Interest rate (12_interest_rate)¶

• Table of contents
• Interest rate (12_interest_rate)
  • Description
  • Interfaces
    • Input
    • Output
    • Interface plot
  • Realizations
    • (A) glo (default)
    • (B) reg
  • Defintions
  • Developer(s)
  • See Also
  • Reference

Description¶

The interest rate module describes interest rates and the annuity-due used in the model. The data of interest rates is used as interest rates, a risk-accounting factor associated with long-term investment (Wang et al¹ 2015). These two factors are required for inter-temporal calculations in the model such as shifting investment from one time step to another or distribution one-time investments over several time steps. An annuity-due is an annuity whose payments are made at the beginning of each period (Jordan et al²2000). The annuity due is then used in the modules (13_tc, 39_landconversion, 41_area_equipped_for_irrigation, and 57_maccs) to compute the present value of annual costs.

Interfaces¶

Input¶

Name	Description	Unit	A	B
$sm\_invest\_horizon$	investment horizon	years	x	x

_{The last columns of the table indicate the usage in the different realizations (numbered with capital letters)}

Output¶

Name	Description	Unit
$pm\_interest(i)$	interest rate in each region	-
$pm\_annuity\_due(i)$	Annuity-due annual cash flows over n years in each region	-

Interface plot¶

Figure 0: Information exchange among modules

Realizations¶

(A) glo (default)¶

The glo realization is the default setting, in which the interest rate is the interest rate of 7% applied globally (Florian et al³ 2014). Therefore the annuity-due is identical for each region.

\begin{equation}
\begin{split}
p12\_annuity\_due = \frac{1-(1+s12\_interest)^{-sm\_invest\_horizon}}{\frac{s12\_interest}{1+s12\_interest}} \\
pm\_interest(i) = s12\_interest \\
pm\_annuity\_due(i) = p12\_annuity\_due
\end{split}
\end{equation}

(B) reg¶

In the reg realization, the interest rates can be regionally specific. Therefore the annuity-due can also be regionally specific.

\begin{equation}
\begin{split}
p12\_annuity\_due(i) = \frac{1-(1+f12\_interest(i))^{-sm\_invest\_horizon}}{\frac{f12\_interest(i)}{1+f12\_interest(i)}} \\
pm\_interest(i) = f12\_interest(i) \\
pm\_annuity\_due(i) = p12\_annuity\_due(i)
\end{split}
\end{equation}

The country level data of real interest rates, from the World Development Indicators, is aggregated to regional interest rates using countries' GDP as a weight. Then the average is taken between the aggregated discount rates for each MAgPIE region between 1995 and 2005 (Figure 1).

Figure 1: Regionally specified interest rates

Defintions¶

Name	Description	Unit	A	B
$sm\_invest\_horizon$	investment horizon	-	x	x
$s12\_interest$	global interest rate	-	x
$f12\_interest(i)$	interest rate in each region	-		x
$p12\_annuity\_due(i)$	annuity factor for each region	-		x
$p12\_annuity\_due$	annuity factor for each region	-	x

_{The last columns of the table indicate the usage in the different realizations (numbered with capital letters)}

Developer(s)¶

Xiaoxi Wang, Florian Humpenöder, Jan Philipp Dietrich

See Also¶

13_tc, 39_landconversion, 41_area_equipped_for_irrigation, 57_maccs

Reference¶

¹ Wang, Xiaoxi; Biewald, Anne; Dietrich, Jan P., Schmitz, Christoph; Lotze-Campen, Hermann; Humpenöder, Florian; Bodirsky, Benjamin L.; Popp, Alexander. Taking Account of Governance: Implications for Land-Use Dynamics, Food Prices, and Trade Patterns. Ecological Economics. Under revision.

² Jordan, Bradford D.; Ross, Stephen David; Westerfield, Randolph (2000). Fundamentals of corporate finance. Boston: Irwin/McGraw-Hill. p. 175. ISBN 0-07-231289-0.

³ Humpenöder,Florian; Popp, Alexander; Dietrich, Jan P.; Klein,David; Lotze-Campen,Hermann; Bonsch,Markus; Bodirsky, Benjamin L.; Weindl,Isabelle; Stevanovic,Miodrag; Müller,Christoph (2014). Investigating afforestation and bioenergy CCS as climate change mitigation strategies. Environmental Research Letters 9 (6): 064029.