1      Context

The course is taught in the ENGAGE consortium and is therefore designed for a mixed cohort with heterogeneous backgrounds in macroeconomics, public finance, and climate economics. Target participants are PhD candidates and Research Master students from participating universities, e.g. Universität Mannheim, WU Wien, Tilburg University, Toulouse University.

The course will be taught online. The course is first taught from 19 October 2026 to 7 December 2026. It covers 3 ECTS, or 75 hours for students, including 22.5 pure contact hours (a time slot 10:30-12:30 counts for 1.5 hours as we start at 45 minutes after full hour and we have a 15 min break. That is there are 15 lecture slots of 2 academic hours.

At the TiU RM, it is labelled “Topics in Macro-Environment”. 

2      Lecture hours

In the table below, we use colors to identify the lecturers Armon Rezai and Reyer Gerlagh. Students are expected to have prepared by reading the lecture slides, reading the lecture notes, and reading and running the python code (if applicable).

3      Prerequisites

Before the course starts,

• students need to be able to optimize dynamic models, using Lagrangian and Knowledge of dynamic programming is of advantage. They also need to understand the interpretation of dual variables; students are expected to complete basic problem sets and follow derivations of assigned readings.
• students must be able to run codes in python; students are expected to run, modify, and extend these notebooks in certain week.

4      Reading materials

Course material will be made available via Canvas. For various lectures, there will be lecture notes with required readings and optional background readings; students should prioritise the required readings. Readings will be listed with DOI/CEPR/working-paper links to facilitate access through each student’s home-institution library. TiU is adamant that we cannot distribute copyrighted material.

5      Course learning goals

After completing the course, students should be able to:

1. Understand core concepts and theoretical foundations of climate change as a macroeconomic
   • Explain why climate change is an intertemporal macroeconomic
   • Understand the main contributions in the macro-climate literature and recognize the conceptual limitations of models.
   • Identify the diferences between uncertainty and disagreement in research and policy communities and how these afect the validity of model interpretations.
   • Derive and interpret simple analytical rules for the social cost of
   • Understand the structure of analytical Integrated Assessment Models (IAMs) and DICE-style numerical IAMs.
   • Apply standard methods of dynamic macro models to climate
   • Distinguish between first-best carbon pricing and second-best climate policy under constrained
   • Build tractable models by making deliberate choices about model elements like constraints, choice margins, and state variables.
2. Develop technical and computational methods for modeling and
   • Program, implement, calibrate, test and simulate simple climate-macro models in
   • Critically assess the strengths and limitations of quantitative macro-climate
3. Analyze policy questions and their macroeconomic
   • Translate policy questions—such as emission caps, instrument choice, cross-industry dynamics, revenue recycling, carbon budgets, and temperature caps—into model objects like constraints, wedges, state variables, and equilibrium conditions.
   • Derive and explain the equilibrium efects of policy
   • Understand the role of Hotelling-style scarcity pricing in climate
   • Assess how public finance, distortionary taxation, revenue recycling, and the marginal cost of public funds influence climate-policy design.
   • Evaluate the distributional and political-economy implications of carbon pricing, including efects on households, workers, asset owners, public debt, compensation, and policy
   • Design and evaluate climate policies by connecting theoretical models to practical issues like instrument choice, revenue recycling, and cross-industry dynamics.

6      Course structure

The lectures combine structured exposition with discussion of student questions. They are also sometimes structured as tutorials and provide computational practice and help students connect analytical model objects to numerical implementation.

For each lecture, we provide a lecture note that describes

• what students need to read beforehand (typically 2 hours)
• exercises they need to make and to hand in (typically 2 hours)

The exercises are not assessed, but need to be handed in, and become public information. The lectures begin with a discussion with the lecturer of the exercises from the previous lecture by a student randomly selected.

7      Exam structure and grading

Students will be graded on two components:

• Their submitted course exercises throughout the Students will be asked to discuss their submission at the beginning of the next class.
• An oral exam, with material discussed at the exam to be prepared by the student. The exam may include real-time coding. The lecturers jointly determine the grade. 

8      Detailed class content

8.1      BM72 in python

This session briefly introduces the Brock–Mirman 1972 model with a constant savings rate. The focus is on coding the BM72 model in Python, and on calibrating, simulating, testing predictions, and running sensitivity analyses.

We first present the basic model structural assumptions and analytics. We then generalize the model to shorter period lengths, derive the welfare function for finite-horizon simulations, and translate macroeconomic targets — output, savings rate, and interest rate — into calibration targets for preferences, the capital elasticity, and TFP. These steps are implemented in Python, with charts used to present the results.

We run tests such as:

• Does optimization reproduce the analytically predicted savings rate?
• Are results independent of the truncation period?
• Are results independent of the period length?
• How do transitions depend on the period length?

We provide a base model calibrated to logistic population and output growth, with period lengths of 1, 5, and 10 years.

For the next lecture, students download historical data and future projections, recalibrate the model with 1-year or 5-year periods, and compare the data and projections with the analytical solution and optimization outcome. Students submit their Python code and charts as a PDF, preferably through Canvas.

After the session, students are able to:

• understand normalizations useful for optimization in Python;
• identify model variables that can serve as calibration targets;
• construct tests for checking the consistency of numerical outcomes;
• construct charts that provide basic insight into the

8.2      GHKT14 in python.

We start with brief feedback on the Python codes and graphs submitted for the previous lecture.

We  then  present  a  simple  version  of  the  Golosov–Hassler–Krusell–Tsyvinski 2014 Econometrica model. Building on BM72, we add CO¿ emissions, abatement, climate damages, and past emissions, and show how these determine the Social Cost of Carbon. We derive the analytical rule for optimal emissions from baseline emissions and a simple abatement cost function.

The model is calibrated with baseline emissions proportional to population. We define the marginal productivity of emissions, compare it with the SCC, and compare BAU, the Python-calculated optimum, and the analytical solution. We also run a sensitivity analysis for discounting.

For the next lecture, students complete two exercises: a sensitivity analysis for damages, and a scenario in which the planner has a low discount rate while consumers have a higher discount rate.

After the session, students are able to:

• build a simple climate-economy model in Python;
• identify and test analytical predictions in a quantitative model;
• use scenarios for economic analysis and code testing;
• run sensitivity analyses and construct flexible

Connection to Week 2. After the first week, students should be able to translate theory into applied models and assess its quantitative implications. The focus is on verifying that analytical predictions are reproduced by numerical calculations.

8.3      Climate change as an intertemporal macroeconomic externality

This session introduces climate change as a dynamic macroeconomic externality. Emissions accumulate in the climate system, afect temperature, and reduce output and welfare over time.

The lecture introduces the social cost of carbon as the shadow value of an additional unit of emissions and explains why optimal carbon pricing is an intertemporal Pigouvian policy.

After the session, students understand:

• how emissions, carbon stocks, temperature, damages, output, and welfare are connected in a macro-climate model;
• why climate change is an intertemporal externality rather than a static pollution problem;
• why the optimal carbon tax is linked to the present value of future marginal damages;
• how to interpret the social cost of carbon as a shadow

8.4      Simple SCC rules and analytical IAMs

This session studies analytical integrated assessment models, with emphasis on GHKT-style tractability and simple rules for the social cost of carbon. The lecture explains when the capital accumulation problem and the climate externality can be separated, why the SCC may be proportional to output, and how discounting, growth, carbon persistence, and damages enter the SCC.

After the session, students understand:

• the basic structure of analytical IAMs;
• the logic of the GHKT model and related simple SCC rules;
• why the SCC is often approximately proportional to GDP;
• how the SCC responds to damage parameters, discounting, growth, and carbon persistence;
• what is gained and what is lost by using simple analytical

8.5      Temperature caps, carbon budgets, and DICE-style IAMs

This session moves from SCC rules to temperature targets and carbon budgets. It explains how cumulative-emissions constraints can be represented as shadow prices, why the scarcity component of the carbon price follows a Hotelling logic, and how this relates to DICE-style numerical IAMs. The lecture also discusses uncertainty, disagreement, and the criticism that IAMs may create a false sense of precision.

After the session, students understand:

• the relationship between temperature caps, cumulative emissions, and carbon budgets;
• why a binding carbon budget introduces a scarcity rent into the carbon price;
• how DICE-style models extend analytical IAMs;
• how parameter choices on damages, discounting, abatement costs, and climate dynamics afect optimal policy;
• the main conceptual criticisms of IAM-based climate policy

8.6      Second-best climate policy: missing instruments and public finance

This session introduces second-best climate policy. The first-best carbon-tax rule is an implementation result that relies on a suficiently rich set of instruments. When some instruments are missing, climate policy must address several wedges at once. The session introduces learning-

by-doing, the social benefit of learning, renewable subsidies, and the interaction between climate policy and fiscal constraints.

After the session, students understand:

• the diference between first-best and second-best climate policy;
• why the carbon tax is not always the only relevant policy instrument;
• how learning-by-doing creates a separate deployment externality;
• why renewable subsidies and carbon taxes address diferent wedges;
• how missing instruments change the interpretation of optimal climate

8.6     Overlapping generations, incidence, and the political economy of carbon pricing

This session studies climate policy in overlapping-generations economies. Representative-agent models are useful for deriving aggregate optimal policy, but they hide conflicts between currently alive generations, future generations, workers, asset owners, debtors, and Carbon pricing afects wages, asset values, transfers, public debt, and future climate damages, so aggregate welfare gains need not imply majority support.

After the session, students understand:

• why representative-agent models hide intergenerational and intragenerational conflicts;
• how carbon pricing afects diferent cohorts through income, assets, and climate damages;
• why aggregate welfare gains need not imply Pareto improvements or majority support;
• how fiscal instruments can redistribute the burden of climate policy;
• why incidence and political feasibility may difer between creditor and debtor

8.8      Ramsey climate policy, MCPF, and fiscal climate damages

This session studies climate policy in a Ramsey public-finance setting. The lecture explains how climate policy interacts with distortionary taxation, labour supply, public spending, and the marginal cost of public funds. It clarifies when the standard SCC rule survives in a second-best fiscal environment and when fiscal climate damages or public-expenditure channels modify the optimal carbon price.

After the session, students understand:

• how implementability constraints enter climate-policy problems;
• the meaning and role of the marginal cost of public funds;
• why distortionary taxation alone does not automatically invalidate the SCC rule;
• how climate damages to public finances can afect optimal policy;
• how revenue recycling, labour taxation, and fiscal constraints shape policy

8.9      Distribution, compensation, and political feasibility

This session studies selected distributional and political-economy implications of climate policy. Carbon pricing afects wages, asset values, sectoral rents, consumption prices, and government revenues. These efects shape the incidence of policy across households, workers, firms, asset owners, and generations. The session discusses carbon dividends, labour-tax recycling, compensation, public debt, and political feasibility.

After the session, students understand:

• why the incidence of carbon pricing depends on factor prices, asset ownership, and fiscal recycling;
• how compensation and revenue recycling afect political feasibility;
• why public debt can shift the intergenerational burden of climate policy;
• how distributional conflict can arise between workers, asset owners, young households, old households, debtors, and creditors;
• why distribution is not an add-on to climate policy but part of

8.10   Policy instruments and synthesis

This session synthesises the theoretical part of the course. It compares carbon taxes, emission trading, renewable subsidies, clean R&D subsidies, standards, mandates, and fiscal instruments. The session asks how diferent policy instruments map into model objects: prices, constraints, wedges, shadow values, and state variables. It also briefly revisits technology policy as a bridge, while keeping the main emphasis on climate-policy design under realistic constraints.

After the session, students understand:

• how carbon taxes, permits, subsidies, standards, and mandates difer as implementation devices;
• why instrument choice depends on market failures, fiscal constraints, missing instruments, and political feasibility;
• how the SCC benchmark is modified by second-best considerations;
• how the course’s main themes fit together: analytical IAMs, SCC rules, carbon budgets, public finance, distribution, and policy instruments;
• which results are robust and which depend on modelling

8.11   Welfare and Sustainability

This session discusses welfare analysis and sustainability from the perspective of a social planner. Are optimal climate policies sustainable? The answer depends on the welfare function, the definition of agents, and the reference scenario against which sustainability is evaluated.

Climate policy can improve aggregate welfare while redistributing consumption from present generations, who pay abatement costs, to future generations, who benefit from lower climate damages. This raises the question whether the future can compensate the present, and whether such compensation is meaningful when generations are separated in time.

We compare diferent sustainability concepts. A standard BAU reference protects current generations against policy costs. A sustainability reference protects future generations’ rights to inherit a high-quality environment. We compare both approaches in our numerical model.

We then discuss the welfare function. What changes if preferences are time-inconsistent, if discount rates difer between planner and agents, or if social preferences are not constant over time?

After the session, students are able to:

• explain optimality and sustainability in climate economics;
• explain why the choice of reference path afects optimal climate policy;
• distinguish policies that protect present generations from policies that protect future generations;
• understand climate policies for time-inconsistent or non-constant preferences;
• use numerical scenarios to guide intuition for all above questions

8.12   Planner versus decentralized

This session studies the relation between the planner’s solution and a decentralized economy. A social planner chooses savings, emissions, abatement, and transfers to maximize welfare. In a decentralized economy, these choices are made by households and firms, and eficiency is constructed through the Pareto criterion.

For Pareto eficiency, a key question is who counts as an agent: individuals, generations, or groups within generations. This matters because climate policy afects both intergenerational and intragenerational distribution. A decentralized allocation may be eficient relative to one definition of agents, but not relative to another.

We also discuss whether the representative infinitely lived agent of the Ramsey–Cass–Koopmans model is realistic for a decentralized economy. OLG models with changing demography suggest a diferent BAU scenario, because households difer by age, assets, income, horizon, and exposure to future climate damages.

The session also studies implementation. We ask which carbon taxes, transfers, asset markets, or property rights are needed to decentralize the planner’s solution. We discuss when compensation across generations is possible, when it is only hypothetical, and how missing markets or missing instruments prevent the decentralized economy from reaching the planner’s allocation.

After the session, students are able to:

• understand Pareto eficiency in a climate-economy model;
• explain why the definition of agents matters for eficiency and compensation;
• distinguish intergenerational from intragenerational distribution in decentralized economies;
• understand how OLG models with changing demography can change the view on reference scenarios;
• explain that an eficient climate policy in a decentralized economy need not be a Pareto

8.13   Endogenous population

This session studies endogenous fertility in climate-economy models. We ask how climate policy changes when households choose fertility and when population becomes part of the economic response to climate change.

We introduce a climate-economy model with endogenous fertility through a quality–quantity trade-of.  Fertility  decisions  afect future  population,  aggregate  output,  and  future  emissions.  This creates an additional externality: individual households do not fully internalize the climate-related costs of having more children.

Decentralizing the social optimum requires two complementary instruments. Carbon pricing internalizes the emissions externality, while family-planning interventions address the fertility externality.

We discuss the quantitative implications of the model. Population peaks difer substantially across policy regimes: lower in the social optimum and higher when only carbon prices are implemented.

After the session, students are able to:

• understand the quality–quantity trade-of and endogenous fertility;
• explain in what sense family planning could be part of climate policies;
• explain how fertility choices afect future emissions, output, and climate damages;
• distinguish the emissions externality from the fertility externality;
• interpret fertility costs as the climate-related social costs of an additional child;
• understand how endogenous population changes BAU scenarios and optimal climate

8.14   Endogenous Innovation

This session studies endogenous innovation in climate-economy models. What if climate change afects not only the level of output, but also the growth of productivity.

We extend the Brock–Mirman framework with endogenous growth through variety expansion. Research investments increase the number of varieties and thereby raise productivity. Climate change afects both the level of total factor productivity and the build-up of future TFP. This introduces an additional channel through which emissions reduce welfare: current climate damages may slow down future knowledge accumulation and long-run growth.

The model also includes human capital and endogenous fertility. This makes it possible to study the interaction between two large externalities: climate change and knowledge creation. Additional children increase future population and emissions, but they may also contribute to future innovation and knowledge production. The welfare efect of population growth therefore depends on the balance between accelerated climate change and additional knowledge creation.

We discuss the analytical results for capital investment, research, and the Social Cost of Carbon. A key implication is that SCC estimates become substantially larger when climate change reduces TFP growth, not only the level of TFP. The session compares this growth-damage channel with standard climate-economy models in which damages mainly reduce contemporaneous output.

After the session, students are able to:

• explain how endogenous innovation can be added to a climate-economy model;
• distinguish climate damages to the level of TFP from damages to TFP growth;
• explain why growth damages can strongly increase the Social Cost of Carbon;
• understand how fertility, human capital, and innovation interact in long-run climate policy;
• compare the climate externality with the knowledge-creation externality;

8.15   Recap

We discuss all learning goals and how we achieved these.