Total Factor Productivity in AK Models

patriks

Heya guys,

Just another quick question: In a basic AK model (Y = AKαL1-α), A is total factor productivity. This total factor productivity engenders the technological level of the economy. If this is true, it follows that the state of technology is not accounted for in factor inputs.
The question is, if technology isn't accounted for in inputs (L and K), is the state of human capital (namely, education) accounted for in inputs (most likely in L) or would it, too, be considered as part of A (total factor productivity)?

Thanks in advance!;)

Yes, there are some models which are

Y = AK^aL^bE^c

where E is human capital, however unless it is expressly stated assume that human capital levels are represented by A.
Think of A more like a measure of efficiency rather then technology, L as people and K as machines. Throwing more machines at a problem won't (in the long run, assuming decreasing returns to scale) lead to sustainable growth however putting in a series of better machines over time will lead to that. The 'better' qualification is the A factor. Human education is the corresponding case for the L.

patriks

Thanks a million! That's exactly the reply I was looking for.

I'm not sure what level you are at, but look at www.karlwhelan.com - teaching - TCD 4010 - Solow Model Notes

That gives a really good intro into all of this.

patriks

Thanks again. Those resources are quite helpful.

On a different note, does anybody have any idea where I could get my hands on a programme that would enable me to derive qualitative graphical illustrations?
I'm familiar with Excel, but this is purely to illustrate a concept rather than graphically quantify a particular situation.

Also, anybody have any suggestions for variables in a regression which is concerned with technological change?
I've gathered a number of statistics, but I'm not quite sure which would be appropriate for a regression. I've got statistics on technological infrastructure, but, really, they're probably only applicable as dummy variables.
Also, I'm not sure what β1 would be appropriate (i.e. the level of technology in place when another variable is equal to 0).

Sorry about all the questions.:o

Flamed Diving

patriks wrote: »

Thanks again. Those resources are quite helpful.

On a different note, does anybody have any idea where I could get my hands on a programme that would enable me to derive qualitative graphical illustrations?
I'm familiar with Excel, but this is purely to illustrate a concept rather than graphically quantify a particular situation.

Also, anybody have any suggestions for variables in a regression which is concerned with technological change?
I've gathered a number of statistics, but I'm not quite sure which would be appropriate for a regression. I've got statistics on technological infrastructure, but, really, they're probably only applicable as dummy variables.
Also, I'm not sure what β1 would be appropriate (i.e. the level of technology in place when another variable is equal to 0).

Sorry about all the questions.:o

Firstly, what do you need to graphically represent? Many other qualitative social science fields like to use SPSS, so that might be suitable.

Secondly, you should base your decision to include variables on available literature and theory. So what does this say? The last thing you should do is throw variables in for the hell of it. Remember, when you write up your paper, you need to justify why you did what you did. This is much easier to do when you have published work backing your case.

Thirdly, why are your variables 'probably' only applicable as dummys?

Finally, I'm not sure what you mean by 'appropriate' beta1.

patriks

Flamed Diving wrote: »

Firstly, what do you need to graphically represent? Many other qualitative social science fields like to use SPSS, so that might be suitable.

Well, basically, I'd like to insert a Solow-Swan model with technological progress. It's basically just to demonstrate that economies with a lower level of capital per capita grow at faster rates than economies with a higher rate of capital per capita. To show this, all one needs is the [s.f(k)/k] curve and the [x + n + δ] line.

Flamed Diving wrote: »

Secondly, you should base your decision to include variables on available literature and theory. So what does this say? The last thing you should do is throw variables in for the hell of it. Remember, when you write up your paper, you need to justify why you did what you did. This is much easier to do when you have published work backing your case.

As above, the empirical data suggests that less technologically advanced countries converge due to faster growth rates. It also reinforces the theory of developing countries as imitators not innovators, given by the GERD and BERD statistics.

Flamed Diving wrote: »

Thirdly, why are your variables 'probably' only applicable as dummys?

You see, I've got a lot of data on technological improvement, but it's predominantly concerned with ICT statistics and transport infrastructure, figures like: internet access and broadband penetration as percentages of the nation, goods carried by road and rail in millions of tonnes per kilometer, etc.
I figured that if something like internet access were greater than, say 60%, in a regression, it would manifest as 1; however, if it were less than 60%, it would manifest as 0. Perhaps I'm way off the mark here.
I've also got other statistics like GERD, BERD, GDP per capita over time, etc.

Flamed Diving wrote: »

Finally, I'm not sure what you mean by 'appropriate' beta1.

Well, technically, isn't beta1 representative of the level of the dependent variable (y) when the independent variable (x) is equal to 0?
I'm not sure what this would look like in a technological regression.

Flamed Diving

patriks wrote: »

Well, basically, I'd like to insert a Solow-Swan model with technological progress. It's basically just to demonstrate that economies with a lower level of capital per capita grow at faster rates than economies with a higher rate of capital per capita. To show this, all one needs is the [s.f(k)/k] curve and the [x + n + δ] line.

The theory suggests this, but the empirical data doesn't hold this model up, I'm afraid. If anything, both sets of countries are diverging. The reasons are, well, not really well understood. But institutions would appear to be key. Of course, demonstrating that low-capital countries do not always converge is just as useful a result. If you wish to demonstrate high-capital countries reaching lower levels in capital investment growth, just collect such data from Penn World Tables, convert it to 'mean deviation' format and stick it in a line graph. You will witness the deviations get smaller, over time, which is an example of 'steady-state' being reached.

Anyway, you mentioned qualitative methods. This is quantitative, you know?

patriks wrote: »

As above, the empirical data suggests that less technologically advanced countries converge due to faster growth rates. It also reinforces the theory of developing countries as imitators not innovators, given by the GERD and BERD statistics.

No, I'm afraid the data shows that low-capital countries lag far behind, in growth terms, and are regressing, in many cases. What studies have you been reading?

patriks wrote: »

You see, I've got a lot of data on technological improvement, but it's predominantly concerned with ICT statistics and transport infrastructure, figures like: internet access and broadband penetration as percentages of the nation, goods carried by road and rail in millions of tonnes per kilometer, etc.
I figured that if something like internet access were greater than, say 60%, in a regression, it would manifest as 1; however, if it were less than 60%, it would manifest as 0. Perhaps I'm way off the mark here.
I've also got other statistics like GERD, BERD, GDP per capita over time, etc.

You are trying to guess or impose the beta here? If so, this defeats the purpose, no? Why not just focus on one aspect of technology? It will make things a lot easier. The rest will just end up in the residual anyway, don't worry about it.

patriks wrote: »

Well, technically, isn't beta1 representative of the level of the dependent variable (y) when the independent variable (x) is equal to 0?
I'm not sure what this would look like in a technological regression.

Ok, if you have a single dummy variable regression:

Y = B0 + B1X + e

When X = 1, then Y = B0 + B1 + e

B0 is the deterministic unobserved part of Y and (e) is the stochastic unobserved part of Y.

When X = 0, then Y = B0 + e

Therefore, B0 will contain the deterministic element of your model that was not observed. That's what X = 0 is.

patriks

Flamed Diving wrote: »

The theory suggests this, but the empirical data doesn't hold this model up, I'm afraid. If anything, both sets of countries are diverging. The reasons are, well, not really well understood. But institutions would appear to be key. Of course, demonstrating that low-capital countries do not always converge is just as useful a result. If you wish to demonstrate high-capital countries reaching lower levels in capital investment growth, just collect such data from Penn World Tables, convert it to 'mean deviation' format and stick it in a line graph. You will witness the deviations get smaller, over time, which is an example of 'steady-state' being reached.

To be totally honest, my study is based on two sets of economies in the E.U.: developed economies (France, Germany, U.K.) and underdeveloped economies (Lithuania, Latvia, Estonia). I've looked at technological infrastructure statistics for both tiers, and they appear to be rising in the underdeveloped areas, but stagnating in the developed areas. On top of this, I've looked at figures like GDP per capita; again, they appear to be rising faster in underdeveloped economies, but stagnating - and in some cases decreasing - in developed economies. I had presumed that this would be indicative of convergence, but, now, according to what you've been saying, I guess that this is inaccurate.

Flamed Diving wrote: »

Anyway, you mentioned qualitative methods. This is quantitative, you know?

Well, yes, the calculation is quantitative, but I meant that the graphical representation would be qualitative (i.e. illustrate the economic theory).

Flamed Diving

Try get this paper, it might help you get an idea of how you should approach presenting your work, and it is fairly easy to follow:

http://ideas.repec.org/a/aea/aecrev/v76y1986i5p1072-85.html

Beware, though. Note that he does not include many poor nations and he was caught out for excluding countries like Portugal and Spain (IIRC) because they would have depressed his estimates. In addition, he puts too much weight on the importance of R-squared, so keep that in mind. Despite all that, it is a good paper to begin with.

Here is a copy:

http://abacus.bates.edu/~daschaue/baumol86.pdf

patriks

Thanks for that link. It's appreciated.

One other thing: if the empirical data suggests that economies don't converge and that, in fact, divergence is more of a reality, would I be better off changing the focus of my thesis to something like the role of technological progress in economic growth in developed countries, and lose the area on underdeveloped countries?
I mean, the theory seems pretty redundant if it's not substantiated by empiricism, right?

Flamed Diving

patriks wrote: »

Thanks for that link. It's appreciated.

One other thing: if the empirical data suggests that economies don't converge and that, in fact, divergence is more of a reality, would I be better off changing the focus of my thesis to something like the role of technological progress in economic growth in developed countries, and lose the area on underdeveloped countries?
I mean, the theory seems pretty redundant if it's not substantiated by empiricism, right?

Well the theory isn't redundant it's just wrong. But all theories are wrong, even evolution, relativity, etc. The point is whether they can help us describe reality, in spite of their flaws. The Solow-Swan model does make some accurate predictions, but it does obviously fall down, on many matters. But half an eye, is better than no eye, at all.

Anyway, I would agree with reducing your scope somewhat, on two counts. One would be to focus on industrialised nations, and second I would narrow the bundle of technology goods you are looking at. Remember that if your number of observations are low (usually the case with Macro models) then each parameter (ind variable) k that you add, increases the risk of sampling error. So if you throw a ton of technology parameters into the model, you might just do that. However, when writing your methodology be sure to mention your realisation of the limits of omitting the poorer nations.

My only worry is that by selecting the "winners" you are performing selection bias? Perhaps not so if you argue that data prevented you from using them anyway, I dunno. Try get another opinion, either here or from your supervisor.

patriks

Yeah, I will. Thanks again for all you help.

patriks

Sorry for commencing this thread again.
I just wanted to clarify something:
Even though economic convergence may not be a property replicated all over the world, wouldn't the increase in GDP per capita in developing economies (Latvia, Lithuania, Estonia) - relative to developed E.U. economies - imply that convergence has been a feature of the E.U.'s developing nations?
I mean, for example, take Ireland, surely, the Irish economy has, in recent history, exhibited convergence properties?

nesf

patriks wrote: »

Sorry for commencing this thread again.
I just wanted to clarify something:
Even though economic convergence may not be a property replicated all over the world, wouldn't the increase in GDP per capita in developing economies (Latvia, Lithuania, Estonia) - relative to developed E.U. economies - imply that convergence has been a feature of the E.U.'s developing nations?
I mean, for example, take Ireland, surely, the Irish economy has, in recent history, exhibited convergence properties?

Ireland has, as have many of the Baltic States. What's different about these countries and say Zimbabwe or Nigeria? It's an interesting question.

Time Magazine

Also it's important to note that although countries may display divergence, when you adapt for population, there is convergence. (China and India count for more than Lesotho.)

patriks

Hello again,

I've been doing some research on appropriate regressions for convergence and I chanced upon this:

1/T In yT/y0 = α0 + α1 In y0



It's supposed to "verify the existence of β-convergence"; the thing is: I'm not quite sure what it means or how to use it.
I mean, I guess T is time, y is output per capita and "In" is the natural log, but I'm not sure what the α (alpha) parameters are or how the regression would work.
If that's not clear, maybe you'd like to have a look at the paper yourself, if so, here it is (the regression model is on page 8).

Could anybody elaborate on how to use this model?

Thanks again!

Flamed Diving

patriks wrote: »

Hello again,

I've been doing some research on appropriate regressions for convergence and I chanced upon this:

1/T In yT/y0 = α0 + α1 In y0


Could anybody elaborate on how to use this model?

Thanks again!

From the paper:

This equation allows us to verify the existence of b-convergence. The explained variable is the average annual growth rate of real GDP per capita between period T and 0 while the explanatory variable is GDP per capita level in period 0. If parameter a1 is negative, b- convergence exists.

The explained variable is the term on the left.

1/T: T is the number of time periods you have e.g. 1990-1999: T = 10

yt: GDP per capita in 1999
y0: GDP per capita in 1990

Combining the terms in the manner described gives you the average annual growth rate. e.g.

yt = €10,000
y0 = €5,000

€10,000/€5,000 = 2

ln(2) = 0.69

0.69/10 = 0.069 or 6.9%, which is your average annual growth rate in this simple example.

Ok, back the right hand side. a0 is just a constant, and a1 is your coefficient. As the authors put it, if parameter a1 is negative, b- convergence exists. Remember that lny0 is the growth rate in 1990. The higher the growth rate early on, the lower the rate will be, over the next ten years, according to Solow, right?

So if it is negative, convergence is occuring. Nice little model, actually.

Time Magazine

patriks wrote: »

but I'm not sure what the α (alpha) parameters are or how the regression would work.

They're the coefficients on the variables. [latex]\alpha_0 [/latex] is the intercept and [latex]\alpha_1[/latex] is the effect of (the log of) initial GDP per capita on the average growth rate.

patriks

Flamed Diving wrote: »

Ok, back the right hand side. a0 is just a constant, and a1 is your coefficient. As the authors put it, if parameter a1 is negative, b- convergence exists.

Okay, the explained variable side is okay, but if I were to use this model, how would I apply the right-hand side?
I mean, what value would the constant (a0) and the coefficient (a1) take?
To go back to your example:

.069 = a0 + a1 In y0

Now, what values will the right-hand side take? How does one know if a1 is negative if they don't have a value for a1?
Perhaps i'm missing something pretty obvious here.

Thanks!

Time Magazine

patriks wrote: »

Okay, the explained variable side is okay, but if I were to use this model, how would I apply the right-hand side?
I mean, what value would the constant (a0) and the coefficient (a1) take?
To go back to your example:

.069 = a0 + a1 In y0

Now, what values will the right-hand side take? How does one know if a1 is negative if they don't have a value for a1?
Perhaps i'm missing something pretty obvious here.

Thanks!

You would regress the left-hand side on the right-hand side. The actual numbers chosen (assuming you regress them using the Ordinary Least Squares method) will be those that give the model the "best fit".

Flamed Diving

patriks wrote: »

Okay, the explained variable side is okay, but if I were to use this model, how would I apply the right-hand side?
I mean, what value would the constant (a0) and the coefficient (a1) take?
To go back to your example:

.069 = a0 + a1 In y0

Now, what values will the right-hand side take? How does one know if a1 is negative if they don't have a value for a1?
Perhaps i'm missing something pretty obvious here.

Thanks!

Ok, let's say you are assessing 100 countries and back to my simple example.

1. Collect GDP per capita data for 1990 and 1999.

2. Put into Excel

3. Create a column which divides 1999 by 1990

4. Create a column which takes the natural log of the previous column

5. Create a column which divides this by 10.

These are all your 'Y' observations.

6. Create another column for ln(GDP 1990)

These are your 'X' observations.

Then just run a simple OLS regression (perhaps GLS) and get your a1.

If it is negative, then GDP per cap is converging in this region.

I assume that if it is positive, it is diverging.

patriks

Oh, okay! That's perfect!
So, it's just like the general principle of the right-hand side is just like any other OLS/GLS regression.

Thanks a million, guys!

Flamed Diving

I ran a quick regression of 164 countries for 1988-2007, and got:

a1 = .0920834

I guess that translates to no convergence, across the world. Just what we find in other studies.

patriks

I know this is bordering obsessive, but I'd just like to make absolutely sure I've interpreted all the directives accurately.
Four very small, very quick questions:

Flamed Diving wrote: »

1. Collect GDP per capita data for 1990 and 1999.

1. Hypothetically, You would only need to collect the data from the beginning of the period and the end of the period under analysis; You don't need the periods in between, right?
i.e. You'd need the 1990 GDP per capita and the 1999 GDP per capita, not the GDP per capita for 1990, 1991, 1992, 1993, ..., 1999.

Flamed Diving wrote: »

5. Create a column which divides this by 10.
These are all your 'Y' observations.

2. You only put the data from this final column in as your "Y" observations (the column which has divided the values of the previous column by 10), right?
i.e. You don't put all the previous columns into the Y input section of the regression as well.

3. Now, let's say you were using data from three countries, the spreadsheet would look like this, right?

Y Observations:
Country 1: In(y1999/y1990)/10
Country 2: In(y1999/y1990)/10
Country 3: In(y1999/y1990)/10

X observations:
Country 1: In(y1990)
Country 2: In(y1990)
Country 3: In(y1990)

Then, I just run the OLS/GLS regression.

4. Hypothetically, if I had 5 years worth of GDP stats for each country, I could run the convergence regression 4 times (Year1-Year2,Year2-Year3,Year3-Year4,Year4-Year5) to get different levels of convergence/divergence, right?

Again, I'm really sorry about all the questions. You're previous post was very clear, it;s just that I haven't done much work with regression models (like you couldn't tell:o), and I just want to make absolutely sure I've fully comprehended it.

Thanks again!

Flamed Diving

patriks wrote: »

I know this is bordering obsessive, but I'd just like to make absolutely sure I've interpreted all the directives accurately.
Four very small, very quick questions:



Hypothetically, You would only need to collect the data from the beginning of the period and the end of the period under analysis; You don't need the periods in between, right?
i.e. You'd need the 1990 GDP per capita and the 1999 GDP per capita, not the GDP per capita for 1990, 1991, 1992, 1993, ..., 1999.

Correct.

patriks wrote: »

You only put the data from this final column in as your "Y" observations (the column which has divided the values of the previous column by 10), right?
i.e. You don't put all the previous columns into the Y input section of the regression as well.

Now, let's say you were using data from three countries, the spreadsheet would look like this, right?

Y Observations:
Country 1: In(y1999/y1990)/10
Country 2: In(y1999/y1990)/10
Country 3: In(y1999/y1990)/10

X observations:
Country 1: In(y1990)
Country 2: In(y1990)
Country 3: In(y1990)



Then, I just run the OLS/GLS regression.

Correct.

patriks wrote: »

Hypothetically, if I had 5 years worth of GDP stats for each country, I could run the convergence regression 4 times (Year1-Year2,Year2-Year3,Year3-Year4,Year4-Year5) to get different levels of convergence/divergence, right?

Yeah, but that's fairly pointless. You could just take year 1 and year 5, to get roughly the same result. But, you could do something like 1970-79, 1980-89, 1990-99. This regression is about intervals, so you should do it like this.

e.g. Did EU countries converge since 1973? So data for 1973 and 2007 would most likely be your data periods. More examples:

NATFA countries? Asian Free Trade Countries? OECD and lowest 20%?

Stuff like that.

patriks wrote: »

Again, I'm really sorry about all the questions. You're previous post was very clear, it;s just that I haven't done much work with regression models (like you couldn't tell:o), and I just want to make absolutely sure I've fully comprehended it.

Thanks again!

No problem.

patriks

Out of curiosity, if we take a developed nation, say France. If we ran the beta-convergence regression, wouldn't we expect to find a negative alpha1? i.e. given that beta-convergence is convergence towards a steady state, when we ran the regression, we would discover that France have converged towards their steady state.
I guess the question I'm asking is: Does steady state convergence even apply to nations already in their steady state?
I mean, we may take it for granted that developed nations are in their steady state, so we wouldn't need to run the regression, but, technically, would the negative alpha1 confirm what we already knew?

Flamed Diving

patriks wrote: »

Out of curiosity, if we take a developed nation, say France. If we ran the beta-convergence regression, wouldn't we expect to find a negative alpha1? i.e. given that beta-convergence is convergence towards a steady state, when we ran the regression, we would discover that France have converged towards their steady state.
I guess the question I'm asking is: Does steady state convergence even apply to nations already in their steady state?
I mean, we may take it for granted that developed nations are in their steady state, so we wouldn't need to run the regression, but, technically, would the negative alpha1 confirm what we already knew?

Bear in mind that you need to keep the number of observations (n) you have as high as possible. Of course, you could do this by slicing the data into decades, but this would only give you have 5-6 observations. The bare minimum you should have is 30. You could reduce the intervals to five years, giving you 10-12. No. Three years gives you twenty. Two years gives you the bare minimum. But you don't really have a range any more. Plus, you would need to run this type of model in panel data form, I think.

I don't think this model can do what you want it to, tbh. It is for studying cross-sections of several countries.

Anyway, take a bunch of developed nations and you would expect a negative alpha, if you started from an earlier spot. There may even still be convergence, due to globalisation, etc. Furthermore, if you have an expected result, you should always test your model on this, don't assume it.