Solving SDEs

Stochastic Differential Equations (SDEs) solved.

Fiscal Multiplier

The Economist explains the Keynesian fiscal multiplier.

Ito's Lemma

The key is to do the second order Taylor expansion.

Diffusions and Diffusion Models

Good news: Now you can enjoy the online course "Asset Pricing" by Professor John H. Cochrane at University of Chicago (at no charge)! Very instructive and understandable!

Start now!!

Studying Macroeconomics

I major in macroeconomics. So, it may be a good idea to share my experience, i.e. how I studied (and am studying!) macroeconomics.

If you are new to macroeconomics, you are highly recommended to begin with Mankiw's principles of macroeconomics. You don't see any mathematics in this text, so don't have to worry about math!

After reading principles of macro, you should go either Blanchard's Macroeconomics or Mankiw's intermediate Macroeconomics (I read both, by the way). At this stage, you can say that you are familiar with undergraduate macro and see the world through the lens of macro! Read blogs by macroeconomists: you can understand now. (I read Mankiw and Cochrane every day.)

If you want to continue (i.e. graduate macro), you cannot escape from mathematics. But there are many good textbooks on math for economists. I recommend Dowling's Introduction to Mathematical Economics. This is wonderful and very easy to follow, but covers most math tools you'll need (if time allows, also read Chiang and Wainwright's Fundamental Methods of Mathematical Economics and Chiang's Elements of Dynamic Optimization). I didn't study Math III and Math C at high school, but after reading these three books, I'm really equipped with math tools for (macro)economics.

After mastering most math tools, you want to try either Benassy's Macroeconomic Theory or David Romer's Advanced Macroeconomics. And if time allows, read the classic: Lectures on Macroeconomics by Blanchard and Fischer (mathematically speaking, Benassy is very friendly, Romer is not that diffiicult, and Blanchard-Fischer is very technical). At this stage, you know what macroeconomics is (almost) all about.

Actually, three textbooks above present collection of various macro models. If you want to specialize in one specific topic, you have to look for other materials. In my case, I major in New Keynesian DSGE models. So, I study lecture notes by leaders in this field, Gali, Christiano, and Moll.

FYI:

Leaders in Growth Theory - Acemoglu and Charles Jones (Jones has excellent data on standard of livings across countries!).

Leaders in Computational Macroeconomics - Jesus Fernandez-Villaverde.

Leaders in Macroeconomics - Chris Edmond, Ivan Werning, Michael Woodford, and John Cochrane.

Sorry, but I cannot introduce all...(Google yourself!)

Poverty and Economic Growth

Why are some countries rich and other are poor? Economic growth theory has been developed to answer this question. In this post I provide useful sources to know about growth and poverty.

First, you have to start with Banerjee and Duflo's Poor Economics. Building schools in poor countries? Okay, it's definitely important. But is it the end of the story? No. You have to think, think, and think. Build schools, then what? Build schools, then hire teachers. Okay, then if you suppose that they will work hard for children, read this book. The book let you think radically. The problem is not easy.

Then, read non-technical books - Acemoglu and Robinson's Why Nations Fail, Jeffrey Sachs' The End of Poverty, and Robert Allen's Global Economic History. You may also enjoy Michael Spence (Nobel Prize Winner in Economics)'s The Next Convergence.

After reading non-technical books and being interested in more, then read textbooks on economics. Many intermediate textbooks on macroeconomics, such as Mankiw and Blanchard, have chapters on economic growth. More specialized (yet accessible) books are Charles Jones and David Weil.

At this stage, you are advised to see data. The best data is provided in the Penn World Table, which is widely used by professional economists. Plus, Charles Jones has a kind of dictionary of economic growth. If you read this, you are done.

But if you want to pursue more, try graduate-level textbooks on economic growth. Barro and Martin is still easy to follow, so is Aghion and Howitt. The most challenging one - Introduction to Modern Economic Growth - is written by one of the leaders in the field, Daron Acemoglu. If you can read this book, you must be a researcher of poverty and economic growth!

Dynamic Programming

Dynamic programming is the very powerful mathematical tool. When applied to economics, we can use that method to solve, well, (almost) all problems (even if the model is stochastic!). The problem is that many books on this method are too technical for economists and it's hard to understand it.

The most accessible introduction to dynamic programming is, in my opinion, George McCandless's "ABCs of RBCs" (his lecture notes are also nice). The second best is Klaus Walde's Applied Intertemporal Optimization (AIO for short, available for free!). McCandless doesn't explain the continuous-time dynamic programming, so if you work with continuous-time models, you should read AIO as well. The final book on dynamic programming is the bible - Recursive Methods in Economic Dynamics. However, this classic is too technical. Unless you are familiar with abstract mathematics, this book cannot be recommended.

By the way, dynamic programming is developed by Richard E. Bellman. That's why you have Bellman equation when solving problems using dynamic programming.