Peaking Interest: How awareness drives the effectiveness of - - PowerPoint PPT Presentation
Peaking Interest: How awareness drives the effectiveness of time-of-use electricity pricing Brian C. Prest Ph.D. Candidate, Duke University brian.prest@duke.edu USAEE 2017 Annual Conference November 13, 2017 Brian C. Prest (USAEE 2017)
Brian C. Prest
Ph.D. Candidate, Duke University brian.prest@duke.edu
USAEE 2017 Annual Conference November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Time-of-use (TOU) electricity pricing: charge more during peak hours
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Time-of-use (TOU) electricity pricing: charge more during peak hours Goal: reduce costs associated with timing of load
Investment in “peaker” power plants Managing intermittent renewables (without expensive battery storage)
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Time-of-use (TOU) electricity pricing: charge more during peak hours Goal: reduce costs associated with timing of load
Investment in “peaker” power plants Managing intermittent renewables (without expensive battery storage)
Literature shows consumers do respond, but only modestly Why?
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Time-of-use (TOU) electricity pricing: charge more during peak hours Goal: reduce costs associated with timing of load
Investment in “peaker” power plants Managing intermittent renewables (without expensive battery storage)
Literature shows consumers do respond, but only modestly Why?
1
Neoclassical idea: “Get the prices right” and peak load will be solved
Small responses indicate real costs of shifting ⇒ Charge correct prices to induce conservation
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Time-of-use (TOU) electricity pricing: charge more during peak hours Goal: reduce costs associated with timing of load
Investment in “peaker” power plants Managing intermittent renewables (without expensive battery storage)
Literature shows consumers do respond, but only modestly Why?
1
Neoclassical idea: “Get the prices right” and peak load will be solved
Small responses indicate real costs of shifting ⇒ Charge correct prices to induce conservation
2
Behavioral idea: People are boundedly rational
Small responses indicate insufficient information or attention ⇒ Provide nudges, information, or automation
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Time-of-use (TOU) electricity pricing: charge more during peak hours Goal: reduce costs associated with timing of load
Investment in “peaker” power plants Managing intermittent renewables (without expensive battery storage)
Literature shows consumers do respond, but only modestly Why?
1
Neoclassical idea: “Get the prices right” and peak load will be solved
Small responses indicate real costs of shifting ⇒ Charge correct prices to induce conservation
2
Behavioral idea: People are boundedly rational
Small responses indicate insufficient information or attention ⇒ Provide nudges, information, or automation
So which is closer to the truth?
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Theory ambiguous ⇒ agnostic, data-driven approach
Let the data suggest the mechanism, not imposing assumptions Identify what factors drive heterogeneous responses
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Theory ambiguous ⇒ agnostic, data-driven approach
Let the data suggest the mechanism, not imposing assumptions Identify what factors drive heterogeneous responses
Apply (and extend) new machine learning algorithm for estimating heterogeneous causal effects, designed by Athey and Imbens (2016)
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Theory ambiguous ⇒ agnostic, data-driven approach
Let the data suggest the mechanism, not imposing assumptions Identify what factors drive heterogeneous responses
Apply (and extend) new machine learning algorithm for estimating heterogeneous causal effects, designed by Athey and Imbens (2016) Data: TOU pricing experiment on Irish households
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Theory ambiguous ⇒ agnostic, data-driven approach
Let the data suggest the mechanism, not imposing assumptions Identify what factors drive heterogeneous responses
Apply (and extend) new machine learning algorithm for estimating heterogeneous causal effects, designed by Athey and Imbens (2016) Data: TOU pricing experiment on Irish households Testing >150 dimensions of observable characteristics from survey data for heterogeneous responses
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
3
Information amplifies effects up to 2x (even conditional on awareness)
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
3
Information amplifies effects up to 2x (even conditional on awareness)
4
Consumers are extremely insensitive to the size of the price change
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
3
Information amplifies effects up to 2x (even conditional on awareness)
4
Consumers are extremely insensitive to the size of the price change
5
Conditional on above, nothing else matters (of 150+ characteristics)
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
3
Information amplifies effects up to 2x (even conditional on awareness)
4
Consumers are extremely insensitive to the size of the price change
5
Conditional on above, nothing else matters (of 150+ characteristics)
Implications:
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
3
Information amplifies effects up to 2x (even conditional on awareness)
4
Consumers are extremely insensitive to the size of the price change
5
Conditional on above, nothing else matters (of 150+ characteristics)
Implications:
These generally point towards behavioral explanations
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
3
Information amplifies effects up to 2x (even conditional on awareness)
4
Consumers are extremely insensitive to the size of the price change
5
Conditional on above, nothing else matters (of 150+ characteristics)
Implications:
These generally point towards behavioral explanations Can’t reliably predict awareness
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Average TOU pricing effect: -9% peak consumption Key Drivers of Heterogeneity:
1
Key result: Unaware households don’t respond (-2%, insignif.)
2
Low energy consuming households don’t respond
3
Information amplifies effects up to 2x (even conditional on awareness)
4
Consumers are extremely insensitive to the size of the price change
5
Conditional on above, nothing else matters (of 150+ characteristics)
Implications:
These generally point towards behavioral explanations Can’t reliably predict awareness “Getting prices right” might not be sufficient
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Treatment and Control Group Assignments
Bi-Monthly Bill and Energy Statement Monthly Bill and Energy Statement In-Home Display (IHD) Load Reduction Incentive Control Tariff A 195 216 205 216 Tariff B 80 87 72 81 Tariff C 222 217 202 213 Tariff D 80 87 78 77 Control 678
Energy Statement Example Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Treatment and Control Group Assignments
Bi-Monthly Bill and Energy Statement Monthly Bill and Energy Statement In-Home Display (IHD) Load Reduction Incentive Control Tariff A 195 216 205 216 Tariff B 80 87 72 81 Tariff C 222 217 202 213 Tariff D 80 87 78 77 Control 678
10 20 30 40
Hour of Day Price (€ cents per kWh) 2 4 6 8 10 12 14 16 18 20 22 24
20 26 32 38 14.1
Tariff D Tariff C Tariff B Tariff A Control (No Change)
Energy Statement Example Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Treatment and Control Group Assignments
Bi-Monthly Bill and Energy Statement Monthly Bill and Energy Statement In-Home Display (IHD) Load Reduction Incentive Control Tariff A 195 216 205 216 Tariff B 80 87 72 81 Tariff C 222 217 202 213 Tariff D 80 87 78 77 Control 678
10 20 30 40
Hour of Day Price (€ cents per kWh) 2 4 6 8 10 12 14 16 18 20 22 24
20 26 32 38 14.1
Tariff D Tariff C Tariff B Tariff A Control (No Change)
Energy Statement Example Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Household Electricity Consumption (N × T ≈ 77 million)
Data both pre- and during treatment N ≈ 3, 000 households T ≈ 26, 000 half-hours each
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Household Electricity Consumption (N × T ≈ 77 million)
Data both pre- and during treatment N ≈ 3, 000 households T ≈ 26, 000 half-hours each
Survey data: > 150 complete variables on...
Family characteristics: Employment, education, class, household size, etc. House characteristics: age, rooms, style, insulation, window glazing, etc. Appliance and electronics characteristics: heating type, water heating type, immersion heaters, washers, dryers, TVs (by size), computers, game consoles, internet access, etc. Attitudinal/Behavioral: Attitudes towards energy/environment, appliance/electronics usage, reasons for participation, etc. Post-experiment survey: questions about experience with program
Selected summary statistics Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
ln(kWhi,h,t) = βhTreatmenti,h,t + αi,h + λw,h + ǫi,h,t
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
ln(kWhi,h,t) = βhTreatmenti,h,t + αi,h + λw,h + ǫi,h,t
Hour of Day Treatment Effect (Log Points: ∆ln(Yi))
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20
Point Estimate (Insigificant) Point Estimate (Sigificant)
Night Day Day Peak
Seasonal TEs Placebo Test Individual TEs Pre-trend check Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Athey and Imbens (2016) Extended regression trees to causal inference Estimates CATEs Extensions in this paper Diff-in-diff (vs. “diff”) Multiple treatment groups
Details Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
TE: −8.9% SE: (0.9%) n: 2328 TE: −10.3% SE: (1.4%) n: 2029 TE: −11.2% SE: (1.3%) n: 1933 TE: −14.6% SE: (1.6%) n: 474 TE: −10.1% SE: (1.3%) n: 1459 TE: −11.7% SE: (1.5%) n: 513 TE: −9.3% SE: (1.4%) n: 946 TE: −10.7% SE: (1.4%) n: 477 TE: −7.9% SE: (1.6%) n: 469 TE: 8.4% SE: (12.4%) n: 96 TE: −2.3% SE: (1.7%) n: 299 TE: −4.2% SE: (1.4%) n: 202 TE: −0.2% SE: (4.5%) n: 97 yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Robustness Checks: Propensity Tree “Honest” Tree Temp.-binned Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
TE: −8.9% SE: (0.9%) n: 2328 TE: −10.3% SE: (1.4%) n: 2029 TE: −11.2% SE: (1.3%) n: 1933 TE: −14.6% SE: (1.6%) n: 474 TE: −10.1% SE: (1.3%) n: 1459 TE: −11.7% SE: (1.5%) n: 513 TE: −9.3% SE: (1.4%) n: 946 TE: −10.7% SE: (1.4%) n: 477 TE: −7.9% SE: (1.6%) n: 469 TE: 8.4% SE: (12.4%) n: 96 TE: −2.3% SE: (1.7%) n: 299 TE: −4.2% SE: (1.4%) n: 202 TE: −0.2% SE: (4.5%) n: 97 yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Robustness Checks: Propensity Tree “Honest” Tree Temp.-binned Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
TE: −8.9% SE: (0.9%) n: 2328 TE: −10.3% SE: (1.4%) n: 2029 TE: −11.2% SE: (1.3%) n: 1933 TE: −14.6% SE: (1.6%) n: 474 TE: −10.1% SE: (1.3%) n: 1459 TE: −11.7% SE: (1.5%) n: 513 TE: −9.3% SE: (1.4%) n: 946 TE: −10.7% SE: (1.4%) n: 477 TE: −7.9% SE: (1.6%) n: 469 TE: 8.4% SE: (12.4%) n: 96 TE: −2.3% SE: (1.7%) n: 299 TE: −4.2% SE: (1.4%) n: 202 TE: −0.2% SE: (4.5%) n: 97 yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Robustness Checks: Propensity Tree “Honest” Tree Temp.-binned Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
TE: −8.9% SE: (0.9%) n: 2328 TE: −10.3% SE: (1.4%) n: 2029 TE: −11.2% SE: (1.3%) n: 1933 TE: −14.6% SE: (1.6%) n: 474 TE: −10.1% SE: (1.3%) n: 1459 TE: −11.7% SE: (1.5%) n: 513 TE: −9.3% SE: (1.4%) n: 946 TE: −10.7% SE: (1.4%) n: 477 TE: −7.9% SE: (1.6%) n: 469 TE: 8.4% SE: (12.4%) n: 96 TE: −2.3% SE: (1.7%) n: 299 TE: −4.2% SE: (1.4%) n: 202 TE: −0.2% SE: (4.5%) n: 97 yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Robustness Checks: Propensity Tree “Honest” Tree Temp.-binned Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill?
Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
TE: −8.9% SE: (0.9%) n: 2328 TE: −10.3% SE: (1.4%) n: 2029 TE: −11.2% SE: (1.3%) n: 1933 TE: −14.6% SE: (1.6%) n: 474 TE: −10.1% SE: (1.3%) n: 1459 TE: −11.7% SE: (1.5%) n: 513 TE: −9.3% SE: (1.4%) n: 946 TE: −10.7% SE: (1.4%) n: 477 TE: −7.9% SE: (1.6%) n: 469 TE: 8.4% SE: (12.4%) n: 96 TE: −2.3% SE: (1.7%) n: 299 TE: −4.2% SE: (1.4%) n: 202 TE: −0.2% SE: (4.5%) n: 97 yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Robustness Checks: Propensity Tree “Honest” Tree Temp.-binned Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill? Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
Monthly Bill? Overall Load Reduction Incentive? Baseline Average Peak Consumption >= 0.25 kWh (24th pctile)
TE: −8.9% SE: (0.9%) n: 2328 TE: −10.3% SE: (1.4%) n: 2029 TE: −11.2% SE: (1.3%) n: 1933 TE: −14.6% SE: (1.6%) n: 474 TE: −10.1% SE: (1.3%) n: 1459 TE: −11.7% SE: (1.5%) n: 513 TE: −9.3% SE: (1.4%) n: 946 TE: −10.7% SE: (1.4%) n: 477 TE: −7.9% SE: (1.6%) n: 469 TE: 8.4% SE: (12.4%) n: 96 TE: −2.3% SE: (1.7%) n: 299 TE: −4.2% SE: (1.4%) n: 202 TE: −0.2% SE: (4.5%) n: 97 yes no
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
Robustness Checks: Propensity Tree “Honest” Tree Temp.-binned Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 Consumption (kwh per 30 minutes) Price (€ cents per kWh)
Day Hours Night Hours
Heterogeneous Demand Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 Consumption (kwh per 30 minutes) Price (€ cents per kWh)
Day Hours Night Hours
Commonly used constant elasticity assumption is invalid Concern that consumers won’t respond to real-time price changes
Heterogeneous Demand Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Cannot reliably predict who will be aware
Lasso Model Selection:
Lasso table Lasso fitted values
Removes almost all covariates Few remaining are modest in size
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Cannot reliably predict who will be aware
Lasso Model Selection:
Lasso table Lasso fitted values
Removes almost all covariates Few remaining are modest in size
Consumer surplus loss is small
CS Loss
∼e3 per h.h. annually on average
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Cannot reliably predict who will be aware
Lasso Model Selection:
Lasso table Lasso fitted values
Removes almost all covariates Few remaining are modest in size
Consumer surplus loss is small
CS Loss
∼e3 per h.h. annually on average
Capacity benefits substantial
Capacity benefits
∼e100 per h.h. in avoided capacity costs (one-time benefit) IHD increases this benefit by about e80 (e130 with vs. e50 w/o) Effects would likely be 2-3x larger in U.S. than in Ireland
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
1 Awareness of TOU pricing is key to effectiveness
⇒ Awareness is not predictable, so focus on information
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
1 Awareness of TOU pricing is key to effectiveness
⇒ Awareness is not predictable, so focus on information
2 Small consumers don’t respond (in levels or percentages)
⇒ Target larger consumers
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
1 Awareness of TOU pricing is key to effectiveness
⇒ Awareness is not predictable, so focus on information
2 Small consumers don’t respond (in levels or percentages)
⇒ Target larger consumers
3 Information provision amplifies effects up to 2x, even among aware
⇒ Information is important
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
1 Awareness of TOU pricing is key to effectiveness
⇒ Awareness is not predictable, so focus on information
2 Small consumers don’t respond (in levels or percentages)
⇒ Target larger consumers
3 Information provision amplifies effects up to 2x, even among aware
⇒ Information is important
4 Consumers are extremely insensitive to the size of the price change
⇒ Raises concern about effectiveness of real-time pricing ⇒ Caveat: steeper price hikes and/or automation
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
1 Awareness of TOU pricing is key to effectiveness
⇒ Awareness is not predictable, so focus on information
2 Small consumers don’t respond (in levels or percentages)
⇒ Target larger consumers
3 Information provision amplifies effects up to 2x, even among aware
⇒ Information is important
4 Consumers are extremely insensitive to the size of the price change
⇒ Raises concern about effectiveness of real-time pricing ⇒ Caveat: steeper price hikes and/or automation
Getting prices exactly right isn’t as important as getting people to pay attention
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest Ph.D. Candidate Duke University brian.prest@duke.edu
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Mean
Min Max Age Group: 18-25 (Indicator) 0.003 0.06 1 Age Group: 26-35 (Indicator) 0.08 0.28 1 Age Group: 36-45 (Indicator) 0.20 0.40 1 Age Group: 46-55 (Indicator) 0.25 0.43 1 Age Group: 56-65 (Indicator) 0.22 0.42 1 Age Group: 65+ (Indicator) 0.24 0.43 1 Social Class: AB, Manager/Professional (Indicator) 0.15 0.35 1 Social Class: C1, White collar (Indicator) 0.27 0.44 1 Social Class: C2, Skilled manual (Indicator) 0.16 0.37 1 Social Class: DE, Unskilled manual/other (Indicator) 0.39 0.49 1 Social Class: Farmer (Indicator) 0.03 0.16 1 Education: None (Indicator) 0.01 0.11 1 Education: Primary (Indicator) 0.12 0.32 1 Education: Secondary without Cert. (Indicator) 0.29 0.45 1 Education: Secondary to Cert. (Indicator) 0.17 0.37 1 Education: Third (Indicator) 0.36 0.48 1 Education: Refused (Indicator) 0.05 0.23 1 Number of Adults in Home 2.22 1.04 1 7 Number of Children Under 15 in Home 0.50 0.96 6 Has Children Under 15 in Home (Indicator) 0.27 0.44 1
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Mean
Min Max Own home outright (Indicator) 0.55 0.50 1 Own home with mortgage (Indicator) 0.39 0.49 1 Home Age: Less than 5 years (Indicator) 0.05 0.21 1 Home Age: 5-9 years (Indicator) 0.14 0.34 1 Home Age: 10-29 years (Indicator) 0.29 0.45 1 Home Age: 30-74 years (Indicator) 0.41 0.49 1 Home Age: More than 75 years (Indicator) 0.12 0.32 1 Home Style: Apartment (Indicator) 0.01 0.12 1 Home Style: Bungalow (Indicator) 0.27 0.44 1 Home Style: Detached (Indicator) 0.27 0.44 1 Home Style: Semi-Detached (Indicator) 0.31 0.46 1 Home Style: Terraced/Townhome (Indicator) 0.14 0.35 1 Number of Bedrooms 3.48 0.84 1 5
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Mean
Min Max Home Heat: Electric, Central (Indicator) 0.04 0.20 1 Home Heat: Electric, Plug-in (Indicator) 0.03 0.18 1 Home Heat: Oil (Indicator) 0.60 0.49 1 Home Heat: Gas (Indicator) 0.31 0.46 1 Home Heat: Solid Fuel (Indicator) 0.27 0.44 1 Water Heat: Electric, Central (Indicator) 0.13 0.34 1 Water Heat: Electric, Immersion (Indicator) 0.56 0.50 1 Water Heat: Oil (Indicator) 0.40 0.49 1 Water Heat: Gas (Indicator) 0.24 0.42 1 Water Heat: Solid Fuel (Indicator) 0.16 0.37 1 Washing Machine (Indicator) 0.99 0.11 1 Tumble Dryer (Indicator) 0.69 0.46 1 Dishwasher (Indicator) 0.67 0.47 1 Stand alone freezer (Indicator) 0.51 0.50 1 Cook stove type: Electric (Indicator) 0.70 0.46 1 Cook stove type: Gas (Indicator) 0.25 0.44 1 Cook stove type: Oil (Indicator) 0.02 0.15 1 Cook stove type: Solid (Indicator) 0.02 0.15 1 Number of TV’s (Less than 21 inches) 1.01 0.98 4 Number of TV’s (More than 21 inches) 1.29 0.88 4 Number of Desktop Computers 0.52 0.58 4 Number of Laptop Computers 0.69 0.79 4 Number of Game Consoles 0.47 0.77 4 Internet Access in Home (Indicator) 0.70 0.46 1
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.0 0.1 0.2 0.3 0.4 0.5 Hour of Day Consumption (kwh per 30 minutes) 2 4 6 8 10 12 14 16 18 20 22 24
Control Group Baseline Period Treatment Period
Night Rate (9−12¢) Night Rate (9−12¢) Day Rate (12.5−14¢) Day Rate (12.5−14¢) Peak Rate (20−38¢)
Balance Checks: t-tests LPM Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.0 0.1 0.2 0.3 0.4 0.5 Hour of Day Consumption (kwh per 30 minutes) 2 4 6 8 10 12 14 16 18 20 22 24
Control Group Treatment Group Baseline Period Treatment Period
Night Rate (9−12¢) Night Rate (9−12¢) Day Rate (12.5−14¢) Day Rate (12.5−14¢) Peak Rate (20−38¢)
Balance Checks: t-tests LPM Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.0 0.1 0.2 0.3 0.4 0.5 Hour of Day Consumption (kwh per 30 minutes) 2 4 6 8 10 12 14 16 18 20 22 24
Control Group Treatment Group Baseline Period Treatment Period
Night Rate (9−12¢) Night Rate (9−12¢) Day Rate (12.5−14¢) Day Rate (12.5−14¢) Peak Rate (20−38¢)
Balance Checks: t-tests LPM
Treatment/control are unbalanced ⇒ need diff-in-diff
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Variable Control Mean Treatment Mean t-statistic p-value Unbalanced Variables (α < 0.05) 1 Employment status: Retired (Indicator) 0.38 0.31 3.40 0.001 2 Number of Large Televisions (21+ inch) 1.19 1.31
0.001 3 Number of Electronics 3.74 4.04
0.003 4 Age Group: 65+ (Indicator) 0.28 0.23 2.79 0.01 5 Has Children Under 15 in Home (Indicator) 0.23 0.28
0.01 6 Number of Residents 2.60 2.76
0.01 7 Social Class: AB (Highest) (Indicator) 0.12 0.15
0.01 8 Education: Primary only (Indicator) 0.15 0.11 2.51 0.01 9 Baseline Average Consumption (Night Hours) 0.14 0.15
0.02 10 Internet Access in Home (Indicator) 0.66 0.71
0.02 11 Number of Desktop Computers 0.48 0.53
0.03 12 Number of Children Under 15 in Home 0.43 0.52
0.04 13 Housing Status: Own with Mortgage (Indicator) 0.35 0.40
0.04 14 Others in Household Use Internet Regularly (Indicator) 0.53 0.57
0.04 Selected Balanced Variables (α ≥ 0.05) 15 Baseline Average Consumption (Peak Hours) 0.42 0.44
0.07 16 Number of Adults in Home 2.16 2.24
0.08 17 Cook stove type: Electric (Indicator) 0.72 0.69 1.62 0.10 18 Number of Laptop Computers 0.65 0.71
0.11 19 Baseline Average Consumption (Day Hours) 0.29 0.30
0.12 20 Unemployed, not seeking job (Indicator) 0.03 0.04
0.13 21 Home Heat: Solid Fuel (Indicator) 0.29 0.26 1.46 0.14 22 Interested in changing energy use for environment* 1.38 1.34 1.41 0.16 23 Female (Indicator) 0.47 0.50
0.31 24 Education: Secondary to Certificate (Indicator) 0.16 0.17
0.39 25 Satisfied with billing frequency* 2.84 2.86
0.64 Observations 3,006 Number of Variables Tested 122 Number of Variables Not Shown 97 Number of Variables Significant (5% level) 14 Share of of Variables Significant (5% level) 11.5%
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Dependent variable: Treated (Indicator) Baseline Average Consumption (Peak Hours) 0.03 (0.07) Baseline Average Consumption (Night Hours) 0.14 (0.15) Baseline Average Consumption (Day Hours)
(0.12) Number of Large Televisions (21+ inch) 0.02∗∗ (0.01) Age Group: 65+ (Indicator) 0.13 (0.11) Number of Adults in Home 0.01 (0.01) Internet Access in Home (Indicator) 0.01 (0.02) Number of Desktop Computers in Home 0.01 (0.02) Others in Household Use Internet Regularly (Indicator)
(0.02) Cook stove type: Electric (Indicator)
(0.06) Observations 3,006 R2 0.03 Adjusted R2
Number of Covariates 109 Number of Covariates Not Shown 100 Number of Covariates Significant (5% level) 2 Share of Covariates Significant (5% level) 1.8% Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Hour of Day Treatment Effect (Log Points: ∆ln(Yi))
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20
Point Estimate (Insigificant) Point Estimate (Sigificant)
Night Day Day Peak
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Week of Year Treatment Effect (Log Points: ∆ln(Yi))
4 8 12 16 20 24 28 32 36 40 44 48 52 −0.20 −0.15 −0.10 −0.05 0.00 0.05 0.10 0.15 0.20
Estimated Treatment Effect 95% Confidence Interval Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Tariff A, Bi−monthly Bill
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff A, Monthly Bill
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff A, Bi−monthly Bill + IHD
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff A, Bi−monthly Bill + OLR
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff B, Monthly Bill
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff B, Bi−monthly Bill + IHD
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff B, Bi−monthly Bill + OLR
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff C, Bi−monthly Bill
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff C, Monthly Bill
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff C, Bi−monthly Bill + IHD
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff D, Bi−monthly Bill
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff D, Bi−monthly Bill + IHD
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Tariff D, Bi−monthly Bill + OLR
2 4 6 8 10 12 14 16 18 20 22 24 −0.20 −0.10 0.00 0.10 0.20Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.1 0.2 0.3 0.4 0.5 0.6 Time Consumption (kWh per 30 minutes) Jul−2009 Sep−2009 Nov−2009 Jan−2010 Mar−2010 May−2010 Jul−2010 Sep−2010 Nov−2010
Treatment Group
Baseline Period Treatment Period
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
yes no [1] [2] [3] [4] [5] [6] [7]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.12 kWh (5th pctile)
In−Home Display?
TE: −8.9% SE: (0.9%) n: 2328 TE: −10.4% SE: (1.4%) n: 2029 TE: −11.4% SE: (1.3%) n: 1933 TE: −14.7% SE: (1.6%) n: 474 TE: −10.3% SE: (1.3%) n: 1459 TE: 8.6% SE: (12.4%) n: 96 TE: −2.3% SE: (1.7%) n: 299
yes no [1] [2] [3] [4] [5] [6] [7]
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.22 kWh (18th pctile)
In−Home Display?
yes no [1] [2] [3] [4] [5] [6] [7]
Aware of Tariff Change? Baseline Average Peak Consumption >= 0.22 kWh (18th pctile)
In−Home Display?
TE: −8.9% SE: (1.4%) n: 1151 TE: −10.1% SE: (2%) n: 607 TE: −9.6% SE: (2%) n: 508 TE: −12.7% SE: (2.3%) n: 90 TE: −8.6% SE: (1.9%) n: 418 TE: −8.9% SE: (5.8%) n: 99 TE: −1.4% SE: (2.7%) n: 544
yes no [1] [2] [3] [4] [5] [6] [7]
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.0 0.1 0.2 0.3 0.4 0.5 0.6 10 20 30 40 Consumption (kwh per 30 minutes) Price (€ cents per kWh)
Monthly Bill Group, Peak Hours OLR Group, Peak Hours Bi−monthly Bill Group, Peak Hours Unaware, Large User Group, Peak Hours All Households, Day Hours All Households, Night Hours Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
−0.3 −0.2 −0.1 0.0 0.1 Temperature Bin (Degrees Celsius) Treatment Effect (Log Points: ∆ln(Yi)) (−4,−1] (−1,2] (2,5] (5,8] (8,11] (11,14] (14,17] (17,20]
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
−0.3 −0.2 −0.1 0.0 0.1 Temperature Bin (Degrees Celsius) Treatment Effect (Log Points: ∆ln(Yi)) (−4,−1] (−1,2] (2,5] (5,8] (8,11] (11,14] (14,17] (17,20]
No Electric Home Heat
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
−0.3 −0.2 −0.1 0.0 0.1 Temperature Bin (Degrees Celsius) Treatment Effect (Log Points: ∆ln(Yi)) (−4,−1] (−1,2] (2,5] (5,8] (8,11] (11,14] (14,17] (17,20]
No Electric Water Heat
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
−0.3 −0.2 −0.1 0.0 0.1 Temperature Bin (Degrees Celsius) Treatment Effect (Log Points: ∆ln(Yi)) (−4,−1] (−1,2] (2,5] (5,8] (8,11] (11,14] (14,17] (17,20]
No Electric Cook Stove
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
−0.3 −0.2 −0.1 0.0 0.1 Temperature Bin (Degrees Celsius) Treatment Effect (Log Points: ∆ln(Yi)) (−4,−1] (−1,2] (2,5] (5,8] (8,11] (11,14] (14,17] (17,20]
No Tumble Dryer
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
−0.3 −0.2 −0.1 0.0 0.1 Temperature Bin (Degrees Celsius) Treatment Effect (Log Points: ∆ln(Yi)) (−4,−1] (−1,2] (2,5] (5,8] (8,11] (11,14] (14,17] (17,20]
No Dishwasher
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
(−4,−1] (−1,2] (2,5] (5,8] (8,11] (11,14] (14,17] (17,20] Temperature Bin (Degrees Celsius) Share of Peak Hours 0.00 0.05 0.10 0.15 0.20 0.25
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Aware of Tariff Change (Indicator) LPM Lasso-Min Lasso-1SE Internet Access in Home (Indicator) 0.06 0.06 0.13 Use Internet Regularly (Indicator) 0.02 0.01 Water Heating Fuel: Oil (Indicator; “none” omitted) 0.05 0.04 Number of Dishwashers in Home 0.03 0.04 Number of Desktop Computers in Home 0.02 0.01 Expect Participating in Trial Will Reduce My Bill (Indicator) 0.05 0.06 Female Respondent (Indicator) 0.04 0.04 Social Class: AB (Highest) (Indicator)
0.02 Education: Third (e.g., University) (Indicator) 0.05 0.04
0.05 0.05
0.04 0.05
R2 0.12 0.07 0.03 Adjusted R2 0.07 0.07 0.03 Observations 2,328 2,328 2,328 Number of Covariates 123 17 1 Number of Covariates Not Shown 111 6 Number of Covariates Significant (5% level) 14 (11.4%) na na
Return to main Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Predicted Probability of Awareness (%) Frequency 20 40 60 80 100 200 400 600 800 1000 400 800 1200 1600 2000 Frequency Full Model Lasso (RMSE Min.) Lasso (1 Std. Error, right axis)
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Heterogeneous consumer impacts (trt. period), computed half-hourly. Annual Household Impacts
Average Household Loss in CS Excluding Transfer (b) Loss in CS Including Transfer (a + b) Change in Bill (a − d)
CS-E Dist. CS-I Dist. Bill Dist. Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Heterogeneous consumer impacts (trt. period), computed half-hourly. Annual Household Impacts
Average Household Loss in CS Excluding Transfer (b) e3 Loss in CS Including Transfer (a + b) Change in Bill (a − d)
CS-E Dist. CS-I Dist. Bill Dist. Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Heterogeneous consumer impacts (trt. period), computed half-hourly. Annual Household Impacts
Average Household Loss in CS Excluding Transfer (b) e3 Loss in CS Including Transfer (a + b) e19 Change in Bill (a − d)
CS-E Dist. CS-I Dist. Bill Dist. Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Heterogeneous consumer impacts (trt. period), computed half-hourly. Annual Household Impacts
Average Household Loss in CS Excluding Transfer (b) e3 Loss in CS Including Transfer (a + b) e19 Change in Bill (a − d) e5
CS-E Dist. CS-I Dist. Bill Dist. Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Heterogeneous consumer impacts (trt. period), computed half-hourly. Annual Household Impacts
Average Household Bi-Monthly Bill Loss in CS Excluding Transfer (b) e3 e2 Loss in CS Including Transfer (a + b) e19 e19 Change in Bill (a − d) e5 e9
CS-E Dist. CS-I Dist. Bill Dist. Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Heterogeneous consumer impacts (trt. period), computed half-hourly. Annual Household Impacts
Average Household Bi-Monthly Bill IHD Loss in CS Excluding Transfer (b) e3 e2 e4 Loss in CS Including Transfer (a + b) e19 e19 e18 Change in Bill (a − d) e5 e9 e1
CS-E Dist. CS-I Dist. Bill Dist. Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
e100 per household average capacity benefit
≈ (-9% peak load)*(1200 Watt peak load)*(e0.86/Watt)
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
e100 per household average capacity benefit
≈ (-9% peak load)*(1200 Watt peak load)*(e0.86/Watt)
One-Time Capacity Benefits per Household, with and without IHD Capacity Benefit
Note: Benefits are estimated assuming the estimated treatment effect for each group: all households (-8.9%), the bi-monthly bill group (-4.8%), and the IHD group (-12.5%).
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
e100 per household average capacity benefit
≈ (-9% peak load)*(1200 Watt peak load)*(e0.86/Watt)
One-Time Capacity Benefits per Household, with and without IHD Capacity Benefit Average Household e100
Note: Benefits are estimated assuming the estimated treatment effect for each group: all households (-8.9%), the bi-monthly bill group (-4.8%), and the IHD group (-12.5%).
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
e100 per household average capacity benefit
≈ (-9% peak load)*(1200 Watt peak load)*(e0.86/Watt)
One-Time Capacity Benefits per Household, with and without IHD Capacity Benefit Average Household e100 Bi-Monthly Bill e50
Note: Benefits are estimated assuming the estimated treatment effect for each group: all households (-8.9%), the bi-monthly bill group (-4.8%), and the IHD group (-12.5%).
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
e100 per household average capacity benefit
≈ (-9% peak load)*(1200 Watt peak load)*(e0.86/Watt)
IHD adds about e80 to capacity benefit One-Time Capacity Benefits per Household, with and without IHD Capacity Benefit Average Household e100 Bi-Monthly Bill e50 In-Home Display e130
Note: Benefits are estimated assuming the estimated treatment effect for each group: all households (-8.9%), the bi-monthly bill group (-4.8%), and the IHD group (-12.5%).
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
500 1000 1500 2000 Hour of Day Consumption (kWh) 2 4 6 8 10 12 14 16 18 20 22 24
kWh, Flat 14.1 cents/kWh (left) kWh, TOU Pricing (left) kWh, Real Time Pricing (left)
10 20 30 40 50 60 cents/kWh
14.1 cents/kWh Fixed Tariff (right) Marginal Price (right)
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.0 0.1 0.2 0.3 0.4
Euro (€) Density −6 −4 −2 2 4 6 8 10 12 14 16 Bi−monthly Bill Group (Avg = €1.78) IHD Group (Avg = €3.61)
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.00 0.01 0.02 0.03 0.04 0.05
Euro (€) Density −50 −30 −10 10 20 30 40 50 60 70 80 90 100 Bi−monthly Bill Group (Avg = €19.18) IHD Group (Avg = €17.66)
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
0.00 0.01 0.02 0.03 0.04 0.05 Euro (€) Density −50 −30 −10 10 20 30 40 50 60 70 80 90 100 Bi−monthly Bill Group (Avg = €8.61) IHD Group (Avg = €1.38)
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
For each control observation i and treatment m ∈ {1, ..., M}, generate a new pseudo-observation im with Yim ≡ Yi Xim ≡ Xi Wim ≡ Wi ( = 0) For m′ ∈ {1, ..., M} W m′
im
≡
for m′ = m for m′ = m, for a total of M × nC control observations, replacing the nC original ones
Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017
Transformed LATE: 1 nT
Yi − 1 M × nC
SC
Yi = 1 nT
Yi − 1 M × nC M
Yi = 1 nT
Yi − 1 nC
Yi = ˆ τ, which is the same as the LATE estimate of the untransformed data.
Return Brian C. Prest (USAEE 2017) Peaking Interest November 13, 2017