at least n firms in each circle. The projects is based on the creation of an algorithm which gives an unbiased measure to be used in the empirical analysis. The regression we are interested in takes the following form:
The dependent variable is a measure of growth of the firms. This measure could be investment forwarded one period or growth in investment. The control variables include the number of the startups firms, m, the agglomeration measure, A and a vector of other control variables affecting the growth of firms at time t. Because of the endogeneity in the circle area or the measure of agglomeration, A, there is a need for an instrumental variable to get consistent estimates of the effects we are interested in. The proposed instrument is the presence of a river, or road in between the points representing geographical locations of the venture capital backed up firms. The instrument affects agglomeration without having a direct impact on the growth. This makes it good candidate for a valid instrument. The next tasks are determining the additional control variables to include in the regression, years to include in the analysis and methods of finding an unbiased measure of agglomeration.
Data
Making the circle input data
Ed's additional datawork is in
Z:\VentureCapitalData\SDCVCData\vcdb2\ProcessingCoLevelSimple.sql
The key table for circle processing is CoLevelBlowout, which is restricted (to include cities with greater than 10 active at some point in the data) to make CoLevelForCircles.
We need to:
- Winsorize CoLevelBlowout
- Compute the circles!
- Make the Bay Area (over time) data
- Plot the Bay Area data (with colors per Bay Area city) for 1985 to present
- Combine the plots to make an animated gif
To winsorize the data we need the formula for Great Circle Distance. The radius of the earth is 6,378km (half of diameter: 12,756 km). So:
GCD = acos( sin(lat1) x sin(lat2) + cos(lat1) x cos(lat2) x cos(long1-long2) ) x r
Main Sources
The primary sources of data for this project are:
- SDC VentureXpert - from VC Database Rebuild, the key table is
- GIS City Data
- Data on NSF, NIH, population, income, clinical trials, employment, schooling, R&D expenditures and revenue of firms can be found in Hubs.
VC data
Data on the number of new vc backed firms in each city and year is in:
Z:\Hubs\2017\clean data The name of the file is firm_nr.txt.
Database is cities SQL script is: nr_firms.sql
Raw data is in:
Z:\VentureCapitalData\SDCVCData\vcdb2 The file is colevelsimple.txt
In order to see if there are outliers, I get the average coordinates for all cities and find the differences of the firm's coordinates from the city coordinate. The script for the average city coordinates is in
Z:\Hubs\2017\sql scripts and the file name is newcolevel.sql.
The differences are taken in excel. The file containing the differences is in
Z:\Hubs\2017 and the file name is new_colevel.txt.
- Data on the circle area in each city and year is in:
Z:\Hubs\2017\clean data The name of the file is circles.txt. (It contains only 106 observations)
Database is cities SQL script is: circles.sql
The script for joining the two tables on the VC table is in:
Z:\Hubs\2017\sql scripts The name of the file is new_firm_nr_circles.sql
- We use the cities with greater than 10 active VC backed firms. Data on the cities and number of active firms is in:
E:\McNair\Projects\Hubs\Summer 2017 The file is CitiesWithGT10Active.txt
The script for joining the final data with this file is located in
Z:\Hubs\2017\sql scripts The file name is final_joined_kerda.sql.
The final data is in
Z:\Hubs\2017\clean data The file name is new_final_kerda.txt.
Accelerator data
Accelerators data is in
Z:\Hubs\2017\clean data The file name is accelerators.txt The table is accelerators
The joined accelerators data with the VC table is in joined_accelerators table. The script is in
Z:\Hubs\2017\sql scripts The file name is join_accelerators.sql
The do file is in
Z:\Hubs\2017\kerda The name is agglomeartion_kerda.do
It includes the graphs, tables and the preliminary FE regressions with VC funding amount and growth rate. It also predicts the hazard rates, matches on the hazard rate in order to create synthetic control and treatment groups. What is left to do is to add 2 lagged and 3 forward observations for the cities which do have a match. Remove the overlapping observations for the years that get a treatment but which at the same time serve as a control.
See also
Also:
- Enclosing Circle Algorithm
- Normalizer
- Geocode.py
Unbiased measure
The number of startups affects the total area of the circles according to some function. The task is to find an unbiased measure of the area, which is not affected by the number of the startups, given the size and their distribution.
For the unbiased calculation of a measure in a different context see: http://users.nber.org/~edegan/w/images/d/d0/Hall_(2005)_-_A_Note_On_The_Bias_In_Herfindahl_Type_Measures_Based_On_Count_Data.pdf
GIS Resources
- https://www.census.gov/geo/maps-data/data/tiger-line.html
- https://www.census.gov/geo/maps-data/data/tiger.html
- http://postgis.net/features/
- https://en.wikipedia.org/wiki/GIS_file_formats
Useful functions for spatial joins
sum(expression): aggregate to return a sum for a set of records count(expression): aggregate to return the size of a set of records ST_Area(geometry) returns the area of the polygons ST_AsText(geometry) returns WKT text ST_Buffer(geometry, distance): For geometry: Returns a geometry that represents all points whose distance from this Geometry is less than or equal to distance. Calculations are in the Spatial Reference System of this Geometry. For geography: Uses a planar transform wrapper. ST_Contains(geometry A, geometry B) returns the true if geometry A contains geometry B ST_Distance(geometry A, geometry B) returns the minimum distance between geometry A and geometry B ST_DWithin(geometry A, geometry B, radius) returns the true if geometry A is radius distance or less from geometry B ST_GeomFromText(text) returns geometry ST_Intersection(geometry A, geometry B): Returns a geometry that represents the shared portion of geomA and geomB. The geography implementation does a transform to geometry to do the intersection and then transform back to WGS84 ST_Intersects(geometry A, geometry B) returns the true if geometry A intersects geometry B ST_Length(linestring) returns the length of the linestring ST_Touches(geometry A, geometry B) returns the true if the boundary of geometry A touches geometry B ST_Within(geometry A, geometry B) returns the true if geometry A is within geometry B geometry_a && geometry_b: Returns TRUE if A’s bounding box overlaps B’s. geometry_a = geometry_b: Returns TRUE if A’s bounding box is the same as B’s. ST_SetSRID(geometry, srid): Sets the SRID on a geometry to a particular integer value. ST_SRID(geometry): Returns the spatial reference identifier for the ST_Geometry as defined in spatial_ref_sys table. ST_Transform(geometry, srid): Returns a new geometry with its coordinates transformed to the SRID referenced by the integer parameter. ST_Union(): Returns a geometry that represents the point set union of the Geometries. substring(string [from int] [for int]): PostgreSQL string function to extract substring matching SQL regular expression. ST_Relate(geometry A, geometry B): Returns a text string representing the DE9IM relationship between the geometries. ST_GeoHash(geometry A): Returns a text string representing the GeoHash of the bounds of the object.
Native functions for geography
ST_AsText(geography) returns text ST_GeographyFromText(text) returns geography ST_AsBinary(geography) returns bytea ST_GeogFromWKB(bytea) returns geography ST_AsSVG(geography) returns text ST_AsGML(geography) returns text ST_AsKML(geography) returns text ST_AsGeoJson(geography) returns text ST_Distance(geography, geography) returns double ST_DWithin(geography, geography, float8) returns boolean ST_Area(geography) returns double ST_Length(geography) returns double ST_Covers(geography, geography) returns boolean ST_CoveredBy(geography, geography) returns boolean ST_Intersects(geography, geography) returns boolean ST_Buffer(geography, float8) returns geography [1] ST_Intersection(geography, geography) returns geography [1]
Functions for Linear Referencing
ST_LineInterpolatePoint(geometry A, double measure): Returns a point interpolated along a line. ST_LineLocatePoint(geometry A, geometry B): Returns a float between 0 and 1 representing the location of the closest point on LineString to the given Point. ST_Line_Substring(geometry A, double from, double to): Return a linestring being a substring of the input one starting and ending at the given fractions of total 2d length. ST_Locate_Along_Measure(geometry A, double measure): Return a derived geometry collection value with elements that match the specified measure. ST_Locate_Between_Measures(geometry A, double from, double to): Return a derived geometry collection value with elements that match the specified range of measures inclusively. ST_AddMeasure(geometry A, double from, double to): Return a derived geometry with measure elements linearly interpolated between the start and end points. If the geometry has no measure dimension, one is added.
3-D Functions
ST_3DClosestPoint — Returns the 3-dimensional point on g1 that is closest to g2. This is the first point of the 3D shortest line. ST_3DDistance — For geometry type Returns the 3-dimensional cartesian minimum distance (based on spatial ref) between two geometries in projected units. ST_3DDWithin — For 3d (z) geometry type Returns true if two geometries 3d distance is within number of units. ST_3DDFullyWithin — Returns true if all of the 3D geometries are within the specified distance of one another. ST_3DIntersects — Returns TRUE if the Geometries “spatially intersect” in 3d - only for points and linestrings ST_3DLongestLine — Returns the 3-dimensional longest line between two geometries ST_3DMaxDistance — For geometry type Returns the 3-dimensional cartesian maximum distance (based on spatial ref) between two geometries in projected units. ST_3DShortestLine — Returns the 3-dimensional shortest line between two geometries
Relevant PostgreSQL Commands
\dt *.* Show all tables \q Exit table
Specifities/ Outliers to consider
New York (decompose) Princeton area (keep Princeton unique) Reston, Virginia (keep) San Diego (include La Jolla) Silicon Valley (all distinct)
To make a circle
SELECT ST_Buffer([desired point], [desired radius], 'quad_segs=8') FROM [desired table]
quad_segs=8 indicates circle
For more precision in circle:
SELECT ST_Transform(geometry(
ST_Buffer(geography(
ST_Transform( [desired point], 4326 )),
[desired radius]')),
900913) FROM [desired table]
4326 and 900913 represent particular precision.
Decimal Degrees
We are working with longitude and latitude in decimal degrees. See https://en.wikipedia.org/wiki/Decimal_degrees
When converting radius to km, multiply by 111.3199. For area, multiple by (111.3199)^2=12,392.12013601.
Census Data
Population
The Census Gazetteer files for 2010, 2000 and 1990 can give use population by census place. See https://www.census.gov/geo/maps-data/data/gazetteer.html
The places file contains data for all incorporated places and census designated places (CDPs) in the 50 states, the District of Columbia and Puerto Rico as of the January 1, 2010. The file is tab-delimited text, one line per record. Some records contain special characters. Download the National Places Gazetteer Files (1.2MB) Download the State-Based Places Gazetteer Files: Column Label Description Column 1 USPS United States Postal Service State Abbreviation Column 2 GEOID Geographic Identifier - fully concatenated geographic code (State FIPS and Place FIPS) Column 3 ANSICODE American National Standards Insititute code Column 4 NAME Name Column 5 LSAD Legal/Statistical area descriptor. Column 6 FUNCSTAT Functional status of entity. Column 7 POP10 2010 Census population count. Column 8 HU10 2010 Census housing unit count. Column 9 ALAND Land Area (square meters) - Created for statistical purposes only. Column 10 AWATER Water Area (square meters) - Created for statistical purposes only. Column 11 ALAND_SQMI Land Area (square miles) - Created for statistical purposes only. Column 12 AWATER_SQMI Water Area (square miles) - Created for statistical purposes only. Column 13 INTPTLAT Latitude (decimal degrees) First character is blank or "-" denoting North or South latitude respectively Column 14 INTPTLONG Longitude (decimal degrees) First character is blank or "-" denoting East or West longitude respectively.
Relationships
See https://www.census.gov/geo/maps-data/data/relationship.html
These text files describe geographic relationships. There are two types of relationship files; those that show the relationship between the same type of geography over time (comparability) and those that show the relationship between two types of geography for the same time period.
ACS (American Community Survey) Data
Steps to download:
1) Go to https://factfinder.census.gov/faces/nav/jsf/pages/download_center.xhtml 2) Select 'I know the dataset or table(s) that I want to download.' 3) Press Next 4) For 'Select a program:' choose 'American Community Survey' 5) For 'Select a dataset and click Add to Your Selections:' choose '<YEAR OF INTEREST> ACS 1-year estimates' 6) Press 'Add To Your Selections' 7) Press Next 8) For 'Select a geographic type:' choose 'Place - 160' 9) For Select a state: Don't choose a state, as we wish to download all. 10) For 'Select one or more geographic areas...' choose 'All Places within United States and Puerto Rico' 11) Press Next
Other
Counts of firms by NAICS code at the county level may be useful: https://www2.census.gov/geo/pdfs/education/cbp12gdbs.pdf
Tax Increment Finance Zones
- State by state enabling statues: https://www.cdfa.net/cdfa/tifmap.nsf/index.html
