# Model Documentation

### | Version 4.0

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# 12_interest_rate

# Interest rate (12_interest_rate)

## Description

Interest rates are used in MAgPIE as a risk-accounting factor associated with investment activities (Wang et al. 2016). Interest rates are required for inter-temporal calculations in the model such as shifting investment from one time step to another or distribution of one-time investments over several time steps (e.g. in the modules 13_tc, 39_landconversion and 41_area_equipped_for_irrigation).

## Interfaces

Interfaces to other modules

### Input

module inputs (A: glo_jan16 | B: reg_feb18)
| Description | Unit | A | B
--- | --- | --- | --- | ---
im_development_state (t, i) | Development state according to the World Bank definition where 0=low income country 1=high income country in high income level | \(1\) |  | x
im_gdp_pc_ppp (t, i) | Per capita income in purchasing power parity | \(USD_{05PPP}/cap/yr\) | x |

### Output

module outputs
| Description | Unit
--- | --- | ---
pm_interest (i) | Current interest rate in each region | \(\%/yr\)

## Realizations

### (A) glo_jan16

In the glo_jan16 realization, interest rates are identical in all regions. The initial global interest rate is 7% (in 1995) for all scenarios defined in `scen12`. It undergoes a transition towards 4%, 7% and 10% until 2030 for the low-, medium- and high- interest rate scenarios, respectively.

> Limitations There are no known limitations.

### (B) reg_feb18

The reg_feb18 realization is the default setting, in which the interest rate depends on the development state `im_development_state`, which is calculated based on GDP per capita. Thus, interest rates are regionally specific and dynamic over time.

    s12_min_dev = smin(i,im_development_state("y1995",i));
    s12_max_dev = smax(i,im_development_state("y1995",i));
    s12_slope_a = (f12_interest_bound("y1995","high")-f12_interest_bound("y1995","low"))/(s12_min_dev-s12_max_dev);
    s12_intercept_b = f12_interest_bound("y1995","high")-s12_slope_a*s12_min_dev;
    p12_interest(t,i) = s12_slope_a *im_development_state(t,i) + s12_intercept_b;

> Limitations There are no known limitations.

## Definitions

### Objects

module-internal objects (A: glo_jan16 | B: reg_feb18)
| Description | Unit | A | B
--- | --- | --- | --- | ---
f12_interest_bound (t, bound12) | Lower and higher bounds of interest rates | \(\%/yr\) |  | x
f12_interest (t_all, scen12) | Interest rate scenarios | \(\%/yr\) | x |
p12_interest (t, i) | Interest rate | \(\%/yr\) | x | x
s12_intercept_b | Intercept of the linear relationship between development state and interest rate | \(1\) |  | x
s12_max_dev | Maximum development_state of all regions in 1995 | \(1\) |  | x
s12_min_dev | Minimum development_state of all regions in 1995 | \(1\) |  | x
s12_slope_a | Slope of the linear relationship between development state and interest rate | \(1\) |  | x

### Sets

sets in use
| description
--- | ---
bound12 | Bound for interest rate
i | World regions
scen12 | Interest rate scenarios
t_all | 5-year time periods
t(t_all) | Simulated time periods

## Authors

Xiaoxi Wang

## See Also

09_drivers, 12_interest_rate, 13_tc, 39_landconversion, 41_area_equipped_for_irrigation

## References

Wang, Xiaoxi, Anne Biewald, Jan Philipp Dietrich, Christoph Schmitz, Hermann Lotze-Campen, Florian Humpenöder, Benjamin Leon Bodirsky, and Alexander Popp. 2016. “Taking Account of Governance: Implications for Land-Use Dynamics, Food Prices, and Trade Patterns.” Ecological Economics 122 (February): 12–24. doi:10.1016/j.ecolecon.2015.11.018.