By Stanislav Anatolyev
Journal of Economic Surveys
Volume 21 Issue 1, Pages 143 - 173
This article surveys estimation in stationary time-series models usingthe approach of optimal instrumentation. We review tools that allow constructionand implementation of optimal instrumental variables estimators in variouscircumstances – in single- and multiperiod models, in the absence and presence ofconditional heteroskedasticity, by considering linear and non-linear instruments.We also discuss issues adjacent to the theme of optimal instruments. The articleis directed primarily towards practitioners, but econometric theorists and teachersof graduate econometrics may also find it useful.
See the paper at:
http://www3.interscience.wiley.com/journal/117999553/abstract
Saturday, February 28, 2009
Understanding Modern Econometrics
By Yongmiao Hong, 2006
WISE Working Paper, China
Econometrics has become an integral part of training in modern economics and business.Together with microeconomics and macroeconomics, econometrics has been taught as one of thethree core courses in most undergraduate and graduate economic programs in North America. InChina, the importance of econometrics has been increasingly recognized and econometric toolsand methods have been widely employed in empirical studies on Chinese economy. However,there is a substantial gap between Chinese econometrics and modern econometrics. There stillexists conceptual misunderstanding of econometrics among Chinese economic profession, andthere exist some problems in Chinese econometric teaching and research. This paper discussesthe philosophy and methodology of econometrics, the roles and limitations of econometrics,and the di¤erences between econometrics and mathematical economics as well as mathematicalstatistics. A variety of illustrative econometric examples are given, which cover various …eldsof economics and …nance The paper also suggests how to improve and strengthen econometricteaching and research in China.
See this paper at: http://wise.xmu.edu.cn/discourse/20060831/%E7%90%86%E8%A7%A3%E7%8E%B0%E4%BB%A3%E8%AE%A1%E9%87%8F%E7%BB%8F%E6%B5%8E%E5%AD%A6.pdf
WISE Working Paper, China
Econometrics has become an integral part of training in modern economics and business.Together with microeconomics and macroeconomics, econometrics has been taught as one of thethree core courses in most undergraduate and graduate economic programs in North America. InChina, the importance of econometrics has been increasingly recognized and econometric toolsand methods have been widely employed in empirical studies on Chinese economy. However,there is a substantial gap between Chinese econometrics and modern econometrics. There stillexists conceptual misunderstanding of econometrics among Chinese economic profession, andthere exist some problems in Chinese econometric teaching and research. This paper discussesthe philosophy and methodology of econometrics, the roles and limitations of econometrics,and the di¤erences between econometrics and mathematical economics as well as mathematicalstatistics. A variety of illustrative econometric examples are given, which cover various …eldsof economics and …nance The paper also suggests how to improve and strengthen econometricteaching and research in China.
See this paper at: http://wise.xmu.edu.cn/discourse/20060831/%E7%90%86%E8%A7%A3%E7%8E%B0%E4%BB%A3%E8%AE%A1%E9%87%8F%E7%BB%8F%E6%B5%8E%E5%AD%A6.pdf
Philosophy and objectives of econometrics
by Arnold Zellner
Journal of EconometricsVolume 136, Issue 2, February 2007, Pages 331-339
In this paper, the philosophy and objectives of econometrics are discussed. The roles of induction, deduction and reduction in economic research are explained. Further, the roles of sophisticated simplicity and predictive performance in model building are described. Many examples, drawn from the work of leading scientists, are provided to illustrate general points. In addition, the work that has been done leading to the formulation of a disaggregate Marshallian Macroeconomic Model is briefly described. It is concluded that greater emphasis in teaching to explain the roles of deduction, induction and reduction in economic research would be very beneficial in terms of producing more valuable and useful research results. Also, development and use of many more sophisticatedly simple models and further use of Bayesian inference and decision techniques will do much to promote more rapid progress in economic science.
Journal of EconometricsVolume 136, Issue 2, February 2007, Pages 331-339
In this paper, the philosophy and objectives of econometrics are discussed. The roles of induction, deduction and reduction in economic research are explained. Further, the roles of sophisticated simplicity and predictive performance in model building are described. Many examples, drawn from the work of leading scientists, are provided to illustrate general points. In addition, the work that has been done leading to the formulation of a disaggregate Marshallian Macroeconomic Model is briefly described. It is concluded that greater emphasis in teaching to explain the roles of deduction, induction and reduction in economic research would be very beneficial in terms of producing more valuable and useful research results. Also, development and use of many more sophisticatedly simple models and further use of Bayesian inference and decision techniques will do much to promote more rapid progress in economic science.
Friday, February 27, 2009
Approximate Fixed Point
In functional analysis and topology, the very important and very basic theorem is the fixed point theorem. It has been extensively used to guarantee the existence of the solution of some equation systems. Economists like Debreu and Nash borrow the idea of fixed point to shape the existence of the general equilibrium in economic theory. Along with assumptions about consumer preferences and production techlogoly, fixed point theory, such as Brower fixed point theorem and Kakutani fixed point theorem are utilized to prove the existence of the equilibrium. Nash applies the similar ideas in Game Theory to show the existence of Nash equilibrium.
You might feel overwhelmed by the statements above if you have never get to know these background economic nuisance. To state fixed point theorem simply, as cited from Wikipedia, "it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point." See http://en.wikipedia.org/wiki/Fixed_point_theorem
To give a simple example, when we put the World map on the desk, then there should be one point on the map that exactly coincides with the exact corresponding geographical real point.
However, albeit useful in expanding areas of scientific research today, it has its limitations. The fixed point theorem deals with deterministic functions. There has been a litterature trying to incorporate randomness into fixed point theorem. Bharucha-Reid (1976) has a great review of this litterature and Tan and Yuan (1993) explore into the relationship between the deterministic and random fixed point theorem. Random fixed point theorem introduce a stochastic sample space and make the function and variable all dependent on the realizatioin of the sample space. That is, instead of having f(x)=x, we have f(w,x(w))=x(w), equavalent to say that x(w) is a fixed point of f. Some conditions sufficient for the existence of random fixed point have been explored since 1950s.
Though as if it is complicated, with a realization of w, the random fixed point theorem degenerates to fixed point theorem in deterministic case. Another way of extending the fixed point theorem into stochastic situation is what called approximate fixed point. This is a new term I'd like to introduce to the litterature. What term means is that, instead of getting x via f(.) when input is x, we have f(x)->x in probability, as some index goes to infinity. This would be of great interest as many functions we have in Econometrics are random functions. It would be hard to get f(x)=x. While when f(x) approaches x in probability, some properties can be established. For an illustration, iteration via f(.), will give x when sample size is large enough, with an input of x. The idea is rather new and not much can be said at the moment. However, I believe that this will be an important point in probability, and especially in Econometrics, in a few years time.
When you can not get the exact solution to the problem anoying you, try to circumvent to an approximate one!
You might feel overwhelmed by the statements above if you have never get to know these background economic nuisance. To state fixed point theorem simply, as cited from Wikipedia, "it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point." See http://en.wikipedia.org/wiki/Fixed_point_theorem
To give a simple example, when we put the World map on the desk, then there should be one point on the map that exactly coincides with the exact corresponding geographical real point.
However, albeit useful in expanding areas of scientific research today, it has its limitations. The fixed point theorem deals with deterministic functions. There has been a litterature trying to incorporate randomness into fixed point theorem. Bharucha-Reid (1976) has a great review of this litterature and Tan and Yuan (1993) explore into the relationship between the deterministic and random fixed point theorem. Random fixed point theorem introduce a stochastic sample space and make the function and variable all dependent on the realizatioin of the sample space. That is, instead of having f(x)=x, we have f(w,x(w))=x(w), equavalent to say that x(w) is a fixed point of f. Some conditions sufficient for the existence of random fixed point have been explored since 1950s.
Though as if it is complicated, with a realization of w, the random fixed point theorem degenerates to fixed point theorem in deterministic case. Another way of extending the fixed point theorem into stochastic situation is what called approximate fixed point. This is a new term I'd like to introduce to the litterature. What term means is that, instead of getting x via f(.) when input is x, we have f(x)->x in probability, as some index goes to infinity. This would be of great interest as many functions we have in Econometrics are random functions. It would be hard to get f(x)=x. While when f(x) approaches x in probability, some properties can be established. For an illustration, iteration via f(.), will give x when sample size is large enough, with an input of x. The idea is rather new and not much can be said at the moment. However, I believe that this will be an important point in probability, and especially in Econometrics, in a few years time.
When you can not get the exact solution to the problem anoying you, try to circumvent to an approximate one!
Thursday, February 26, 2009
Economist Jokes---What are economists doing now?
The following is taken from a website that collects jokes for economists and economics:
http://netec.mcc.ac.uk/JokEc.html
TOP 10 REASONS TO STUDY ECONOMICS
1. Economists are armed and dangerous: "Watch out for our invisible hands."
2. Economists can supply it on demand.
3. You can talk about money without every having to make any.
4. You get to say "trickle down" with a straight face.
5. Mick Jagger and Arnold Schwarzenegger both studied economics and look how they turned out.
6. When you are in the unemployment line, at least you will know why you are there.
7. If you rearrange the letters in "ECONOMICS", you get "COMIC NOSE".
8. Although ethics teaches that virtue is its own reward, in economics we get taught that reward is its own virtue.
9. When you get drunk, you can tell everyone that you are just researching the law of diminishing marginal utility.
10. When you call 1-900-LUV-ECON and get Kandi Keynes, you will have something to talk about.
I find that the third reason is especially funny to me. It turns out that I do not even talk about money as an economic researcher. Although we have written and read papers about money, interest rate, yield curve, stock return, inflation, etc., we did not know much about what's going on in the money market, as evidenced by the financial crisis prevailing over the world.
Indeed that we are researching into different blocks of the complicated economic world, and no one is able to link one senario with all others. To me, the quantitative methods are more interesting and I understand that there are so many difficulties to apply them in empirical work. So, to stay safe in the academic world is my dominant strategy. We economist are not sure that if we could really understand the economics. This is true for all branches of scientific research. It's a phylosophical question to answer. The world may be known to us, yet may be not. Then what should we do is really a more basic question relating to the source of the world and our human beings. The question is never fully answered and answeres are accepted highly on a religious basis.
Yet, I do believe the world should be known to us and we are right in the process, although it might take us forever to reach the knowledgable state of mind. We march on as we believe that we are in the right direction.
http://netec.mcc.ac.uk/JokEc.html
TOP 10 REASONS TO STUDY ECONOMICS
1. Economists are armed and dangerous: "Watch out for our invisible hands."
2. Economists can supply it on demand.
3. You can talk about money without every having to make any.
4. You get to say "trickle down" with a straight face.
5. Mick Jagger and Arnold Schwarzenegger both studied economics and look how they turned out.
6. When you are in the unemployment line, at least you will know why you are there.
7. If you rearrange the letters in "ECONOMICS", you get "COMIC NOSE".
8. Although ethics teaches that virtue is its own reward, in economics we get taught that reward is its own virtue.
9. When you get drunk, you can tell everyone that you are just researching the law of diminishing marginal utility.
10. When you call 1-900-LUV-ECON and get Kandi Keynes, you will have something to talk about.
I find that the third reason is especially funny to me. It turns out that I do not even talk about money as an economic researcher. Although we have written and read papers about money, interest rate, yield curve, stock return, inflation, etc., we did not know much about what's going on in the money market, as evidenced by the financial crisis prevailing over the world.
Indeed that we are researching into different blocks of the complicated economic world, and no one is able to link one senario with all others. To me, the quantitative methods are more interesting and I understand that there are so many difficulties to apply them in empirical work. So, to stay safe in the academic world is my dominant strategy. We economist are not sure that if we could really understand the economics. This is true for all branches of scientific research. It's a phylosophical question to answer. The world may be known to us, yet may be not. Then what should we do is really a more basic question relating to the source of the world and our human beings. The question is never fully answered and answeres are accepted highly on a religious basis.
Yet, I do believe the world should be known to us and we are right in the process, although it might take us forever to reach the knowledgable state of mind. We march on as we believe that we are in the right direction.
Monday, February 23, 2009
The source of Joy
It is always a wonderful experience to open THE ANALECTS to get some quaint but fresh understanding of life.
In chapter one, the Master said:" Is it not a pleasure, having learned something, to try it out at due intervals? Is it not a joy to have friends come from afar? Is it not gentlemanly not to take offence when others fail to appreciate your abilities?"
I was reading this when I was in Peking International Airport back to Sep 4, 2007. That was the first time that I have the chance to take a plane to come to America, leaving my parents, sister and brother at the check-in gate. I still remember the strong feelings I had when I passed the entrance and sit alone on a chair, waiting for my plan to take me to my bright future. I decided to read the book to keep me away from missing my family.
It is indeed a pleasure to try what I have learned, at due intervals. This is just what I have been feeling when I was in Wuhan University. Back to 2003, it was the time that I first get to know economics at Instute of Advanced Study (IAS). At that time, many courses at IAS were taught by graduate students. It was and still is my dream to teach thus I was passioned to be one of those graduate students. I started to teach Econometrics in Sep 2005, although I got into this area for only about 16 months. I was indeed lucky at that time. It is still very clear to me that I was preparing for my first lecture in the libary. I wrote my notes and then practice them, since it was the first time that I started to teach economics. Also, it was the first time that I taught Econometrics, using a (an excellent) book written in English. Though I have known all the materials well and even had some advanced training in the subject, I felt it was good to think everything over and over again, to gain a better intuition and understanding. It was then exciting to practice what I have learned for the lectures I have the chance to give. It was a wonderful memory. Since I started everything from the beginning, and every point came later had some source of what I have presented earlier. I present preliminaries, ask questions, prompt the stuents to think, and offer intuition behind the stories. My understanding in Econometrics has been greatly enhanced, my intuition is getting better and my pleasure in the area is exploding, reaching others too.
It was through my practice of what I have learned that I had the chance to share with others the valuable journey in Econometrics. Although I had hard times to learn, to practice and to make it perfect, it is through the experience of sharing that I realized the value of life and find the source of pleasure.
In chapter one, the Master said:" Is it not a pleasure, having learned something, to try it out at due intervals? Is it not a joy to have friends come from afar? Is it not gentlemanly not to take offence when others fail to appreciate your abilities?"
I was reading this when I was in Peking International Airport back to Sep 4, 2007. That was the first time that I have the chance to take a plane to come to America, leaving my parents, sister and brother at the check-in gate. I still remember the strong feelings I had when I passed the entrance and sit alone on a chair, waiting for my plan to take me to my bright future. I decided to read the book to keep me away from missing my family.
It is indeed a pleasure to try what I have learned, at due intervals. This is just what I have been feeling when I was in Wuhan University. Back to 2003, it was the time that I first get to know economics at Instute of Advanced Study (IAS). At that time, many courses at IAS were taught by graduate students. It was and still is my dream to teach thus I was passioned to be one of those graduate students. I started to teach Econometrics in Sep 2005, although I got into this area for only about 16 months. I was indeed lucky at that time. It is still very clear to me that I was preparing for my first lecture in the libary. I wrote my notes and then practice them, since it was the first time that I started to teach economics. Also, it was the first time that I taught Econometrics, using a (an excellent) book written in English. Though I have known all the materials well and even had some advanced training in the subject, I felt it was good to think everything over and over again, to gain a better intuition and understanding. It was then exciting to practice what I have learned for the lectures I have the chance to give. It was a wonderful memory. Since I started everything from the beginning, and every point came later had some source of what I have presented earlier. I present preliminaries, ask questions, prompt the stuents to think, and offer intuition behind the stories. My understanding in Econometrics has been greatly enhanced, my intuition is getting better and my pleasure in the area is exploding, reaching others too.
It was through my practice of what I have learned that I had the chance to share with others the valuable journey in Econometrics. Although I had hard times to learn, to practice and to make it perfect, it is through the experience of sharing that I realized the value of life and find the source of pleasure.
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