Toolkit for Quantitative Spatial Models

© Gabriel M. Ahlfeldt, Tobias Seidel

Version 0.91, 2024

General remarks

This toolkit covers a class of quantitative spatial models established by Monte, Redding, Rossi-Hansberg (2018). We aim to provide an accessible and easy-to-use simulation framework within MATLAB (Monte, Reeding, Rossi-Hansberg use Mathematica) that helps developing the intuition for the key mechanisms in the model as well as the programming implementation of the model. To this end, this toolkit contains a codebook which summarizes the various exogenous and endogenous objects of the model, its equilibrium conditions, and various solvers used to take the model to the data. We build on Seidel and Wickerath (2020) who apply a variant of the Monte, Redding, Rossi-Hansberg (2018) model to Germany. The toolkit introduces a subset of codes that are crucial for the quantification and simulation of the model, with applications that serve didactic purposes and are unrelated to the substantive analyses in both papers. For more general applicability, the toolkit is designed to also work in instances where the researcher does not observe bilateral commuting flows (and possibly not even wages).

This toolkit has been developed as core component of the course Quantitative Spatial Economics taught by Gabriel Ahlfeldt to research students at the Berlin School of Economics and Humboldt University. The course is taught in the German summer term and is open to visiting PhD students.

General instructions

Before you can start, you need to install the following MATLAB toolboxes:

• Global optimization toolbox
• Optimization toolbox
• Mapping toolbox
• Statistics and machine learning toolbox

To install a MATLAB toolbox, open MATLAB and go to the 'Home' tab. Click on 'Add-Ons' in the menu. From there, browse or search for the toolbox you want to install. Click on the toolbox to view its details. Then, proceed by clicking 'Install.' Follow the on-screen instructions, which will include accepting the license agreement and selecting the installation path. After the installation is complete, the toolbox will be ready to use. Make sure you have the appropriate licenses for the toolbox you've selected.

How to Use the Toolkit

The toolkit is designed as a didactic journey through the codes essential for the quantification and simulation of this class of models. The aim is to convey how to quantify the model and conduct simple counterfactuals.

Once you are set up, execute the codes in the order in which they are being called by MRRH2018_toolkit.m in the scripts folder. When you use the toolkit for the first time, it is especially important that you execute the scripts exactly in the order outlined by MRRH2018_toolkit.m as intermediate inputs will be generated that will be used at later stages. There are also didactic reasons for proceeding in the given order since the structure broadly follows the use of the model in the paper and codes become progressively more complex. For the best learning experience, we recommend that you open the scripts and go through the code line by line (instead of calling scripts from MRRH2018_toolkit.m). Plenty of comments have been added to refer to the relevant equations in the paper. It will likely be beneficial to triangulate between the code, the pseudo codes summarized in the codebook, and the Monte, Redding, Rossi-Hansberg (2018) and Seidel, Wickerath (2020) papers to understand how the code implements the model.

Throughout the quantification of the model, we use the MAPIT program to illustrate selected variables recovered using the structure of the model. You can use MAPIT to conveniently plot any model input or output at any stage of the analysis to develop your intuition for the various endogenous and exogenous objects. MAPIT is relatively slow. If you want to experiment with the code and reduce the computational time, you may find it convenient to outcomment the use of MAPIT.

After recovering the unobserved exogenous location characteristics, we use various solution algorithms to solve for the spatial equilibrium. For illustrative purposes, we perform a series of simple counterfactuals. Specifically, we implement a hypothetical border along the former border between East and West Germany that may either prevent commuting, trade, or both. Notice that the population remains mobile across residences. This way, the model provides insights into who the population would like to reoptimize their location choices in light of the asymmetry of the strength of the shock that arises from the two different parts home market size. You can use MAPIT to inspect the effects on any endogenous outcome and execute similar counterfactuals by changing other primitives of the model. The toolkit will hopefully be sufficiently transparent for you to conveniently run your own counterfactuals.

Monte, Redding, Rossi-Hansberg (2020) and Seidel, Wickerath (2020) quantify the model using observed commuting flows. They rationalize zero commuting flows by setting commuting costs to infinity. The advantage of this approach is that it allows for arbitrary commuting costs on routes with positive commuting flows. Depending on your application, you may wish to use commuting cost matrices that are smooth functions of network distance, travel time, or other distance measures. This will be particularly desirable in counterfactuals if you wish to allow for changes in commuting flows at the extensive margin. For example, a new road or rail may lead to commuting flows on certain routes changing from zero to positive values. You may also simply not observe bilateral commuting flows. To facilitate the applicability of the toolkit in such instances, you can use Algorithm getBiTK to predict bilateral commuting flows that are consistent with observed workplace employment, residence population and commuting costs. The algorithm recovers a measure of workplace amenities, that ensures that workplace employment predicted by the model matches data. Please run the script OwnData.m in the scripts folder in these instances. Make sure that the code reads your commuting cost matrix (basline) as well as workplace employment (L_n) and residence population (R_n) measures. You also not observe wages in your application. In this case, you may interpret the inverted fundamental as transformed wages as in Ahlfeldt, Redding, Sturm, Wolf (2015) from which you can recover model-consistent wages. Please refer to the codebook for further detail.

When using the toolkit in your work, please cite this toolkit as:

G. M. Ahlfeldt, Seidel, T. (2024): Toolkit for quantitative spatial models. https://github.com/Ahlfeldt/MRRH2018-toolkit.

Please also consider citing Monte, Redding, Rossi-Hansberg (2018) and Seidel and Wickerath (2020).

Data and Data Folders

Directory	File	Description	Additional Information
matlab/data/input		Folder containing required data inputs to execute this toolkit	-
matlab/data/input	commuting_wide.csv	CSV file containing bilateral commuting flows	-
matlab/data/input	CountyArea.csv	CSV file containing county geographic area in sq. km	-
matlab/data/input	CountyBorderDist.csv	CSV file containing distance from the inner-German border n km	-
matlab/data/input	distance_matrix.csv	CSV file containing bilateral distances between counties	-
matlab/data/input	house_prices.csv	CSV file containing county house prices	-
matlab/data/input	labor_tidy.csv	CSV file containing labour market outcomes	-
matlab/data/input	roundtrip_time_base.csv	CSV file containing bilateral commuting times	-
matlab/data/output		Folder containing data files generated by the scripts in this toolkit.	Will be populated while you execute the MATLAB programs
matlab/figs		Folder containing figures and maps	Will be populated while you execute the MATLAB programs

MATLAB scripts

Scripts are MATLAB programmes that execute substantive parts of the analysis and call functions

Script	Description	Special Instructions
scripts	Folder containing MATLAB scripts	-
MRRH2018_toolkit.m	Meta file that calls other scripts to execute the analysis.	Your journey through the toolkit starts here!
ReadData.m	Loads various data files used by Seidel, Wickerath (2020).	You do not need to execute this program if you wish to use your own continuous travel time matrices and/or population and employment measures (in this case proceed to OwnData.m
Descriptives.m	Explores the data set: generates various maps and descriptive statistics	You can also execute this data set after OwnData.m
BorderData.m	Adds data and generates variables needed for the border counterfactuals	You must execute this script before Counterfactuals.m; you may use it after ReadData.m or OwnData.m
Counterfactuals	Performs the border counterfactuals	-

MATLAB functions

Functions are MATLAB programmes that return outputs for given intputs according to a programming syntax and are being called by scripts (they may also call each other)

Script	Description	Special Instructions
progs	Folder containing MATLAB functions	-
MAPIT.m	Function that can be called to create simple maps that illustrate county outcomes	You may use it at any stage of the analysis to inspect any exogenous or endogenous variable
getBiTK.m	Function used for the quantification of the model; generates commuting flows that are consistent with your commuting cost matrix	Useful if you wish to work with continuous commuting cost matrices and/or do not observe commuting flows (and wages)
solveProductTradeTK.m	Function used for the quantification of the model; inverts fundamental productivity and solves for trade shares and the tradable goods price index	-
counterFactsTK.m	Main solver that solves for relative changes from the initial to the counterfactual equilibrium	Calls the functions below in an iterative procedure
updateEmplTK.m	Updates workplace employment	Nested within counterFactsTK.m
updateHousePriceTK.m	Updates housing price	Nested within counterFactsTK.m
updateLamTK.m	Updates unconditional commuting probabilities	Nested within counterFactsTK.m
updatePricesTK.m	Updates tradable goods price index	Nested within counterFactsTK.m
updateResidentsTK.m	Updates residential employment	Nested within counterFactsTK.m
updateResWageTK.m	Updates residential wage	Nested within counterFactsTK.m
updateTradeshTK.m	Updates trade shares	Nested within counterFactsTK.m
updateWageTK.m	Updates wage	Nested within counterFactsTK.m

Shapefiles

Name	Description
shape	Folder containing shape files
VG250_KRS_clean_final	County shapefile (Kreise und kreisfreie Städte, 2018 definition), indexed in the same way as MATLAB data set
states	State shapefile (Bundesländer, 2018 definition)

Other files

File	Description
Codebook.pdf	This codebook summarizes the primitives and endogenous objects of the models and introduces selected numerical algorithms in pseudo-code. The focus is on algorithms that are essential for the quantification and simulation of the respective quantitative models.

Further resources:

Ahlfeldt, Redding, Sturm, Wolf (2015): The Economics of Density: Evidence from the Berlin Wall, Econometrica, 83(6), p. 21272189. https://doi.org/10.3982/ECTA10876

Monte, Redding, Rossi-Hansberg (2018): Commuting, Migration, and Local Employment Elasticities, American Economic Review, 108(12), pp. 3855-90, https://doi.org/10.1257/aer.20151507

Seidel, Wickerath (2020): Rush hours and urbanization, Regional Science and Urban Economics, 85, https://doi.org/10.1016/j.regsciurbeco.2020.103580

Version history:

Version 0.90: Public release version

Version 0.91: MAPIT programme improved by implementing Jenks Breaks for categorization