Research Demonstration: The Impacts of Irrigation Costs on Irrigation Demand

# Research Demonstration: The Impacts of Irrigation Costs on Irrigation Demand
### AECN 396/896-002

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Understand the impact of pumping cost on groundwater use for irrigated agriculture

Well-level groundwater use observed annually in Eastern Colorado

---
class: middle

# Data

```r
(data <- readRDS("final_data_CO.rds") %>%
 dplyr::select(site_no, year, pumpingAF, pc, precip, et, gpm, REA, tier))
```

```
##               site_no year pumpingAF       pc    precip       et       gpm REA tier
##    1: 393510102431000 2013    308.17 3.612525 12.204731 37.17223 1489.3279 Y-W    2
##    2: 393510102431000 2011    358.25 1.888933 14.921268 34.40002 1403.8981 Y-W    3
##    3: 393510102431000 2015    364.01 2.885766 18.779538 32.68950 1489.3279 Y-W    3
##    4: 393510102431000 2016    391.91 2.396533  9.724415 34.12479 1489.3279 Y-W    3
##    5: 393510102431000 2014    244.08 3.445902 15.590560 34.93238 1489.3279 Y-W    2
##   ---                                                                              
## 5924: 393630102454000 2011    200.34 3.365769 14.094496 34.53151  743.3990 Y-W    2
## 5925: 393630102454000 2013    265.91 2.466798 12.204731 37.26833  835.3989 Y-W    3
## 5926: 393630102454000 2012    246.91 1.792938  5.866145 43.65690  730.0590 Y-W    3
## 5927: 393630102454000 2015    177.45 4.519144 19.055128 32.71948  772.9989 Y-W    2
## 5928: 393630102454000 2016    197.94 2.937017  9.645674 34.14341  842.7288 Y-W    3
```

+ `site_no`: well id 
+ `year`: year 
+ `pumpingAF`: groundwater use (acre-feet)
+ `pc`: pumping cost ($/acre-feet)
+ `precip`: total precipitation (inches) during the growing season
+ `et`: total evapotranspiration (inches) during the growing season
+ `gpm`: well yield (gallons per minute)
+ `REA`: energy supplier name
+ `tier`: price tier (explained later)

---
class: middle

# Exploratory Data Analysis

---

# Econometric Model (univariate)

`$W = \beta_0 + \beta_1 IC + v$`

+ `$W$`: irrigation amount 
+ `$IC$`: irrigation cost 
+ `$v$`: error term.

---
class: middle

# Endogeneity: Omitted Variable Bias

`$W_{i,t} = \beta_0 + \beta_1 IC_{i,t} + v_{i,t}$`

What is in `$v$`? Are they going to cause bias on `$\beta_1$` estimation?

+ soil type
+ well yield
+ precipitation

---
class: middle

# Econometric Model (multi-variate)

`$W_{i,t} = \beta_0 + \beta_1 IC_{i,t} + \beta_2 WY_{i,t} + \beta_3 Precip_{i,t} + \beta_4 ET_{i,t} + \varepsilon_{i,t}$`

+ `$W$`: irrigation amount 
+ `$IC$`: irrigation cost 
+ `$WY$`: well yield
+ `$Precip$`: total precipitation during the production season
+ `$ET$`: total evapotranspiration during the production season
+ `$\varepsilon$`: error term

---
class: middle

# Can Individual (well) Fixed Effects help?

---
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# Endogeneity

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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-20335fba{width:54.8pt;background-color:transparent;vertical-align: middle;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-20335fce{width:60.9pt;background-color:transparent;vertical-align: middle;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table class='cl-2038d7c4'><thead><tr style="overflow-wrap:break-word;"><td class="cl-20335fce">Supplier</td><td class="cl-20335f9d">Year</td><td class="cl-20335fba">Price 1</td><td class="cl-20335fba">Price 2</td><td class="cl-20335fba">Price 3</td><td class="cl-20335f9c">Threshold 1</td><td class="cl-20335f9c">Threshold 2</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="6"class="cl-20335ed4">Highline</td><td class="cl-20335eb6">2,011</td><td class="cl-20335ea2">0.1592</td><td class="cl-20335ea2">0.1185</td><td class="cl-20335ea2">0.0727</td><td class="cl-20335eac">300</td><td class="cl-20335eac">600</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,012</td><td class="cl-20335ed6">0.1626</td><td class="cl-20335ed6">0.1261</td><td class="cl-20335ed6">0.0727</td><td class="cl-20335ed5">300</td><td class="cl-20335ed5">600</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,013</td><td class="cl-20335ed6">0.1347</td><td class="cl-20335ed6">0.0981</td><td class="cl-20335ed6"></td><td class="cl-20335ed5">400</td><td class="cl-20335ed5"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,014</td><td class="cl-20335ed6">0.1347</td><td class="cl-20335ed6">0.0981</td><td class="cl-20335ed6"></td><td class="cl-20335ed5">400</td><td class="cl-20335ed5"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,015</td><td class="cl-20335ed6">0.1347</td><td class="cl-20335ed6">0.0981</td><td class="cl-20335ed6"></td><td class="cl-20335ed5">400</td><td class="cl-20335ed5"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335f27">2,016</td><td class="cl-20335f25">0.1152</td><td class="cl-20335f25">0.0981</td><td class="cl-20335f25"></td><td class="cl-20335f24">400</td><td class="cl-20335f24"></td></tr><tr style="overflow-wrap:break-word;"><td rowspan="6"class="cl-20335f60">Y-W</td><td class="cl-20335f7e">2,011</td><td class="cl-20335f4d">0.2107</td><td class="cl-20335f4d">0.0973</td><td class="cl-20335f4d">0.0496</td><td class="cl-20335f4c">500</td><td class="cl-20335f4c">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,012</td><td class="cl-20335ed6">0.2206</td><td class="cl-20335ed6">0.1019</td><td class="cl-20335ed6">0.0520</td><td class="cl-20335ed5">500</td><td class="cl-20335ed5">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,013</td><td class="cl-20335ed6">0.2206</td><td class="cl-20335ed6">0.1019</td><td class="cl-20335ed6">0.0520</td><td class="cl-20335ed5">500</td><td class="cl-20335ed5">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,014</td><td class="cl-20335ed6">0.1071</td><td class="cl-20335ed6">0.0972</td><td class="cl-20335ed6">0.0814</td><td class="cl-20335ed5">500</td><td class="cl-20335ed5">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335ede">2,015</td><td class="cl-20335ed6">0.1071</td><td class="cl-20335ed6">0.0972</td><td class="cl-20335ed6">0.0814</td><td class="cl-20335ed5">500</td><td class="cl-20335ed5">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20335f1a">2,016</td><td class="cl-20335f06">0.1384</td><td class="cl-20335f06">0.1016</td><td class="cl-20335f06">0.0676</td><td class="cl-20335f07">500</td><td class="cl-20335f07">1,000</td></tr></tbody></table></div></template>
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Threshold 1 and 2 refer to the threshold electricity uses (kwh/HP) over which the users move on to the next tier. For example, for a farmer served by Highline who has a pump of 100 HP, the farmer would be at the second tier after using 40,000 kwh.

---
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# Endogeneity

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1</td><td class="cl-2043bbbd">Threshold 2</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="6"class="cl-2043bb1c">Highline</td><td class="cl-2043bafe">2,011</td><td class="cl-2043bab8">0.1592</td><td class="cl-2043bab8">0.1185</td><td class="cl-2043bab8">0.0727</td><td class="cl-2043baea">300</td><td class="cl-2043baea">600</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,012</td><td class="cl-2043bb31">0.1626</td><td class="cl-2043bb31">0.1261</td><td class="cl-2043bb31">0.0727</td><td class="cl-2043bb30">300</td><td class="cl-2043bb30">600</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,013</td><td class="cl-2043bb31">0.1347</td><td class="cl-2043bb31">0.0981</td><td class="cl-2043bb31"></td><td class="cl-2043bb30">400</td><td class="cl-2043bb30"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,014</td><td class="cl-2043bb31">0.1347</td><td class="cl-2043bb31">0.0981</td><td class="cl-2043bb31"></td><td class="cl-2043bb30">400</td><td class="cl-2043bb30"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,015</td><td class="cl-2043bb31">0.1347</td><td class="cl-2043bb31">0.0981</td><td class="cl-2043bb31"></td><td class="cl-2043bb30">400</td><td class="cl-2043bb30"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb81">2,016</td><td class="cl-2043bb78">0.1152</td><td class="cl-2043bb78">0.0981</td><td class="cl-2043bb78"></td><td class="cl-2043bb77">400</td><td class="cl-2043bb77"></td></tr><tr style="overflow-wrap:break-word;"><td rowspan="6"class="cl-2043bb9e">Y-W</td><td class="cl-2043bbbc">2,011</td><td class="cl-2043bb83">0.2107</td><td class="cl-2043bb83">0.0973</td><td class="cl-2043bb83">0.0496</td><td class="cl-2043bb82">500</td><td class="cl-2043bb82">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,012</td><td class="cl-2043bb31">0.2206</td><td class="cl-2043bb31">0.1019</td><td class="cl-2043bb31">0.0520</td><td class="cl-2043bb30">500</td><td class="cl-2043bb30">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,013</td><td class="cl-2043bb31">0.2206</td><td class="cl-2043bb31">0.1019</td><td class="cl-2043bb31">0.0520</td><td class="cl-2043bb30">500</td><td class="cl-2043bb30">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,014</td><td class="cl-2043bb31">0.1071</td><td class="cl-2043bb31">0.0972</td><td class="cl-2043bb31">0.0814</td><td class="cl-2043bb30">500</td><td class="cl-2043bb30">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb44">2,015</td><td class="cl-2043bb31">0.1071</td><td class="cl-2043bb31">0.0972</td><td class="cl-2043bb31">0.0814</td><td class="cl-2043bb30">500</td><td class="cl-2043bb30">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-2043bb6d">2,016</td><td class="cl-2043bb4f">0.1384</td><td 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A well in Highline's service area with 100 HP will be on the second price tier after using 40,000 kWh.

---
class: middle

# Endogeneity

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1</td><td class="cl-20575439">Threshold 2</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="6"class="cl-20575384">Highline</td><td class="cl-2057537b">2,011</td><td class="cl-20575352">0.1592</td><td class="cl-20575352">0.1185</td><td class="cl-20575352">0.0727</td><td class="cl-2057537a">300</td><td class="cl-2057537a">600</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-205753ac">2,012</td><td class="cl-2057538e">0.1626</td><td class="cl-2057538e">0.1261</td><td class="cl-2057538e">0.0727</td><td class="cl-20575385">300</td><td class="cl-20575385">600</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-205753ac">2,013</td><td class="cl-2057538e">0.1347</td><td class="cl-2057538e">0.0981</td><td class="cl-2057538e"></td><td class="cl-20575385">400</td><td class="cl-20575385"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-205753ac">2,014</td><td class="cl-2057538e">0.1347</td><td class="cl-2057538e">0.0981</td><td class="cl-2057538e"></td><td class="cl-20575385">400</td><td class="cl-20575385"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-205753ac">2,015</td><td class="cl-2057538e">0.1347</td><td class="cl-2057538e">0.0981</td><td class="cl-2057538e"></td><td class="cl-20575385">400</td><td class="cl-20575385"></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-20575407">2,016</td><td class="cl-205753fd">0.1152</td><td class="cl-205753fd">0.0981</td><td class="cl-205753fd"></td><td class="cl-205753fc">400</td><td class="cl-205753fc"></td></tr><tr style="overflow-wrap:break-word;"><td rowspan="6"class="cl-2057542f">Y-W</td><td class="cl-20575438">2,011</td><td class="cl-2057542e">0.2107</td><td class="cl-2057542e">0.0973</td><td class="cl-2057542e">0.0496</td><td class="cl-20575424">500</td><td class="cl-20575424">1,000</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-205753ac">2,012</td><td class="cl-2057538e">0.2206</td><td 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Would this cause bias in estimating `$\beta_1$`?

---
class: middle

# Fixed-Effects estimation

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---
class: middle

# (individual) Fixed Effects Estimation

+ Including individual (cross-sectional units) dummies (here, they are wells represented by `wdid`) in the model

+ This is equivalent to do within-transformation of the data (deviation from the individual means) and then regress deviation on deviation

+ What the within-transformation does is to effectively  divide the observations into groups (wells) and you look at variations .red[within] each of the groups (wells observed over time).

+ Since including individual dummies are equivalent to the within-transformation approach, that means including individual (well) dummies also effectively divides the observations into groups (wells) and you look at variations .red[within] each of the groups (wells observed over time).

---
class: middle

# Fixed Effect Estimation (in general)

Including dummies variables effectively divide the observations into groups and you look at variations .red[within] each of the groups

---
class: middle

# Beyond individual (well) FEs

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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-208f4c77{width:76.8pt;background-color:transparent;vertical-align: middle;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-208f4c80{width:66.4pt;background-color:transparent;vertical-align: middle;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table class='cl-20976eec'><thead><tr style="overflow-wrap:break-word;"><td class="cl-208f4c5a">wdid</td><td class="cl-208f4c59">year</td><td class="cl-208f4c77">pumpingAF</td><td class="cl-208f4c62">pc</td><td class="cl-208f4c76">tier</td><td class="cl-208f4c80">pump_hp</td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td rowspan="5"class="cl-208f4b72">4,905,044</td><td class="cl-208f4b5e">2,012</td><td class="cl-208f4b9a">250.07</td><td class="cl-208f4b22">1.843734</td><td class="cl-208f4b54">3</td><td class="cl-208f4b4a">75</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4b5e">2,013</td><td class="cl-208f4b9a">218.01</td><td class="cl-208f4b22">2.399341</td><td class="cl-208f4b54">3</td><td class="cl-208f4b4a">75</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4b5e">2,014</td><td class="cl-208f4b9a">149.69</td><td class="cl-208f4b22">3.755891</td><td class="cl-208f4b54">3</td><td class="cl-208f4b4a">75</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4b5e">2,015</td><td class="cl-208f4b9a">174.95</td><td class="cl-208f4b22">4.548531</td><td class="cl-208f4b54">2</td><td class="cl-208f4b4a">100</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4bea">2,016</td><td class="cl-208f4bd7">215.48</td><td class="cl-208f4bcc">3.163381</td><td class="cl-208f4bf5">3</td><td class="cl-208f4bd6">100</td></tr><tr style="overflow-wrap:break-word;"><td rowspan="6"class="cl-208f4c58">4,905,049</td><td class="cl-208f4c3a">2,011</td><td class="cl-208f4c12">159.82</td><td class="cl-208f4c26">3.555504</td><td class="cl-208f4c30">2</td><td class="cl-208f4c31">100</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4b5e">2,012</td><td class="cl-208f4b9a">232.43</td><td class="cl-208f4b22">1.900167</td><td class="cl-208f4b54">3</td><td class="cl-208f4b4a">100</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4b5e">2,013</td><td class="cl-208f4b9a">175.85</td><td class="cl-208f4b22">3.963672</td><td class="cl-208f4b54">2</td><td class="cl-208f4b4a">100</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4b5e">2,014</td><td class="cl-208f4b9a">138.14</td><td class="cl-208f4b22">3.780853</td><td class="cl-208f4b54">2</td><td class="cl-208f4b4a">100</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4b5e">2,015</td><td class="cl-208f4b9a">102.94</td><td class="cl-208f4b22">4.165940</td><td class="cl-208f4b54">1</td><td class="cl-208f4b4a">100</td></tr><tr style="overflow-wrap:break-word;"><td class="cl-208f4baf">2,016</td><td class="cl-208f4ba5">92.98</td><td class="cl-208f4ba4">5.929217</td><td class="cl-208f4bb0">1</td><td class="cl-208f4bae">100</td></tr></tbody></table></div></template>
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+ Does including individual dummies (well fixed effects) help?

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