Price Elasticity of Electricity Revisited: A Meta-Analysis

• Název práce v češtině: Cenová elasticita elektřiny přehodnocena: Metaanalýza
• Název v anglickém jazyce: Price Elasticity of Electricity Revisited: A Meta-Analysis
• Klíčová slova: meta-analýza, energie, elektřina, poptávka po elektřině, cenová elasticita, publikační zkreslení, endogenní zkreslení
• Klíčová slova anglicky: meta-analysis, energy, electricity, electricity demand, price elasticity, publication bias, endogeneity bias
• Akademický rok vypsání: 2021/2022
• Typ práce: bakalářská práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: doc. PhDr. Zuzana Havránková, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 15.06.2022
• Datum zadání: 15.06.2022
• Datum a čas obhajoby: 11.06.2024 09:00
• Místo konání obhajoby: Opletalova, O105, místnost č. 105
• Datum odevzdání elektronické podoby: 30.04.2024
• Datum proběhlé obhajoby: 11.06.2024
• Oponenti: Dipl.-Ing. Mathieu Petit, B.Sc.

Seznam odborné literatury

Acton, J.P., Mitchell, B. & R. Mowill (1976): “Residential Demand for Electricity in Los Angeles: An Econometric Study of Disaggregated Data.” Rand Corporation, Santa Monica, California, Rand Corporation, Santa Monica, California
van Aert, R.C. & M. van Assen (2021). Correcting for publication bias in a meta-analysis with the p-uniform* method. Working paper, Tilburg University & Utrecht University, available online at osf.io/preprints/metaarxiv/zqjr9/download (oned on December 22, 2021).
Ajanovic, A., Hiesl, A. & R. Haas (2020): “On the role of storage for electricity in smart energy systems.” Energy 200: art. 117473.
Andrews, I. & M. Kasy (2019): “Identification of and Correction for Publication Bias.” American Economic Review 109(8): pp. 2766–2794.
Bom, P. R. D. & H. Rachinger (2019): “A Kinked Meta-Regression Model for Publication Bias Correction.” Research Synthesis Methods 10(4): pp. 497–514.
Borenstein, S. & J. Bushnell (2015): “The U.S. Electricity Industry After 20 Years of Restructuring.” Annual Review of Economics 7(1): pp. 437–463.
Cuddington, J.T. & L. Dagher (2015): “Estimating Short and Long-Run Demand Elasticities: A Primer with Energy-Sector.” The Energy Journal 36(1): pp. 185–209.
Dahl, C.A. (2011a): “A Global Survey of Electricity Demand Elasticities.” Paper presented at the 34th IAEE International Conference: Institutions, Efficiency and Evolving Energy Technologies, June 19-23, 2011, at the Stockholm School of Economics, Sweden
Dahl, C.A. (2011b): “DEDD-El.xls.” in Dahl Energy Demand Database, http://dahl.mines.edu/courses/dahl/dedd, Mineral and Energy Economics Program, Colorado School of Mines, Colorado: Golden.
Egger, M., Smith, G.D., Schneider, M. & C. Minder (1997): “Bias in meta-analysis detected by a simple, graphical test.” British Medical Journal 315(7109), pp. 629–634.
Elliott, G., Kudrin, N., & K. Wuthrich (2022): “Detecting p-hacking.” Econometrica 90(2): pp. 887–906.
Espey, J.A. & M. Espey (2004): “Turning on the Lights: A Meta-Analysis of Residential Electricity Demand Elasticities.” Journal of Agricultural and Applied Economics 36(1): pp. 65–81.
Furukawa, C. (2019): “Publication Bias under Aggregation Frictions: Theory, Evidence, and a New Correction Method.” MIT working paper, Massachusetts Institute of Technology.
George, E. I. (2010): “Dilution priors: Compensating for model space redundancy. In Borrowing Strength: Theory Powering Applications–A Festschrift for Lawrence D. Brown” (pp. 158–165). Institute of Mathematical Statistics.
Gowrisankaran, G., Reynolds S.S. & M. Samano (2016): “Intermittency and the Value of Renewable Energy.” Journal of Political Economy 124(4): pp. 1187–1234.
IEA (2019): “Nuclear Power in a Clean Energy System” International Energy Agency, Agency Report as of May 2019, accessed on June 13, 2022 at https://www.iea.org/reports/nuclear-power-in-a-clean-energy-system.
Ioannidis, J.P., T.D. Stanley & H. Doucouliagos (2017): “The Power of Bias in Economics Research.” Economic Journal 127(605): pp. 236–265.
Ito, K. (2014): “Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing.” American Economic Review 104(2): pp. 537–563.
Labandeira, X., Labeaga, J.M. & X. López-Otero (2017): “A meta-analysis on the price elasticity of energy demand.” Energy Policy 102: pp 549–568.
Lijesen, M.G. (2007): “The real-time price elasticity of electricity.” Energy Economics 29: pp. 249–258.
Mathews, J. & H. Tan (2014): “Economics: Manufacture renewables to build energy security.” Nature 513: pp. 166–168.
Stanley, T.D. (2005): “Beyond Publication Bias.” Journal of Economic Surveys 19(3), pp. 309–345.
Steel, M.F. (2020): “Model averaging and its use in economics.” Journal of Economic Literature 58(3): pp. 644–719.
Taylor, L.D. (1975): “The Demand for Electricity: A Survey.” Bell Journal of Economics 6(1): pp. 74–110.
Zhu, X., Li, L., Zhou, K., Zhang, X. & S. Yang (2018): “A meta-analysis on the price elasticity and income elasticity of residential electricity demand.” Journal of Cleaner Production 201: pp. 169–177.

Předběžná náplň práce v anglickém jazyce

Research question and motivation

Matching demand with supply gets difficult in electricity markets. Demand for electricity changes rapidly throughout the day while electricity generated by suppliers is hard and costly to store (Ajanovic et al., 2020). To increase efficiency on the power grid one has to know how consumer demand responds to price changes. The response is measurable and economists call it the price elasticity of electricity demand. This parameter informs policy makers how tax revenues or consumption change with pricing policies. The parameter is also used in calibrations of economic models of climate change, mitigation, and adaptation.

The power grid went through great structural changes during the past 15 years. First, in pursuit to limit their carbon footprint, countries increasingly use renewables to generate electricity (and less so the nuclear generators, see IEA, 2019). The trouble is that countries using renewables battle with intermittency (Gowrisankaran et al., 2016). As pointed out by Mathews & Tan (2014) and many others, if country wants a reliable power grid based on renewables, it has to compensate the phases of no sun and no wind with fossil fuel generators which can be turned on and off at will. Second, the energy mix-up and technological advancement call for an increasing usage of the time-of-day or time-of-use pricing (as shown in Borenstein & Bushenell, 2015, e.g. the off-peak electricity hours tend to be cheaper) and real-time pricing (Lijesen, 2007). Indeed, both technological change and elaborated pricing schemes present a challenge for the estimation of the price elasticity. The rising amount of newly produced articles documents to the importance of the parameter.

The pattern of increasing article production manifests in the previously conducted meta-analyses of Espey et al. (2004), Labandeira et al. (2017), and Zhu et al. (2018) and the literature reviews by Taylor (1975), Dahl (2011a), and Huntington et al. (2019). All of them suggest the elasticity estimates vary widely when one uses different methods, data, pricing schemes, or considers the socio-economic characteristics of consumers. They also suggest that any researcher wanting to calibrate their climate model can easily find values ranging from huge negative (as much as -30) to large positive (such as +3) although the simple average falls close to -0.3 for the short-term and -0.6 for the long-term effects. None of these published surveys, nonetheless, corrects its simple average for publication selection bias and the management of outliers is rather unclear.

Publication selection arises when there is a preference to publish certain type of results: those that are either in line with a strong theory or that are statistically significant. The literature at question is driven by the law of demand, the strongest economic theory of all. To no surprise, many authors of primary studies are reluctant to interpret positive elasticities that deem electricity a Giffen good. But none of the previous surveys comments on the fact that the outlying negative values in the literature are 10-fold larger than the outlying positive values. In fact, it is noteworthy that such wide distribution of estimates produces a simple average that is so far from the negative end of the distribution.

In my work, I will explore this pattern of the literature and use novel techniques that detect and correct for the selection bias. I will also explore how do the elasticity estimates vary with energy mix used to produce the electricity in the grid. In doing so, I am going to collect the time-of-use estimates besides the short-run and long-run elasticities and control for this dimension of elasticity. Finally, I plan to create a database of calibration studies that would show how large are the elasticities used for calibrations and compare the distribution of calibration parameters (there could be hundreds of calibration choices) to my dataset of the actual representation of the estimated elasticities collected from primary studies (there could be thousands of estimates). This last point is, nevertheless, a workload possibly well beyond what I can manage in this bachelor thesis.

Contribution

I want to address two important issues of the literature estimating the price elasticity of electricity demand: publication bias and calibration bias. I will take advantage of Dahl (2011b) dataset, I will recode, restructure, and complete it to fit the needs of bstandard meta-analysis and enlarge it including the most recent studies (the other available surveys did not publish their datasets). I will use the state-of-the-art methods for publication bias detection and correction (including Furukawa, 2019, an MIT dissertation, Andrews & Kasy, 2019, published in American Economic Review, and Elliot et al. 2022 published in Econometrica). Secondly, I will analyze the heterogeneous study design including correction for endogeneity and aggregation bias. To do so I will use model averaging techniques that deal with the model uncertainty. I will also estimate the best-practice derived from the literature based on what is considered to be the best practice in estimation. Last, I will show how the empirical literature differs from the calibrations used for climate models.

Methodology

Researchers estimate the demand equation with watts demanded on the left hand-side and the price of electricity on the right hand-side. The price is usually accompanied by other covariates that could matter for demand, such as income, price of other substitutes for electricity, some representation of temperature, socio-economic variables, or even the stock of appliances. Most researchers use the log-log specification which has a convenient property of providing direct estimate of the elasticity (log Demand is a linear function of log Price and the regression coefficient beta is the elasticity, such as in log Demand = intercept + beta * log Price + whatever remains). To say something about the publication bias I will also collect the estimates of standard errors reported with each elasticity. The idea is that in the absence of publication bias there should be no systematic relation between estimates and their standard errors (Stanley, 2005).

Publication bias can be addressed well in the direct estimates of elasticity produced by the static models such as those that used the log-log specification. Once the original coefficient beta does not represent the elasticity---ie. the estimate is calculated indirectly from the inverse demand equation (which rarely happens; for example, when expressing price as a function of demand where the elasticity would equal 1/beta) or as a long-term estimate from the error correction model---the relationship between the elasticity and its standard error becomes mechanical and the search for the correlation between the estimate and its standard error could be skewed. Once the data is collected I will decide what treatment to use for elasticities that are recalculated from the reported coefficients.

The common visual method to identify the publication bias is a funnel plot of Egger et al. (1997). But the assessment of any visual test is in the eye of the beholder, thus I will apply more rigorous tests as well to address the issue. I will start with the simple linear test of funnel asymmetry (Stanley, 2005) which tests for the correlation between the estimate and its standard error. The linearity of the relationship between the estimate and its standard error is, nevertheless, hard to argue for: there could be, for example, jumps at conventional significance level suggesting p-hacking. I will use the weighted average of adequately powered by Ioannidis et al. (2017), the stem-based method by Furukawa (2019), the selection model by Andrews & Kasy (2019), and the endogenous kink by Bom & Rachinger (2019) that do drop the linearity assumption. The non-linear tests still incorporate one strong assumption: the assumption that the standard error is exogenous. In medicine, where meta-analysis was originally developed, this assumption is rarely questioned but in economics, it is not the case: for one, methodology that is used to estimate the effect can influence both the effect and its standard error. The answer comes from psychology: van Aert & van Assen (2020) provide p-uniform* estimation based on the p-values reported for the effects.

Besides publication bias, I will support my arguments with the analysis of heterogeneity behind the estimates that comes from the different study design. I will follow the preceding surveys but enlarge the list of coded variables representing the study design by factors such as country level variables, decomposition of energy sources that are used to produce the electricity, definition of demand (could be electricity consumption, load per capita, household expenditures normalized by demanded quantity, or distribution company electricity sales), measurement of prices (could be average price or marginal price or index, see Ito, 2014), whether the estimate is short-run, long-run, or time-of-day (reviewed in Cuddington & Dagher, 2015), whether the data is subject to aggregation that might suppress the micro-level variation (Acton et al., 1976), whether the elasticities are industry-, commercial-, or household-relevant, and so on. The one important part of the study design will be coding for treatment of potential endogeneity of the electricity price measure, inherent in any demand rule.

The idea behind the analysis of variation stemming from study design is to take the reported elasticities and regress them on the coded variables. This approach should show us if some systematic variation in elasticities comes from the study design. Given that I will code for tens of design aspects, I will have a large number of explanatory variables in the regression which introduces model uncertainty. I want to keep the important variables inside my model and keep the unimportant ones away but I do not know ex-ante which variables are important (there is no solid theory that would promote, for example, the number of citations as an important aspect of study design but one can argue that the number of citations can pick up on some intricate study quality that cannot be captured by any other aspect of method variation). Thus, I will use methods that do tackle the model uncertainty formally, such as model averaging techniques (Steel, 2020). For Bayesian application of model averaging, for example, I will use the dilution prior suggested by George (2010) which corrects for collinearity in the data.

The final part of my thesis will include the best-practice estimation conditional on two things: first, what the previous results from model averaging are and second, what the best practice is of how the estimation should be conducted (I can synthetically estimate an elasticity using the design of the best studies in my sample). I want to show that once I get rid of publication bias which I hypothesize is present in this literature (which sets the impact of standard error to zero), taking care of the measurement error and endogeneity bias (for example by using instrumental variable estimation), using as disaggregated data as possible (so that I keep the micro variation that is lost in aggregation), and so on, the best-practice estimate will differ from the simple average reported by previous surveys. I also hypothesize that what is used in the calibration exercises does not necessarily represent what the literature has to say about the elasticity.

Outline

1. Introduction
2. Price elasticity of electricity demand
• significance of the topic (punchy and brief, citing the most prominent studies)
• how do researchers estimate the effect
• existing surveys of the effect and my contribution
3. Collecting the dataset for meta-analysis
• selection criteria, summary statistics with estimates distribution and what can we learn from the birds-eye-view of the literature
• prima facie patterns in data if any, putting emphasis on the simple average from the literature
4. Is publication bias present in the literature?
• reasons why any meta-analyst should care about publication selection in this literature: law of demand and statistical significance
• what does the funnel plot suggest, what about linear and non-linear tests, what about the tests that do not need the exogeneity assumption of the standard error, are the tests consistent in any way, is there a difference in methods that treat and do not treat for endogeneity of the price inside the demand equation
• thus: is there a publication bias, how large it is and how much it skews the simple average from the literature
5. What else could drive the estimated effects?
• this will be my literature review: coding the variables that capture various aspects of study design – if the discussions and descriptions of why I chose different variables became overwhelming, I will transfer some parts of this into the appendix and keep just the discussion of what is important or interesting in the main text of the thesis
• what do the results of model averaging imply and are these implications robust across different models (say simple frequentist econometrics of OLS estimation, lasso, possibly different subsamples of the dataset.. )
6. Do the calibrations in climate models represent numbers consistent with the empirical research?
• estimating the best-practice effect either by choosing a subjective study design or following a design of the best studies in my sample, how does the synthetic effect differ from the simple average of the literature
• what does the distribution of calibration parameters imply when I compare it to what we see in the empirical literature
7. Conclusion