Speaking about the road I'm traveling right now, it would be interesting to know if there's any trend on the subfields in economics chosen by PhD students for their dissertation. Well, one study finds that there is and the factor that is influencing this trend is also the trends in papers being published among the top-notched research journals.
Sheng Guo (Florida International University) and Jungmin Lee (Sogang University) conducted an analysis of recent trends on the subfields of study that doctoral students in economics choose for their dissertation between 1991 and 2007:
"[W]e find that the trends in the subfields of study of doctoral dissertations follow those of articles published at five major general-interest journals (American Economic Review, Quarterly Journal of Economics, Journal of Political Economy, Review of Economic Studies, and Review of Economics and Statistics)... Our findings show that the subfield trends in dissertations are in accordance with the research trends in journal articles. The relationships hold strong even after we control for the job openings for the various subfields."
Guo and Lee used some simple regression methods to arrive at their conclusion. They emphasized, however, that they are not claiming any causality here. The beauty of the results for them is that they may lead to some sense of what is really going on. I for one would not be surprised if this was really the case. If I need any suggestions for a dissertation topic, the journals would be among the first that I will look at. The journals are a great source of learning what are the frontiers of economics that you can try to help contribute. Things you learn in the university are not enough to know that. Professors can only tell you as much as his fields of interest is.
With regards to the subfields with which the co-movements were more pronounced:
"In particular, we find strong relationships between the dissertation topics and the published article topics in the subfields of Microeconomics; Health, Education and Welfare; and, Economic Development and Growth. It is interesting to note that each of these subfields have undergone substantial changes during the last twenty years."
So it would be interesting to see if there are new trends among the top journals with regards to the topic or subfields being published. I could certainly use a topic or two to start thinking about my own dissertation.
By the way, Guo and Lee's paper is also useful for one of their tables. Appendix Table 1 shows the annual average of economics PhD degrees granted from 1991 to 2007. Here are some universities included in the list:
Harvard University (32.9)
University of California, Berkeley (29.8)
University of Illinois (28.8)
University of Chicago (28.2)
Stanford University (25.9)
Massachusetts Institute of Technology (25.5)
University of Wisconsin (22.5)
Indiana University (9.8)
University of Missouri (8.2)
University of Massachusetts (7.7)
April 19, 2011
April 1, 2011
Forecast Error Variance Decomposition in STATA
A very related concept to impulse response functions (IRF) is forecast error variance (FEV) and forecast error variance decomposition (FEVD). To understand these two terms, let's go through each word per word.
Let Γt denote an information set containing yt, as well as earlier values of y. The forecast of yt+1 made at time t is Ε[yt+1|Γt]. This is called a one-step-ahead forecast. Then, the forecast error is the difference between what is the forecasted value, and what the value turned out to be eventually:
εt+1 = yt+1 - Ε[yt+1|Γt]
Generally speaking, and if we consider an autoregression (AR) process, the k-step-ahead forecast error is:
where Φi is, if you remember from a previous post, a matrix that contains the effects of a one-unit increase in innovation on the value of the y variable.
We have to treat positive and negative forecast errors symmetrically, so we square them. The result is none other than the FEV:
To illustrate, let's go back to the example we used in our impulse response analysis. The resulting IRF's of up to 3 periods ahead were:
If we look only at yt up to 3 periods ahead, the FEV's are:
If you notice, since we're only looking at yt, calculating the FEV is just adding up the square of the elements of the first rows of the matrices (the first rows correspond to yt for each period t). Just remember, as we move further from one time period, the sum is cumulative--we add the FEV in period t as well as all other previous periods.
Now, as the FEV corresponds to effects on yt from all sources of impluse shocks, FEVD basically separates FEV into components attributed to each of these sources. In our example, since we have a bivariate VAR system, impulse shocks will come from two sources, (ety,etx):
Of course, it is much easier to understand FEVD if we express them in ratios. So, for example, the contribution of x's structural innovation to the FEV of y in t = 1 is 3.75 ÷ (6.25 + 3.75) = 0.375 or 37.5%. The contribution of y's structural innovation to its own in t = 2 is 6.5 ÷ (6.5 + 3.75) = 0.63414 or 63.414%.
Much like the IRF, FEV is easy to implement in STATA. Just use the IRF TABLE command with the FEVD option. So if we use the real GDP and real oil price data we had before, the commands and results are as follows:
Again, the NOCI option is there to supress reporting of the confidence intervals. So, similar to the IRF table results, you use the footnotes as a guide to identify which variables are the impulse sources and which variables are the affected ones. In this bivariate system, it should be that for each row (which corresponds to time periods), columns (1) and (3) should add up to 1 and columns (2) and (4) should add up to 1 as well.
Let Γt denote an information set containing yt, as well as earlier values of y. The forecast of yt+1 made at time t is Ε[yt+1|Γt]. This is called a one-step-ahead forecast. Then, the forecast error is the difference between what is the forecasted value, and what the value turned out to be eventually:
εt+1 = yt+1 - Ε[yt+1|Γt]
Generally speaking, and if we consider an autoregression (AR) process, the k-step-ahead forecast error is:
where Φi is, if you remember from a previous post, a matrix that contains the effects of a one-unit increase in innovation on the value of the y variable.
We have to treat positive and negative forecast errors symmetrically, so we square them. The result is none other than the FEV:
To illustrate, let's go back to the example we used in our impulse response analysis. The resulting IRF's of up to 3 periods ahead were:
If we look only at yt up to 3 periods ahead, the FEV's are:
If you notice, since we're only looking at yt, calculating the FEV is just adding up the square of the elements of the first rows of the matrices (the first rows correspond to yt for each period t). Just remember, as we move further from one time period, the sum is cumulative--we add the FEV in period t as well as all other previous periods.
Now, as the FEV corresponds to effects on yt from all sources of impluse shocks, FEVD basically separates FEV into components attributed to each of these sources. In our example, since we have a bivariate VAR system, impulse shocks will come from two sources, (ety,etx):
Of course, it is much easier to understand FEVD if we express them in ratios. So, for example, the contribution of x's structural innovation to the FEV of y in t = 1 is 3.75 ÷ (6.25 + 3.75) = 0.375 or 37.5%. The contribution of y's structural innovation to its own in t = 2 is 6.5 ÷ (6.5 + 3.75) = 0.63414 or 63.414%.
Much like the IRF, FEV is easy to implement in STATA. Just use the IRF TABLE command with the FEVD option. So if we use the real GDP and real oil price data we had before, the commands and results are as follows:
Again, the NOCI option is there to supress reporting of the confidence intervals. So, similar to the IRF table results, you use the footnotes as a guide to identify which variables are the impulse sources and which variables are the affected ones. In this bivariate system, it should be that for each row (which corresponds to time periods), columns (1) and (3) should add up to 1 and columns (2) and (4) should add up to 1 as well.
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