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Climate Macro (DICE)

puremacro.climate.simulate_dice_model is a compact forward simulator of Nordhaus's DICE-2016R model. You supply a carbon-tax path, a climate sensitivity and a damage coefficient; it returns the joint 2020-2165 trajectory of output, emissions, the three carbon reservoirs, warming and damages, plus a social cost of carbon (SCC) computed as DICE defines it: the present value of the consumption lost to one extra ton of CO2 emitted today, obtained by perturbing the emissions path and discounting with the Ramsey factor.

It is a scenario tool, not an optimiser: nothing is maximised, the savings rate is fixed and the abatement rate follows DICE's first-order condition against the tax you pass in. Within that scope the blocks are the published DICE-2016R ones, applied on their published time basis (see "Model blocks").

from puremacro.climate import simulate_dice_model

res = simulate_dice_model()   # defaults: 2020-2165, $40/tCO2 growing 2%/yr, ECS 3.1
print(res.summary())
res.plot()

`simulate_dice_model()` — every argument is keyword-only

argument	default	meaning
`n_periods`	`30`	number of steps; with 5-year steps 30 covers 2020-2165
`time_step_years`	`5`	years per step. DICE's constants are per 5-year step; for other values the carbon-cycle and temperature operators are raised to the power `dt/5` (matrix fractional power), so a 10-year run samples the same dynamics
`start_year`	`2020`	calendar year of the initial state
`carbon_tax_initial`	`40.0`	carbon price in the start year, $/tCO2; `0.0` is the no-policy path
`carbon_tax_growth`	`0.02`	annual growth rate of the tax
`climate_sensitivity`	`3.1`	equilibrium warming per CO2 doubling, °C (DICE-2016R)
`damage_coef`	`0.00236`	`a2` in the quadratic damage function `D(T) = a2 T^2`
`discount_rate`	`0.015`	pure rate of time preference `rho` used in the SCC
`elasticity_marginal_utility`	`1.45`	`eta` in the Ramsey discount factor used in the SCC
`savings_rate`	`0.22`	fixed gross savings rate
`scc_horizon_years`	`300`	horizon over which marginal damages are integrated for the SCC

Inputs are validated: a non-positive n_periods, time_step_years or climate_sensitivity, or a negative carbon tax, raise ValueError.

What comes back

DICEResult is a frozen dataclass:

field / method	what it is
`trajectories`	`DataFrame` indexed by `year` with `output_gross`, `output_net`, `capital`, `consumption`, `population`, `emissions` (GtCO2/yr), `atmospheric_carbon`, `upper_ocean_carbon`, `deep_ocean_carbon` (GtC), `radiative_forcing` (W/m2), `temperature_anomaly`, `ocean_temperature` (°C), `climate_damages` ($T/yr), `damage_fraction`, `abatement_rate` (`mu`), `abatement_fraction`, `carbon_tax` and `social_cost_of_carbon` ($/tCO2)
`peak_temperature`	max of `temperature_anomaly` over the horizon
`scc_initial`	SCC in the start year
`end_century_damages`	`damage_fraction` in 2100
`parameters`	the arguments the run used
`summary()`, `to_frame()`, `to_markdown()`, `to_latex()`, `to_typst()`, `plot()`	the standard puremacro presentation interface

Running a baseline and a policy scenario

from puremacro.climate import simulate_dice_model

base = simulate_dice_model(
    n_periods=30, time_step_years=5, start_year=2020,
    carbon_tax_initial=40.0, carbon_tax_growth=0.02,
)
policy = simulate_dice_model(
    n_periods=30, time_step_years=5, start_year=2020,
    carbon_tax_initial=80.0, carbon_tax_growth=0.035,
)
no_policy = simulate_dice_model(carbon_tax_initial=0.0, carbon_tax_growth=0.0)

print(base.summary())
warming_saved = (base.trajectories["temperature_anomaly"]
                 - policy.trajectories["temperature_anomaly"])
print(warming_saved.loc[2100])

What the runs produce (default calibration, 5-year steps):

	baseline ($40, +2%/yr)	accelerated ($80, +3.5%/yr)	no policy
abatement rate `mu` in 2020	0.194	0.300	0.000
first year `mu` reaches 1.0	2130	2070	never
emissions 2020, GtCO2	32.4	28.5	39.6
emissions 2100, GtCO2	23.1	0.4	70.1
`atmospheric_carbon` 2100, GtC	1325	996	1679
warming 2100, °C	3.36	2.68	3.91
`peak_temperature`, °C	4.13	2.96	5.94
`end_century_damages`	2.66%	1.70%	3.62%
`scc_initial`, $/tCO2	34.7	33.5	35.2

The SCC is almost the same across the three runs because it is a marginal damage evaluated on each path, not a function of the tax: the no-policy path is slightly warmer, so its marginal ton does slightly more harm. The no-policy peak of about 6 °C and the 2100 value of about 3.9 °C are in line with DICE-2016R's own baseline.

Model blocks

Macro

L(t)     : logistic path from 7.79 to 11.5 billion
A(t)     : TFP growing at 0.076/5yr, declining 0.5%/yr
Y_gross  = A K^0.30 L^0.70                              $T/yr
K'       = (1 - 0.10)^dt K + dt * savings_rate * Y_net

Emissions and abatement

sigma(t) : carbon intensity, GtCO2 per $T, declining at DICE's rate
p_back(t): backstop price, 550 $/tCO2 in 2015 declining 0.5%/yr
tau(t)   = carbon_tax_initial * (1 + carbon_tax_growth)^(t - t0)
mu       = min(1, (tau / p_back)^(1/(theta2 - 1))),   theta2 = 2.6
abatement_fraction = theta1 * mu^theta2,  theta1 = p_back * sigma / (1000 theta2)
E_ind    = sigma * (1 - mu) * Y_gross ;  E_land = 2.6 GtCO2/yr declining 11.5%/5yr

Carbon cycle

Three reservoirs, initialised at [851, 460, 1740] GtC. DICE-2016R's transfer coefficients b12 = 0.12, b23 = 0.007 per 5-year step, with the reverse flows pinned to the equilibrium stocks (b21 = b12 * 588/360, b32 = b23 * 360/1720). The operator is applied so that carbon is conserved exactly: with zero emissions the three stocks always sum to the same total. Emissions are converted at 3.666 GtCO2 per GtC and injected into the atmosphere.

Temperature

Two layers with DICE-2016R's per-step coefficients c1 = 0.1005, c3 = 0.088, c4 = 0.025 (they are not multiplied by the step length; for time_step_years != 5 the whole 5-year operator is raised to the power dt/5). Forcing is 3.68 log2(M_AT / 588) plus DICE's exogenous non-CO2 path. The recursion is stable and monotone for any positive climate sensitivity: at climate_sensitivity=1.0 warming peaks at 1.45 °C, and at 5.0 at 5.91 °C.

Damages

damage_fraction = min(0.90, damage_coef * T_atm^2) — quadratic only; no other damage form is provided.

For each period t the emissions path is perturbed by one extra ton of CO2, the model is re-run, and the consumption losses over the next scc_horizon_years are discounted with (1 + rho)^-(s-t) (c_t / c_s)^eta. The SCC therefore responds to the discount rate and to the climate parameters:

`discount_rate`	0.001	0.015 (default)	0.05	0.10
`scc_initial`, $/tCO2	151	34.7	6.1	1.8

Raising climate_sensitivity from 3.1 to 5.0 raises the initial SCC from $34.7 to $60.3 (+74%) and the peak warming from 4.13 °C to 5.91 °C.

What is simplified relative to published DICE

No optimisation: the savings rate is fixed and the abatement rate follows the supplied tax; DICE's optimal-policy runs are not reproduced.
The population, TFP, carbon-intensity, backstop and land-emission paths are the closed-form approximations of DICE-2016R's exogenous processes.
One quadratic damage function; no tipping points, no catastrophic damages.
The SCC is a marginal-damage calculation along the simulated path with a fixed 300-year horizon; DICE reports it from the optimiser's shadow prices.

Gotchas

time_step_years other than 5 changes the sampling of the same continuous-time dynamics, not the dynamics themselves; a 10-year run reports a peak of 4.25 °C against the 5-year run's 4.13 °C because it samples the path at different dates.
carbon_tax_initial=0.0 still prices carbon in the SCC column: the SCC is a damage, not the tax.

The rest of `puremacro.climate`

The subpackage also holds four empirical modules, added in 0.52.0, that have nothing to do with DICE. They are not re-exported — puremacro.climate.__all__ is ["DICEResult", "simulate_dice_model"] only, so from puremacro.climate import compute_annual_cdd_hdd raises ImportError. Import from the submodule:

from puremacro.climate.degree_days import compute_monthly_cdd_hdd, compute_annual_cdd_hdd
from puremacro.climate.annual_lp import climate_annual_lp
from puremacro.climate.mediation import climate_mediation_lp
from puremacro.climate.monthly_dl import monthly_dl, make_dl_lags

function	what it does
`compute_monthly_cdd_hdd(df, *, temp_col="temp_c", threshold=18.0)`	adds `cdd = max(T-18, 0)` and `hdd = max(18-T, 0)` columns
`compute_annual_cdd_hdd(df, *, temp_col, threshold, region_col="region", year_col="year", month_col="month")`	sums those to `annual_cdd` / `annual_hdd` per region-year
`climate_annual_lp(panel, *, response, cdd_col="annual_cdd", hdd_col="annual_hdd", horizons=range(0,11), n_lags=2, controls=(), region_col="region", year_col="year", alpha=0.10)`	returns `{"cdd": ..., "hdd": ...}`, each a `panel_lp_dk` frame with `[h, beta, se, t, lo, hi]`
`climate_mediation_lp(panel, *, mediator_col, response, ..., n_bins=5)`	baseline vs top-quintile-interacted LP plus `mediation_share_cdd` / `mediation_share_hdd` arrays
`monthly_dl(df, *, shock_cols=("cdd","hdd"), response_col="log_births", n_lags=12, ...)`	distributed-lag OLS; HC1 for one region, cluster-by-region in panel mode

climate_annual_lp runs the CDD regression with HDD as a control and vice versa, so each reported IRF is the partial response — heating and cooling degree days are strongly negatively correlated within a region-year and an unconditional CDD response is largely the absence of winter.

One dead parameter here too: climate_mediation_lp(..., top_quintile_only=True) is accepted and never read. The top quintile is always the one interacted.