[RD] Daily Graphs and Charts
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% of atheists who feel qualified to tell Christians what Christian values are.
According to this I don't exist. If that's the case, then who was keyboard?
Monsterzuma
the sly one
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http://economistsview.typepad.com/economistsview/2012/02/potential-output-measuring-the-gap.html
The third of these makes the least sense to me.
Mise
isle of lucy
I don't understand why you would have a "quadratic exponential" increase anyway. When you fit a trend line to a graph, you're not just looking for the prettiest fit. You're fitting a model to the data, calibrating the parameters of the model to best fit the data. I don't understand why the author thinks that the economy's size would be described by eb0 + b1*t +b2*t2. What does the extra term actually represent in his model? At least the last one has a model that it's trying to fit, with a hypothesis backing it up. The "quadratic" fit doesn't make sense IMO. I mean, why stop at quadratic? Why not add a t3 term? We all know that the more terms you add to the polynomial, the better the fit (this is trivially true), so why not add a 6 more terms, and get a really, really awesome fit 
And anyway, the point of being "below trend" isn't that we're below where a model would predict we should be, based on certain parameters. Because, as I kind of alluded to, you can create a model that exactly fits the data; you could even come up with a theory that describes the economy as exactly as theories that describe planetary motion. But in that case, all the model will say is that the economy is exactly where you would expect it to be, based on the model.... It wouldn't tell you anything about whether we were "above trend" or "below trend" at all, because the trend exactly predicts (and subsequently fits) the data. Not very enlightening, is it!
That's why I think a linear fit of log-GDP makes the most sense when discussing whether and how far we're "below trend". It's intuitively compelling, doesn't overfit the data, and depends on time and a single parameter that is supposed to encapsulate the "natural" growth rate of a country. If growth is lower than its "natural" rate, then you have to say that something is wrong. If you try to predict and model how the "natural" rate changes over time (by adding terms and parameters or changing the curve's form), then you can't really say we're "below trend" on that basis; you have to look at the model itself, and how the parameters have changed over time instead.
And anyway, the point of being "below trend" isn't that we're below where a model would predict we should be, based on certain parameters. Because, as I kind of alluded to, you can create a model that exactly fits the data; you could even come up with a theory that describes the economy as exactly as theories that describe planetary motion. But in that case, all the model will say is that the economy is exactly where you would expect it to be, based on the model.... It wouldn't tell you anything about whether we were "above trend" or "below trend" at all, because the trend exactly predicts (and subsequently fits) the data. Not very enlightening, is it!
That's why I think a linear fit of log-GDP makes the most sense when discussing whether and how far we're "below trend". It's intuitively compelling, doesn't overfit the data, and depends on time and a single parameter that is supposed to encapsulate the "natural" growth rate of a country. If growth is lower than its "natural" rate, then you have to say that something is wrong. If you try to predict and model how the "natural" rate changes over time (by adding terms and parameters or changing the curve's form), then you can't really say we're "below trend" on that basis; you have to look at the model itself, and how the parameters have changed over time instead.
Integral
Can't you hear it?
Great pictures.
What about HP filtering makes little sense to you? I could try to explain.
What about HP filtering makes little sense to you? I could try to explain.
Monsterzuma
the sly one
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Is it so much different from a moving average with a relatively small subset size (I hope this is the right word; I mean the stretch over which the average is taken for each point on the graph)? My objection is mainly just that when "subset size" is very small, the graph is only an indication of a very short term trend in the data, so it doesn't say very much. Or as Mise put it, it risks "overfitting" the model to the data.
the way I see it, the challenge is to keep the model as simple as possible while still getting a reasonably good fit. adding a term to polynomial the first time improves the fit considerably, whereas the effect of adding more beyond that is less great. so I could see an argument that the quadratic fit displayed is an ideal compromise between simplicity and good fitting.
Mise said:
the way I see it, the challenge is to keep the model as simple as possible while still getting a reasonably good fit. adding a term to polynomial the first time improves the fit considerably, whereas the effect of adding more beyond that is less great. so I could see an argument that the quadratic fit displayed is an ideal compromise between simplicity and good fitting.
Mise
isle of lucy
Well, one would have to come up with a real-world interpretation for what the extra t^2 term means. Same as when you decide whether your curve should go through zero - is there a good reason for it to go through zero? And if not, what's the physical interpretation of the constant? Personally I can't think of a good interpretation for what the t^2 might represent... I'm not sure why the GDP would be described by ~exp(t+t^2) and not ~exp(t).
Monsterzuma
the sly one
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what seems to differentiate the quadratic graph from the linear one is the gradual tapering off of the speed of growth over time, so I think there is a very simple real world interpretation: limits to growth issues.
Mise
isle of lucy
Okay, but it looks like the t^2 term has a negative coefficient (since it looks curved downwards), which means that, at some point, the curve will start going down... I.e. GDP reaches the point of inflection, explicitly falls over the long term, and eventually hits zero again... which doesn't make sense to me!
Integral
Can't you hear it?
The quadratic trend will have an implicit max point, and there's little theoretical justification for one. Even if there were (limits to growth, whatever) then surely the max would be time-varying, which is unappealing from an empirical point of view.
HP filtering isn't great, but it has the advantage of simplicity. There is one free parameter, the smoothing factor, and the literature has converged on particular values of the smoothing factor for annual, quarterly, and monthly data. I'm not saying those values are a priori any good, but at least there's consistency.
An alternative is to use band-pass filters, in which you can capture fluctuations at a per-specified frequency, typically 6 to 32 quarters. The results of a BP filter are qualitatively and quantitatively similar to an HP filter with the usual smoothing factors.
A third way to get time-varying filters is to use some theory, like the Permanent Income Hypothesis, to tease out cycle from trend. These are neat procedures, but somewhat new and not widely used.
If you want to talk theory, a Solow model with transitory productivity shocks will generate data that looks an awful lot like the postwar US experience, and the underlying model implies a linear model for log(GDP). I know exactly what log GDP = a + 2.2*t means: it implies that the average rate of productivity advancement is 2.2%. I don't know how to so cleanly map a quadratic-exponential trend to the usual theories.
HP filtering isn't great, but it has the advantage of simplicity. There is one free parameter, the smoothing factor, and the literature has converged on particular values of the smoothing factor for annual, quarterly, and monthly data. I'm not saying those values are a priori any good, but at least there's consistency.
An alternative is to use band-pass filters, in which you can capture fluctuations at a per-specified frequency, typically 6 to 32 quarters. The results of a BP filter are qualitatively and quantitatively similar to an HP filter with the usual smoothing factors.
A third way to get time-varying filters is to use some theory, like the Permanent Income Hypothesis, to tease out cycle from trend. These are neat procedures, but somewhat new and not widely used.
If you want to talk theory, a Solow model with transitory productivity shocks will generate data that looks an awful lot like the postwar US experience, and the underlying model implies a linear model for log(GDP). I know exactly what log GDP = a + 2.2*t means: it implies that the average rate of productivity advancement is 2.2%. I don't know how to so cleanly map a quadratic-exponential trend to the usual theories.
Winner
Diverse in Unity
Not that I want to discourage you, but I'd like to remind you that not all of us are economists. I don't mind discussion, but let's keep it to a level most college-educated people can understand, okay? 
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Speaking of The Economist:
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Speaking of The Economist:
Mise
isle of lucy
Just "lots of cows" I guess. Size of the dairy industry? Maybe France and Italy have better things to do with their farmland (wine?) than let cows graze.
Oh and I'd like to remind you all that I'm not an economist
Oh and I'd like to remind you all that I'm not an economist
Traitorfish
The Tighnahulish Kid
Agricultural subsidies might have something to do with it. I'm told that the British dairy sector is quite heavily subsidised.
Mise
isle of lucy
The predominance of a small number of very large supermarkets keeps prices down as well. Tesco for example are known to drive farm gate prices to barely above cost.
Murky
Deity
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How did they obtain the data? A survey of people's daily dietary intake?
Mise
isle of lucy
WTH... The RDA for adults is 2000 for women and 2500 for men... How the hell are people eating nearly double that??
It's good that getting enough calories isn't the big nutritional problem is most parts of the world though.
EDIT: A guy in the comments says this: "These numbers are incorrect. These are the numbers for AVAILABLE kcal per person, not actual intake (source: Euromonitor)"
EDIT2: Graph looks basically the same as this one: http://www.fao.org/fileadmin/templates/ess/ess_test_folder/Publications/yearbook_2010/maps/map07.pdf
It's good that getting enough calories isn't the big nutritional problem is most parts of the world though.
EDIT: A guy in the comments says this: "These numbers are incorrect. These are the numbers for AVAILABLE kcal per person, not actual intake (source: Euromonitor)"
EDIT2: Graph looks basically the same as this one: http://www.fao.org/fileadmin/templates/ess/ess_test_folder/Publications/yearbook_2010/maps/map07.pdf
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