Neighborhood Effects and Social: The case of Irrigated and Rainfed Rice Farners in Bohol

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    Neighborhood Effects and Social Behavior :

    The Case of Irrigated and Rainfed Rice Farmers in Bohol

    Takuji W. Tsusaka

    ~Emergence of Social Norms and Community Mechanisms~

    Accepted by 2012AAEA (Agricultural and

    Applied Economics Association of USA)

    Valerien O. Pede

    Keitaro Aoyagi

    Thanks:

    JICA

    Lolit Garcia

    Elmer Suaz

    Edmund Mendez

    Evangeline Austria

    Ma. Indira JoseNeale Paguirigan

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    Experimental methods, spatial econometrics, and survey methods are nicely

    blended in a single study.

    The study provides innovative approaches to investigate the spillover effect ofsocial behaviors.

    Excellent job!!

    According to the reviewers of the conference,

    1

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    Social Behavior

    Social Interaction Mutual Trust

    Social Behavior Social Relationship

    Often used as synonyms and are considered to be forms ofsocial capital,

    2

    Empirical and theoretical supports:

    Grootaert & van-Bastelaer (2008), Krishna (2007), Chou (2006), Isham et al. (2002),

    Zack & Knack (2001), Knack & Keefer (1997), etc. etc.

    y m y y n nn n nn ,

    Plays a crucial role in rural development and poverty reduction.

    Mechanism to induce effective collective actions and reduce

    transaction costs in a variety of ways (Hayami 2009, Arrow 1999,

    Solow 1999).

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    Neighborhood Effect and Social Behavior

    (Objective)Our View: Since social behavior takes place between people, it is natural to suppose that such

    behavior may affect other peoples behavior; i.e., there must be spillovers and externalities of

    social behavior.

    3

    Blume, Bandiera, Brock, Durlauf, Moffitt,

    Raudenbush, Sampson, Cook, Manski etc.

    Bandiera, Rasul, Conley, Udry, Anselin,

    Griffith, etc.

    Neighborhood Effects

    using spatial econometrics..

    Hayami, Grootaert, van-Bastelaer,

    Krishna, Chou, Isham, Zack,

    Knack, Arrow, Solow, Keefer, etc.

    Social Behavior/Social Capital

    Ionnides,Topa

    using behavioral game experiments

    Onesa, Putterman, Dufwenberg, Muren,

    Cook, Cooper, Eckel, Wilson, Bohnet,

    Zeckhauser, Ben-Ner, etc.

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    Neighborhood Effect

    Yi = Social Behavior

    (e.g. Trusting)

    Yi

    Xi = Individual Profile

    (e.g. Age)

    For example,

    XjXj

    YjYj

    i = Residual

    Endogenous Social Effector Spatial Lag Effect

    Xi

    Xj Xj

    Yj Yj

    Exogenous Social Effect or

    Cross Effect or ContextualEffect

    Correlated Social Effect or

    Perturbation Effect

    j

    i

    j

    j

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    Spatial Econometric Approach

    (1) Neighborhood Definition Weight Matrix

    n observations

    n

    0

    0 0

    1

    1

    0

    0

    Wafter normalization

    5

    Spatial Lag Operator

    WX =

    n

    X =

    x1x

    2x3

    xn

    x averaged over neighbors for obs 1

    x averaged over neighbors for obs 2x averaged over neighbors for obs 3

    x averaged over neighbors for obs n

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    Spatial Econometric Approach

    (2) Model Specification1) a-Spatial ModelY= 1X+ 1

    2) Cross Regression Model

    Y= 2X+2WX+ 2

    Lagrange Multiplier Tests

    Morans I

    Lag Test

    Error Test

    Spatial Diagnostics

    6

    a) Lag Model (w/Cross) ( Spatial Durbin Model)

    b) Error Model (w/Cross)

    c) ARAR Model (w/Cross)

    Y= 3WY+ 3X+3WX+ 3

    Y= 4X+4WX+ 4 , 4 = 4W4 + 4

    Y= 5WY+ 5X+5WX+ 5, 5 = 5W5 + 5

    Robust Error Test SARMA Test

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    Behavioral Game Experiment

    General Instructions

    All participants receive a pre-paid show-up fee of P50 at the beginning. The games deal with actual money. Whatever money participants win in games will be theirs to take home.

    The amount they win depends on the decisions they make during the games.

    The games must be taken seriously. They are not allowed to talk to other participants during the entire

    event. If the fail to follow the rule the will not be iven the ost- aid show-u fee P100 at the end of all

    Purpose: To elicit individuals social behavior quantitatively.

    7

    experiments.

    Dictator Game

    The game is played by pairs. Your anonymous partner is in a separate room. You never know who it is.

    At the beginning, you (sender) get P100/Your partner (receiver) gets nothing.

    Your partner will receive a transfer from you/You will not receive any money from your partner. The amount you keep is your payoff of this game/The amount your partner receives is his/her payoff of

    this game.

    How much do you transfer to your partner, if your partner is someone in your barangay?

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    B

    ?A (You)

    ?

    Your Room (Senders) The other Room (Receivers)

    Keep: P50Receive: P50

    Keep: P100 Receive: P0

    Send: P50

    Send: P0

    Dictator Game Example

    C ?Keep: P0

    Receive: P100

    The amount you keep

    is your payoff of this

    game

    The amount they

    receive is their payoff

    of this game

    Send: P100

    The transferred amount is recorded as

    the game result, and is interpreted as a

    measure of your altruistic behavior.

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    10

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    Behavioral Game Experiment

    Public Goods Game (Two Rounds)

    The game is played by groups of four people of which you are one. The three

    anonymous partners are in a separate room. You never know who they are.

    At the beginning, you (sender) and your partners (receivers) get P100 each.

    1st Round

    11

    .

    The total amount contributed will be doubled, and the doubled amount will be

    shared equally among all members, regardless of your contribution.

    The amount you keep plus the amount you receive back from the group is your

    payoff of this game.

    How much do you contribute to the group, if your partners are some ones in yourbarangay?

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    (50+50+50+50)

    P 200

    Contribute P 50 Contribute P 50 Contribute P 50 Contribute P 50

    Keep P 50

    You A B C

    Keep P 50 Keep P 50 Keep P 50

    The contributed amount is

    recorded as the game result,

    and is interpreted as aPublic Goods Game

    Round 1, Example

    P 400

    Receive P 100 Receive P 100 Receive P 100Receive P 100

    P 50

    P 150

    P 50

    P 150

    P 50

    P 150

    P 50

    P 150Payoff Payoff Payoff Payoff

    behavior to public goods.

    12

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    Behavioral Game Experiment

    Public Goods Game (Contd)

    Therefore, the game has an aspect ofinvestment.

    What if you increase/decrease your contribution, others contributions kept unchanged?

    Case1 You Partner A Partner B Partner CContribution 50 50 50 50

    Pa off 150 150 150 150

    13

    Case2 You Partner A Partner B Partner CContribution 20 50 50 50

    Payoff 165 135 135 135

    Case3 You Partner A Partner B Partner C

    Contribution 80 50 50 50Payoff 135 165 165 165

    Case4 You Partner A Partner B Partner CContribution 80 80 80 80

    Payoff 180 180 180 180

    Incentive for cheating (free-riding)

    Importance of Collective Action

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    Behavioral Game Experiment

    Public Goods Game (Contd)

    You can secretly check the contribution from each partner by paying P1.

    Then, you can send a message to particular partners to indicate that youare unhappy with that persons contribution, by paying P1 per message.

    After the 1st Round

    We will consider two variables in the analysis

    14

    The contributed amount is recorded as the result of the second round,

    and is interpreted as a measure of your contributory behavior to public

    goods in the presence ofmonitoring mechanism.

    with the same partners as in the 1st round.Then, Play the 2nd Round

    Free-riding Index (FRI) Group Members

    Average Contribution

    Your

    Contribution

    Check

    Dummy

    Indicator for degree of awareness of own free-riding

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    Our Study Site

    San Miguel/Trinidad/Ubay, Bohol

    Thanks to

    15

    Figure by Barkada Tours

    Arnel & Nel !

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    Our Data

    Primary Data

    Agricultural and Socioeconomic Data (X)

    4 crop seasons from 2009 to 2010 One half of the irrigated farmers (randomly selected): Volumetric pricing system

    The other half: Area size based flat rate

    Volumetric Pricing Dummy

    16

    Geographical Coordinates (W) Both farm plots and residences. Two types of neighborhood can be defined

    Behavioral Game Results ( Y) 243 randomly selected farmers

    Irrigated (N= 132) & Rain-fed (N= 111) The sample for this study

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    Data: Descriptive Statistics

    Overall

    (N=243)

    Irrigated

    Areas

    (N=132)

    Rainfed

    Areas

    (N=111)

    t-test for mean

    difference

    [p-value]

    Volumetric Pricing Dummy

    0.561(0.498)

    Age 51.062 49.689 52.694 3.004 *

    (12.019) (12.248) (11.585) [0.052]

    Gender Dummy 0.708 0.758 0.649 0.109 *

    Agricultural & Socioeconomic Variables (X)

    Sample Mean

    (Standard Deviation)

    17

    (0.456) (0.430) (0.480) [0.063]

    Years of Schooling 6.395 6.144 6.694 0.550

    (3.0384) (2.922) (3.159) [0.160]

    Ln Asset 10.578 10.444 10.738 0.295

    (1.132) (1.193) (1.038) [0.718]

    Field Size (ha) 1.585 1.167 1.754 0.586 ***

    (1.058) (0.682) (1.228) [0.000]

    Household Size (head count) 5.936 6.144 5.689 0.455

    (2.302) (2.321) (2.265) [0.125]

    Household Female Ratio 0.500 0.484 0.519 0.035 *

    (0.162) (0.148) (0.176) [0.092]

    Value for the last season

    Averaged over the 4 seasonsStatistical Significance: *** 1 %, * 10%

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    Data: Descriptive Statistics

    Overall

    (N=243)

    Irrigated

    Areas

    (N=132)

    Rainfed

    Areas

    (N=111)

    t-test for mean

    difference

    [p-value]

    Dependent Variables (Y)

    Dictator Game 30.041 32.197 27.477 4.719 *

    (20.236) (21.555) (18.314) [0.070]

    PGG Round 1 54.403 53.182 55.856 2.674

    Behavioral Game Results (Y)& Control Variables

    Sample Mean

    (Standard Deviation)

    18

    (23.033) (22.080) (24.139) [0.368]

    PGG Round 2 52.140 51.818 52.523 0.704

    (24.350) (23.633) (25.279) [0.823]

    Controls for PGG

    Risk Preference 53.786 54.470 52.973 1.497

    (25.898) (24.380) (27.686) [0.655]

    PGG R1 Message Receipt Dummy 0.280 0.273 0.288 0.016(0.450) (0.447) (0.455) [0.789]

    PGG R1 Free-riding Index -0.110 0.455 -0.781 1.235

    (15.335) (14.746) (16.049) [0.533]

    Statistical Significance: * 10%

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    Defining the Neighbors

    Weight Matrices (W)

    2 types of neighborhood

    Residential Neighborhood

    Plot Neighborhood

    2 Areas

    Irrigated

    Rainfed = 4 Weight Matrices

    How did we choose neighbors?? Threshold Distance

    19

    Too short Some people will have no neighbor

    Those observations will be dropped.

    Too long Boundary Bias Problem

    (e.g. Griffith, 1983)

    You

    d

    You

    d

    Impose the shortest possible threshold distance.(GeoDa does it)

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    Defining the Neighbors

    Individually Calculated 4 Threshold Distances

    0.959

    1.302

    0.956

    1.376

    (a) Plot Neighborhood/Irrigated Farmers

    (b) Plot Neighborhood/Rainfed Farmers

    (c) Residential Neighborhood/Irrigated Farmers

    (d) Residential Neighborhood/Rainfed Farmers.

    km

    Use this as a uniform

    threshold distance

    Field Plot Neighborst-test for

    Residential Neighborst-test forNeighborhood Structures;

    20

    mean

    difference[p-value]

    mean

    difference[p-value]

    IrrigatedAreas

    RainfedAreas

    IrrigatedAreas

    RainfedAreas

    Weight Code (a) (b) (c) (d)

    Number of Observations 131 109 132 110

    Total Number of Neighbor Relations 860 1166 866 1292

    Nonzero Weights (%) 5.01 9.81 4.97 10.68Avg. Num. of Neighbors 6.565 10.697 4.132 6.561 11.746 5.185

    (2.649) (4.309) [0.000] (3.119) (5.409) [0.000]

    Avg. Distance bet. Neighbors (km) 0.603 0.587 0.016 0.583 0.574 0.009(0.236) (0.239) [0.293] (0.243) (0.252) [0.564]

    Statistics@Threshold Distance = 0.956km

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    Defining the Neighbors

    0

    5

    10

    15

    20

    1 2 3 4 5 6 7 8 9 10111213141516171819202122

    0

    5

    10

    15

    20

    (a) Plot/Irrigated

    Distribution of the Number of Neighbors(b) Residential/Irrigated

    21

    0

    5

    10

    15

    20

    1 2 3 4 5 6 7 8 9 10111213141516171819202122

    0

    5

    10

    15

    20

    1 2 3 4 5 6 7 8 9 10111213141516171819202122

    (c) Plot/Rainfed (d) Residential/Rainfed

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    Defining the Neighbors

    Graphical Representations

    (b) Plot/Rainfed (d) Residential/Rainfed

    22

    (a) Plot/Irrigated (c) Residential/Irrigated

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    Summarized Hypotheses

    H1) Social behaviors of individual farmers are influenced by their neighbors social

    behaviors and personal attributes.

    H2) Neighborhood effects on social behaviors, particularly contribution to public

    goods, are higher in the irrigated areas vis--vis in the rain-fed areas.

    23

    H3) In the irrigated areas, farmers are more contributory to public goods when they are

    engaged in volumetric water pricing system than in area-based flat rate system.

    H4) The endogenous social effects on public goods contribution are larger among farm

    plot neighbors than among residential neighbors.

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    Results: Spatial Model Diagnostics

    Game Experiment Dictator Game Public Goods Game, Round 1 Public Goods Game, Round 2

    Neighborhood Plot Residential Plot Residential Plot Residential

    Ecosystem Irrigated Rainfed Irrigated Rainfed Irrigated Rainfed Irrigated Rainfed Irrigated Rainfed Irrigated Rainfed

    Moran's I 0.042 * -0.031 0.131 *** -0.126 -0.087 0.060 *** 0.004 -0.010 0.119 *** -0.016 0.162 *** 0.014 *

    (0.050) (0.385) (0.001) (0.990) (0.849) (0.004) (0.246) (0.219) (0.000) (0.241) (0.000) (0.081)

    Error Correlation 0.616 5.332 ** 1.511 5.001 ** 8.135 *** 0.083

    (0.433) (0.021) (0.219) (0.025) (0.004) (0.773)

    La Correlation 3.034 * 7.854 *** 1.831 10.961 *** 9.849 *** 0.974

    Lagrange Multiplier Tests on Cross Regression Residuals for Spatial Dependence Identification

    . . . . . .

    (0.082) (0.005) (0.176) (0.001) (0.002) (0.324)

    Error Correlation 12.977 *** 2.540 0.623 0.375 0.214 1.165

    Robust (0.000) (0.111) (0.430) (0.540) (0.644) (0.281)

    Lag Correlation 15.395 *** 5.062 ** 0.943 6.335 ** 1.928 2.0555

    Robust (0.000) (0.024) (0.332) (0.012) (0.165) (0.152)

    SARMA 16.011 *** 10.394 *** 2.453 11.336 *** 10.062 *** 2.138

    (0.000) (0.006) (0.293) (0.003) (0.007) (0.343)

    Spatial Model of

    Our Choice

    Lag

    &

    Cross

    Cross

    Lag

    &

    Cross

    Cross Cross Cross Cross Cross

    Lag

    &

    Cross

    Cross Cross Cross

    For RobustnessCheck

    ARAR&

    Cross

    Lag&

    Cross(Statistical Significance: *** 1 %, ** 5%, * 10%, 15% )

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    Results: Spatial Estimation

    Dictator Game Neighborhood Plot Residential

    Ecosystem Irrigated Rainfed Irrigated Rainfed

    Spatial ModelLag &

    Cross Cross

    Lag &

    Cross

    ARAR &

    Cross Cross

    Endogenous Social Effect () 0.239*

    0.352***

    0.331

    Correlated Social Effect () 0.034

    Neighbors' Characteristics ()

    Volumetric Pricing Dummy -13.630 * -11.492 -11.601

    Age 0.123 0.060 -0.105 -0.128 0.445

    Gender Dumm 4.382 -24.624 * 11.062 11.584 8.701

    WYW

    Years of Schooling -0.750 -4.222 * -1.288 -1.322 1.294

    Ln Asset -0.887 10.944 * 5.075 5.230 -1.344

    Field Area (ha) 16.206 *** 3.016 8.419 8.361 4.183

    Household Size -2.513 -2.327 -1.876 -1.895 -2.070

    Household Female Ratio -2.364 -2.837 21.705 23.196 -5.491

    Own Characteristics ()

    Volumetric Pricing Dummy -2.131 -0.327 -0.371

    Age -0.201 -0.091 -0.263 * -0.266 * -0.121

    Gender Dummy 2.914 3.098 3.526 3.605 5.631 Years of Schooling 0.610 0.282 0.221 0.213 0.334

    Ln Asset -0.374 0.854 -0.308 -0.290 -0.347

    Field Area (ha) -0.118 2.322 -0.956 -0.920 2.324

    Household Size -0.323 0.261 -0.377 -0.387 0.462

    Household Female Ratio 29.147 ** 3.188 30.608 ** 30.845 ** -4.975

    WX

    X

    Statistical Significance:

    *** 1 %, ** 5%, * 10%, 15%.

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    Results: Spatial Estimation

    Public GoodsGame, Round 1

    WY

    W

    Neighborhood Field Plot Residential

    Ecosystem Irrigated Rainfed Irrigated Rainfed

    Spatial Model Cross Cross Cross Cross

    Endogenous Social Effect ()

    Correlated Social Effect ()

    Neighbors' Characteristics ()

    Volumetric Pricing Dummy -9.637 -11.411

    Age -0.623 0.548 -0.682 * -0.520

    Gender Dummy -9.676 19.125 -10.821 35.160 **

    Years of Schooling -0.152 -0.088 0.533 -1.508

    X

    Statistical Significance:*** 1 %, ** 5%, * 10%, 15%.

    Ln Asset 0.013 -3.671 3.425 -3.891

    Field Area (ha) 8.575 -7.042 2.966 5.672Household Size -1.822 -0.502 1.453 0.633

    Household Female Ratio 11.186 11.712 -8.118 31.177

    Own Characteristics ()

    Volumetric Pricing Dummy 0.221 0.217

    Age -0.450 *** -0.713 *** -0.441 *** -0.743 ***

    Gender Dummy -4.709 -3.032 -5.778 -2.514

    Years of Schooling 0.112 -0.194 0.236 -0.044

    Ln Asset 2.323 2.589 1.307 0.981

    Field Area (ha) 5.586 * -2.125 5.754 * -1.965

    Household Size -0.742 -0.717 -0.575 -0.889

    Household Female Ratio 20.000 -18.463 18.812 -14.913

    Control

    Risk-Taking Behavior 0.227 *** 0.132 0.215 *** 0.135

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    Results: Spatial Estimation

    WY

    W

    WX

    Neighborhood Field Plot Residential

    Ecosystem Irrigated Rainfed Irrigated Rainfed

    Spatial Model

    Lag &

    Cross Cross Cross

    Lag &

    Cross Cross

    Endogenous Social Effect () 0.332 *** 0.284 ***

    Neighbors' Characteristics ()

    Volumetric Pricing Dummy 1.337 -11.436 * -6.470

    Age -0.317 -0.584 -0.276 -0.221 -0.579

    Gender Dummy 0.439 14.381 -3.750 -1.077 25.875

    Years of Schooling -2.103 * 3.266 1.360 0.428 1.365

    Ln Asset 2.964 -0.095 -1.520 -1.265 -3.677

    Public GoodsGame, Round 2

    WY

    W

    WX

    X

    Statistical

    Significance:

    *** 1 %, ** 5%,

    * 10%, 15%.

    . . . . .

    Household Size -0.577 3.104 0.798 0.224 4.020

    Household Female Ratio -8.270 19.684 -35.690 -28.779 -19.813

    Own Characteristics ()

    Volumetric Pricing Dummy 3.199 3.314 4.083

    Age 0.167 -0.169 0.179 0.187 -0.089

    Gender Dummy 2.492 0.145 0.690 2.059 -0.156

    Years of Schooling 0.371 0.214 0.385 0.366 0.322

    Ln Asset 1.746 0.954 1.110 1.330 0.387

    Field Area (ha) -0.716 -2.529 1.028 0.302 -2.671

    Household Size 0.613 0.219 0.567 0.517 0.144

    Household Female Ratio 7.872 -5.448 2.114 5.034 -6.961

    Controls

    Risk-Taking Behavior 0.126 ** 0.252 *** 0.193 *** 0.161 *** 0.240 ***

    Round 1 Message Receipt Dummy 7.312 ** 11.574 ** 7.139 * 7.416 ** 11.731 **

    Round 1 Free Riding Index 0.212 * 0.014 0.232 * 0.266 ** 0.093

    Round 1 MRD x FRI 0.440 ** -0.358 0.471 * 0.419 ** -0.289

    Round 1 Own Contribution 0.847 *** 0.542 *** 0.821 *** 0.840 *** 0.584 ***

    X

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    Summary of the Results

    H1) Social behaviors of individual farmers are influenced by their neighbors social behaviors and

    personal attributes. The endogenous social effects among irrigated farmers are found in dictator game and monitored public goods game.

    The exogenous social effects are minor on the whole. No correlated social effects are found.

    H1 is accepted to the extent that it depends on the irrigation availability and the type of social

    behavior.

    H2) Neighborhood effects on social behaviors, particularly contribution to public goods, augment in

    the irrigated areas vis--vis in the rain-fed areas. There exists a clear contrast in the result between the two ecosystems.

    Hypothesis Verification

    H1

    H2

    28

    The endogenous social effects and the impact of FRI are found only in the irrigated areas.

    H2 is definitely supported.

    H3) In the irrigated areas, farmers are more contributory to public goods when they are engaged in

    volumetric water pricing system than in area-based flat rate system Volumetric water pricing makes no difference in the outcome of dictator game and pre-monitoring public goods game

    It has a minimal positive effect in monitored public goods game.

    H3 is only weakly supported.

    H4) The endogenous social effects on public goods contribution are more salient among farm plot

    neighbors than among residential neighbors. The spillover of public goods contribution under monitoring is stronger among plot neighbors than among residential

    neighbors.

    H4 is clearly accepted.

    H3H3

    H4H4

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    Concluding Remarks

    I. Emergence ofsocial norms and community mechanisms in irrigated society.

    i. Farmers altruistic behavior and contributory behavior spill over to their neighbors,

    indicating that collective actions required in irrigation water management induce the

    emergence ofsocial norm: farmers decide on their social behavior more or less by

    following the way their neighbors behave socially.

    ii. Cooperative resource management also promotes a community mechanism: free

    riding acts are corrected.

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    iii. This irrigation system was introduced in 2008. It is implied that, by intervention

    schemes such as the construction of gravity irrigation, changes in social norm and

    community mechanism occur rather shortly than slowly.

    Essential Assumption: There was no intrinsic difference in behavioral spillover among

    irrigated farmers and among rainfed farmers prior to the construction of irrigation,

    which is partially supported by the descriptive tables.

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    Concluding Remarks

    II. Limitations & Possible Extensions:

    i. The contrasting result between the two ecosystems may be partially attributed to the

    relative concentration of neighbors in the rainfed areas, (in addition to the relatively

    independent agricultural practices). The result would be more convincing if we could

    separate out the former factor.

    ii. Number of neighbors (k-nearst neighbors) and Distance to neighbors (threshold

    distance) are 2 conflicting criteria commonly used in constructing weight matrices.

    30

    e ave assume t e a rness o mpos ng t e same t res o stance across t e

    types of neighborhood. It may be interesting to use a k-nearest neighbor criterion,though the choice of k has to be justified some way.

    iii. The next step of this research may be to estimate social behaviors using social

    distance instead of geographical distance. Such a study will explore how personal

    relationship affects the spillover of social behavior (and will also be applicable tosituations in which geographical distance is not a hard constraint).

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    Appendix

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    Order of Approximation bias (%)

    7th 0.5000 0.5217 4.35

    5th 0.5217 4.34

    3rd 0.5208 4.17

    Marginal Effect vs. Coefficient

    Consider the endogenous social effects.

    Let be the marginal effect.

    + 3 + 5 + 7 + = = 1

    k1

    k2

    1

    k3

    1

    j=1

    2k-1

    kj-1

    7th 0.4000 0.4110 2.745th 0.4110 2.74 marginal effect () coefficient () bias (%)

    3rd 0.4107 2.67 0.5000 0.5217 4.35

    0.4000 0.4110 2.74

    7th 0.3000 0.3046 1.52 0.3000 0.3046 1.52

    5th 0.3046 1.52 0.2000 0.2013 0.67

    3rd 0.3045 1.50 0.1000 0.1002 0.17

    7th 0.2000 0.2013 0.67

    5th 0.2013 0.67

    3rd 0.2013 0.67

    7th 0.1000 0.1002 0.17

    5th 0.1002 0.17

    3rd 0.1002 0.17

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    Marginal Effect vs. Coefficient

    Consider the exogenous social effects.

    Let be the marginal effect.

    =

    1-

    (1+ + 2 + 3 + 4 + .........) = j = (if 0 < < 1)j=0

    When = 0.3 , then 1.4

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