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===City Growth Rates===
 
A code section was added to E:\project\vcdb3\Ranking.sql to explore city growth rates.
 
The main problem with estimating the average of <math>\frac{dollars_t - dollars_{t-1} }{dollars_{t-1}}<\math>, where dollars is growth VC dollars invested in a cit-year, is a truncation issue. <math>dollars_{t-1}<\math> is often zero, and it is impossible for value to be below -100% while it can be above +100%.
 
I experimented with various ways to limit this issue, including considering:
*Only cities that have had more than $10m in a given year
*City-year pairs with more than $10m
*The top 100, 50 or 20 cities in 2017, for years from 1990 to 2017 or 2000 to 2017.
*Only cities that had $10m or more for every year from 2000 to 2017
 
The growth rate for cities that had $10m or more for every year from 2000 to 2017 was 0.334 per year, implying that such "established" ecosystems double their VC every three years. There are 47 such cities. The list of average growth rates by city for these cities is below. The average growth rate increases to 39.17% for the 61 cities which have $10m or more for at least all bar one years, and to 51.43% for the 72 cities that have it fro all bar two years.
 
city | avg
---------------------+--------------------
Malvern | 0.993156571636778
La Jolla | 0.610594418156654
Woburn | 0.603879780755441
Scottsdale | 0.575267305240787
Hayward | 0.541730108455613
Carlsbad | 0.523716703358772
Pleasanton | 0.509316345882909
Denver | 0.501050394443719
Burlingame | 0.500020365810236
Watertown | 0.472356466716033
Bedford | 0.463504586546262
Minneapolis | 0.458034053534397
Menlo Park | 0.456066638196533
North Waltham | 0.443317946821974
Palo Alto | 0.425111728982036
Emeryville | 0.421690271365118
Boston | 0.412678555600625
Seattle | 0.381774873244813
Los Gatos | 0.374521134293509
Lexington | 0.369969174443311
Los Angeles | 0.365024808593637
Atlanta | 0.351405016195985
South San Francisco | 0.321407553118583
Durham | 0.298104095936328
Morrisville | 0.297076835403358
Pittsburgh | 0.285423923204106
Boulder | 0.284022977435934
Rockville | 0.254953079027088
Campbell | 0.252975908859599
Waltham | 0.235784276400949
San Francisco | 0.231574232838588
Cambridge | 0.226097618461997
Burlington | 0.225559858389355
Chicago | 0.222048532754601
New York | 0.222000093754721
Irvine | 0.208556113551383
Houston | 0.206415333165726
Fremont | 0.204771682823134
San Mateo | 0.196399732252421
Cupertino | 0.18040546805283
Mountain View | 0.159432352723845
San Jose | 0.152962850233141
Redwood City | 0.0888134263293376
San Diego | 0.0711881806017128
Santa Clara | 0.0566618949392164
Sunnyvale | 0.0318692877947854
Austin | 0.0254452013443905
(47 rows)
 
Note that if we exclude 2000 (i.e. consider 2001 to 2017 inclusive), the overall average growth rate drops to 0.2812, and some cities, like Houston, have materially lower growth rates. It is worth noting that Houston had one big up year in 2013, where growth VC investment levels where 2.168 times the previous year, but then suffered a about a 50% mean reversion in the following years. Without 2013, Houston's average 2001 to 2017 growth rate is - -0.0197349989630022.
 
city | state | avg
---------------------+-------+----------------------
La Jolla | CA | 0.680031123241241
Woburn | MA | 0.64163859928389
Malvern | PA | 0.548552704731425
Menlo Park | CA | 0.504383164761797
Bedford | MA | 0.504211517175831
Hayward | CA | 0.49942185834955
Carlsbad | CA | 0.488399093032109
North Waltham | MA | 0.479226357065314
Minneapolis | MN | 0.473356376707567
Scottsdale | AZ | 0.434025239485977
Watertown | MA | 0.409908014646241
Emeryville | CA | 0.403333541766609
Pleasanton | CA | 0.402025316290345
Burlingame | CA | 0.401579348905957
Seattle | WA | 0.398842474741046
Boston | MA | 0.378228024530469
Morrisville | NC | 0.354372777597948
Palo Alto | CA | 0.350685408163029
Atlanta | GA | 0.336685642867238
Denver | CO | 0.332644416223719
Los Angeles | CA | 0.304585103537747
Boulder | CO | 0.28880663996075
South San Francisco | CA | 0.248595987210001
Campbell | CA | 0.245514436831657
Rockville | MD | 0.24315823017573
Los Gatos | CA | 0.233216007276288
Pittsburgh | PA | 0.225499709366802
Burlington | MA | 0.223634772577002
San Francisco | CA | 0.219993519832261
Lexington | MA | 0.205000361475032
New York | NY | 0.203868079937506
Chicago | IL | 0.203682874006923
Cupertino | CA | 0.191836717363744
San Mateo | CA | 0.187723172713732
Mountain View | CA | 0.166926239441008
Irvine | CA | 0.16644409093795
Fremont | CA | 0.150247623895727
Cambridge | MA | 0.140990253943638
Houston | TX | 0.109011554442698
San Diego | CA | 0.067832637853121
Redwood City | CA | 0.0666242814798974
San Jose | CA | 0.0471224685794607
Durham | NC | 0.0331127017373814
Waltham | MA | 0.0258917169868607
Austin | TX | 0.00294040411546173
Santa Clara | CA | -0.00296623469124349
Sunnyvale | CA | -0.00667850429419462
(47 rows)
==2017 and 2018 Q1/2 updates==

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