Karsten Neuhoff

German Institute for Economic Research (DIW Berlin)

Mohrenstraße 58

Berlin, 10117

Germany

  • German Institute for Economic Research (DIW Berlin)

SCHOLARLY PAPERS

44

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Scholarly Papers (44)

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1.

Balancing and Intraday Market Design: Options for Wind Integration

DIW Berlin Discussion Paper No. 1162
Number of pages: 38 Posted: 18 Oct 2011
Frieder Borggrefe and Karsten Neuhoff
Independent and German Institute for Economic Research (DIW Berlin)
Downloads 473 (76,625)
Citation 36

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Power market design, integrating renewables, wind energy, balancing, intraday

2.

Carbon Markets and Technological Innovation

Number of pages: 25 Posted: 26 Jan 2009 Last Revised: 24 May 2014
Thomas A. Weber and Karsten Neuhoff
Ecole Polytechnique Federale de Lausanne - MTEI and German Institute for Economic Research (DIW Berlin)
Downloads 398 (93,812)
Citation 8

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Carbon Emissions, Carbon Taxes, Cap-and-Trade, Environmental Regulation, Induced Technological Innovation, Price Caps, Price Floors, Prices vs. Quantities

3.

Border Carbon Adjustments and Alternative Measures for the EU ETS: An Evaluation

DIW Berlin Discussion Paper No. 1855
Number of pages: 23 Posted: 30 Mar 2020
Roland Ismer, Karsten Neuhoff and Alice Pirlot
German Institute for Economic Research (DIW Berlin), German Institute for Economic Research (DIW Berlin) and University of Oxford - Said Business School
Downloads 334 (115,128)
Citation 2

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Carbon pricing, Climate policy, International trade, WTO

4.

Rural Electrification in India: Economic and Institutional Aspects of Renewables

Number of pages: 37 Posted: 10 Apr 2016
James Cust, Anoop Singh and Karsten Neuhoff
University of Oxford - Oxford Centre for the Analysis of Resource Rich Economies (OXCarre), Department of Industrial & Management Engineering and German Institute for Economic Research (DIW Berlin)
Downloads 290 (133,072)
Citation 14

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Rural Electrification, Distributed Generation, Renewable Energy, India

5.

Intraday Markets for Power: Discretizing the Continuous Trading?

DIW Berlin Discussion Paper No. 1544
Number of pages: 22 Posted: 28 Jan 2016
Karsten Neuhoff, Nolan Ritter, Aymen Salah-Abou-El-Enien and Philippe Vassilopoulos
German Institute for Economic Research (DIW Berlin), Rhine-Westphalia Institute for Economic Research (RWI-Essen), EPEX Spot SE - Product Design and EPEX Spot SE - Product Design
Downloads 274 (141,068)
Citation 17

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Auctions, electricity, empirical analysis, market design

6.

Mediating Market Power in Electricity Networks

UC Berkeley, Center for Competition Policy Working Paper No. CPC02-32
Number of pages: 37 Posted: 17 Feb 2004
Richard Gilbert, Karsten Neuhoff and David M. G. Newbery
University of California, Berkeley - Department of Economics, German Institute for Economic Research (DIW Berlin) and University of Cambridge - Department of Applied Economics
Downloads 220 (174,980)
Citation 7

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Electricity, market power, transmission rights, nodal pricing

7.

Banking of Surplus Emissions Allowances: Does the Volume Matter?

DIW Berlin Discussion Paper No. 1196
Number of pages: 23 Posted: 15 Mar 2012
Karsten Neuhoff, Anne Schopp, Rodney Boyd, Kateryna Stelmakh and Alexander Vasa
German Institute for Economic Research (DIW Berlin), German Institute for Economic Research (DIW Berlin), affiliation not provided to SSRN, affiliation not provided to SSRN and German Institute for Economic Research (DIW Berlin)
Downloads 216 (178,047)
Citation 14

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European emission trading scheme, banking, discount rates

8.

Congestion Management in European Power Networks: Criteria to Assess the Available Options

DIW Berlin Discussion Paper No. 1161
Number of pages: 25 Posted: 18 Oct 2011
Karsten Neuhoff, Benjamin F. Hobbs and David M. G. Newbery
German Institute for Economic Research (DIW Berlin), Johns Hopkins University and University of Cambridge - Department of Applied Economics
Downloads 188 (202,161)
Citation 18

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Power market design, integrating renewables, congestion management

9.

Modelling a Market Stability Reserve in Carbon Markets

DIW Berlin Discussion Paper No. 1483
Number of pages: 23 Posted: 10 Jun 2015
Anne Schopp, William W. Acworth, Daniel Huppmann and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin), Independent, International Institute for Applied Systems Analysis (IIASA) and German Institute for Economic Research (DIW Berlin)
Downloads 166 (225,048)
Citation 11

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Computational Model, Emissions trading, Environmental Regulation, Market stability reserve

10.

The Role of Hedging in Carbon Markets

DIW Berlin Discussion Paper No. 1271
Number of pages: 26 Posted: 27 Mar 2013
Anne Schopp and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 160 (232,179)
Citation 5

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Emissions trading schemes, banking, power hedging, discount rates

11.

Renewable Electric Energy Integration: Quantifying the Value of Design of Markets for International Transmission Capacity

DIW Berlin Discussion Paper No. 1166
Number of pages: 49 Posted: 29 Oct 2011
Karsten Neuhoff, Rodney Boyd, Thilo Grau, Julian Barquin, Francisco Echavarren, Janusz Bialek, Chris Dent, Christian von Hirschhausen, Benjamin F. Hobbs, Friedrich Kunz, Hannes Weigt, Christian Nabe, Georgios Papaefthymiou and Christoph Weber
German Institute for Economic Research (DIW Berlin), affiliation not provided to SSRN, German Institute for Economic Research (DIW Berlin), Comillas Pontifical University, affiliation not provided to SSRN, affiliation not provided to SSRN, affiliation not provided to SSRN, German Institute for Economic Research (DIW Berlin) - Department of International Economics, Johns Hopkins University, German Institute for Economic Research (DIW Berlin), WWZ, Wirtschaftswissenschaftliche Fakultät der Universität Basel, Ecofys, affiliation not provided to SSRN and University of Duisburg-Essen
Downloads 141 (257,429)
Citation 22

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Power market design, renewable power integration, congestion management, transmission economics

12.

Survey of Photovoltaic Industry and Policy in Germany and China

DIW Berlin Discussion Paper No. 1132
Number of pages: 47 Posted: 24 Jun 2011 Last Revised: 04 Nov 2011
Thilo Grau, Molin Huo and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin), affiliation not provided to SSRN and German Institute for Economic Research (DIW Berlin)
Downloads 130 (274,024)
Citation 4

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Photovoltaics, Technology Policy, Innovation, Investment Support

13.

Use of Long-Term Auctions for Network Investment

Number of pages: 34 Posted: 22 Apr 2003
Tanga McDaniel and Karsten Neuhoff
Appalachian State University - Department of Economics and German Institute for Economic Research (DIW Berlin)
Downloads 122 (287,416)

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Auctions, Gas, Investment, Networks, Regulation

14.

Structuring International Financial Support for Climate Change Mitigation in Developing Countries

DIW Berlin Discussion Paper No. 976
Number of pages: 41 Posted: 03 May 2010
Karsten Neuhoff, Sam Fankhauser, Emmanuel Guerin, Jean-Charles Hourcade, Helen Jackson, Ranjita Rajan and John Ward
German Institute for Economic Research (DIW Berlin), London School of Economics & Political Science (LSE) - Grantham Research Institute on Climate Change and the Environment, affiliation not provided to SSRN, CIRED, International Research Center on Environment & Development, France, affiliation not provided to SSRN, affiliation not provided to SSRN and Northwestern University
Downloads 121 (290,857)
Citation 3

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Financial mechanism, risk guarantee, development, climate policy

15.

Power Market Design Beyond 2020: Time to Revisit Key Elements?

DIW Berlin Discussion Paper No. 1456
Number of pages: 34 Posted: 12 Mar 2015
Karsten Neuhoff, Sophia Ruester and Sebastian Schwenen
German Institute for Economic Research (DIW Berlin), European University Institute - Florence School of Regulation and Technische Universität München (TUM)
Downloads 96 (338,481)
Citation 6

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Power market design, regulation, investment framework

16.

Impact of Renewable Energy Act Reform on Wind Project Finance

DIW Berlin Discussion Paper No. 1387
Number of pages: 36 Posted: 19 Jun 2014
Matthew Tisdale, Thilo Grau and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin), German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 96 (338,481)
Citation 3

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Feed in tariff, financing renewables, project finance

17.

Quantifying Impacts of Consumption Based Charge for Carbon Intensive Materials on Products

DIW Berlin Discussion Paper No. 1570
Number of pages: 32 Posted: 15 May 2016
Stefan Pauliuk, Karsten Neuhoff, Anne Owen and Richard Wood
University of Freiburg, German Institute for Economic Research (DIW Berlin), University of Leeds and Norwegian University of Science and Technology (NTNU)
Downloads 95 (340,694)
Citation 4

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Material flow analysis, material flow cost accounting, carbon pricing, inclusion of consumption

18.

Climate Neutral Production, Free Allocation of Allowances under Emissions Trading Systems, and the WTO: How to Secure Compatibility with the ASCM

DIW Berlin Discussion Paper No. 1948
Number of pages: 20 Posted: 03 Jun 2021
Roland Ismer, Harro van Asselt, Jennifer Haverkamp, Michael Mehling, Karsten Neuhoff and Alice Pirlot
German Institute for Economic Research (DIW Berlin), affiliation not provided to SSRN, affiliation not provided to SSRN, Massachusetts Institute of Technology (MIT), German Institute for Economic Research (DIW Berlin) and University of Oxford - Said Business School
Downloads 89 (354,957)

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WTO, ASCM, Carbon Pricing, Free allowance allocation, Climate Contribution, Carbon Contracts for Difference

19.

Flexible Short-Term Power Trading: Gathering Experience in EU Countries

DIW Berlin Discussion Paper No. 1494
Number of pages: 25 Posted: 04 Aug 2015
Karsten Neuhoff, Carlos Batlle, Gert Brunekreeft, Christos Konstantinidis, Christian Nabe, Giorgia Oggioni, Pablo Rodilla, Sebastian Schwenen, Tomasz Siewierski and Goran Strbac
German Institute for Economic Research (DIW Berlin), Comillas Pontifical University - Institute for Research in Technology (IIT), Tilburg Law and Economics Center (TILEC), Imperial College London, Ecofys, University of Brescia, Comillas Pontifical University - Institute for Research in Technology (IIT), Technische Universität München (TUM), Technical University of Lodz and Imperial College London
Downloads 86 (362,525)
Citation 9

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Electricity trading, Power system operation, Institutional analysis

20.

Carbon Pricing of Basic Materials: Incentives and Risks for the Value Chain and Consumers

DIW Berlin Discussion Paper No. 1935
Number of pages: 30 Posted: 18 Mar 2021
Jan Stede, Stefan Pauliuk, Gilang Hardadi and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin), University of Freiburg, Aalborg University and German Institute for Economic Research (DIW Berlin)
Downloads 70 (411,214)

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Emissions trading, border carbon adjustment (BCA), excise duty, carbon intensity, carbon leakage, distributional effects, fiscal revenues

21.

Time-Consistent Carbon Pricing: The Role of Carbon Contracts for Differences

DIW Berlin Discussion Paper No. 1859
Number of pages: 37 Posted: 15 Apr 2020
Olga Chiappinelli and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 69 (411,214)
Citation 1

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Carbon pricing, time-inconsistency, green technology, climate policy, carbon contracts

22.

How EU Trade Policy Can Enhance Climate Action: Options to Boost Low-Carbon Investment and Address Carbon Leakage

CEPS Policy Priorities for 2019-2024, 2019
Number of pages: 12 Posted: 10 Nov 2019
Susanne Dröge, Karsten Neuhoff, Christian Egenhofer and Milan Elkerbout
affiliation not provided to SSRN, German Institute for Economic Research (DIW Berlin), Centre for European Policy Studies (CEPS) and Centre for European Policy Studies (CEPS)
Downloads 69 (411,214)
Citation 1

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climate neutrality, EU ETS, EU framework for low-carbon investment, European Green Deal, carbon border tax

23.

Renewable Energy Policy in the Age of Falling Technology Costs

DIW Berlin Discussion Paper No. 1746
Number of pages: 24 Posted: 08 Aug 2018
Karsten Neuhoff, Nils May and Joern Constantin Richstein
German Institute for Economic Research (DIW Berlin), German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 65 (424,352)

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Investments under uncertainty, financing costs, renewable energy policy, contracts for difference

24.

Financing Power: Impacts of Energy Policies in Changing Regulatory Environments

DIW Berlin Discussion Paper No. 1684
Number of pages: 29 Posted: 03 Oct 2017
Nils May and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 56 (456,402)
Citation 6

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Investments, long-term contracts, financing costs, liberalization of power markets, renewable energy policies

25.

Facilitating Low-Carbon Investments: Lessons from Natural Gas

DIW Berlin Discussion Paper No. 1154
Number of pages: 15 Posted: 07 Oct 2011
Anne Neumann and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 52 (471,738)
Citation 1

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investment, low-carbon economy, natural gas

26.

Lessons from Conditionality Provisions for South-North Cooperation on Climate Change

EPRG (Electricity Policy Research Group) Working Paper No. 0825, Cambridge Working Paper in Economics No. 0849
Number of pages: 26 Posted: 28 Feb 2010
Maike Sippel and Karsten Neuhoff
University of Stuttgart - Institute of Energy Economics and the Rational Use of Energy (IER) and German Institute for Economic Research (DIW Berlin)
Downloads 48 (488,054)

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International cooperation, incentive schemes, mechanism design

27.

Can Governments Ban Materials with Large Carbon Footprint? Legal and Administrative Assessment of Product Carbon Requirements

DIW Berlin Discussion Paper No. 1834 (2019)
Number of pages: 30 Posted: 12 Dec 2019
Timo Gerres, Manuel Haussner, Karsten Neuhoff and Alice Pirlot
Comillas Pontifical University, University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg, Law School, Students, German Institute for Economic Research (DIW Berlin) and University of Oxford - Said Business School
Downloads 45 (501,266)
Citation 1

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Embodied Carbon, Climate Policy, Standards, Technical Regulations, WTO

28.

Sozialverträglicher CO2-Preis: Vorschlag für einen Pro-Kopf-Bonus durch Krankenversicherungen (Creating Social Acceptance for a CO2 Price: How to Implement a Per Capita Health Insurance Bonus)

DIW Berlin Discussion Paper No. 1819
Number of pages: 22 Posted: 06 Nov 2019
Roland Ismer, Manuel Haussner, Klaus Messerschmidt and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin), University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg, Law School, Students, Friedrich-Alexander-Universität Erlangen-Nürnberg and German Institute for Economic Research (DIW Berlin)
Downloads 42 (514,822)

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CO2-Steuer, Verteilungswirkung, Rückerstattung, Krankenkasse CO2-Price, distributional effect, reimbursement, health insurance

29.

Inclusion of Consumption into Emissions Trading Systems: Legal Design and Practical Administration

DIW Berlin Discussion Paper No. 1579
Number of pages: 25 Posted: 25 May 2016
Roland Ismer, Manuel Haussner, Karsten Neuhoff and William W. Acworth
German Institute for Economic Research (DIW Berlin), University of Erlangen-Nuremberg-Friedrich Alexander Universität Erlangen Nürnberg, Law School, Students, German Institute for Economic Research (DIW Berlin) and Independent
Downloads 37 (538,972)
Citation 5

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Carbon pricing, value chain, consumption charge

30.

A Coordinated Strategic Reserve to Safeguard the European Energy Transition

DIW Berlin Discussion Paper No. 1495
Number of pages: 29 Posted: 04 Aug 2015
Karsten Neuhoff, Jochen Diekmann, Friedrich Kunz, Sophia Ruester, Wolf-Peter Schill and Sebastian Schwenen
German Institute for Economic Research (DIW Berlin), German Institute for Economic Research (DIW Berlin) - Energy, Transportation, Environment, German Institute for Economic Research (DIW Berlin), European University Institute - Florence School of Regulation, DIW Berlin - Department of Energy, Transportation, Environment and Technische Universität München (TUM)
Downloads 35 (549,408)
Citation 3

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Capacity mechanisms, strategic reserve, market design, energy policy, energy transition

31.

FTR Allocations to Ease Transition to Nodal Pricing: An Application to the German Power System

DIW Berlin Discussion Paper No. 1418
Number of pages: 28 Posted: 21 Oct 2014 Last Revised: 22 Oct 2014
Friedrich Kunz, Karsten Neuhoff and Juan Rosellon
German Institute for Economic Research (DIW Berlin), German Institute for Economic Research (DIW Berlin) and Centro de Investigacion y Docencia Economicas
Downloads 34 (554,784)
Citation 2

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Electricity market, financial transmission right, congestion management, market design, Germany

32.

Pricing Carbon Consumption: A Review of an Emerging Trend

DIW Berlin Discussion Paper No. 1620
Number of pages: 36 Posted: 30 Nov 2016
Clayton Munnings, William Acworth, Oliver Sartor, Yong-Gun Kim and Karsten Neuhoff
Resources for the Future, Adelphi, CDC Climat Research, Korea Environment Institute and German Institute for Economic Research (DIW Berlin)
Downloads 32 (565,581)

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Carbon pricing, consumption based policy, review

33.

A Green COVID-19 Recovery of the EU Basic Materials Sector: Identifying Potentials, Barriers and Policy Solutions

DIW Berlin Discussion Paper No. 1921
Number of pages: 38 Posted: 16 Dec 2020
Olga Chiappinelli, Timo Gerres, Karsten Neuhoff, Frederik Lettow, Heleen de Coninck, Balázs Felsmann, Eugénie Joltreau, Gauri Khandekar, Pedro Linares, Joern Constantin Richstein, Alexander Sniegocki, Jan Stede, Tomas Wyns, Cornelis Zandt and Lars Zetterberg
German Institute for Economic Research (DIW Berlin), Comillas Pontifical University, German Institute for Economic Research (DIW Berlin), affiliation not provided to SSRN, Radhoud University, affiliation not provided to SSRN, Université Paris Dauphine, affiliation not provided to SSRN, Universidad Pontificia Comillas, German Institute for Economic Research (DIW Berlin), Warszawski Instytut Studiów Ekonomicznych (WISE), German Institute for Economic Research (DIW Berlin), affiliation not provided to SSRN, affiliation not provided to SSRN and IVL Swedish Environmental Research Institute
Downloads 31 (571,183)

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Green COVID-19 recovery, industrial decarbonisation, policy package, EU green deal, technology readiness

34.

Trust and Virtual Districts: Evidence from the Milan Internet Exchange

Metroeconomica, Vol. 58, No. 3, pp. 436-456, July 2007
Number of pages: 21 Posted: 28 Jun 2007
Emanuele Giovannetti, Karsten Neuhoff and Giancarlo Spagnolo
Anglia Ruskin University, German Institute for Economic Research (DIW Berlin) and Stockholm School of Economics (SITE)
Downloads 31 (571,183)
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35.

Pricing Carbon Consumption

Resources for the Future Discussion Paper 16-49
Number of pages: 36 Posted: 30 Nov 2016
Clayton Munnings, William Acworth, Oliver Sartor, Yong-Gun Kim and Karsten Neuhoff
Resources for the Future, Adelphi, Institute for Sustainable Development and International Relations, Korea Environment Institute and German Institute for Economic Research (DIW Berlin)
Downloads 30 (576,884)

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Carbon Emissions, Carbon Pricing, Carbon Consumption, Carbon Production, Downstream Abatement, Emissions Leakage

36.

Assessing Energy Price Induced Improvements in Efficiency of Capital in OECD Manufacturing Industries

World Bank Policy Research Working Paper No. 6929
Number of pages: 57 Posted: 20 Apr 2016
Jevgenijs Steinbuks and Karsten Neuhoff
World Bank - Development Research Group (DECRG) and German Institute for Economic Research (DIW Berlin)
Downloads 26 (601,566)

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Energy Production and Transportation, Political Economy, Climate Change Economics, Economic Theory & Research, Markets and Market Access

37.

Benchmarks for Emissions Trading – General Principles for Emissions Scope

DIW Berlin Discussion Paper No. 1712
Number of pages: 25 Posted: 12 Jan 2018
Vera Zipperer, Misato Sato and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin), London School of Economics & Political Science (LSE) and German Institute for Economic Research (DIW Berlin)
Downloads 25 (608,160)
Citation 3

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Emissions Trading, Emission Benchmarking, Free allocation, Incentives, Low-Carbon Innovation

38.

Time-Consistent Carbon Pricing

DIW Berlin Discussion Paper No. 1710
Number of pages: 20 Posted: 12 Jan 2018
Olga Chiappinelli and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 16 (671,640)

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Carbon pricing, Time-inconsistency, Low-carbon innovation, Environmental regulation, Repeated games, Carbon contracts

39.

Coordination of Renewable Energy Remuneration Schemes Through Information Exchange

DIW Berlin Discussion Paper No. 1574
Number of pages: 26 Posted: 15 May 2016
Thilo Grau and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin) and German Institute for Economic Research (DIW Berlin)
Downloads 15 (679,078)

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Renewable energy, feed-in tariff, coordinated remuneration schemes

40.

An Auction Story: How Simple Bids Struggle with Uncertainty

DIW Berlin Discussion Paper No. 1765
Number of pages: 32 Posted: 06 Nov 2018
Joern Constantin Richstein, Casimir Lorenz and Karsten Neuhoff
German Institute for Economic Research (DIW Berlin), TU Berlin - Workgroup for Infrastructure Policy (WIP) and German Institute for Economic Research (DIW Berlin)
Downloads 13 (694,640)
Citation 2

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Market design, electricity markets, bidding formats, auctions

41.

International Support for Domestic Climate Policies: Policy Summary

IOP Conference Series: Earth and Environmental Science Volume 6, Session 58, 2009
Posted: 26 Aug 2019
Anoop Singh, Karsten Neuhoff and Grant M. Kopec
Department of Industrial & Management Engineering, German Institute for Economic Research (DIW Berlin) and University of Cambridge - Department of Engineering

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42.

Take-or-Pay Contracts for Renewables Deployment

Energy Policy, Vol. 36, p. 2481, 2008
Posted: 26 Jan 2010
Angus Johnston, Amalia Kavali and Karsten Neuhoff
University of Oxford - Faculty of Law, University of Cambridge and German Institute for Economic Research (DIW Berlin)

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Renewable Support Policy, Property rights, Transition, Regulatory Risk, Law

43.

The Proposed New EU Renewables Directive: Interpretation, Problems and Prospects

European Energy and Environmental Law Review, p. 126, 2008
Posted: 26 Jan 2010 Last Revised: 23 Nov 2010
Angus Johnston, Karsten Neuhoff, Doerte Fouquet, Mario Ragwitz and Gustav Resch
University of Oxford - Faculty of Law, German Institute for Economic Research (DIW Berlin), affiliation not provided to SSRN, Fraunhofer Institut für Systemtechnik und Innovationsforschung and Vienna University of Technology

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EU Law, Environmental Law, Renewables policy, Electricity generation

44.

Large-Scale Deployment of Renewables for Electricity Generation

Oxford Review of Economic Policy, Vol. 21, Issue 1, pp. 88-110, 2005
Posted: 29 Feb 2008
Karsten Neuhoff
German Institute for Economic Research (DIW Berlin)

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Griffith crack, rectangular layer, shear stress, stress intensity factors