Economic Growth
IN THE UNITED STATES OF AMERICA
A County-level Analysis
Objective
•To explore the factors driving differences in regional economic
growth across the United States.
•To replicate the analysis in the OECD paper, “The Sources of
Economic Growth in OECD Regions: A Parametric Analysis,”
(December 2008) for the U.S. case.
Agenda
1. Theory
2. Data
3. Summary Statistics
4. Results
5. Findings/Conclusion
6. Future research/Recommendations
7. Questions
What theories explain economic
growth?
1. Neo-Classical Theory
2. Endogenous Growth Theory
3. New Economic Geography (NEG)
Neo-Classical Theory Assumes Diminishing
Returns And Exogenous Technology
• Key assumptions:
• Capital is subject to diminishing returns
• Perfect competition
• An exogenously determined constant rate reflects the
progress made in technology
•3 Key factors:
•Capital intensities
•Human capital
•Technology (not included in the model; exogenous)
Neo-Classical Theory Predicts Convergence
• Long-run growth is the result of continuous technological
progress, which is determined exogenously
• Key implication: Conditional convergence
• Problems
•Limited empirical evidence of convergence
•Leaves technological progress out of the model
Endogenous Growth Theory Assumes Diminishing
Returns and Endogenous Technology
• Key assumptions:
• Capital is subject to diminishing returns
•In many endogenous growth models the assumption of perfect
competition is relaxed, and some degree of monopoly power is thought to
exist.
•3 Key factors:
•Physical capital
•Human capital
•Technology (included in the model: endogenous)
Endogenous Growth Theory: Internal factors are
the main sources of economic growth
•Investing in human capital  the development of new forms of technology
& efficient and effective means of production  economic growth
•Investment in human capital (education and training of the workforce) is
an essential ingredient of growth
•The main implication: policies which embrace openness, competition,
change and innovation will promote growth.
•Theory emphasizes that private investment in R&D is the central source of
technical progress
•No convergence is predicted.
New Economic Geography: Why is
manufacturing concentrated in a few regions?
•
Economic geography: the location of factors of production in space
•
Key factors
• Economies of scale
• Transportation costs
• Location of demand
• Population
New Economic Geography predicts that the
right mix of key factors causes growth
Key implications
• Agglomeration raises wages in the core region
relative to the periphery
• Despite early similarity regions can become quite
different
• Large nearby demand causes more growth
• Producing near one’s main market minimizes
transportation costs
How does NEG differ from Neo-Classical and
Endogenous Growth Theories?
• NEG takes scale into account
• NEG models propose that external increasing returns to scale incentivize
agglomeration
• Agglomeration captures, via scale effects, how small initial differences
cause large growth differentials over time
We obtained data on 3,079 counties between
1998-2007
Variable
Source
Year(s)
Annualized per capita personal
income growth
Bureau of Economic Analysis
1998-2007
Log of income in the initial year
Bureau of Economic Analysis
1998
Physical capital/infrastructure
ESRI Data and Maps 9.3 Media
Kit
2008
Education rates
U.S. Census
2000
Innovation Index
Economic Development
Administration
Employment rate
Employment specialization
Accessibility to
Markets/Distance to Markets
Census of Employment and
Wages
1998-2007
Per Capita Personal Income
•Ranges from $8,579 in Loup County, NE to $132,728 in Teton County, WY
• Used to create three variables:
• Dependent variable: annualized per capita personal income growth
1/10 * ln(income in 2007) – ln(income in 1998)
• Highest: 7% in Sublette, WY
• Lowest: -3% in Crowley, CO
• Mean: 1%
• Independent variable: log of income in the initial year, 1998
• Highest: $76,450 in New York, NY
• Lowest: $7,756 in Loup, NE
• Independent variable: per capita personal income in nearby counties,
weighted by distance and other spatial measures
Per Capita Personal Income By County 1998
Legend
Per Capita Personal Income 1998
income_1998
$7,756.00 - $17,986.00
$17,986.01 - $21,883.00
$21,883.01 - $26,732.00
$26,732.01 - $35,888.00
$35,888.01 - $76,450.00
Per Capita Personal Income By County 2007
Legend
Per Capita Personal Income 2007
income_2007
$6,777.41 - $20,522.62
$20,522.63 - $25,391.39
$25,391.40 - $32,690.20
$32,690.21 - $47,484.53
$47,484.54 - $104,855.10
Total Per Capita Personal Income Growth Rate By County 1998-2007
Legend
Total PCPI Growth
1998-2007
-0.035588 - 0.002768
0.002769 - 0.011047
0.011048 - 0.019209
0.019210 - 0.031769
0.031770 - 0.070344
Infrastructure
•A measure of Physical Capital.
•Mileage of major roads by county
•Airports by county
200
0
100
Frequency
300
400
Major Road Mileage by County
0
. sum
1000
2000
3000
Major roads in miles
4000
5000
high_length_miles
Variable
Obs
Mean
high_lengt~s
3079
380.8334
Std. Dev.
280.9239
Min
Max
32.13309
4584.723
1500
1000
0
500
Number of Counties
2000
2500
Number of airports by County
0
1
2
3
Number of airports
4
Number of
airports
Freq.
Percent
Cum.
0
1
2
3
4
6
2,543
458
62
8
7
1
82.59
14.87
2.01
0.26
0.23
0.03
82.59
97.47
99.48
99.74
99.97
100.00
Total
3,079
100.00
5
6
Education Rates
• Source: 2000 Census
• Percent of population with less than high school degree
• Highest: 62.5% in Starr, TX
• Lowest: 4.4% in Douglas, CO
• Median: 21.6%
• Percent of population with a high school diploma
• Highest: 53.5% in Carroll, OH
• Lowest: 12.4% in Arlington, VA
• Median: 34.7%
• Percent of population with more than a high school degree
• Highest: 82.1% in Los Alamos, NM
• Lowest: 17.2% in McDowell, WV
• Median: 41.4%
• These three variables add up to 1
(Capture above info in bar graph)
Innovation Index
[COMING SOON]
Employment Rate
• Source: 2000 Census (for cross-section)
• Youth employment rate: population aged 16 – 20 that is working divided by total
population 16 – 20
• Highest: 100% in Loving, TX
• Lowest: 8.78% in Shannon, SD
• Median: 46.2%
• Working age employment rate: population aged 21 – 65 that is working divided by
total population 21 – 65
• Highest: 88.4% in Stanley, SD
• Lowest: 35.9% in McDowell, WV
• Median: 73%
• Total employment rate
• Highest: 86.7% in Stanley, SD
• Lowest: 33.6% in McDowell, WV
• Median: 69.9%
(NEED BAR GRAPH!)
Employment Specialization: Measure of Industrial
Concentration of Region
• Meant to capture notion of agglomeration
• The spatial concentration of industry
• A determinant of economic growth in NEG growth theory.
• How is it modeled?
• Specialization indices
• Herfindahl Index
• Krugman Index
Herfindahl Index
•
The Herfindahl index is the sum across industrial sectors of the square of that
sector’s share of employment
• Ranges from 0 to 1.0
• 0 = large number of very small firms
• (perfect competition)
• 1 = a single monopolistic producer
• (complete monopoly by a single firm)
Krugman Index
• KI = ∑j|aij-b-ij|
• a = the share of industry j in county i’s total employment
• b = the share of the same industry in the employment of all other
counties, -i
• KI = the absolute values of the difference between these shares,
summed over all industries
• Ranges from 0 to 2.0
• 0 = county i has industrial composition identical to its comparison counties
• 2 = county i has industrial composition without any similarity (no common
industries) to its comparison counties
To Measure Employment Specialization We Chose
the Krugman Index
Pros
Cons
Herfindahl Index
Captures industrial specialization
Is an absolute measure; Does not
take neighbors into account
Krugman Index
Captures industrial specialization.
Argued that the absolute size of
clusters should be the basis for
calculation.
Is a relative measure; Compares to
one’s neighbors
Objections hold that this level is
systematically underestimated for
larger metropolitan areas when
relative levels of concentration are
used.
Accessibility to Markets/Distance to Markets
[PENDING]
OLS Results
. reg totalpcpigrowth lninitialincome
Source
SS
df
MS
Model
Residual
.001620368
.293232788
1
3077
.001620368
.000095298
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
lninitiali~e
_cons
-.003361
.0447189
Std. Err.
.0008151
.008105
t
-4.12
5.52
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.000
=
=
=
=
=
=
3079
17.00
0.0000
0.0055
0.0052
.00976
[95% Conf. Interval]
-.0049592
.0288272
-.0017628
.0606106
0
.05
-.05
totalpcpigrowth
.1
Scatter Plot
9
9.5
10
10.5
lninitialincome
11
11.5
OLS Results
. reg totalpcpigrowth high_length_miles
Source
SS
df
MS
Model
Residual
.000529396
.294323761
1
3077
.000529396
.000095653
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
high_lengt~s
_cons
1.48e-06
.0107438
Std. Err.
6.28e-07
.0002969
t
2.35
36.18
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
3079
5.53
0.0187
0.0018
0.0015
.00978
P>|t|
[95% Conf. Interval]
0.019
0.000
2.46e-07
.0101616
2.71e-06
.0113261
OLS Results
. reg
totalpcpigrowth lninitialincome percentlessthanhs percenthsdiploma percentmorethanhs
Source
SS
df
MS
Model
Residual
.0219857
.272867456
3
3075
.007328567
.000088737
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
lninitiali~e
percentles~s
percenthsd~a
percentmor~s
_cons
-.0109003
.0231712
(dropped)
.0401284
.0973624
Std. Err.
t
Number of obs
F( 3, 3075)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
=
=
=
=
=
=
3079
82.59
0.0000
0.0746
0.0737
.00942
[95% Conf. Interval]
.0010488
.0035923
-10.39
6.45
0.000
0.000
-.0129567
.0161277
-.0088438
.0302147
.0028069
.0104257
14.30
9.34
0.000
0.000
.0346248
.0769203
.0456319
.1178044
OLS Results
. reg totalpcpigrowth airports
Source
SS
df
MS
Model
Residual
.002081988
.292771168
1
3077
.002081988
.000095148
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
airports
_cons
.0016204
.0109692
Std. Err.
.0003464
.00019
t
4.68
57.74
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
3079
21.88
0.0000
0.0071
0.0067
.00975
P>|t|
[95% Conf. Interval]
0.000
0.000
.0009412
.0105968
.0022995
.0113417
OLS Results
. reg totalpcpigrowth high_length_miles airports
Source
SS
df
MS
Model
Residual
.002104477
.29274868
2
3076
.001052238
.000095172
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
high_lengt~s
airports
_cons
-3.76e-07
.0017429
.0110871
Std. Err.
7.74e-07
.0004284
.000308
t
-0.49
4.07
36.00
Number of obs
F( 2, 3076)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.627
0.000
0.000
=
=
=
=
=
=
3079
11.06
0.0000
0.0071
0.0065
.00976
[95% Conf. Interval]
-1.89e-06
.0009029
.0104832
1.14e-06
.0025829
.0116909
OLS Results
. reg totalpcpigrowth totalemprate
Source
SS
df
MS
Model
Residual
.003059628
.291793528
1
3077
.003059628
.000094831
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
totalemprate
_cons
-.0134318
.0206125
. reg totalpcpigrowth
Source
Std. Err.
.0023647
.0016478
t
-5.68
12.51
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.000
=
=
=
=
=
=
3079
32.26
0.0000
0.0104
0.0101
.00974
[95% Conf. Interval]
-.0180683
.0173816
-.0087952
.0238434
youthemprate
SS
df
MS
Model
Residual
.00935219
.285500966
1
3077
.00935219
.000092785
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
youthemprate
_cons
-.0166641
.0188594
Std. Err.
.0016598
.0007721
t
-10.04
24.43
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.000
=
=
=
=
=
=
3079
100.79
0.0000
0.0317
0.0314
.00963
[95% Conf. Interval]
-.0199186
.0173455
-.0134096
.0203734
OLS Results
. reg totalpcpigrowth
Source
workingageemprate
SS
df
MS
Model
Residual
.001864752
.292988405
1
3077
.001864752
.000095219
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
workingage~e
_cons
-.0107746
.0191127
. reg
Std. Err.
.0024347
.0017728
t
-4.43
10.78
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.000
=
=
=
=
=
=
3079
19.58
0.0000
0.0063
0.0060
.00976
[95% Conf. Interval]
-.0155485
.0156367
-.0060007
.0225888
totalpcpigrowth youthemprate workingageemprate totalemprate
Source
SS
df
MS
Model
Residual
.010864542
.283988615
3
3075
.003621514
.000092354
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
youthemprate
workingage~e
totalemprate
_cons
-.0204913
.033683
-.0228014
.0119877
Std. Err.
.0039113
.0217282
.0243243
.0018895
t
-5.24
1.55
-0.94
6.34
Number of obs
F( 3, 3075)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.121
0.349
0.000
=
=
=
=
=
=
3079
39.21
0.0000
0.0368
0.0359
.00961
[95% Conf. Interval]
-.0281604
-.0089204
-.070495
.008283
-.0128222
.0762863
.0248922
.0156925
OLS Results
. reg totalpcpigrowth hi
Source
SS
df
MS
Model
Residual
.000901317
.29395184
1
3077
.000901317
.000095532
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
hi
_cons
.0034814
.0104854
Std. Err.
.0011334
.00032
t
3.07
32.76
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
3079
9.43
0.0021
0.0031
0.0027
.00977
P>|t|
[95% Conf. Interval]
0.002
0.000
.0012591
.0098579
.0057037
.0111128
. reg totalpcpigrowth ki
Source
SS
df
MS
Model
Residual
.002731506
.29212165
1
3077
.002731506
.000094937
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
ki
_cons
.0027874
.0090671
Std. Err.
.0005197
.0004528
t
5.36
20.02
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
3079
28.77
0.0000
0.0093
0.0089
.00974
P>|t|
[95% Conf. Interval]
0.000
0.000
.0017685
.0081792
.0038063
.009955
OLS Results
. reg
totalpcpigrowth accessibility
Source
SS
df
MS
Model
Residual
.001546966
.293306191
1
3077
.001546966
.000095322
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
accessibil~y
_cons
-.00061
.0173707
Std. Err.
.0001514
.0015157
t
-4.03
11.46
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
3079
16.23
0.0001
0.0052
0.0049
.00976
P>|t|
[95% Conf. Interval]
0.000
0.000
-.000907
.0143988
-.0003131
.0203426
OLS Results
. reg totalpcpigrowth distance_to_market
Source
SS
df
MS
Model
Residual
.01258184
.282271316
1
3077
.01258184
.000091736
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
distance_t~t
_cons
8.36e-14
.0042186
Std. Err.
7.14e-15
.0006293
t
11.71
6.70
Number of obs
F( 1, 3077)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
3079
137.15
0.0000
0.0427
0.0424
.00958
P>|t|
[95% Conf. Interval]
0.000
0.000
6.96e-14
.0029846
9.76e-14
.0054525
OLS Results
Source
SS
df
MS
Model
Residual
.031777513
.263075644
9
3069
.003530835
.00008572
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
distance_t~t
high_lengt~s
percentles~s
percentmor~s
lninitiali~e
ki
youthemprate
workingage~e
airports
_cons
4.25e-14
-4.46e-07
.0095969
.0277121
-.0068983
.0027824
-.0116003
.0025639
.0011786
.0634634
Std. Err.
8.05e-15
7.87e-07
.0041919
.0031681
.0011938
.000657
.002529
.0043352
.0004263
.0111748
t
5.28
-0.57
2.29
8.75
-5.78
4.23
-4.59
0.59
2.76
5.68
Number of obs
F( 9, 3069)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.571
0.022
0.000
0.000
0.000
0.000
0.554
0.006
0.000
=
=
=
=
=
=
3079
41.19
0.0000
0.1078
0.1052
.00926
[95% Conf. Interval]
2.67e-14
-1.99e-06
.0013777
.0215003
-.0092391
.0014941
-.0165589
-.0059364
.0003428
.0415525
5.82e-14
1.10e-06
.0178161
.0339239
-.0045576
.0040706
-.0066417
.0110642
.0020143
.0853743
OLS Results
> i youthemprate workingageemprate
Source
SS
df
MS
Model
Residual
.031122181
.263730976
8
3070
.003890273
.000085906
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
distance_t~t
high_lengt~s
percentles~s
percentmor~s
lninitiali~e
ki
youthemprate
workingage~e
_cons
4.20e-14
5.45e-07
.010242
.029272
-.0068954
.0025355
-.0117032
.0020258
.0631671
Std. Err.
8.05e-15
7.02e-07
.0041899
.0031208
.0011951
.0006516
.0025314
.0043356
.0111864
t
5.22
0.78
2.44
9.38
-5.77
3.89
-4.62
0.47
5.65
Number of obs
F( 8, 3070)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.437
0.015
0.000
0.000
0.000
0.000
0.640
0.000
=
=
=
=
=
=
3079
45.29
0.0000
0.1056
0.1032
.00927
[95% Conf. Interval]
2.62e-14
-8.31e-07
.0020267
.0231529
-.0092386
.0012577
-.0166667
-.0064751
.0412335
5.78e-14
1.92e-06
.0184573
.0353911
-.0045521
.0038132
-.0067397
.0105267
.0851007
OLS Results
Source
SS
df
MS
Model
Residual
.030269749
.264583407
9
3069
.003363305
.000086212
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
distance_t~t
high_lengt~s
percentles~s
percentmor~s
lninitiali~e
hi
youthemprate
workingage~e
airports
_cons
4.67e-14
-1.22e-06
.0102764
.0267372
-.0081632
.0007522
-.0144924
.007201
.0009525
.0762806
Std. Err.
8.02e-15
7.77e-07
.0042013
.0031696
.0011864
.0012876
.0025074
.0043019
.0004248
.0110451
t
5.82
-1.57
2.45
8.44
-6.88
0.58
-5.78
1.67
2.24
6.91
Number of obs
F( 9, 3069)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.118
0.015
0.000
0.000
0.559
0.000
0.094
0.025
0.000
=
=
=
=
=
=
3079
39.01
0.0000
0.1027
0.1000
.00929
[95% Conf. Interval]
3.10e-14
-2.74e-06
.0020388
.0205225
-.0104894
-.0017724
-.0194087
-.001234
.0001196
.0546241
6.24e-14
3.07e-07
.018514
.032952
-.0058371
.0032769
-.0095761
.0156359
.0017853
.0979372
OLS Results
Source
SS
df
MS
Model
Residual
.030072747
.26478041
8
3070
.003759093
.000086248
Total
.294853157
3078
.000095794
totalpcpig~h
Coef.
distance_t~t
high_lengt~s
percentles~s
percentmor~s
lninitiali~e
ki
totalemprate
airports
_cons
4.55e-14
-3.64e-07
.0117685
.0300993
-.0068724
.0036642
-.0089656
.0012035
.0635042
Std. Err.
8.02e-15
7.90e-07
.0042226
.0031391
.0012303
.0006237
.0036322
.0004274
.0113212
t
5.67
-0.46
2.79
9.59
-5.59
5.88
-2.47
2.82
5.61
Number of obs
F( 8, 3070)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.000
0.645
0.005
0.000
0.000
0.000
0.014
0.005
0.000
=
=
=
=
=
=
3079
43.58
0.0000
0.1020
0.0997
.00929
[95% Conf. Interval]
2.98e-14
-1.91e-06
.0034891
.0239443
-.0092848
.0024413
-.0160873
.0003654
.0413063
6.12e-14
1.18e-06
.0200479
.0362543
-.0044601
.004887
-.0018438
.0020416
.085702
Modeling Spatial Relationships
Inverse Distance
…
 K-Nearest Neighbor
…
 Contiguity
…
Contiguous Counties
The average county has 5 to 6 neighbors (main point)
How many neighbors does the…
Number of Contiguous Neighbors
1200
Number of Counties
1000
800
600
400
200
0
1
2
3
4
5
6
7
8
9
Number of Neighbors
10
11
12
13
14
Global Spatial Autocorrelation
Growth rates display spatial dependence…Moran’s
I…Null hypothesis
. spatgsa totalpcpigrowth, weights(W) moran
Measures of global spatial autocorrelation
Weights matrix
Name: W
Type: Imported (binary)
Row-standardized: No
Moran's I
Variables
totalpcpigrowth
*1-tail test
I
0.432
E(I)
sd(I)
-0.000
0.010
z
41.176
p-value*
0.000
Own growth rates depend on neighbors (idea)
Moran scatterplot (Moran's I = 0.439)
totalpcpigrowth
5
1122
4
2653
3063
3
Wz
2
1
0
228
-1
-2
3074
1116
2719
1104
1114
3066
2736
3059
3061
3069
3068
25561999 3078
3065
2602
1967
3071
1993
3075
2647
3079
2006
1981
1986
1961
3062 2639
3058
2367
2541
2336
1601 1972
2000
1968
1774
1980
3072
30601962
2726
2546
1977
1133
2704
2747
2721
2622
1569
2606
256
1966
2571
1985
2666
1979
1956
3057
1976
2384
2358
1123
1990
1963
1984
1992
333
3070
267
21302656
1982
1983
2683
1576
1974
1995
2158
1129
2613
1135 2106
2002
2159
2099
1959
1957
2490
1125
1978
2714
2329
1769 3073
2379
2371
526
538
1082
2557
1960
334 2008
2792
2128
2657
2540
244
238
1610
3077
2146
2619
195
1390
2351
2620
2543
2137
2695
2121
557
2677
1128
2612
2505
1998
1600
2380
1568
2696
2641
2382
1971
1618
2650
2111
2333
1975
2741
2624
1295
1988
3064
2337
2157
2356
1107
2144
1566
2131
2512
269
2703
2151
1614
2391
2365
2706
2615
1582
1565
1130
2372
1596
2343
1101
1773
1597
2163
1612
2142
1586
2135
2122
2702
1987
1110
2592
2363
2739
1139
2110
2344
2519
2742
1577
1762
346
1606
2895
1585
2574
1970
1619
2728
2674
2527
2551
1572
1589
2148
1958
1584
2160
1997
1421
1117
2644
1609
1182
2161
2559
1571
1174
996
2357
1102
2881
72
1871
2883
1570
2124
239
2712
1964
1185
2328
2625
2349
1084
2355
2147
1991
1579
198
1598
1605
2638
1095
2150
2140
2710
1608
1445
531
2170
2518
1081
1607
1778
2590
1602
2105
2737
2730
1611
2573
17231989
2393
1567
2167
2291
1615
2554
1441
2643
1097
2621
2127
2113
77
2007
2537
2115
1593
2341
33
1083
1096
1613
2759
80
1126
1581
2764
2711
1564
2373
2697
1592
2669
2720
2350
1320
1996
290
1763
2780
1575
1578
159
2003
1698
2610
1091
2165
2585
1100
2596
2156
2345
1599
2552
2566
1587
2534
1099
2978
2133
1106
2502
2375
1389
2658
2670
301
2681
1088
1093
2607
2611
1432
2004
2561
1793
1195
1623
2342
2138
1657
2572
1780
2884
2348
556
2630
1119
1131
2777
2885
1087
2779
2693
1784
1121
768
271
2637
2727
2675
2347
1748
2528
1594
2705
1183
1118
1574
1595
2783
2152
2626
1141
2629
315
1080
1718
1367
2930
21
1132
2153
1705
234
2975
1113
73
2886
2493
1175
1111
261
2500
2642
2378
1171
2332
2589
2648
2168
1090
2933
2295
2171
2155
1617
1796
2097
240
1127
2184
2694
2169
2567
1173
2634
2623
68
2526
936
2828
2664
347
2654
2775
2817
1120
2814
2279
2339
69
316
529
2498
1603
1973
2352
2524
2709
201
2164
1588
2108
2766
1103
2838
2145
250
226
2806
2522
382
1094
2785
2361
2112
2671
383 2139
2579
1676
2335
2810
2849
1092
1194
1785
2386
535
1665
2684
2672
257
63
2646
1761
2584
2774
2117
2536
2782
2976
2731
2346
1965
357
296
2134
2280
2717
549
230
206
1604
336
2538
2459
2136
59
2514
197
2618
1969
1124
1591
2560
2119
1741
134
452
4
1369
520
1089
463
1160
863
2289
2235
1167
254
1420
109
2496
1161
96
1193
1108
1583
2555
2959
2570
2501
2326
258
2515
1086
534
2740
2580
1764
2652
119
975
81
2366
57
2772
8
1426
2103
1105
1098
2910
1140
2746
2665
2211
1191
178
287
177
171
1085
20
2299
241
312
2931
1776
79
2359
1580
871
2513
544
2162
2832
1654
2932
1447
2913
2655
6
1590
2968
2001
2529
541
2839
2288
2890
1782
1702
2603
878
2370
2851
951
1886
1670
1316
2149
1380
1526
1448
2761
1442
548
172
1163
2609
299
2821
2778
2971
213
1824
2107
2101
203
2768
2967
89
2861
1768
46
166
2855
2277
2564
2698
1511
1515
1134
66
1137
232
283
1079
2492
58
2114
2132
1386
2852
2503
2377
2532
1790
199
2941
242
2509
2784
524
1385
2954
212
2950
325
272
2938
1882
800
78
1833
2882
71
2980
2389
2334
2927
2633
2635
2776
1645
527
968
341
765
1339
1438
2946
1994
1681
205
1787
32
2102
2203
31
2125
295
1746
2381
3067
324
2752
2640
18
1074
849
1018
2368
2963
485
2588
249
2725
2239
1293
793
2281
1187
2940
51
2120
145
2880
934
1627
355
2627
1321
192
2533
2141
16
377
1025
2686
1722
190
952
2787
43
2661
248
2587
1739
1162
24
2116
1138
184
2781
2504
558
1724
848
830
1508
971
2773
219
196
1423
2793
2506
85
1851
1188
1324
779
2651
53
279
2822
2154
264
2362 16771771
1838
1384
1346
2878
2232
1755
1759
815
778
1338
759
978
551
1435
1
1166
2815
2718
903
1779
1333
142
1922
1626
174
167
2208
281
522
2616
2732
331
305
1853
2594
1788
769
381
91
1903
1944
1907
2369
1725
2577
2321
2786
1377
1159
1803
982
162
2507
1770
2689
837
2303
335
1024
2788
2608
1514
1176
842
2508
2324
1715
99
545
2118
916
2510
835
2842
2734
2415
2957
912
2939
2800
200
121
61
150
1314
555
1150
274
188
1666
1735
1757
539
2827
117
282
2530
1883
2360
92
1142
1791
809
990
286
2645
2905
1405
1112
2819
130
112
2296
176
2392
2960
356
884
1357
170
207
3
1642
1949
1751
1030
1551
838
550
1342
1807
2953
306
755
791
1396
185
136
2398
1672
2981
108
2841
2716
1835
1880
14
102
1323
536
2692
1789
183
103
2865
2809
1749
1180
2581
1179
1753
1399
853
2260
1520
2104
75
1190
420
986
337
27
2789
2535
2578
448
767
1678
1772
2636
595
1864
786
245
327
1732
2937
1149
1466
2858
2846
1559
1398
2836
2593
2834
2935
1189
50
284
2682
1038
1418
2847
1829
2894
1804
2483
2376
546
19
1460
105
2475
1837
2435
2799
2871
1647
319
1633
1169
54
128
2005
70
1178
2331
2206
125
773
2462
1076
2397
2553
214
41
1845
1164
2875
521
2274
173
2495
135
2862
2820
5896
1147
2306
1730
2190
1736
2700
94
2312
1294
1409
2550
2936
1006
1750
1412
1783
262
126
1318
29
954
2943
307
2763
1165
1463
2691
789
1529
2688
60
2576
1184
11
547
795
2385
2868
193
1012
1834
1616
2404
1538
1196
1056
1168
55
2663
823
1009
1381
2811
864
2919
1696
1055
160
851
1795
1388
1330
994
2864
1823
1177
2218
132
2542
227
37
332
1434
1721
300
38
2549
2472
1926
1443
832
2735
151
23
115
2278
518
2482
813
1444
339
2419
1700
1501
1016
1155
1760
935
1302
2813
1862
762
1062
2660
814
1325
2219
423
1403
2272
2198
1394
26
2750
1855
787
1483
2942
2921
288
2213
2723
1181
2870
15
1639
2447
147
1809
1737
1282
928
187
2308
2340
2520
2268
1801
2265
532
2856
2179
49
1573
209
1410
2951
340
1777
2874
2569
7
2173
2767
693
1379
1635
285
771
2790
957
2212
1332
797
1053
280
2474
154
1136
1850
2662
776
533
1433
799
965
1152
191
1336
1115
1429
2539
1717
1068
1393
2521
622
210
2830
1689
1308
65
2986
354
1440
487
83
1374
2441
2201
208
1831
82
2934
2964
2977
2857
168
829
161
772
2917
2863
1172
84
852
2237
2685
821
1335
1283
826
867
2956
2807
2979
2129
2702180
2394
885
1355
1307
917
1370
88
2974
1692
920
1311
215
1153
2952
455
604
2904
2315
1510
725
2833
211
519
2751
794
393
1154
1523
2599
525
2902
2427
2601
2497
1481
1775
408
1148
1077
2183
2469
1817
2876
2850
1109
1376
2525
93
1383
1555
2945
764
834
2313
1494
796
847
97
528
2802
1144
289
2844
1752
2255
164
1071
44
1495
2908
530
1549
2465
1632
2879
1525
2724
2383
657
3005
949
1742
122
2948
189
2632
2598
2290
2631
2749
1000
1840
1863
1548
2958
2877
1539
828
2955
1408
1358
1192
1343
181
1836
1158
1818
763
766
788
2455
86
1422
2966
2949
1186
2563
1366
2918
2804
1622
2715
1543
294
2649
2614
1382
2791
2973
1359
2988
1813
2729
2181
165
756
1341
517
2907
293
801
2887
2916
874
1439
775
2214
1521
542
757
861
2297
1708
2143
2458
2451
1424
688
1716
2238
845
2972
559
2354
2745
1644
2982
111
1811
182
3054
1870
297
1157
784
76
1679
2240
180
202
2970
2188
1022
1145
2984
2758
1419
2962
446
2276
3037
770
1756
87
641
1920
12
1457
543
2969
590
1937
2859
1924
179
825
1709
1285
95
148
158
1701
1740
1203
2266
1912
428
890
1690
13
2388
1734
611
1305
1371
2174
1033
2835
2757
169
727
204
1476
1415
2446
1558
1413
824
345
1842
537
349
235
985
2396
1875
2411
2944
2204
1731
1035
2052
2228
1143
218
344
1849
153
1893
1942
2860
152
478
2387
1909
1362
785
1638
3053
1738
1794
819
2837
2733
2287
1877
2467
28
1636
2770
1021
140
1046
624
2241
223
2256
1895
909
2307
1407
1151
2922
1218
2407
984
1682
2701
1156
3003
1301
1402
2310
2600
3050
1037
3006
3020
3035
488
3019
1686
1484
831
2795
643
919
1028
100
2889
1026
627
744
62
1814
1223
2191
1232
662
1743
2319
836
2965
2390
2796
2470
1720
107
277
608
2754
1819
368
1843
3008
1630
2426
855
1373
2258
321
807
1848
1262
593
163
45
2302
540
879
303
3013
2460
1298
2123
1291
792
820
3046
2224
876
3028
2338
1372
338
1628
1075
2098
1467
1563
2254
2210
3043
2322
3048
1680
854
2250
1356
1808
311
660
1729
1810
1758
1296
1170
194
2824
523
320
419
67
1767
3051
758
1797
2267
472
2985
911
2253
2867
3034
1640
1391
175
1513
52
1392
2187
2999
328
372
774
146
976
1344
922
1892
3024
1800
2248
2798
1841
899
2220
233
1806
343
3029
560
3030
1534
2831
509
2866
1703
1069
2196
1013
1674
1846
1653
2448
2708
3021
1348
761
987
1238
3009
1387
1697
2491
1286
972
138
2269
243
1378
1646
1464
781
3010
736
1227
897
106
1876
2990
326
1334
676
980
1032
291
2690
1054
2305
2765
2464
2516
2989
475
1805
3015
353
34
2424
3055
123
1747
2517
2794
907
411
2192
118
255
3016
1673
2257
2216
561
429
42
681
893
1905
3044
1414
1671
2466
1694
640
973
1733
1453
1459
974
1310
2485
1822
943
3022
675
1727
155
1765
2417
2454
2722
2872
1040
812
2743
2755
1641
2869
1719
923
2911
901
1315
3000
875
704
2840
144
2992
3041
860
905
64
114
1019
323
1431
1449
2215
120
739
1146
508
816
2244
141
2678
98
803
2995
3018
2756
850
2456
1711
2432
362
1001
2461
3027
1925
3004
2909
104
2193
588
883
2816
749
137
1322
2753
1349
811
1516
2261
651
3025
1070
217
942
2227
626
684
2812
783
1446
36
2489
370
1364
298
636
1347
1820
1527
1485
2998
2480
3032
1928
2801
1888
1375
1828
1299
1498
2301
827
1914
1300
2243
2848
940
342
186
1643
514
2805
2929
562
2176
798
724
937
461
926
1902
129
231
1881
1533
2486
1491
2263
2264
672
131
2217
846
1832
1815
1329
2325
47
650
2412
2797
1406
804
1562
1401
1561
2562
1290
48
1658
1303
1067
2418
10
1839
2400
2185
1844
2586
712
2207
1522
1437
2226
1812
780
1531
1631
2259
22
1933
585
268
566
2893
2064
856
1340
2262
1400
3023
225
633
2200
1554
709
594
1436
157
589
620
447
817
584
3017
806
2249
292
474
2713
782
1816
966
569
962
1472
1898
2499
2440
90
1826
3031
2748
2430
2996
2463
2275
318
844
600
2481
2906
350
946
113
615
156
3040
2762
1496
2568
2429
950
2597
777
2924
580
489
1528
25
808
9
2808
2406
2223
309
1003
2309
2582
1317
1008
2425
2558
2408
1685
2273
552
412
2488
1929
398
1058
2479
977
841
2457
2300
1938
1292
802
880
621
1541
596
110
1504
1707
609
656
2222
959
1799
1544
1404
1395
2997
1847
1020
1667
565
1798
1854
1363
2031
694
2468
1353
734
658
981
1368
1478
3047
1502
635
1313
40
2738
1430
2205
2472029
931
1206
216
2947
2399
1545
617
1473
2039
2983
1887
477
1427
124
578
2317
2246
1865
2961
2845
3042
502
1002
2478
1505
1621
1288
721
1913
3033
2294
1465
1352
322
1281
30
2409
563
648
603
630
632
1553
869
1860
2364
149
2744
843
1825
2987
2994
3011
1675
2473
1304
2803
139
1287
3056
17
760
988
1695
2477
2920
638
1023
921
1197
2442
101
1251
623
1852
2015
1899
2416
586
1041
722
948
713
2199
701
3002
1802
2403
143
2471
348
741728
1891
1745
2016
1475
567
895
1057
1480
690
237
1072
602
1951
1306
35
2298
1547
673
575
3039
1754
2854
958
715
2548
572
839
1354
927
1474
1289
862
1927
553
127
822
2531
2873
708
1489
629
1004
597
1872
591
873
1540
1524
2628
405
1492
2022
655
2172
571
646
1456
2476
634
805
56
1519
330
1361
2439
2353
881
384
2993
1918
2896
2900
2245
2189
945
2405
476
574
1220
2314
886
2086
1506
1360
1943
933
2079
2316
3036
568
647
2221
2081
2423
2901
1212
1497
1652
707
1691
1365
810
1699
2956
451
2194
275
1493
1537
222
425
1319
2023
1231
2617
2195
317
1029
1458
1207
872
750
2843
2252
1532
1714
642
740
1629
2914
1668
465
628
1048
3012
302
2292
1490
1827
932
3052
914
133
1856
2912
314
1470
369
2853
1550
924
422
1487
2595
2899
466
637
1005
1861
2074
2178
1948
1509
2286
1625
573
2182
599
427
2667
2431
1649
991
2898
2270
859
619
2009
818
1897
1879
2073
2484
790
2818
2428
511
481
2048
2395
3007
3045
2231
610
2760
2437
1726
2673
313
2061
1451
583
1462
840
1683
1050
2771
1693
1542
2892
587
379
614
1469
1425
2401
1921
1014
1350
1428
482
490
2230
1488
1906
1461
1932
1859
3001
1557
930
1953
1047
441
1455
2445
2436
2293
1411
2236 1662
691
1637
2051
1280
2283
116
639
1659
308
1786
1052
1479
1337
371
462
1821
2186
2915
1546
1486
1065
645
653
2282
468
2017
2434
2323
2769
2826
2823
2197
997
1499
2209
1471
1704
1500
1397
877
1268
731
2829
904
1512
2175
1210
2177
2414
1901
618
703
1454
592
1217
1222
606
944
1249
1328
581
2021
3026
1036
1017
1669
699
685
892
652
1297
1830
669
2044
2247
2903
436
702
2449
745
1560
2928
1031
2202
1624
2707 870
2024
1265
2825
649
450
418
2092
2926
601
501
910
979
993
963
480
1684
1620
1919
898
3014
644
380
1051
698
1450
1663
2037
1452
1650
2422
2494
2438
2100
1200
717
2327
2035
1713
858
683
1890
1015
2565
666
1503
746
953
1468
2320
39
576
577
1955
1894
1507
2251
570
737
654
2225
1044
1064
1517
386
1201
365
1239
1482
733
1331
310
2330
1868
2234
723
2991
1923
2605
1656
515
2402
1263
273
2242
833
2413
1858
2687
1908
716
960
1010
1878
1345
582
1477
2604
2897
1351
1244
389
894
373
2433
598
1214
2026
459
1706
416
720
970
2075
1530
2925
251
2032
1061
2066
486
678
1655
1250
1556
2049
387
1248
613
2090
868
1216
266
1660
2058
1536
2511
1011
2166
512
2229
1712
2057
1326
500
1063
1327
2420
421
1417
1900
503
1518
682
748
220
735
399
612
493
276
430
431
498
407
2085
2036
1552
1261
1416
2374
2452
955
456
253
1256
605
686
1874
726
236
304
2318
229
908
440
2583
2042
964
1257
470
2285
983
625
2045
1224
925
364
1255
900
2084
2076
390
1258
665
2450
1276
2311
2033
449
729
506
2126
1271
1253
1939
469
414
1241
947
1648
891
1947
492
677
687
1027
1904
1045
1930
1915
1247
409
961
2069
439
1945
992
1279
438
484
2091
1535
718
2041
445
1198
1934
1917
1312
2284
1873
3038
1954
1059
889
2304
1661
467
1651
2443
2093
3049
1936
616
1039
1211
1950
2019
1869
2923
929
554
906
939
2012
2271
659
938
680
1940
1946
887
989
2077
1202
2545
1884
395
1073
1941
406
2487
1688
1284
1866
352
728
1260
424
454
1236
385
1066
2060
741
1043
1916
1252
496
918
2591 2668 2547
607
969
913
1309
711
396
1766
376
1266
1225
2062
1245
882
1264
388
747
497
442
460
705
464
2018
2027
695
358
1235
410
2089
1060
1233
415
394
2095
2233
1034
967
378
400
2087
2050
444
2038
692
1710
667
2053
999
998
752
2013
359
866
2011
458
754
392
2070
1267
433
1910
252
1078
2888
224
2025
753
1935
329
1931
2410
1007
1199
579
2068
2040
2088
351
495
1204
403
631
732
374
714
435
865
663
505
1911
1042
2444
2676
2421
2010
504
453
751
1889
1857
2020
1219
2096
2043
2080
473
941
1254
413
2072
1952
221
265
719
2055
2453
263
697
902
888
2046
2109
375
2014
1885
471
2071
743
2047
1687
2065
564
494
2028
510
516
995
361 1243
671
2056
2067
1744
674
1867
1215
1273
857
1205
2891
664
2054
730
1230
397
668
443
670
1896
689
710
363
1781
661
1277
483
700
706
507
513
1237
2059
1209
1049
1664
2063
742
1278
696
1234
2078
1229
417
1242
499
1226
1246
2082
426
2030
915
2034
2083
434
1213
360
1208
367
246
437
2544
479
457
1274
402
738
259
432
679
1228
4911221
1269
2699
1792
1634
1270
1275
2094
404
401 2659
1272
391 1240 1259 2679
278
366 260
2523
2575
3076
2680
-3
-5
-4
-3
-2
-1
0
1
z
2
3
4
5
6
7
Main Findings
Future Research
Questions