Optimal incentives for a multi-task Agent with possible unawareness 

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Cognitive biases related to energy behavior

Various factors explain the observed EPG: technical failures, non-optimal renovation works, harsh weather conditions, etc. However, behavioral factors seem to play a significant role, as pointed out in previous literature. These behaviors often emerge due to cognitive biases.
Cognitive biases refer to individuals’ mistakes occurring when reasoning and making decisions. They are generally induced by mental shortcuts (i.e. heuristics), emerging when the brain tries to process and simplify information it is receiving. These shortcuts do not always lead us to make optimal decisions, and can event unconsciously alter someone’s behavior. A number of these cognitive biases can directly impact energy consumption behaviors and indirectly impact energy savings of renovated buildings. In this study, we focus on four biases, namely (1) the Status Quo Bias, (2) the Optimism Bias, (3) the Attitude-Behavior Gap and (4) the Intention-Behavior Gap. Our analysis applies these cognitive biases to energy consumption related behaviors, because they can intuitively induce occupants to consume more and save less energy than initially predicted. They were selected in order to analyze a combination of largely studied cognitive biases that could be applied to energy consumption behaviors (1 and 2), and often studied pro-environmental related behaviors (3 and 4). We consider the two behavioral gaps as cognitive biases: as stated by Frederiks et al. (2015b), attitudes and intentions (i.e. a motivation toward a goal-directed behavior) are psychological factors, which potentially affect occupant’s energy behavior, and thus their energy consumption.
Note that the literature recognizes that it is difficult to exactly measure cognitive biases, even though the concept behind them seems clear. It has mostly been studied through experiments in controlled environments. In this chapter, we propose to measure cognitive biases through self-declarations. These self-reported behaviors are only possible indicators, measuring cognitive biases indirectly. We present the selected self-declarations in Section 1.5. In the following, we define the concept of the fours above mentioned biases and deduce testable hypotheses from psychology and the theory of behavior.
The status quo bias: It refers to the behavioral tendency of preferring to do nothing, or to exert no effort to adapt a behavior (Samuelson and Zeckhauser, 1988), although doing nothing may lead to a change (Baron and Ritov, 2004). This tendency might arises due to people’s general loss aversion (Thaler, 1980; Kahneman and Tversky, 1984; Samuelson and Zeckhauser, 1988; Kahneman et al., 1991). Individuals perceive losses as being bigger than the potential gains they can obtain by adapting their behavior.

A new database on deep energy renovation in France

The survey and its questionnaire led to the elaboration of a database. This section explains how it has been compiled and how theoretical energy consumption were calculated. To minimize missing observations on actual energy consumption, we asked households to prepare their energy bills (e.g. electricity, gas) in advance. During the interviews, the investigators filled out paper questionnaires to discuss more fluently with the respondents.
They should feel comfortable to answer honestly. The compilation of the collected data into an Excel file was done with Adobe Acrobat Pro. The PDF version of the questionnaire was transformed into an interactive ‘PDF form’, where every button was programmed under the needed form (e.g. binary, categorical, text, single answer) and with an appropriate variable name. This form being fillable on the computer, we manually copied the completed paper questionnaires. After gathering all the electronic PDF forms, the software creates a corresponding Excel file. This method has two advantages: (1) the number of transcription errors are drastically decreased and limited, and (2) the time needed to elaborate the Excel file containing the entire database is remarkably reduced.

The predicted energy consumption

Households’ predicted energy consumption were calculated through energy audits by external energy consultation firms during the planning of the renovation works.
The energy audits are made with the TH-C-E ex standard calculation method based on the French thermal Regulation entered into force in 2012 (Centre scientifique et technique du bâtiment (CSTB), 2008)17. The method predicts the energy consumption of existing buildings after renovation measures. It takes into account specific set points, standard building characteristics and real values for all the replaced and renovated elements. On the household side, standard behavioral and occupants’ characteristics are considered: any evolution or change of the household are not included. It thus represents a static prediction where real conditions of use are not considered. Concerning heating habits, a standard heating temperature of 19°C during occupation times (i.e. 16 hours per day during weekdays, and 24 hours per day during weekends), and 16°C otherwise are taken into account. These temperature settings are optimal in terms of comfort in isolated buildings, but are low enough to permit energy savings.

Socio-demographic characteristics

From the 139 households having participated in the survey, about 89% live as a couple (married or not), and an average of 3.38 persons live per renovated house. Indeed, 90% of the households have children under the age of 18 living with them. No couples aged between 18 and 24 were interrogated: young people generally do not have the financial capacity to become landlord, and on top of that, finance a deep energy renovation. However, 16% of the respondents are between 25 and 34 years old, which shows that deep energy renovation can also be accessible to younger landlords. The vast majority of the households are between 35 and 59 (71%), and only 13% are older. Nearly half of the respondents (i.e. 47%) work as an executive, liberal or executive intellectual. Interestingly, higher educated households seem predominant in the JRBBC program: 83% of the panel have a higher education, among which 39% have a Master’s degree or more. Only 1% have no diploma at all. Figure 1.4 shows that a majority (53%) of the households have a monthly net revenue lying between 3 000e and 5 000e.

Energy Performance Gap and proxies for the cognitive biases

In this section, we present the variable of interest and the proxy variables used to test the cognitive biases.
Our dependent variable is the Energy Performance Gap (EPG) of the individual household measured as the logarithmic ratio of the ex-post actual and predicted total energy consumption. Actual energy consumption is normalized by heating degree days, altitude and location of the individual building.
Figure 1.12 depicts the relationship between the EPG and actual energy consumption of our sample. A positive and increasing relationship between both measures can be observed. This means that the higher the actual energy consumption of a household, the more likely is the underestimation of the predicted energy consumption. An EPG greater (lower) than zero represents the Net Losing (Gaining) Energy Savings of the individual household (Sunikka-blank and Galvin, 2012). This observation is in line with the one made by Raynaud (2014). The likelihood of achieving at least the required energy performance is approximately 62% as a relatively large percentage of households of our sample actually consume lower levels of energy than predicted. However, 38% of the sample reveals an over-consumption pattern.


Selecting control variables using learning models

To curb adverse effects from confounding variables and to control for observed heterogeneity among occupants, we have a wide range of socio-demographic and technical covariates available as controls.
However, our sample size is small, which might lead to the problem of overfitting in the subsequent estimation model, especially when the number of parameters is too large for a particular dataset. While there exists no exact rule about the number of covariates to be included in a model, we apply the thumb rule in accordance with Koebel et al. (2016) by using 10 observations per covariate. To prevent the problem of overfitting, we seek to select a restricted number of control variables constituting a common classification problem.
Instead of using a forward selection method to select covariates, we apply a more data-driven approach, by employing machine learning and predictive modeling. These are powerful tools helping to identify strong predictors of the EPG, and therefore to select most relevant variables affecting the Net Losing Energy Savings (NLS) on the one hand, and the Net Gaining Energy Savings (NGS) on the other hand. Data-driven approaches are receiving widespread attention from scholars in different fields, and the success of their application is due to the effective use of models capable of detecting complex data dependencies and capturing non-linear or non-monotonic data patterns (Breiman, 2001; Cranmer and Desmarais, 2017; Varian, 2014). To this purpose, we apply a set of most widely used supervised machine learning algorithms: (i) random forest (RF), (ii) gradient tree boosting (GTB), and (iii) non-linear (radial) support vector machine (SVM).
The basic procedure of machine learning can be summarized as follows. First, the data is split into ‘training sets’ (to train the model) and ‘test sets’ (to evaluate/validate the trained model). Various validation methods are available to divide the data. We use the Leave One Out Cross Validation (LOOCV) method, because it constitutes an effective internal validation method when the sample size is relatively small. It uses one single observation from the original sample as a validation data (i.e. ‘test set’) and the remaining are used as training data (i.e. ‘training set’). This is repeated N-times, such that every single observation from the sample is used as a ‘test set’. Second, the algorithm of the LOOCV attempts to predict the value of interest Y (the outputs NLS and NGS in our case) given an input of a feature set X (variables). The aim is to develop a finely tuned function h(X) that maps input data into the output of interest. The algorithm optimizes this function, given the input data, to accurately predict the target value Y , by using the ‘training set’. For each ‘training set’, we evaluate the difference between the predicted value h(X) and the output Y from the ‘test set’. By doing so, the algorithm can learn from the ‘training set’ in order to measure and minimize the wrongness of h(X).
Once the data is divided, we apply a machine learning algorithm. We implement the three algorithms (i.e. learning models) mentioned earlier, to finally select the one with the highest performance, using the Root-Mean-Square Error (RMSE). This method compares forecasting errors of different models for one particular dataset (Hyndman and Koehler, 2006). Hence, a lowest RMSE indicates the best model.

Table of contents :

1 How cognitive biases affect the Energy Performance Gap in low energy buildings 
1.1 Related literature
1.2 Cognitive biases related to energy behavior
1.3 « Je rénove BBC » renovation program: survey, questionnaire and database
1.3.1 The survey
1.3.2 The questionnaire
1.3.3 A new database on deep energy renovation in France
1.4 Descriptive statistics of the « Je rénove BBC » panel
1.4.1 Socio-demographic characteristics
1.4.2 Importance of financial aids and tax benefits
1.4.3 Renovation motivations
1.4.4 Households’ satisfaction
1.4.5 Habits in the renovated houses
1.4.6 Households’ energy consumption
1.5 Energy Performance Gap and proxies for the cognitive biases
1.6 Control variables and modeling approach
1.6.1 Selecting control variables using learning models
1.6.2 Modeling approach
1.7 Empirical analysis
1.7.1 Parametric and non-parametric statistical tests
1.7.2 Results
1.7.3 Model selection
1.8 Robustness Analysis
1.9 Policy implications and conclusion
Appendix A 
A.1 « Je rénove BBC » survey questions in English
A.2 « Je rénove BBC » original questionnaire in French
A.3 Conventional data in energy audits: the TH-C-E ex software
A.4 Actual ex-post energy consumption
A.5 Variable Definitions
A.6 Tuning Plots
A.7 Missing values imputation
A.8 Statistical Tests
A.9 Regression Results
A.9.1 Status quo bias
A.9.2 Optimism bias
A.9.3 Attitude-Behaviour gap
A.9.4 Intention-Behaviour gap
A.10 Feature ranking
2 Optimal incentives for a multi-task Agent with possible unawareness 
2.1 Introduction
2.2 Related literature
2.3 A two-task Principal-Agent model with complete awareness
2.3.1 The baseline model
2.3.2 Optimal compensation with a risk neutral Principal
2.3.3 Optimal compensation with a risk averse and prudent Principal
2.4 A two-task Principal-Agent model with possible unawareness
2.4.1 The possible unawareness model
2.4.2 Optimal compensation
2.5 Discussion and concluding remarks
Appendix B 
B.1 Proofs of Propositions and equation computations
B.2 A two-task Principal-Agent model with complete unawareness: the case of an observable second task
B.2.1 The complete unawareness model
B.2.2 Optimal compensation
B.2.3 Computation related to the complete unawareness model
3 Knowledge acquisition or incentive to foster coordination ? A real-effort weak-link experiment with craftsmen 
3.1 Introduction
3.2 Experimental design
3.2.1 The individual productivity elicitation
3.2.2 The repeated real-effort game
3.2.3 Procedures
3.3 Predictions
3.4 Results
3.4.1 Descriptive statistics
3.4.2 Non-parametric analysis
3.4.3 Econometric analysis
3.5 Discussion and concluding remarks
Appendix C 
C.1 Instructions of the experiment in French
C.1.1 Informations générales
C.1.2 Instructions de la Partie 1
C.1.3 Instructions de la Partie 2
C.1.4 Instructions de la Partie 3
C.1.5 Instructions de la Partie 4
C.2 Post-experimental questionnaire in French
General Conclusion 


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