# Technological change module (13_tc)¶

**Table of contents**- Technological change module (13_tc)

## Description¶

The technological change module describes the relation between agricultural land use intensity represented by the $\tau$ factor and the costs which have to be paid for further intensification (technological change costs). Besides cropland expansion (39_landconversion) and trade (21_trade) it describes the third major option of the model to increase regional supply. In order to calculate this relation, the module needs to receive information about the assumed interest rate and assumed investment horizon currently provided by module 12_interest_rate and the core.

Calculated $\tau$ factors are then used for yields calculation by 14_yields and by 38_factor_costs for the calculation of factor costs. In addition 90_presolve and core receive the costs assigned to the calculated intensification rates.

## Interfaces¶

### Input¶

Name Description Unit A B $pm\_interest(i)$ real interest reate in each region - x x $pm\_annuity\_due(i)$ Annuity-due annual cash flows over n years in each region - x x $fm\_years(t)$ file containing the years of the t_all set years x x $im\_years(t)$ years between previous and current time step years x x $sm\_invest\_horizon$ investment time 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 $vm\_tech\_costs(i)$ costs of technological change mio. US$ $vm\_tau(i)$ agricultural land use intensity tau - $fm\_tau1995(i)$ agricultural land use intensity tau in 1995 -

### Interface plot¶

Figure 0: Information exchange among modules

## Realizations¶

### (A) endo_APR13 *(default)*¶

The "endo_APR13" realization stands for endogenous implementation of technological change and land use intensification. The intensification rates are calculated endogenously based on an interplay between land use intensity $\tau$ and technological change costs. This module realization contains the implementation as described in Dietrich/Schmitz et al^{1} (2013) with two minor modifications:

- rates of previous investment decisions which still have to be paid are added to the technological change costs
- the planning horizon for investments is unified over all investments in the model.

Figure 1 shows schematically how this process is implemented.

^{1}(2013)]

Initial land use intensity $\tau$ values for the year 2000 come from Dietrich et al^{2} (2012) and are shown in Figure 2.

^{2}(2012)]

Investments into technological change (TC) trigger land use intensification ($\tau$) which triggers in turn yields increases. How much intensification an investment can trigger depends on the investment-yield ratio which depends again on the current agricultural land use intensity. The higher the current intensity level, the more expensive the additional intensification will become. The interaction between land use intensity and production costs per area as shown in the figure is not covered by this module and can be found instead in 38_factor_costs.

Equation 1:

\begin{align}

v13\_cost\_tc(i) &= f13\_crop(i) \cdot s13\_tc\_factor \cdot vm\_tau(i)^{s13\_tc\_exponent} \\

&\cdot (1+pm\_interest(i))^{15}

\end{align}

^{1}(2013)]

Relative technological change costs $v13\_cost\_tc$ are calculated as a heuristically derived power function of the land use intensity $vm\_tau$ for the investment-yield-ratio (Figure 3) multiplied by the initial, regional crop areas in 1995 $f13\_crop$ and shifted 15 years into the future using the region specific interest rate $pm\_interest$. The shifting is performed because investments into technological change require on average 15 years of research before a yield increase is achieved, but the model has to see costs and benefits concurrently in order to take the right investment decisions (see also Dietrich/Schmitz et al^{1} (2013)). Investment costs scale with crop area as a wider areal coverage means typically also higher variety in biophysical conditions and therefore more research required for the same overall intensity boost.

Equation 2:

\begin{align}

v13\_tech\_cost_annuity(i) = (\frac{vm\_tau(i)}{pc13\_tau(i)}-1)\cdot \frac{v13\_cost\_tc(i)}{pm\_annuity\_due(i)}

\end{align}

In order to get the full investments required for the desired intensification the relative technological change costs are multiplied with the given intensification rate. These full costs are then distributed over an estimated planning horizon ($sm\_invest\_horizon$) with the annuity approach and the corresponding annuity factor $pm\_annuity\_due(i)$.

Equation 3:

\begin{align}

vm\_tech\_cost(i) = v13\_tech\_cost\_annuity(i) + pc13\_tech\_cost\_past(i)

\end{align}

Additionally, the technological change costs coming from past investment decisions are added to the technological change costs of the current period.

Limitations

This module significantly reduces the overall computational performance of the model since these endogenous calculations are highly computational intensive.

### (B) exo_JUN13¶

The "exo_JUN13" realization stands for exogenous implementation of technological change and land use intensification. Agricultural land use intensities ($\tau$) for the different regions and years are read from files.

Except for the fixing of agricultural land use intensities $\tau$ and the corresponding replacement of some variables with parameters the calculations are completely identical to the realization "endo_APR13" and the procedure explained in Dietrich/Schmitz et al^{1} (2013).

Limitations

Its use can lead to an infeasibility since fixing the agricultural land use intensities $\tau$ significantly reduces the number of options the model has to fulfill the given demand.

## Definitions¶

Name Description Unit A B $s13\_tc\_factor$ regression factor US\$/ha x x $s13\_tc\_exponent$ regression exponent - x x $f13\_tau(t,i)$ exogenous $\tau$ path - x $f13\_crop(i)$ Regional crop area in 1995 mio. ha x x $f13\_tcguess(i)$ guess for initial annual tc rates - x $v13\_cost\_tc(i)$ technical change costs per region mio. US\$ x $v13\_tech\_cost\_annuity(i)$ annuity costs of technological change mio. US\$ x $p13\_cost\_tc(i)$ technical change costs per region mio. US\$ x $pc13\_tau(i)$ $\tau$ factor of the previous time step - x $p13\_tech\_cost\_past(t,i)$ costs for technological change from past mio. US\$ x x $pc13\_tech\_cost\_past(i)$ current costs for technological change from past mio. US\$ x x $pc13\_tcguess(i)$ guess for annual tc rates in the next time step - x $pc13\_tech\_cost\_annuity(i)$ annuity costs of technological change mio. US\$ x

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

## Developer(s)¶

Jan Philipp Dietrich, Christoph Schmitz, Benjamin Bodirsky

## See Also¶

core, 12_interest_rate, 14_yields, 21_trade, 38_factor_costs, 39_landconversion, 90_presolve, Overview

## References¶

^{1} [Dietrich/Schmitz et al. (2013)] Dietrich J.P., Schmitz C., Lotze-Campen H., Popp A., Müller C.(2013): "Forecasting technological change in agriculture - An endogenous implementation in a global land use model". Technological Forecasting & Social Change doi: 10.1016/j.techfore.2013.02.003

^{2} [Dietrich et al. (2012)] Dietrich J.P., Schmitz C., Müller C., Fader M., Lotze-Campen H., Popp A., "Measuring agricultural land-use intensity – A global analysis using a model-assisted approach", Ecological Modelling, Volume 232, 10 May 2012, Pages 109-118, ISSN 0304-3800, 10.1016/j.ecolmodel.2012.03.002 [Preprint & Online Supporting Material]