Paternalism, Autonomy, or Both?
Experimental Evidence from Energy Saving Programs*
Takanori Ida1 , Takunori Ishihara2 , Koichiro Ito3 , Daido Kido1 ,arXiv:2112.09850v1 [econ.GN] 18 Dec 2021

Toru Kitagawa4 , Shosei Sakaguchi5 , and Shusaku Sasaki6
1
2

Kyoto University

Kyoto University of Advanced Science
3

University of Chicago and NBER
4
5

Brown University

University College London

6

Tohoku Gakuin University

This version: December 21, 2021.
Abstract
Identifying who should be treated is a central question in economics. There are two competing approaches to targeting—paternalistic and autonomous. In the paternalistic approach, policymakers optimally target the policy given observable individual characteristics. In contrast, the autonomous approachacknowledges that individuals may possess key unobservable information on heterogeneous policy impacts, and allows them to self-select into treatment. In this paper, we propose a new approach that mixes
paternalistic assignment and autonomous choice. Our approach uses individual characteristics and empirical welfare maximization to identify who should be treated, untreated, and decide whether to betreated themselves. We apply this method to design a targeting policy for an energy saving programs
using data collected in a randomized field experiment. We show that optimally mixing paternalistic assignments and autonomous choice significantly improves the social welfare gain of the policy. Exploiting
random variation generated by the field experiment, we develop a method to estimate average treatment
effects for each subgroup of individuals who would make the same autonomous treatment choice. Ourestimates confirm that the estimated assignment policy optimally allocates individuals to be treated, untreated, or choose themselves based on the relative merits of paternalistic assignments and autonomouschoice for individuals types.
* Ida and Kido: Graduate School of Economics, Kyoto University, Yoshida, Sakyo, Kyoto 606-8501, Japan (e-mails:
ida@econ.kyoto-u.ac.jp and daido.kido@gmail.com). Ishihara: Faculty of Economics and Business Administration, Kyoto University of Advanced Science, 18 Yamanouchi Gotanda, Ukyo, Kyoto 615-8577, Japan (e-mail: ishihara.takunori@kuas.ac.jp). Ito:
Harris School of Public Policy, University of Chicago, 1307 East 60th St., Chicago, IL 60637 (e-mail: ito@uchicago.edu). Kitagawa: Department of Economics, Brown University, 64 Waterman St., Providence, RI 02912 (e-mail: toru_kitagawa@brown.edu).
Sakaguchi: Department of Economics, University College London, 30 Gordon Street, London WC1H 0AX, United Kingdom(e-mail: s.sakaguchi@ucl.ac.uk). Sasaki: Faculty of Economics, Tohoku Gakuin University, 1-3-1 Tsuchitoi, Aoba-ku, Sendai,
Miyagi 980-8511, Japan (ssasaki.econ@gmail.com). We would like to thank Severin Borenstein, Fiona Burlig, Mark Jacobsen,
Louis Preonas, Frank Wolak, and seminar participants at UC Berkeley for their helpful comments. We thank the Japanese Ministry of Environment for their collaboration for this study. Kitagawa and Sakaguchi gratefully acknowledge financial support from
ERC grant (number 715940) and the ESRC Centre for Microdata Methods and Practice (CeMMAP) (grant number RES-589-280001). Ito gratefully acknowledge support from Research Institute of Economy, Trade and Industry, and note that this project was
conducted as part of a research project “Empirical Research on Energy and Environmental Economics".

1Introduction
Targeting has become a central question in economics and policy design. When policymakers face bud-get constraints, identifying those who should be treated is critical to maximizing policy impacts. Advances
in machine learning and econometric methods have led to a proliferation of targeting methods, which has
contributed to a surge in research on policies including job training programs (Kitagawa and Tetenov, 2018),
social safety net programs (Finkelstein and Notowidigdo, 2019; Deshpande and Li, 2019), energy efficiency
programs (Burlig, Knittel, Rapson, Reguant, and Wolfram, 2020), behavioral nudges for electricity conservation (Knittel and Stolper, 2019), and dynamic electricity pricing (Ito, Ida, and Tanaka, 2021).
In this paper, we begin by highlighting the two competing approaches to effective policy design in theliterature —paternalistic and autonomous. The paternalistic approach involves policymakers using individuals’ observable characteristics to target the program optimally(Kitagawa and Tetenov, 2018; Zhou, Athey,and Wager, 2018). In contrast, the autonomous approach exploits self-selection to accomplish effective
targeting under the belief that individuals’ own choices take into account unobservable information on heterogeneous policy impacts (Heckman and Vytlacil, 2005; Heckman, 2010; Ito, Ida, and Tanaka, 2021).
A priori, it is ambiguous which approach is superior. For example, referring to the paternalistic and autonomous approaches as “planner’s decisions" and “laissez-faire", Manski (2013) summarizes their relative
merits as:“The bottom line is that one should be skeptical of broad assertions that individuals are better
informed than planners and hence make better decisions. Of course, skepticism of such assertions does not imply that planning is more effective than laissez-faire. Their relative merits
depend on the particulars of the choice problem."—Charles F. Manski, Public Policy in an Uncertain World
A common view in the literature, reflected in this quote, is that the appropriate approach depends on thecontext, and therefore, researchers and policymakers need to decide which to use on a case-by-case basis.
We propose a new approach that mixes paternalistic assignment and autonomous choice. Consider atreatment where treating an individual is costly but may generate a social welfare gain. That is, the net
social welfare gain from assigning a particular individual to treatment can be positive or negative. We
consider using observable individual characteristics to identify three types: 1) those who should be treated,12) those who should not be treated, and 3) those who should decide whether to receive treatment themselves.
We build an algorithm based on the empirical welfare maximization (EWM) method developed by Kitagawa and Tetenov (2018). We show that the optimal targeting policy of our approach can be identified andestimated using data obtained from a randomized controlled trial (RCT) or a quasi-experiment with a double
randomization design. If we can obtain data from an RCT in which individuals are randomly assigned to
one of the three arms (compulsory treatment, compulsory no-treatment, and opt-in treatment), we can characterize the expected welfare gain for each observable individual type for each arm. With this informationin hand, we can identify the optimal targeting policy by maximizing an empirical welfare criterion over aclass of assignment policies such as policy trees (Zhou, Athey, and Wager, 2018).
We apply this method to data from a randomized field experiment involving an energy conservation
program. This experiment was conducted in partnership with the Japanese Ministry of the Environment
in the summer of 2020, and involved 3,870 households. Customers participating in the experiment were
eligible to receive a rebate by reducing their electricity consumption during peak demand hours (1 pm to 5pm) on days when the system faced supply shortages relative to demand. Because there is a per-household
implementation cost for this policy, the net social welfare gain from treating an individual can be positive or
negative.
We provide several key findings. First, our experimental results indicate that there is substantial heterogeneity in treatment effect over observable household characteristics. As an example, we compare
intention-to-treat (ITT) estimates for the compulsory treatment group (100% of households were treated)
and the opt-in group (households self-selected into treatment). For some values of the observable variables,
one of these ITTs is larger than the other and the difference between the two is statistically significant. However, for other values of the observable variables, this relationship does not exist or flips. This implies thatthe relative effectiveness of compulsory and opt-in treatment can vary substantially by observable household
type, which suggests that the optimal policy assignment differs across households.
Building upon this insight, we use our algorithm to identify the optimal assignment for each household
type. We begin with a conventional paternalistic approach, where we assign consumers to either of treatment
or no-treatment. Our algorithm finds that 52% of households should be treated and 48% should be untreated.
This optimal policy assignment with two assignment options significantly improves social welfare relative
to treating all households or treating no households.
We then ask if adding an opt-in group (i.e., households who self-select into treatment) further improves2welfare. Our algorithm finds that 37% of households should be treated, 19% should be untreated, and 44%
should be assigned to the opt-in group. Optimal policy assignment with three assignment options further
improves the social welfare relative to the paternalistic approach described above. These results imply that
optimally mixing paternalistic and autonomous approaches can maximize the welfare gain from a policy.
What is the mechanism behind these findings? To explore this question, we develop new methods
that exploit the random variation generated by the field experiment. The key insight that our RCT createdthree randomly-assigned groups (treatment, control, and opt-in) for each observable household types. We
can use this variation to estimate two local average treatment effects (LATEs) that provide insight into themechanism behind our findings.
The first LATE is the ATE for the takers from the opt-in group: households who would take the treatment
if assigned to the opt-in group. The second LATE is the ATE for the non-takers from the opt-in group:
households who would not take the treatment if assigned to the opt-in group. Using the random variationfrom the RCT, we can estimate these two LATEs for each observable household types. We then examine
how these two LATEs differ between the three groups identified by our algorithm.
For households our algorithm assigns to the opt-in group, we find that the LATE for takers is positiveand large, while the LATE for non-takes is negative. That is, for these households, self-selection is very
informative about the effectiveness of the treatment. In contrast, for households assigned to the (compulsory)
treatment group, both LATEs are positive. In this group, there is a positive welfare gain from treating bothtakers and non-takers, so self-selection would not improve social welfare. Similarly, for households assigned
to (compulsory) no-treatment, both LATEs are negative. For these households too, self-selection would not
improve social welfare, and it is optimal for policymakers to leave them untreated.
Using the same method, it is also possible to calculate the ITTs for three counterfactual outcomes (outcomes if assigned to treatment, control, or opt-in) for each group. We confirm that the optimal groud assignment maximizes these ITTs, and alternative treatment assignments would reduce the ITTs of the welfare
gain.
Related literature and our contributions—Our study is related to three strands of the literature. First,
many recent studies in the economics literature have explored targeting based on paternalistic or autonomous
approaches. In addition to the papers cited earlier, recent studies using paternalistic assignment include
Johnson, Levine, and Toffel (2020); Murakami, Shimada, Ushifusa, and Ida (2020); Cagala, Glogowsky,
Rincke, and Strittmatter (2021); Christensen, Francisco, Myers, Shao, and Souza (2021); Gerarden and3

Yang (2021) and studies using autonomous approaches include Alatas, Purnamasari, Wai-Poi, Banerjee,
Olken, and Hanna (2016); Dynarski, Libassi, Michelmore, and Owen (2018); Lieber and Lockwood (2019);
Unrath (2021); Waldinger (2021). We are not aware of any existing study that builds an algorithm to identify
the optimal mix of paternalistic assignment and autonomous choice.
Second, the medical statistics literature has studied hybrid sampling designs that combine randomizationand treatment choice by patients. See, e.g., Janevic, Janz, Dodge, Lin, Pan, Sinco, and Clark (2003), Long,
Little, and Lin (2008), and references therein. In this literature, the sampling process used in our experimentis referred to as a doubly randomized preference trial (Rücker, 1989). An example of a clinical trial that
implements a doubly randomized preference design is the Woman Take Pride study analyzed in Janevic
et al. (2003). These studies focus on assessing whether letting patients choose their own treatment canhave a direct causal effect on their health status beyond the causal effect of the treatment itself. See Knox,
Yamamoto, Baum, and Berinsky (2019) for partial identification analysis in such a context and an application
to political science. Double randomized preference trials have received less attention in economics. The
only paper we are aware of is Bhattacharya (2013), which uses double randomization between randomized
control trials and planner’s allocation to assess the efficiency of the planner’s treatment allocations. To ourknowledge, no work has analyzed double randomized preference trial data to estimate an optimal targeting
policy which mixes paternalistic assignment and autonomous choice.
Third, the econometric framework we use in our empirical analysis builds on the growing statisticaltreatment choice literature. Generally assuming discrete characteristics, earlier studies in this literature(Manski, 2004; Dehejia, 2005; Hirano and Porter, 2009; Stoye, 2009, 2012; Chamberlain, 2011; Tetenov,2012, among others) formulate estimation of a treatment assignment rule as a statistical decision problem.
The empirical welfare maximization approach proposed by Kitagawa and Tetenov (2018) estimates a treatment assignment rule by maximizing the in-sample empirical welfare criterion over a class of assignment
rules. This approach can accommodate multi-armed treatment assignment and a rich set of household characteristics, including continuous characteristics, as is the case for our empirical application. We employ aclass of tree partitions considered in Athey and Wager (2021) and Zhou et al. (2018) as our class of policy
rules.

4

2

Conceptual Framework
Section 2.1 formulates an optimal arm assignment problem that allows for a mixture of paternalism andautonomous choice, and characterizes the optimal arm assignment given observed individual characteristics.
Section 2.2 describes how the EWM method with decision trees can be applied to estimate the optimal arm
assignment from RCT data.

2.1

Optimal Arm Assignment: Paternalism, Autonomy, or Both?
Consider a planner who wishes to introduce a policy intervention (program) to a population of interest.

Instead of the uniform assignment over the entire population, the planner is interested in targeted assignment
over heterogeneous individuals. A novel feature of our setting is that the planner can control not only who iscompulsorily exposed to the program but also who is given an option to opt-in to the program. Interpretingan individual’s take-up of the program as her exposure to the treatment, the planner’s goal is therefore toassign each individual in the population to one of the three arms: compulsory treatment (indexed as T ),compulsory no-treatment (indexed as N T ), and opt-in treatment (indexed as O). An individual assigned tocompulsory treatment or no-treatment is exposed to or excluded from the program with no opt-out or opt-in
option, whereas an individual assigned to opt-in treatment chooses whether to take it up by herself.
The planner’s goal is to optimize a social welfare criterion by assigning individuals to these three arms.
Following the statistical treatment choice literature (Manski, 2004), we specify the planner’s social welfare
criterion to be the sum of individuals’ welfare contributions. An individual’s welfare contribution is aknown function of the individual’s response to being assigned to arm T , N T , or O, and the per-person
cost of the treatment. An individual’s welfare contribution may not correspond to her utility. Hence, if an
individual is assigned to opt-in treatment, her utility maximizing decision may not correspond to the choicethat maximizes the planner’s objective.
Let W (T ), W (N T ), and W (O) denote the potential welfare contributions that would be realized if an
individual were assigned to compulsory treatment, compulsory no-treatment, and opt-in treatment.
We assume that the planner observes a pre-treatment characteristic vector for each individual x ∈ X ,where X denotes the support of the characteristics. Depending on these observable characteristics, theplanner assigns each individual to one of the three arms. Let GT ⊆ X denote a set of the pre-treatment
characteristics x such that any individual whose x belongs to GT is assigned to the compulsory treatment.

5

Similarly, let GN T and GO denote sets of the pre-treatment characteristics x such that the individuals withx ∈ GN T are assigned to compulsory no-treatment and individuals with x ∈ GO are assigned to opt-in
treatment, respectively. We consider non-randomized assignment policies only, so GT , GN T , and GO canbe interpreted as a partition of X , i.e., GT , GN T , and GO are disjoint and GT ∪ GN T ∪ GO = X (see, e.g.,
Figures 2 (a-2) and (b-2)).
We call a partition G := (GT , GN T , GO ) an assignment policy. G describes how individuals are assigned to arms according to their observable characteristics x. The realized welfare contribution after assignment for an individual with characteristics x is either W (T ), W (N T ), or W (O) depending on x ∈ GT ,x ∈ GN T , or x ∈ GO . Hence, her welfare contribution under the policy G can be written asX

W (j) · 1{x ∈ Gj }.

(1)j∈{T,N T,O}

Viewing individual characteristics and their potential welfare contributions as random variables, the average
welfare contribution under assignment policy G can be written asW(G) ≡ E X

W (j) · 1{X ∈ Gj } ,j∈{T,N T,O}

where the expectation is with respect to (W (T ), W (N T ), W (O), X). We define W(G) as our social welfare function. The social welfare function depends on the assignment policy G through the post-assignment
distribution of individual welfare contributions, which can be manipulated by changing which individuals
are assigned to which arms. This form of social welfare is standard in the statistical treatment choice literature. Note that, since we allow the individual welfare contributions to differ from individual utilities,
the interpretation of social welfare is not restricted to be utilitarian. The planner’s objective is to find an
assignment policy G∗ that maximizes the social welfare W(G) over a set of possible assignment policies.
If the planner can implement any assignment policy, this set of assignment policies corresponds to the set ofmeasurable partitions of X . Accordingly, G∗ can be defined byG∗ ∈ arg max W(G),G∈Ge

where Ge := {G = (GT , GN , GO ) : G is a measurable partition of X }.

6(2)

It is desirable that individuals with characteristics x be assigned to an arm that gives the largest conditional mean welfare contribution among {E[W (j) | x] : j ∈ {T, N T, O}}. In the absence of an opt-in
treatment arm, the planner’s paternalistic assignment policy is to allocate them to either compulsory treatment T or compulsory no-treatment N T . The optimal choice is then determined by comparing E[W (T ) | x]
and E[W (N T ) | x]. That is, an optimal paternalistic assignment policy exploits only heterogeneity in the
average welfare contribution conditional on observable characteristics x, which can be assessed by the planner prior to assignment.
Once individuals are permitted to self-select into treatment, social welfare can be improved beyond thelevel attained by paternalistic assignment. This is because an individual may possess private information,
which drives or helps predict her response to the treatment, and choose whether to receive treatment basedon it. On the other hand, such private information is unobservable to the planner, and cannot be exploited
through paternalistic assignment. If an individual’s treatment choice is aligned with the ordering of theirwelfare contributions, then letting each individual autonomously choose between treatment and no-treatment
can dominate paternalistic assignment. This argument, however, relies crucially on the assumption that
individuals’ objective functions are aligned with their social welfare contributions. If this assumption does
not hold, autonomous treatment choice can reduce social welfare, in which case paternalistic assignment
may dominate.
Which of paternalistic and autonomous policies performs better in reality? This is an important empirical question whose answer may well vary across contexts. Furthermore, if the planner can differentiate
between paternalistic and autonomous intervention across individuals, it is desirable to mix paternalistic
and autonomous intervention and assign individuals to the three arms, T , N T , or O, according to theirobservable characteristics x. It may be that, for some values of x, individuals choose by themselves thetreatment that is optimal in terms of the social welfare, so that their choices outperform a planner’s paternalistic assignment based only on x. Assigning such individuals to autonomous opt-in treatment is optimal.
In contrast, for values of x where individuals are likely to choose treatment that is suboptimal in terms of
the social welfare, autonomous choice will underperform a planner’s assignment based on x. Paternalistic
assignment is then optimal. Thus, an optimal assignment policy G∗ that mixes paternalistic assignment(i.e., compulsory treatment and no-treatment) and autonomous choice (i.e., opt-in treatment) depending on
individual observed characteristics x can improve social welfare compared with paternalistic assignment orautonomous choice alone.
7

In the following remark, we present a simple model that clarifies how the optimal assignment policy G∗
mixes paternalistic assignment and autonomous choice in accordance with individual observable characteristics x.
Remark 2.1. Let Z(O) ∈ {T, N T } denote the individual’s autonomous choice of treatment. That is, weobserve Z(O) if she is assigned to opt-in treatment. The autonomous choice Z(O) may depend on bothobservable characteristics X and unobservable characteristics (i.e., private information). We assume that
her welfare contribution at the opt-in arm satisfies

W (O) = W (T ) · 1{Z(O) = T } + W (N T ) · 1{Z(O) = N T }.

An implicit assumption here is that an individual’s response to the treatment is the same irrespective ofwhether she opts-in herself or is assigned to it by the planner. This is similar to the exclusion restriction
for instrumental variables, with an indicator for assignment to the opt-in treatment corresponding to an
instrumental variable. We assume this in the current remark only to simplify exposition, and stress that thevalidity of our method and the estimated optimal assignment policy do not rely on this exclusion restriction.
The optimal arm for individuals with characteristics x attains the highest conditional average welfare
contribution among E[W (T ) | x], E[W (N T ) | x], and E[W (O) | x]. Considering paternalistic assignment policies only, compulsory treatment is superior to compulsory no-treatment if and only if

E[W (T ) − W (N T ) | x] > 0.

(3)

If opt-in treatment is also available, we have the following identities: for j ∈ {T, N T }E[W (j) | x] = E[W (j) | Z(O) = T, x]P (Z(O) = T | x) + E[W (j) | Z(O) = N T, x]P (Z(O) = N T | x),
E[W (O) | x] = E[W (T ) | Z(O) = T, x]P (Z(O) = T | x) + E[W (N T ) | Z(O) = N T, x]P (Z(O) = N T | x).

8

These imply the following equivalence relations:

E[W (O) | x] ≥ E[W (T ) | x] ⇔ E[W (T ) − W (N T ) | Z(O) = N T, x] ≤ 0 or P (Z(O) = T | x) = 1,
(4)E[W (O) | x] ≥ E[W (N T ) | x] ⇔ E[W (T ) − W (N T ) | Z(O) = T, x] ≥ 0 or P (Z(O) = T | x) = 0.
(5)That is, given Pr(Z(O) = T |x) ∈ (0, 1), opt-in treatment dominates compulsory treatment (no-treatment)
if and only if individuals are on average voluntarily making the welfare improving choice, i.e. the mean of
W (T ) is higher than the mean of W (N T ) for those who choose Z(O) = T , and the opposite is true forthose who choose Z(O) = N T . One extreme case where it is immediate that both (4) and (5) hold is a Roymodel where an individual’s latent utility coincides with their social welfare contribution,

Z(O) =

T

if W (T ) ≥ W (N T ),



N T

if W (N T ) > W (T ).

Under this selection equation, W (O) = max{W (T ), W (N T )} holds, and both (4) and (5) follow.
Note that an individual’s autonomous choices Z(O) and their potential welfare contributions (W (T ), W (N T ))can depend on private information. Thus the three conditional average treatment effects E[W (T ) −W (N T ) | x], E[W (T ) − W (N T ) | Z(O) = T, x], and E[W (T ) − W (N T ) | Z(O) = N T, x] in (3)–(5) vary depending the extent to which an individual’s treatment choice is correlated with their underlying
potential welfare contributions.
By (3)–(5), the optimal arm for individuals with X = x can be determined by comparing three conditional average treatment effects: E[W (T ) − W (N T ) | x], E[W (T ) − W (N T ) | Z(O) = T, x], andE[W (T ) − W (N T ) | Z(O) = N T, x], all of which can vary with observed characteristics x. Specifically,an optimal assignment policy G∗ as defined in (2) has the form G∗ = (G∗T , G∗N T , G∗O ) withG∗T = {x ∈ X : E[W (T ) − W (N T ) | x] ≥ 0 and E[W (T ) − W (N T ) | Z(O) = N T, x] > 0},G∗N T = {x ∈ X : E[W (T ) − W (N T ) | x] < 0 and E[W (T ) − W (N T ) | Z(O) = T, x] < 0},G∗O = {x ∈ X : E[W (T ) − W (N T ) | Z(O) = T, x] ≤ 0 and E[W (T ) − W (N T ) | Z(O) = N T, x] ≥ 0}.

9

Figure 1 illustrates an example of an optimal policy G∗ for X ⊆ R2 .
[Figure 1 about here]

2.2

Policy Learning by the EWM with Decision Trees
Our goal is to find an optimal assignment policy G∗ by choosing the optimal arm for each value ofobserved characteristics x. Using data from an RCT in which treatment arms T , N T , and O are randomly
assigned, we apply an EWM method (Kitagawa and Tetenov, 2018) to learn an optimal policy G∗ .
Let the RCT data be a size n random sample of (Wi , Di , Xi ), where Di ∈ {T, N T, O} is individual i’s (randomly assigned) treatment arm, Wi is their observed outcome (welfare contribution), and Xi
their observable pre-treatment characteristics. Letting {Wi (T ), Wi (N T ), Wi (O)} denote potential outP
comes for individual i, the observed outcome Wi is subject to Wi =j∈{T,N T,O} Wi (j)1{Di = j}.
We assume that {Wi (T ), Wi (N T ), Wi (O), Xi }i=1,...,n are independently and identically distributed as{W (T ), W (N T ), W (O), X}.
Using the RCT data and a class G of policies G, the EWM method estimates an optimal policy G∗ bymaximizing the empirical analogue of the social welfare function over G:cĜEW M ∈ arg max W(G),
1
c
W(G)
≡
n

G∈G
n
X

X

i=1 j∈{T,C,O}Wi · 1{Di = j}
· 1{Xi ∈ Gj } ,P (Di = j | Xi )cwhere W(G)is an empirical welfare function of G that produces an unbiased estimate of the populationsocial welfare W(G). Observations are weighted by the inverse of the propensity scores, P (Di = j | Xi ),which are known from the RCT design.
The EWM approach is a model-free: it does not require any assumptions or a functional form specification for the potential outcome distributions. However, the class of policies G must be specified, taking
into account any feasibility constraints for assignment policies. If the class G is too rich, the EWM solution
ĜEW M will overfit the RCT data, and the social welfare attained by the estimated policy falls.
In the paper, we use a class of decision trees (Breiman et al., 2017) as G. The main reasons for thischoice are the ease of interpretation of the decision tree based assignment policies and the availability ofpartition search algorithms from the classification tree literature.
10

To illustrate the interpretation of a decision tree based assignment policy, Figure 2 shows example decision trees of depths 1 and 2 for a two-dimensional X . By traversing a tree from its top node to a bottom
node, we map from x to one of the tree assignment options. This tree structure generates a partition of thecharacteristic space X as in Figures 2 (a-2) and (b-2). Decision trees of depths 1 and 2 partition X into two
and four subspaces, with individuals whose x belongs to each subspace assigned to one of the three options.
Generally, a decision tree of depth L partitions X into 2L subspaces.
[Figure 2 about here]
A decision tree of depth L consists of two components: (i) a set of inequalities allocated to the nodes
in the top L − 1 layers and (ii) a set of options allocated to the terminal nodes. Thus searching an optimal
decision tree of depth L corresponds to searching for an optimal combination of inequalities in the nodes
in the top L − 1 layers and an assignment option for each terminal node. For the example depth 2 decision
tree in Figure 3, searching for the optimal tree is equivalent to optimally choosing an X for each node in
the first and second layers (i.e., triplet of indices (j, k, l) ∈ {1, . . . , K} of the elements of X where K
denotes the dimension of X), threshold values (a1 , a2 , a3 ) for these same nodes, and an assignment option(opt1, . . . , opt4) ∈ {T, N T, O}4 for each of the bottom nodes.
Learning an optimal decision tree of depth L by the EWM method corresponds to finding a tree partition
that maximizes the empirical welfare function W(Ĝ) over a class G of decision trees of depth L. The
complexity of the policy class G can be controlled by fixing the depth of possible decision trees (see, e.g.,
Zhou et al. (2018)).
[Figure 3 about here]

3

Field Experiment and Data
To estimate an optimal arm assignment policy, we use data from a field experiment in Japan involving

an energy savings program. Section 3.1 provides an overview of the field experiment. Section 3.2 presentssummary statistics and balance test results. Section 3.3 reports estimated average treatment effects andpresents evidence of treatment effect heterogeneity.

11

3.1

Field Experiment
Our field experiment was conducted in the summer of 2020 in collaboration with the Ministry of the En-

vironment, Government of Japan. The population was households in the Kinki and Chubu regions of Japan.
The experiment involved compulsory and opt-in schemes that provided monetary rewards for residential
electricity saving. Ex-ante approval for the field experiment was obtained from the ethics committee of theInter-Graduate School Program for Sustainable Development and Survivable Societies, Kyoto University.
In order to include a broad set of households, customers from 2 large regional power companies and 6
start-up1 power companies were invited to participate by letter or email. The homes of customers of thesepower companies are equipped with advanced meters, known as “smart meters,” which record their electricity usage in 30-minute intervals. A total of 4,446 customers pre-registered for the experiment. Amongthem, those who canceled their electricity contracts in the middle of the experiment, those whose electricity
usage data were not accurately recorded in their home energy management systems, and office customers
who used a large amount of electricity, unlike ordinary households, were excluded. This left us with 3,870
households as participants of the entire experiment.
We randomly assigned each of the 3,870 households to one of three groups: No-treatment (N T ), Compulsory treatment (T ), and Opt-in treatment (O).2 All participating customers agreed to provide their electricity usage data and received a participation reward of 2,000 JPY (approximately 19 USD, given 1 USD =105 JPY in the summer of 2020)

No-treatment (N T ): The 1,577 customers in this group did not receive the reward treatment.
Compulsory treatment (T ): The 1,486 customers in this group received monetary rewards for theirelectricity savings.
Opt-in treatment (O): The 807 customers in this group were given the option to complete an application
process in advance and receive the treatment. The opt-in rate, was 37.17% (300 out of 807 customers).

This experiment aimed to reduce residential electricity consumption between 1:00 and 5:00 pm during
the week of August 24 to 30. The 1:00 to 5:00 pm period is when electricity demand peaks in the summer
1

Entry into the Japanese retail electricity sector was fully liberalised in 2016. These 6 companies are post-2016 entrants.
The random assignment process was designed so that N T : T : O= 2: 2: 1. A relatively large number of households wereassigned to the N T and T groups as the data for these groups will also be used in future studies in this project.
212

in Japan, and is known as "peak hours". We set the baseline for each household to be their peak-hourelectricity consumption in July. Households in the Compulsory treatment group, and those in the Opt-in
treatment group who completed the application process, were provided with a monetary reward of 100
JPY per 1 kWh reduction in their peak-hour electricity consumption relative to their baseline. The reward
payment for a household was calculated as follows. Let Ȳibase denote the baseline, which we set to beaverage daily peak-hour electricity consumption (kWh) from July 1 to 31. Let Ȳitreat be the average daily
peak-hour electricity consumption (kWh) from August 24 to 30. We define the average daily peak-hourelectricity saving, ∆Ȳi , to be the difference between Ȳitreat and Ȳibase truncated to be positive, so that∆Ȳi = −min{0, Ȳitreat − Ȳibase }. We multiply the average daily of peak-hour electricity saving, ∆Yi , byseven days, and define this to be the total energy savings for the entire week: ∆Yitotal . The total reward forhousehold i, Qi , is calculated as:
Qi = ∆Yitotal × 100= −min{0, Ȳitreat − Ȳibase } × 100

Information regarding the treatment week, peak hours, and reward calculation procedure was delivered
to the Compulsory-treatment and Opt-in treatment groups by letter or email on July 31. Customers assigned
to the Opt-in treatment group who wished to receive the reward were required to complete an application
process in advance. Customers in this group could complete this process by returning a prepaid postcard3
or online during the two-week period from July 31 to August 11. 300 out of 807 customers (37.17%) in
this group completed the process and expressed their willingness to receive the treatment. This opt-in rateis slightly higher than those for Critical Peak Pricing (CPP) in previous studies, 20% (Potter et al., 2014;
Fowlie et al., 2021) and 16-31% (Ito et al., 2021). Unlike the CPP treatment, where the price of electricity
can increase, the reward amount in this experiment will never be negative, even a customer’s peak-hourelectricity consumption is above their baseline. This feature may have contributed to the high opt-in rate.
The reward calculation procedure was described as follows: “we will pay you a reward of 100 JPY per 1
kWh of electricity saved when you pay your electricity bill,” and “we calculate your electricity savings rateusing your total electricity consumption during these specific hours and your average electricity consumption in the previous month.” In general, experiments featuring reward treatments need to address concerns
3

Specifically, what is known in Japan as a "round-trip postcard."13

regarding baseline manipulation by customers (Wang and Tang, 2018). Customers who are aware how the
reward is calculated have an incentive to increase their electricity consumption during the baseline period
in order to obtain a greater reward. This baseline manipulation is often observed in studies using reward
treatments and could be critical to the estimation of treatment effects (Wolak, 2007). However, such manipulation was difficult in this experiment as the baseline period was a month long, and participants were only
made aware of the calculation process on the final day of this month. Table 1 in the following subsection
shows no difference in baseline period electricity consumption between the three groups, consistent with alack of manipulation.

3.2

Data and Summary Statistics
We used high frequency data of electricity consumption and response data from a survey conductedupon obtaining customers’ agreement to participate in the experiment. Columns 1, 2, 3 of Table 1 present
summary statistics for pre-experiment consumption data and demographic variables by group. The variables
are pre-experiment peak hour-usage, pre-experiment pre-peak hour-usage, pre-experiment post-peak hourusage, number of people at home on weekdays, interest in energy conservation, and household income.4
We observe no significant difference in the first five variables between groups. This indicates that random
assignment has statistically balanced these five observables. For household income, we observe no significant difference between the N T and O groups, or the T and O groups, but we do observe a significant
difference between the N T and T groups. However, we confirmed that the estimated treatment effects did
not substantially vary when controlling for demographic variables including household income.
[Table 1 about here]
We investigated the external validity of our sample by randomly sampling 2,070 customers who did notparticipate in this experiment from the same population and comparing this random sample with our sample.
We found that our sample has larger pre-experiment electricity usage, a larger number of people at home on
weekdays, higher interest in energy conservation, and higher household income. The details are describedin Appendix A.1.
4

The variable peak hour-usage is the average electricity consumption per 30-minutes during peak hours (from 1:00 to 5:00pm), the variable pre-peak hour-usage is the average electricity consumption per 30-minutes during pre-peak hours (from 10:00 am
to 1:00 pm), and the variable post-peak hour-usage is the average electricity consumption per 30-minutes during post-peak hours(from 5:00 to 8:00 pm).

14

3.3

Experimental Results and Heterogeneity
Average treatment effects are estimated using peak-hour electricity consumption data recorded for 30-

minute intervals and the following equation:log Yit =X

τdIT T Zitd + λi + θt + it(6)

d={T,O}

where logYit the natural log of electricity usage for household i in a 30-minute interval t. We included
household fixed effects λi , and time fixed effects θt for each 30-minute interval to control for time-specificshocks such as weather. it is an unobservable error term assumed to follow a normal distribution withmean zero. Zitd equals one if household i is in the Compulsory treatment or the Opt-in treatment in t. τdIT T
represents the treatment effect for each group. In particular, τOIT T represents the Intention-to-Treat (ITT)
estimate, since households in the Opt-in group are required to apply to receive the reward treatment.
[Table 2 about here]
Column 1 of Table 2 shows that the Compulsory treatment led, on average, to a reduction in peak-hourelectricity consumption for the summer treatment week of 0.097 log points and the Opt-in treatment caused
a reduction in consumption of 0.052 log points. The former effect is slightly larger than the latter, and thedifference is statistically significant at the 10% level.
The remaining columns of Table 2 investigate heterogeneity in the treatment effects. Each pair ofcolumns splits the sample into two groups: those with a below median value of a particular variable, andthose with an above median value. The variables used in splitting are the difference between peak-hour andpre-peak-hour average electricity consumptions during the baseline period, the difference between peakhour and post-peak-hour average electricity consumptions during the baseline period, the number of people
at home on weekdays, interest in energy conservation, and household income.
Focusing on the difference between peak-hour and pre-peak-hour average electricity consumption during
the baseline period, the ITT estimate for the lower group is -0.108 for Compulsory treatment and -0.022 for
Opt-in treatment. In contrast, the estimates for the upper group are -0.079 and -0.073. The p-value forthe test of difference between the two ITT estimates is 0.013 for the lower group and 0.880 for the uppergroup. That is, the Compulsory treatment promotes electricity saving more effectively than the Opt-in
treatment for households with a smaller difference between pre-experiment peak-hour and pre-peak-hour
15average electricity consumption. However, there is no such statistically significant difference for the othersub-group, which implies there is heterogeneity in the relative effectiveness of the two treatments between
the two sub-groups.
We also observed statistical differences between the two ITT estimates for some other sub-groups, including the households with a smaller difference between pre-experiment peak-hour and post-peak-hour
average electricity consumptions, those with a smaller number of people at home on weekdays, those with alower interest in energy conservation, and those with a higher household income. This implies that the relative effectiveness of the Compulsory treatment and the Opt-in treatment can vary substantially depending
on households’ pre-experiment electricity usage and demographics, which in turn suggests that the optimaltreatment assignment may differ across households.

4

Optimal Assignment Policy and Welfare Gain: Empirical Results
This section estimates optimal assignment policies using the data from our RCT, and compares the

optimal paternalistic assignment with autonomous choice and a mixture of the two approaches. This analysis
leads us to two findings: (i) paternalistic assignment and aunotonomous choice have similar performance,(ii) mixing the two improves welfare significantly. We then present empirical evidence on the mechanism
driving this gain in welfare.

4.1

Construction of Social Welfare Criterion
We start by setting up a social welfare criterion. Our primary interest is in learning how the total surplus

changes when moving from the status quo (no energy saving program) to an individualized energy saving
program. We hence set the total surplus as the social welfare criterion to be maximized.
For each j ∈ {T, N T, O}, let Y (j) be a household’s potential electricity consumption (kWh) for theexperiment period, and Z(j) ∈ {T, N T }, j ∈ {T, N T, O} be a potential choice variable indicating thetreatment the household would receive if assigned to arm j. Since noncompliance is not possible for thecompulsory arms, Z(j) = j holds for j = T and N T . On the other hand, if a household were assigned tothe opt-in treatment arm, Z(O) indicates their choice of treatment.
We define four parameters: p, c, a, and δ. p is the unit price of electricity. We set to p = 25 JPY/kWh,16

approximately the regulated price of electricity in Japan, which is independent of the time of a day.5 c is themarginal cost of production for electricity. We specify c = 125 JPY/kWh, so that the difference between p
and c is equal to the per kWh rebate. The wholesale price of electricity sometimes soars during peak hours
such as summer afternoons or winter evenings, reflecting supply constraints. In the past, the electricity pricehas occasionally exceeded 100 JPY/kWh in summer afternoons.6
Parameter a represents the administrative cost of implementing our energy saving program. This cost
is comprised of several items, including the installation cost of the Home Energy Management System(HEMS) required to participate. In 2016, the Japanese government estimated the cost of implementing ademand reduction program, including the installation cost of HEMS, to be 291.1 JPY/kWh per household
per season (Ida and Ushifusa, 2017).7 We use this as the value of the administrative cost.
Parameter δ represents the long-term benefits of a unit reduction in energy consumption. Here, we
consider the effect of a unit reduction on the capacity market, where future supply capacity is traded between
the power generation and retail sectors. In Japan, the capacity market was established in 2020, with the firstauction held at that time. In that auction, the Japanese government provided a reference price 9,425 JPY/kW
to bidders. We use this value divided by the total event hours (28 hours) as the value of δ.
With these variables and parameters, we specify the social welfare of assignment policy G to bep−c(Y (T ) − Y (N T )) − a · 1{X ∈ GT }W(G) := E
δ+
2




p−c
+
δ+
(Y (O) − Y (N T )) − a · 1{Z(O) = T } · 1{X ∈ GO }
2





X
p−c
Y (j) − a · 1{Z(j) = T } · 1{X ∈ Gj }
=Eδ+2
j∈{T,N T,O}



p−c
−E δ+
Y (N T ) .
2


(7)

(8)

5
In Japan, until April 1 2016 household electricity was supplied by local power companies and retail prices were regulated.
Since then, entry into the retail electricity industry has been fully liberalized, allowing all households to freely choose their pricemenu. However, as a transitional measure, the regulated price for households is being maintained for the time being, and is set atapproximately 25 JPY/kWh regardless of the time of day.
6
The wholesale electricity market, where the power generation sector and the retail sector trade electricity, is operated by theJapan Electric Power Exchange (JEPX). Most trading takes place in the “day-ahead market” where both sectors trade electricity on
the day before the actual demand period. Trading results are disclosed, and we confirm that the price exceeded 100 JPY/kWh on
July, 25, 2018. Moreover, the price has exceeded even 125 JPY/kWh. For example, it the price reached 250 JPY/kWh on January,15, 2021.
7
We do not include the installation cost for a smart meter in the administrative cost. Since the Great East Japan Earthquake ofMarch 11, 2011 and the accident at the Fukushima Daiichi Nuclear Power Plant, the Japanese government has stipulated that smart
meters be installed in all homes by the end of the decade, so this cost is “sunk” in that it will be paid regardless of whether a demand
reduction program is implemented or not.

17

Equation (7) gives our definition of the change in total surplus. For each j ∈ {T, N T, O}, the termp−c
2 (Y (j) − Y (N T )) represents the household’s contribution to the short-term welfare when it is assigned

to arm j, while the term δ(Y (j) − Y (N T )) measures the household’s contribution to long-term welfare. In
addition, a · 1{Z(j) = T } represents the administrative cost of implementing the energy saving program.
We here assume that this cost is realised when the household actually takes up the program. In total, theterm (δ + p−c
2 )(Y (j) − Y (N T )) − a · 1{Z(j) = T } measures the individual welfare contribution net of
the treatment cost. Equation (8) reveals that setting W (j) = (δ + p−c2 )Y (j) − a · 1{Z(j) = T } allows us
to apply the empirical welfare maximization framework described in Section 2. Note that W(G) = 0 holds
for the uniform compulsory no-treatment policy; i.e., G = (GT , GN T , GO ) = (∅, X , ∅). Hence, the social
welfare of policy G can be interpreted as the welfare gain relative to a policy of uniform no-treatment.
We implement the EWM method using the social welfare function defined above. As stated in Section 3,
our sample consists of 3,870 households. Let Yi denote household i’s observed electricity consumption level(kWh) during the treatment period (i.e., from 1:00 to 5:00 pm on August 24 to 30), and Zi ∈ {T, N T }denote household i’s observed decision about over participation in the energy saving program. As with thepotential choice variables introduced earlier, we have Zi ≡ T or Zi ≡ N T when the household is assigned
to T or N T . On the other hand, when the household is assigned to O, the value of Zi changes depending on
b by maximizing the following objective function
the household’s decision. We estimate the optimal policy G
over a class of policies G:
n

1X
n

X

i=1 j∈{T,N T,O}

Wi · 1{Di = j}
· 1{Xi ∈ Gj },P (Di = j | Xi )

where


p−c
Wi := δ +Yi − a · 1{Zi = T }.
2b by maximizing the sample analog of the first term in (8). Since theThat is, we obtain an optimal policy G
second term in (8) does not depend on the policy G, this is equivalent to maximizing the sample analog ofW(G).
During estimation, we let Yi be the difference between the observed electricity consumption level during
the treatment period and the average consumption level during the baseline period (i.e., from 1:00 to 5:00
pm of July 1 to 31). By defining Yi as the consumption level relative to a baseline, we can control for an ad-18

ditive household specific unobservable without changing the optimal assignment policies for the population.
Eliminating this household specific unobservable results in a more accurate estimate of the empirical welfare
criterion. Since the baseline consumption level is observed before random assignment, this operation does
not affect the expected welfare value. We demean the observed outcome Yi as suggested in Kitagawa andTetenov (2018). In addition, we replace the propensity score P (Di = j | Xi ) with the sample fraction, i.e.,Pn
i=1 1{Di = j}/n.
We specify the policy class to be the class of decision trees of a depth of either 3 or 6. We selectfive variables to be used in constructing the decision trees. These are Peak - Pre-peak, Peak - Post-peak,household income, the number of residents in the same housing unit, and a measure of the households
willingness to participate in the energy saving program. The first four variables are selected based on theirability to predict electricity consumption and the conditional average treatment effects. Specifically, we
select these four variables by running two off-the-shelf machine learning algorithms, lasso and random
forest, with all the available covariates and assessing the importance of each variable. When using lasso
to assess importance, we regress Yi on all the available covariates with a l1 -penalization term. We ordervariables in terms of importance by increasing the penalization parameter step-wise and checking which
variables remain selected for large penalization parameter values. When using random forest, we estimate
the conditional average treatment effects using the causal forest algorithm of (Wager and Athey, 2018) withall available covariates included. We use the frequency with which a variable is used to split nodes as ameasure of its importance. The four selected variables are those that appeared on the lists of importantvariables produced by both methods. The fifth variable, the willingness to participate in the energy saving
program, was included because it is expected to be useful for predicting the opt-in decision. We believe thisis reasonable since the opt-in decision plays an important role in our social welfare function, as is clear fromequation (7).

4.2

Empirical Results on Paternalistic Assignment Policy
We first focus on comparing paternalistic assignment(assigning either T or N T according to household

characteristics) with autonomous choice (uniform assignment of O). We show estimates of the welfare gains
relative to uniform assignment of N T to compare their performance in terms of social welfare.
To find the optimal paternalistic assignment policy, we maximize the estimates of the social welfare overthe class of decision tree policies, with the arms restricted to T and N T . We set the decision tree depth to 3,
19and exactly maximize the empirical welfare criterion by applying the exhaustive search algorithm of Zhou
et al. (2018). We constrain the depth to 3 since, given our sample size, obtaining an exact globally optimal
tree of depth greater than 3 in reasonable time is difficult. We also obtain a (bias-corrected) estimate of thewelfare gain of the optimal paternalistic assignment policy and compare it with the welfare gain of a policyof uniform autonomous choice.
The upper panel of figure 4 presents the decision tree corresponding to the estimated assignment policypat
Ĝpat ≡ (Ĝpat
T , ĜN T , ∅). All variables except Peak - Pre-peak appear at least once in the tree. In particular,

Peak - Post-peak is often used. The lower panel of figure 4 shows the share of households assigned to eachpatarm at Ĝpat . These are estimated as the fractions of households satisfying X ∈ Ĝpat
T and X ∈ ĜN T in

the experimental data. Ĝpat assigns half of the households to compulsory enrollment in the energy saving
program and excludes the other half, highlighting heterogeneity in the sign of welfare contributions among
the households. As show below, this leads paternalistic assignment to dominate uniform assignment totreatment and no-treatment.
[Figure 4 about here]
To assess the welfare performance of the estimated policy, we report point estimates and 95% confidence
intervals for the welfare gain relative to uniform assignment to N T . If an optimal assignment policy isestimated by EWM, the optimized empirical welfare value will be an upwardly biased estimate of the true
welfare attained by the estimated policy. This is known as the winner’s bias (see, e.g., (Andrews et al.,2019)), and is caused by using the same data twice: once to learn the policy and once to infer the policy’s
welfare.8 To control for the winner’s bias in our point estimates and confidence intervals, we create artificial
test data by fitting a causal forest Wager and Athey (2018) to run regressions of the outcome onto all thecovariates, and generating data with permuted regression residuals. See the Appendix for the details. Using
this artificial test data, we compute point estimates and confidence intervals for the welfare gains.
Table 3 reports the welfare performances of the uniform benchmark policies (100% T , 100% N T , and100% O) and the estimated optimal paternalistic assignment policy Ĝpat . The estimated welfare gain of
uniform treatment (100% T assignment) is 63.1 JPY per household, which is not statistically significant inspite of the significant decrease of electricity consumption shown in section 3. This is due to the administrative cost of treatment; for households who respond little to the program, the treatment cost exceeds the8

The estimation and inference procedures proposed by Andrews et al. (2019) cannot be directly applied to decision tree based
policies because the number of candidate policies is infinite.

20

benefit, and the net welfare contribution is negative. This is consistent with the large welfare improvement
under the paternalistic assignment policy Ĝpat . The estimated welfare of the uniform autonomous choice
policy (100% O) is 140.9 JPY per household, and this is also not statistically significant. Furthermore, thedifference between 100% T and 100% O is not statistically significant (p-value is 0.39), implying that there
is no obvious winner among the three uniform policies.
[Table 3 about here]
The fourth row shows the welfare performance of the estimated optimal paternalistic assignment policy.
The estimated welfare is 228.5 JPY, which is significantly different from zero. That is, the paternalistic
assignment policy improves welfare compared to the status quo policy (100% N T ). The remaining rows
show the comparison of the paternalistic assignment policy and the other benchmark policies. The estimatedwelfare gain of the paternalistic policy compared to 100% T is 165.5 JPY per household, and this differenceis statistically significant. This finding implies that the paternalistic policy exploits the heterogeneity in thesign of the net welfare contribution over the observable household characteristics. The final comparison is
between the optimal paternalistic assignment policy and autonomous choice. The estimated welfare gain
is 87.6 JPY per household, and this difference is not statistically significant. That is, we find no evidence
that one approach strictly dominates the other. These results lead to our next empirical question: whether a
mixture of paternalistic and autonomous approaches can outperform both alone.

4.3

The Optimal Mix of Paternalism and Autonomy
Having observed the similar welfare performance of paternalistic assignment Ĝpat and autonomouschoice, we now consider whether or not performance can be improved by a targeted mixing of paternalistic
assignment and autonomous choice. In our framework, a policy assigning arms N T , T , or O in response
to observable household characteristics represents a mixture of paternalistic assignment and autonomouschoice. Similar to the estimation of the optimal paternalistic assignment policy, we search for an optimal
policy in a class of decision trees, now with one of these three possible arms assigned to each terminal node.
To allow for a more flexible policy in line with the increase in available options, we set the tree depth to6. This comes with a computational cost that prevents us from computing the exact global maximizer of
empirical welfare. The exhaustive search algorithm for decision tree of depth 3, as used to estimate the21

optimal paternalistic assignment policy, completes within a reasonable time frame, but increasing the depth
beyond 3 renders exhaustive search infeasible.
We therefore consider a heuristic search procedure to approximately solve the empirical welfare maximization problem. We divide the search for an optimal tree partition into two steps. In the first step, we findan optimal tree of depth 3. In the second, we search within each leaf obtained in the first step for an optimal
subtree of depth 3. The resulting partition is a decision tree of depth 6, but is not guaranteed to maximize
the empirical welfare over the class of decision trees with depth 6. See the Appendix for further details.
We denote a policy estimated by this two-step procedure by Ĝmix . Since Ĝmix is not necessarily a global
maximizer of empirical welfare, the welfare estimate at Ĝmix can be lower than the welfare estimate at a
globally optimal policy. Therefore, the welfare gain estimates reported below can be viewed as conservative
estimates of the welfare gain attained by an optimal targeting policy that mixes paternalistic assignment andautonomous choice.
Figures 5,6, and 7 show the estimated assignment policy. The policy assigns households to arms asfollows. First, the binary conditions of figure 5 assign each household to one node between 8 and 15. Say ahousehold is assigned to node 8, then this household will be assigned to an arm according to the additional
binary conditions for node 8 presented in figure 6. Figure 5 also shows the share of households assigned toeach arm. Under the mixed policy, 44% of the households are assigned to arm O, 37% to arm T , and 19%
to arm N T . In comparison to the paternalistic assignment policy estimated previously, Ĝmix assigns lower
shares of households to T and N T , with almost half of them assigned to arm O.
[Figure 5, 6, and 7 about here]
The decision tree is sufficiently complex that its overall structure is difficult to grasp. To summarize
the assignment policy, we regress the assigned arm on two key covariates, Peak - Pre-peak and Peak - Postpeak, and show how assignment probabilities vary with respect to them. Figure 8 summarizes the probability
estimates. Panels on the left show assignment probabilities for the optimal paternalistic policy, panels on
the right show assignment probabilities for the mixed policy. Each point represents a household observed
from our sample, and the color of the point shows the probability of being assigned to a specific arm. Under
the paternalistic policy, assignment is mainly determined by Peak - Post-peak. On the other hand, under themixed policy, Peak - Pre-peak also plays a role in determining assignment.
[Figure 8 about here]
22

Table 4 presents the estimated welfare performance of Ĝmix and the benchmark policies. The welfare
gain of Ĝmix , shown in the fifth row, is 437.9 JPY and is significantly different from zero. Rows six througheight present comparisons of the welfare gain from the mixed policy with other policies. There are two
important findings. First, Ĝmix attains higher welfare than autonomous choice. The estimated welfare
gain relative to autonomous choice is 297.0 JPY, and the 95% confidence interval does not contain zero.
Second, Ĝopt outperforms the paternalistic assignment policy Ĝpat . The difference of 209.4 JPY, which issignificantly different from zero. We can thus conclude that proper targeting of paternalistic assignment andautonomous choice based on observable household characteristics can significantly improve social welfare
in comparison to either policy alone.
[Table 4 about here]

4.4

What Delivers Welfare Gain?
In this section, we investigate the mechanism driving the welfare gain from the mixed policy Ĝmix . In

particular, we focus on the average welfare effect for subgroups of households who are assigned to arms thatthey would not autonomously choose by Ĝmix .
For a given assignment policy G = (GT , GN T , GO ), the RCT data can be used to identify the average
welfare gain relative to W (N T ) conditional on this assignment policy G, i.e., E[W (k) − W (N T ) | X ∈Gj ], j, k ∈ {T, N T, O}. By the randomization of arms (unconfoundedness) in our RCT data; the followingholds

E[W (k) − W (N T ) | X ∈ Gj ] = E[W | D = k, X ∈ Gj ] − E[W | D = N T, X ∈ Gj ],(9)

The conditional expectations in the right-hand side can be estimated directly from our RCT data. For arm
j, E[W (T ) − W (N T ) | X ∈ Gj ] corresponds to the (conditional) average treatment effect of the energy
saving program, so we denote this quantity ATE. On the other hand, E[W (O) − W (N T ) | X ∈ Gj ]corresponds to the (conditional) intention to treat effect of the energy saving program, so we denote thisquantity by ITT. Note that when k = N T , E[W (k) − W (N T ) | X ∈ Gj ] = 0 always holds. In addition,
we can identify the take-up rate when households were assigned to the opt-in arm,

P (Z(O) = T | X ∈ Gj ) = P (Z = T | D = O, X ∈ Gj ).
23

(10)

Assuming the exclusion restriction holds in the sense that a household’s responses to the treatment is notcausally affected by who makes the treatment choice, the planner or the households themselves, we canestimate the counterfactual average welfare effect for a households who is assigned to arm j by policy G
and would have chosen T if assigned to arm O, as shown below. Identification the counterfactual welfare
effect conditional on the assignment of arm hinges on this exclusion restriction, but identification of the
optimal assignment policy and statistical properties of the estimated policy Ĝmix by EWM are unaffected
no matter whether the exclusion restriction holds or not.
Under the exclusion restriction

W (O) = W (T ) · 1{Z(O) = T } + W (N T ) · 1{Z(O) = N T }.

(11)

Decomposing E[W (O) − W (N T ) | X ∈ Gj 0 ] using the law of iterated expectations and substituting (11)for W (O) gives us

E[W (O)−W (N T ) | X ∈ Gj ] = E[W (T )−W (N T ) | Z(O) = T, X ∈ Gj ]P (Z(O) = T | X ∈ Gj ),Plug in the quantities identified in (9) and (10) to obtain

E[W (T ) − W (N T ) | Z(O) = T, X ∈ Gj ]=E[W | D = O, X ∈ Gj ] − E[W | D = N T, X ∈ Gj ]. (12)P (Z = T | D = O, X ∈ Gj )This identification result is analogous to the identification of the local average treatment effect (LATE) in(Imbens and Angrist, 1994). Specifically, if we view an indicator for being assigned to arm N T or O
as a binary instrumental variable and run two-stage least squares (2SLS) on the subsample of {i : Di ∈{N T, O}, Xi ∈ Gj }, treating the actual treatment take-up as an endogenous variable, we obtain (12) as
the 2SLS estimand. As Z(O) = T corresponds to the subgroup of households who would choose toparticipate in the program if offered the autonomous choice, we refer to this quantity as LATE for takers.
LATE for takers relies on the comparison of households assigned to arms O and N T in the RCT data. A
similar comparison of households assigned to arms O and T identifies the counterfactual average effect for24households who are assigned to arm j by policy G and would choose N T under arm O. Noting

E[W (T ) − W (N T ) | X ∈ Gj ]= E[W (T ) − W (N T ) | Z(O) = T, X ∈ Gj ]P (Z(O) = T | X ∈ Gj )+ E[W (T ) − W (N T ) | Z(O) = N T, X ∈ Gj ]P (Z(O) = N T | X ∈ Gj ),and plugging in the quantities identified in (9), (10), and (12), we obtain

E[W (T ) − W (N T ) | Z(O) = N T, X ∈ Gj ]=E[W | D = T, X ∈ Gj ] − E[W | D = O, X ∈ Gj ]. (13)
1 − P (Z = T | D = O, X ∈ Gj )Analogous to LATE for takers, this quantity corresponds to the estimand from a 2SLS regression using the
subsample of {i : Di ∈ {T, O}, Xi ∈ Gj }, where an indicator for being assigned to arm T or O is used asa binary instrumental variable for the actual treatment take-up. Z(O) = N T corresponds to the subgrouphouseholds who would choose not to participate in the program if assigned to the autonomous choice arm,so we refer to this quantity as LATE for non-takers.9
Panel A of Table 5 presents estimation results. Each column corresponds to a subgroup indexed by theirassigned arm under the estimated optimal policy Ĝmix . The first row shows estimated take-up rates if eachwere group were assigned to autonomous. These are based on the empirical analogue of equation (10). We
observe that variance of the take-up rate across arms is low (p-value is 0.48).
[Table 5 about here]
The second and third rows show LATEs for takers and non-takers as estimated by equations (12) and(13). Unlike the take-up rates, there is large variation in the LATE estimates between the takers and nontakers, and across subgroups.
There are three main findings. First, among households assigned to arm T by Ĝmix , LATE for takers
is 328.4 JPY and not significantly different from zero, whereas LATE for non-takers is 686.9 JPY and
9

Given that the identification of the LATEs for takers and non-takers is analogous to the identification of LATE (for compliers)
shown in Imbens and Angrist (1994), we can derive a necessary testable implication for the exclusion restriction of household’s
responses to being assigned to arm O following the testable implications of the LATE identifying assumptions obtained in Balkeand Pearl (1997) and Heckman and Vytlacil (2005). Following the test approach of Kitagawa (2015), we plot the subdensities ofthe outcome distributions with our data and do not find a notable violation of the testable implications for the exclusion restriction.

25

significantly different from zero. That is, non-takers in this subgroup positively contribute to welfare if they
are exposed to the treatment, even though they would opt-out if given the choice. From the planner’s pointof view, it is preferable to paternalistically assign these households to T instead of letting them choose.
Second, for households assigned to arm O under Ĝmix , the estimated LATEs for takers and non-takers are1369.6 JPY and -678.0 JPY respectively, and both are significantly different from zero. These estimates
are consistent with households who would autonomously choose the treatment that is superior in terms ofsocial welfare being assigned to O. The estimated policy Ĝmix assigns them to arm O in order to benefit
from this welfare gain. Finally, both estimated LATEs for households assigned to arm N T are negative, andthe LATE for takers is significantly different from zero. That is, among this subgroup, negative-selection oftakers reduces social welfare and, for the planner, it is optimal to assign them to N T .
Panel B of Table 5 presents ATE and ITT as estimated by (9). Consistent with the heterogeneity of
LATEs in Panel A, there is considerable variation in the ATEs and ITTs. For the subgroup of households
assigned to arm T , the ATE and ITT estimates are 550.1 JPY and 125.3 JPY, and the difference between
the two is significantly different (p-value 0.003). Consistent with their assignment under Ĝmix , the welfare
maximizing arm for this subgroup is T (Recall that ATE and ITT correspond to the average welfare gains
of arm T and O). For households assigned to arm O, the ATE and ITT are 109.1 JPY and 526.5, and thedifference between these estimates is significantly different from zero (p-value 0.002). In terms of social
welfare, the optimal arm for this subgroup is O, implying that for these households autonomous choicedominates paternalistic assignment, and Ĝmix assigns them accordingly. For households recommended arm
N T , the ATE and ITT are both negative, and both effects are different from zero (p-value is 0.000). The
optimal arm for them is N T .
Hence, the arm recommended by Ĝmix coincides with the arm that attains the highest welfare gain
for every subgroup of {X ∈ Ĝmix}, j ∈ {T, N T, O}. In other words, the estimated policy Ĝmix capj
tures households’ heterogeneous responses, and mixes paternalistic assignments and autonomous choice tomaximize social welfare.

5

Conclusion
We build an algorithm that mixes paternalistic and autonomous approaches to find an optimal targeting

policy that maximizes policy impact. We apply this algorithm to a randomized field experiment involving26

an energy saving program. We show that optimally mixing paternalistic assignment and autonomous choicesignificantly improves the social welfare gain from the policy. To understand the mechanism behind our
findings, we develop a method that exploits the random variation generated by our field experiment toestimate treatment effects. These estimates show that our algorithm optimally allocates individuals to betreated, untreated, or given an opt-in option based on the relative merits of paternalistic assignments andautonomous choice for their individual type.

27

References
A LATAS , V., R. P URNAMASARI , M. WAI -P OI , A. BANERJEE , B. A. O LKEN , AND R. H ANNA (2016):“Self-targeting: Evidence from a field experiment in Indonesia,” Journal of Political Economy, 124, 371–
427.
A NDREWS , I. S., T. K ITAGAWA , AND A. M C C LOSKEY (2019): “Inference on Winners,” NBER working
paper.
ATHEY, S. AND S. WAGER (2021): “Efficient policy learning with observational data,” Econometrica, 89,
133–161.
BALKE , A. AND J. P EARL (1997): “Bounds on treatment effects from studies with imperfect compliance,”
Journal of the American Statistical Association, 92, 1171–1176.
B HATTACHARYA , D. (2013): “Evaluating Treatment Protocols by Combining Experimental and Observational Data,” Journal of Econometrics, 173, 160–174.
B REIMAN , L., J. H. F RIEDMAN , R. A. O LSHEN , AND C. J. S TONE (2017): Classification and regression
trees, Routledge.
B URLIG , F., C. K NITTEL , D. R APSON , M. R EGUANT, AND C. W OLFRAM (2020): “Machine learning from schools about energy efficiency,” Journal of the Association of Environmental and Resource
Economists, 7, 1181–1217.
C AGALA , T., U. G LOGOWSKY, J. R INCKE , AND A. S TRITTMATTER (2021): “Optimal Targeting inFundraising: A Causal Machine-Learning Approach,” arXiv preprint arXiv:2103.10251.
C HAMBERLAIN , G. (2011): “Bayesian aspects of treatment choice,” in The Oxford Handbook of Bayesian
Econometrics, ed. by J. Geweke, G. Koop, and H. van Dijk, Oxford University Press, 11–39.
C HRISTENSEN , P., P. F RANCISCO , E. M YERS , H. S HAO , AND M. S OUZA (2021): “Energy Efficiency
Can Deliver for Climate Policy: Evidence from Machine Learning-Based Targeting,” .
D EHEJIA (2005): “Program evaluation as a decision problem,” Journal of Econometrics, 125, 141–173.
D ESHPANDE , M. AND Y. L I (2019): “Who Is Screened Out? Application Costs and the Targeting of
Disability Programs,” American Economic Journal: Economic Policy, 11, 213–248.
DYNARSKI , S., C. L IBASSI , K. M ICHELMORE , AND S. OWEN (2018): “Closing the gap: The effect ofa targeted, tuition-free promise on college choices of high-achieving, low-income students,” Tech. rep.,National Bureau of Economic Research.
F INKELSTEIN , A. AND M. J. N OTOWIDIGDO (2019): “Take-up and Targeting: Experimental Evidence
from SNAP,” Quarterly Journal of Economics, 134, 1505–1556.

28

F OWLIE , M., C. W OLFRAM , P. BAYLIS , C. A. S PURLOCK , A. T ODD -B LICK , AND P. C APPERS (2021):“Default Effects And Follow-On Behaviour: Evidence From An Electricity Pricing Program,” The Review
of Economic Studies, 88, 2886–2934.
F RIEDBERG , R., J. T IBSHIRANI , S. ATHEY, AND S. WAGER (2021): “Local Linear Forests,” Journal ofComputational and Graphical Statistics, 30, 503–517.
G ERARDEN , T. D. AND M. YANG (2021): “Using Targeting to Optimize Program Design: Evidence froman Energy Conservation Experiment,” Tech. rep., Working Paper.
H ECKMAN , J. J. (2010): “Building Bridges between Structural and Program Evaluation Approaches to
Evaluating Policy,” Journal of Economic Literature, 48, 356–398.
H ECKMAN , J. J. AND E. V YTLACIL (2005): “Structural Equations, Treatment Effects, and Econometric
Policy Evaluation,” Econometrica, 73, 669–738.
H IRANO , K. AND J. R. P ORTER (2009): “Asymptotics for statistical treatment rules,” Econometrica, 77,
1683–1701.
I DA , T. AND Y. U SHIFUSA (2017): “Cost-Benefit Analysis of Price-based Residential Demand Response,”
Proceedings of the Japan Joint Automatic Control Conference, 60, 304–307.
I MBENS , G. W. AND J. D. A NGRIST (1994): “Identification and Estimation of Local Average Treatment
Effects,” Econometrica, 62, 467–475.
I TO , K., T. I DA , AND M. TANAKA (2021): “Selection on Welfare Gains: Experimental Evidence from
Electricity Plan Choice,” NBER Working Paper.
JANEVIC , M. R., N. K. JANZ , J. A. D ODGE , X. L IN , W. PAN , B. R. S INCO , AND N. M. C LARK (2003):“The role of choice in health education intervention trials: a review and case study,” Social Science andMedicine, 56, 1581–1594.
J OHNSON , M. S., D. I. L EVINE , AND M. W. T OFFEL (2020): “Improving regulatory effectiveness throughbetter targeting: Evidence from OSHA,” Harvard Business School Technology & Operations Mgt. Unit
Working Paper.
K ITAGAWA , T. (2015): “A Test for Instrument Validity,” Econometrica, 83, 2043–2063.
K ITAGAWA , T. AND A. T ETENOV (2018): “Who should be treated? Empirical welfare maximization methods for treatment choice,” Econometrica, 86, 591–616.
K NITTEL , C. R. AND S. S TOLPER (2019): “Using machine learning to target treatment: The case ofhousehold energy use,” Tech. rep., National Bureau of Economic Research.
K NOX , D., T. YAMAMOTO , M. A. BAUM , AND A. J. B ERINSKY (2019): “Design, Identification, andSensitivity Analysis for Patient Preference Trials,” Journal of the American Statistical Association, 114,
1532–1546.
29

L IEBER , E. M. AND L. M. L OCKWOOD (2019): “Targeting with in-kind transfers: Evidence from Medicaid
home care,” American Economic Review, 109, 1461–85.
L ONG , Q., R. L ITTLE , AND X. L IN (2008): “Causal Inference in Hybrid Intervention Trials Involving
Treatment Choice,” Journal of the American Statistical Association, 103, 474–484.
M ANSKI , C. (2013): Public Policy in an Uncertain World, Cambridge, MA: Harvard University Press.
M ANSKI , C. F. (2004): “Statistical treatment rules for heterogeneous populations,” Econometrica, 72,
1221–1246.
M URAKAMI , K., H. S HIMADA , Y. U SHIFUSA , AND T. I DA (2020): “Heterogeneous Treatment Effects ofNudge and Rebate: Causal Machine Learning in a Field Experiment on Electricity Conservation,” Kyoto
University, Graduate School of Economics Discussion Paper Series, Discussion Paper No. E-20-003.
P OTTER , J., L. J IMENEZ , AND S. G EORGE (2014): “SmartPricing Options final evaluation: The final reporton pilot design, implementation, and evaluation of the Sacramento Municipal Utility District’s Consumer
Behavior Study,” Sacramento Municipal Utility District.
RÜCKER , G. (1989): “A Two-Stage Trial Design for Testing Treatment, Self-Selection, and Treatment
Preference Effects,” Statistics in Medicine, 8, 477–485.
S TOYE , J. (2009): “Minimax regret treatment choice with finite samples,” Journal of Econometrics, 151,
70–81.
——— (2012): “Minimax regret treatment choice with covariates or with limited validity of experiments,”
Journal of Econometrics, 166, 138–156.
T ETENOV, A. (2012): “Statistical treatment choice based on asymmetric minimax regret criteria,” Journalof Econometrics, 166, 157–165.
U NRATH , M. (2021): “Targeting, Screening, and Retention: Evidence from California’s Food Stamps Program,” .
WAGER , S. AND S. ATHEY (2018): “Estimation and Inference of Heterogeneous Treatment Effects using
Random Forests,” Journal of the American Statistical Association, 113, 1228–1242.
WALDINGER , D. (2021): “Targeting in-kind transfers through market design: A revealed preference analysis of public housing allocation,” American Economic Review, 111, 2660–96.
WANG , X. AND W. TANG (2018): “To Overconsume or Underconsume: Baseline Manipulation in Demand
Response Programs,” North American Power Symposium.
W OLAK , F. A. (2007): “Residential customer response to real-time pricing: The anaheim critical peakpricing experiment,” UC Berkeley: Center for the Study of Energy Markets.
Z HOU , Z., S. ATHEY, AND S. WAGER (2018): “Offline multi-action policy learning: Generalization andoptimization,” arXiv preprint arXiv:1810.04778.
30Figures
Figure 1: Example of G∗
X2

G∗T
G∗N T
G∗O
{x | CAT E(x) ≥ 0}
{x | CAT ET (x) ≥ 0}
{x | CAT EN T (x) ≥ 0}

X1
Notes: CAT E(x) := E[W (T )−W (N T ) | x], CAT ET (x) := E[W (T )−W (N T ) | Z(O) = T, x], and CAT EN T (x) :=E[W (T ) − W (N T ) | Z(O) = N T, x].

31

Figure 2: Examples of depth-1 and -2 decision trees.
(a-2) Partition of X by the depth 1 decision tree in (a-1)(a-1) Depth 1 decision tree

X2

X 1 ≥ a1
True

GN T

False

GT

NT

T

a1

X2

X 1 ≥ a1True

X1(b-2) Partition of X by the depth 2 decision tree in (b-1)(b-1) Depth 2 decision tree

GT

False

X 2 ≥ a2

a2

X 1 ≥ a3

True

False

True

False

T

O

NT

O

GO

GN T
GO
a3

a1

X1

Notes: Panels (a-2) and (b-2) correspond to the partitions of X induced by the decision trees in Panels (a-1) and (a-2), respectively, where we assume X is a two-dimensional space and a1 > a3 .

32

Figure 3: Decision tree of depth 2

X j ≥ a1
True

False

X k ≥ a2X l ≥ a3

True

False

True

False

opt1

opt2

opt3

opt4

Notes: (j, k, l) ∈ {1, . . . , K}3 , (a1 , a2 , a3 ) ∈ R3 , and (opt1, . . . , opt4) ∈ {T, N T, O}4 . Searching for the optimal decision
tree of depth 2 is equivalent to finding the best combination of indices (j, k, l) ∈ {1, . . . , K}3 of X and threshold values(a1 , a2 , a3 ) ∈ R3 in the top 2 layers, and options (opt1, . . . , opt4) ∈ {T, N T, O}4 in the bottom layer.

33

Figure 4: Optimal paternalistic assignment policy
Num. of people<= 2.2447

TRUE

FALSE

Peak − Post−peak<= −0.0543

TRUE

Income<= 744.3019

Peak − Post−peak<= −0.2480

TRUE

T

FALSE

NT

TRUE

FALSE

Interest<= 2.0000

TRUE

NT

Income<= 566.5737

TRUE

FALSE

T

NT

T: 52%

FALSE

Peak − Post−peak<= −0.0909

TRUE

FALSE

T

T

FALSE

NT

NT: 48%Notes: This figure shows the optimal paternalistic policy estimated in Section 4.2. The upper panel illustrates the structure of thepolicy. By following the yes-no questions from the top of the tree down, each household is assigned to a specific arm. The lower
panel shows the estimated share of households assigned to each arm under this policy.

34

Figure 5: Optimal mixture of the paternalistic assignment and autonomous choice: from depth 1 to 3
Income<= 700.0000

TRUE

FALSE

Num. of people<= 3.1216

TRUE

8

TRUE

FALSE

Interest<= 2.0000

TRUE

Peak − Post−peak<= −0.1040

Income<= 593.8629

TRUE

FALSE

9

10

Peak − Pre−peak<= 0.0292

TRUE

FALSE

11

12

T: 37%

O: 44%

FALSE

Peak − Pre−peak<= −0.0004

TRUE

FALSE

13

FALSE

14

15

NT: 19%Notes: This figure shows the optimal mixture of the paternalistic assignment and autonomous choice, which is estimated in
Section 4.3. The upper panel illustrates the upper half of the structure of the policy. By following the yes-no questions fromthe top of the tree down, each household is assigned a number. If the household is assigned a number less than or equal to 11,
the household proceeds to figure 6; otherwise, the household proceeds to figure 7. The lower panel shows the estimated share ofhouseholds assigned to each arm under this policy.

35

Figure 6: Our best mixture of paternalistic and autonomous approaches: from depth 4 to 6, right side
Node ID: 8

Node ID: 9Peak − Post−peak<= −0.0996

Peak − Pre−peak<= 0.0020

TRUE

TRUE

FALSE

Peak − Post−peak<= −0.2575

TRUE

Income<= 300.0000

TRUE

TRUE

FALSE

Peak − Post−peak<= −0.1413

TRUE

FALSE

NT

Income<= 530.5307

T

NT

TRUE

T

Peak − Post−peak<= −0.0917

Num. of people<= 2.0000

TRUE

FALSE

NT

T

TRUE

FALSE

Peak − Pre−peak<= 0.1199

FALSE

Peak − Pre−peak<= −0.0292

TRUE

FALSE

NT

T

Node ID: 10

TRUE

FALSE

Peak − Pre−peak<= −0.0035

TRUE

FALSE

T

Peak − Post−peak<= −0.0544

O

TRUE

O

T

FALSE

Peak − Post−peak<= −0.0094

TRUE

FALSE

O

T

FALSE

T

O

Node ID: 11

TRUE

Peak − Post−peak<= −0.1308

TRUE

FALSE

Peak − Pre−peak<= −0.0203

TRUE

Peak − Post−peak<= −0.1383

NT

Income<= 698.8769

FALSE

Peak − Pre−peak<= 0.0133

TRUE

FALSE

Peak − Pre−peak<= 0.0609

Peak − Post−peak<= −0.1628

TRUE

FALSE

T

TRUE

FALSE

T

Peak − Pre−peak<= 0.0190

TRUE

FALSE

NT

T

Peak − Pre−peak<= 0.0456

TRUE

FALSE

Num. of people<= 4.0000

TRUE

FALSE

NT

FALSE

T

Peak − Post−peak<= −0.3714

TRUE

FALSE

NT

O

Peak − Post−peak<= −0.0464

Peak − Post−peak<= −0.2763

TRUE

FALSE

T

TRUE

FALSE

T

Interest<= 4.0000

TRUE

FALSE

O

O

FALSE

Peak − Pre−peak<= −0.0426

TRUE

FALSE

T

O

FALSE

T

Notes: This figure shows the optimal mixture of the paternalistic assignment and autonomous choice, which is estimated in
Section 4.3. Specifically, it illustrates the lower left section of the decision tree. Households assigned numbers between 8 and
11 in figure 5 are assigned to arms by working down through the yes-no questions in the tree corresponding to their number.

36

Figure 7: Our best mixture of paternalistic and autonomous approaches: from depth 4 to 6, left side
Node ID: 12

Node ID: 13Interest<= 3.0000

Peak − Pre−peak<= 0.0738

TRUE

TRUE

FALSE

Peak − Post−peak<= −0.1456

TRUE

Num. of people<= 3.0000

TRUE

FALSE

NT

TRUE

FALSE

Peak − Post−peak<= −0.5272

TRUE

Peak − Post−peak<= −0.1841

T

TRUE

FALSE

NT

T

TRUE

Income<= 1250.0000

TRUE

FALSE

T

Peak − Pre−peak<= 0.0394

FALSE

Peak − Pre−peak<= −0.0946

NT

FALSE

TRUE

NT

T

Node ID: 14

T

Num. of people<= 4.0000

Income<= 978.9744

TRUE

TRUE

TRUE

FALSE

T

O

TRUE

O

T

FALSE

T

O

Peak − Pre−peak<= 0.0120

TRUE

FALSE

Peak − Post−peak<= −0.0763

TRUE

Income<= 900.0000

TRUE

FALSE

Peak − Post−peak<= −0.0868

O

FALSE

Node ID: 15
Peak − Post−peak<= −0.0266

TRUE

FALSE

Num. of people<= 2.0000

FALSE

O

TRUE

FALSE

Peak − Pre−peak<= 0.0317

FALSE

Interest<= 3.0000

Interest<= 4.0000

TRUE

FALSE

T

O

Peak − Pre−peak<= −0.0336

TRUE

FALSE

T

T

Num. of people<= 2.0000

TRUE

FALSE

Peak − Post−peak<= 0.0332

TRUE

FALSE

O

FALSE

T

Peak − Pre−peak<= 0.0020

TRUE

FALSE

O

NT

Peak − Post−peak<= −0.0441

Peak − Post−peak<= −0.0507

TRUE

FALSE

T

TRUE

FALSE

T

FALSE

NT

Peak − Post−peak<= −0.0606

TRUE

NT

FALSE

Peak − Post−peak<= 0.0269

TRUE

FALSE

T

NT

FALSE

T

Notes: This figure shows the optimal mixture of the paternalistic assignment and autonomous choice, which is estimated in
Section 4.3. Specifically, it illustrates the lower right section of the decision tree. Households assigned numbers between
12 and 15 in figure 5 are assigned to arms by working down through the yes-no questions in the tree corresponding to their
number.

37

Figure 8: Two dimensional summary of the policies
^
Gpat

^
Gmix

0.10

NT

0.05
0.00
−0.05

prob
1.00

0.05
T

0.75
0.50

0.00

0.25
−0.05
0.00
0.10
0.05
O

Peak − Pre−peak

0.10

0.00
−0.05
−0.4

−0.3

−0.2

−0.1

0.0

−0.4

−0.3

−0.2

−0.1

0.0

Peak − Post−peakNotes: This figure shows a two dimensional summary of the policies estimated in Section 4.2 and 4.3. Each row corresponds toa different arm, and each column to a different policy (Ĝpat or Ĝmix ). In each panel, a point represents a household observedin our experimental data, and the color of the point shows the probability of being assigned to a specific arm.

38

Tables
Table 1: Summary Statistics
p-value: H0 : difference in means = 0
NT

T

O

NT vs. T

NT vs. O

T vs. OALL

Peak hour usage (kWh)0.192(0.004)0.190(0.004)0.189(0.005)

0.609

0.633

0.961

0.838

Pre-peak hour usage (kWh)0.179(0.003)0.176(0.004)0.180(0.005)

0.442

0.854

0.417

0.646

Post-peak hour usage (kWh)0.299(0.004)0.297(0.004)0.293(0.006)

0.756

0.426

0.588

0.725

Number of people at home

2.481
(0.031)2.444(0.032)2.470(0.045)

0.406

0.846

0.626

0.703

Interest in energy conservation 3.450(1-5 Likert scale)(0.022)

3.464(0.022)3.488(0.029)

0.647

0.299

0.517

0.584

Household income(10,000JPY)

645.095(10.056)

613.409(9.384)636.641(13.778)

0.022

0.622

0.154

0.066

Number of customers

1,577

1,486

807

Notes: The first three columns present the sample mean and standard errors for the pre-experiment consumption data
and demographic variables. The first column contains values for the group assigned to no-treatment (N T ), the second
contains values for the group assigned to treatment (T ), and the third contains values for the group given the option
to receive treatment (O). We do not observe any significant difference in the first five variables between the groups.
This indicates that random assignment has successfully balanced these five observables. For household income, we
do not observe any significant difference between the N T and O groups, nor the T and O groups, whereas we doobserve a significant difference between the N T and T groups. We confirmed that the treatment effects did not vary
substantially when estimating the effects while controlling for demographic variables including household income.

39

Table 2: Intention-to-Treat Estimates
Peak hour usage− Pre-peak hour usage(in pre-experiment)

Peak hour usage− Post-peak hour usage(in pre-experiment)

All

Low

High

Low

High

100% Treatment-0.097(0.021)-0.108(0.028)-0.079(0.031)-0.089(0.030)-0.094(0.028)

100% Opt-in-0.052(0.027)-0.022(0.034)-0.073(0.041)-0.070(0.037)-0.023(0.037)

Number of customers
Number of observations
p-value (T = O)
Opt-in rate

3,870
1,176,480
0.088
37.2%

1,935
588,240
0.013
36.9%

1,935
588,240
0.880
37.4%

1,937
589,152
0.595
39.9%

1,933
587,328
0.047
34.7%

Number of people at home

Interest inenergy conservation

Household income

Low

High

Low

High

Low

High

100% Treatment-0.096(0.027)-0.098(0.034)-0.134(0.028)-0.057(0.031)-0.071(0.028)-0.125(0.031)

100% Opt-in-0.022(0.034)-0.094(0.042)-0.036(0.035)-0.072(0.040)-0.036(0.038)-0.060(0.037)

Number of customers
2,245
Number of observations 682,480
p-value (T = O)
0.020
Opt-in rate
37.6%

1,625
494,000
0.934
36.6%

1,967
597,968
0.004
33.8%

1,903
578,512
0.715
40.6%

2,036
618,944
0.336
34.8%

1,834
557,536
0.094
39.7%

Notes: This table shows the estimation results for equation (6) using the full-sample (the first column of the upper
panel) or sub-samples (the remaining columns). The dependent variable is the log of household-level electricity
consumption over a 30-minute interval . We include household fixed effects and time fixed effects for each 30-minuteinterval. The standard errors are clustered at the household level to adjust for serial correlation. In order to investigate
the heterogeneity of the treatment effects, we divided the sample into five sets of two sub-groups. For five different
variables, the first sub-group includes households who are below the median of this variable and the second includes
those who are above the median.

40

Table 3: Welfare performance of the best paternalistic assignment
PolicyEst. Welfare Gain

95 % CI

Uniform no-treatment (100% N T )Uniform treatment (100% T )The purely autonomous policy (100% O)
The paternalistic assignment (Ĝpat )

0.0
63.1
140.9
228.5

—
(−97.2, 223.4)(−40.1, 322.0)(109.7, 347.4)

Ĝpat vs 100% TĜpat vs 100% O

165.5
87.6

(58.3, 272.7)(−88.9, 264.1)

Notes: This table shows the estimated welfare gain of the optimal paternalistic assignment along with three benchmark policies.
The unit of these estimates is Japanese yen. 95% confidence intervals are in parentheses. The first four rows show the welfare gain
relative to the status quo (uniform no-treatment), while the remaining two rows show the welfare gain of paternalistic assignment
relative to the other two benchmark policies.

Table 4: Welfare performance of the best mixture of the paternalistic and autonomous approaches
PolicyEst. Welfare Gain

95 % CI

Uniform no-treatment (100% N T )Uniform treatment (100% T )The purely autonomous policy (100% O)
The paternalistic assignment (Ĝpat )The mix of paternalism and autonomy (Ĝmix )

0.0
63.1
140.9
228.5
437.9

—
(−97.2, 223.4)(−40.1, 322.0)(109.7, 347.4)(283.0, 592.8)

Ĝmix vs 100% TĜmix vs 100% O
Ĝmix vs Ĝpat

374.8
297.0
209.4

(238.8, 510.8)(165.9, 428.0)(75.2, 343.5)

Notes: This table shows the estimated welfare gain of the best mixture of paternalistic assignment and autonomous choice, alongwith that of three benchmark policies and the best paternalistic assignment. The unit of these estimates is Japanese yen. 95%
confidence intervals are in parentheses. The first five rows show the welfare gain relative to the status quo (uniform no-treatment),
while the remaining three rows show the welfare gain of the best mixture relative to the other two benchmark policies and the
optimal paternalistic assignment.

41

Table 5: Mechanism behind the algorithm
Recommended arm by Ĝmix
j

NT

T

O

A) Counterfactual analysis of opt-in policy
Opt-in rate (X ∈ Ĝmix
)
43.7%
j
(36%, 52%)
LATE(Z(O) = T, X ∈ Ĝmix)−1629.3
j(−2602.5, −656.2)
LATE(Z(O) = N T, X ∈ Ĝmix)−518.4j(−1268.2, 231.3)

38.2%(33%, 44%)328.4(−462.4, 1119.3)
686.9(231.8, 1142.0)

38.4%(33%, 43%)
1369.6(649.8, 2089.5)−678.0(−1102.4, −253.7)

B) Counterfactual analysis of each policy
ATE(X ∈ Ĝmix)−1004.5
j(−1364.5, −644.4)
ITT(X ∈ Ĝmix)−712.8j(−1117.6, −308.1)

550.1(284.8, 815.5)
125.3(−175.9, 426.6)

109.1(−130.3, 348.5)
526.5(258.5, 794.5)

Notes: This table shows the estimates of the opt-in rate, LATE for takers, LATE for non-takers, ATE, and ITT. Each column
contains estimates for a group of households recommended a particular arm by the estimated policy Ĝmix . The unit of all estimates
except the opt-in rate is JPY. 95% confidence intervals are in parentheses. These estimates are calculated based on the identification
results (9), (10), (12), and (13).

42A

Appendix

A.1

The external validity of the experimental sample

We randomly sampled 2,070 customers from the target population who did not participate in this experiment, and conducted a similar survey to the one for the experimental sample. The purpose of this was
to investigate the external validity of our experimental sample by comparing the mean for each variable
between the control group from our experimental sample and this random sample. Columns 1 and 2 ofTable Appendix 1 show summary statistics for the control group and random sample. Column 3 presents
differences in means, with the standard errors of these differences in brackets. We observe larger means forfour variables in the control group than in the random sample, and the differences are statistically significant.
Our experimental sample has larger pre-experiment electricity usage per month, a larger number of people
at home on weekdays, higher interest in energy conservation, and higher household income. This implies
that our sample includes a larger number of customers who are willing and able to reduce their electricity
consumption, which should be taken into consideration when discussing the generalizability of this study.

Table Appendix 1: The external validity of the experimental sample

Experimental sample
in the control group

Random sample
of population

Difference
between sample
and population

Monthly electricity usage in July (kWh)355.703(205.267)

303.841(176.677)

51.862[6.336]

Number of people at home

2.481
(1.241)

2.313(1.204)0.168[0.041]

Interest in energy conservation(1-5 Likert scale)

3.450(0.854)3.322(0.969)0.128[0.031]

Household income (10,000JPY)

645.095(399.342)

581.264(383.782)

63.832[13.055]

1,577

2,070

Number of customers

43

A.2

Two-step Procedure

We describe the heuristic two-step procedure to obtain a decision tree of depth 6. Our procedure begins
by arbitrarily choosing two arms from the set of all arms. For exposition purpose, suppose these are T
and N T . Given this pair of chosen arms, we first search for the best decision tree of depth 3 that exactly
maximizes the empirical welfare function with the available arms restricted to T and N T . The resulting tree
distributes the training sample among the leaf nodes, and in each leaf node either of T or N T is selected
as the best arm. Next, for each leaf node, we again search for the best decision tree of depth 3, but theavailable arms are modified to the current best arm (T or N T ) and the excluded arm (O). Concatenatingthese decision trees gives us a decision tree of depth 6. Notice that this procedure is dependent on the choiceof the first two arms, (T, N T ), (N T, O), and (T, O). Since our goal is to approximate the decision tree of
depth 6 which attains the highest empirical welfare, we repeat this two step procedure for all possible starting
pairs and choose the one with the highest welfare performance. In our analysis, the decision tree with firststep options N T and O is selected. Although there is no guarantee that our procedure well approximates a
global optimizer, the welfare performance of a policy obtained in this manner constitutes a lower bound forthat of a global optimizer. Therefore, while our decision tree is conservative in terms of welfare, and we do
not regard this as a serious drawback.

A.3

Artificial Test Data

We describe in detail our method for generating artificial test data. To begin with, we describe the sourceof the bias in point estimates. This occurs due to noise in Yi and Zi , which are random components in Wi .
Specifically, the observed outcome Yi can be decomposed as the sum of an essential term and noise as
follows:

Yi = E[Yi (N T ) | Xi ] · 1{Di = N T } + E[Yi (T ) | Xi ] · 1{Di = T } + E[Yi (O) | Xi ] · 1{Di = O}{z}|essential term

+ i (N T ) · 1{Di = N T } + i (T ) · 1{Di = T } + i (O) · 1{Di = O},
{z
}
|
noise

where i (j) := Yi (j) − E[Yi (j) | Xi ] for each j ∈ {T, N T, O}. The observed choice Zi can be similarly
decomposed. While only the first term is necessary for learning an optimal policy, a learning algorithm

44inevitably responds to the noise term and overfits the training sample at hand. When we evaluate the welfare
performance of the estimated policy on the same training sample, the welfare estimate is biased upward
because the policy fits the noise term as well. This implies that, if we replace the noise in the training sample
with a second independent sample, we can eliminate the bias from the estimate of welfare performance.
Motivated by this, we generate test data {Yitest , Zitest , Di , Xi }ni=1 , where Yitest denotes electricity consumption and Zitest denotes treatment choice. For Yitest we use the following procedure to generate artificial
data: For samples i ∈ Ij := {i : Di = j},b i (j) | Xi ] for each i ∈ Ij .
1. Estimate E[Yi (j) | Xi ] and calculate residuals b
i = Yi − E[Y2. Sample {btest
i }i∈Ij with replacement.
i }i∈Ij from {bb i (j) | Xi ] + b
3. Construct Yitest = E[Ytest
i for each i ∈ Ij .
Note that we implicitly assume homoskedasticity. In the first step, we estimate the conditional mean using
a local linear forest (Friedberg et al., 2021). We generate {Zitest }ni=1 as follows: For samples i ∈ IN T andi ∈ IT , we set Zitest = N T and Zitest = T , respectively. For samples i ∈ IO
1. Estimate P (Zi (O) = T | Xi ) for each i ∈ IO .
2. Sample {Zitest }i∈IO such that Zitest ∼ Pb(Zi (O) = T | Xi ).

45