Finally finished my diploma thesis…

It took some time, but today I finally managed to proofread my diploma thesis in economics (which is similar to a master’s thesis) titled “Endogenous growth in heterogeneous-firm trade models.”

Abstract: This thesis aims to demonstrate how a heterogeneous-firm trade and growth model can be used to analyze productivity and welfare effects of trade liberalization. To this end, I first discuss the evolution of trade and growth theories that culminated in a class of comprehensive models capable of accounting for phenomena that are deemed important by both trade and growth theorists. Focusing on one of these models, Gustafsson and Segerstrom (2010), I extend their comparative static analysis to out-of-steady-state dynamics and show that the presence of heterogeneous firms introduces nontrivial complications absent from homogeneous-firm models. Lastly, I present Gustafsson and Segerstrom’s main finding that knowledge spillovers play a pivotal role in determining whether trade liberalization is welfare increasing.

You can download the complete thesis here (PDF, 2.1 MB).

Dynamics in the Solow-Swan growth model

Another Mathematica demonstration: this one visualizes the comparative statics as well as the adjustment dynamics resulting from a parameter change in the Solow-Swan growth model.

I took professor Sorger‘s advanced macro class on growth and business cycle theories last semester, so I noticed that some textbooks (such as Barro/Sala-i-Martin) don’t show the adjustment process of capital, per-capita output, consumption, etc. I think it helps intuition to visualize these variables, which is why I created this demonstration.

You can download the Mathematica notebook (you’ll need either Mathematica or the free Mathematica player to view this), or look at the online version here. (Unfortunately Wolfram changed the demo so only one graph is visible at a time.)

Mathematica demonstration illustrating Melitz’ trade model

Melitz, again. I took a Mathematica class this semester where we had to build a demonstration that could be uploaded to Wolfram’s demonstration project site. I created an animated version of figure 2 from Melitz’ paper (based on the calculations done in one of the Mathematica notebooks presented below), which IMO is well suited to do a comparative statics analysis of autarky and the open economy.

The online demonstration is available here.

Melitz’ heterogeneous firm trade model with Pareto-distributed productivity

The Melitz (2003) trade model is one of the central models of my diploma thesis, so I’ve spent (wasted?) some time derived a closed-form solution for Pareto-distributed firm productivity levels (Melitz himself does not use a particular distribution).  I’ve been able to replicate most of paper’s results, while a few do not hold for the Pareto distribution (using other distributions, though, will generally not produce closed-form solutions). With the Mathematica notebook it is easy to manipulate model parameters and see the effects on equilibrium values.

Download links:  PDF, Mathematica Notebook (ZIP archive)

Update (Dec. 8, 2009): minor changes and error corrections in PDF and Mathematica notebook.

Update (Dec. 14, 2009): Helpman/Melitz/Yeaple (2004) present a similar model with heterogeneous firms and Pareto-distributed firm productivity. It is less complex than Melitz (2003) as it omits the stochastic firm entry and exit process. However, it allows to model firm decisions concerning production for the domestic market and export / FDI in foreign markets depending on firm productivity. The Mathematica notebook below derives this model in greater detail than the original paper.

Download links: PDF, Mathematica notebook/package


  • Helpman, Elhanan/ Melitz, Marc J. and Yeaple, Stephen R. (2004): Export versus FDI with Heterogeneous Firms . In: American Economic Review 94(1), 300 316.
  • Melitz, Marc J. (2003): “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity”. In: Econometrica 71(6), 1695.

An idiot’s guide to Dixit/Stiglitz

While researching for my current diploma thesis on “new new” trade theory I realized that fully understanding (or rather: knowing by heart) the Dixit/Stiglitz (1977) model is a necessary precondition to be able to read most of the relevant papers. Unfortunately, the original Dixit/Stiglitz is not written for undergraduate students (intermediate steps are mostly omitted), and the obsolete Chamberlinian terminology does not exactly promote understanding (obsolete by Austrian university standards, that is).

Consequently I’ve compiled this step-by-step walkthrough of the first and most widely used model (the CES case) covered in Dixit/Stiglitz (1977). This should be sufficient for  most of the “new” and “new new” trade theory models. You can download it here.

Please let me know if you find any mistakes.

Update (Dec. 21, 2009): Minor corrections.


  • Dixit, Avinash K. and Stiglitz, Joseph E. (1977): “Monopolistic Competition and Optimum Product Diversity”. In: American Economic Review 67(3), 297–308.