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Sabtu, 13 April 2013

CONVERGENCE ANALYSIS (Completed by An Example)


Hei friends nice to meet you again. How are you today? Hope that you gonna be okay, right?
Now, I want to declare you an analysis taht must be so interesting to use in your research.. Errr.. what’s that? That’s convergence analysis.

In fact, I use these analysis in my essay in field Economics and Statistics and I think that it’s not a problem to tell you about this analysis..  Okay, let’s go ,, Have a nice reading..
This, convergence theory was begun from Solow Swan Model. What’s that? So, Solow Swan tried to explain that the welfare of developed and developing countries will be convergent someday. Yeah, its growth will meet in one spot. Futhermore, this convergence theory also explains the situation of “catching up effect”.

Just wanna give you a simple ilustration like this; someday the developing countries will succeed to catch up or pursue the developed countries with asumption that the developed countries will suffered a steady state condition. Then, their national income (developed countries) won’t increase anymore because the increase of investment won’t increase income.

Hmmm,, when the developed countries are in steady state condition, while the developing countries; their investment increase will influence their income. Automatically, the developing countries economy will be able to chase and achieve the developed ones. Yeah, that is the flow of thought what is called “catching up effect”. Still puzzled? Just read again and try to brood hahaha..

Identification of whether the convergence will happen or not; owing to Barro and Sala-i-Martin text books, this convergence can be divided by  sigma/gross convergence and beta/unconditional beta convergence). Okay, I will try to explain that.. Just keep calm hehe.. So, this gross convergence is used to observe the dispersion. Owing to its focus (dispersion), we can do this analysis just by observing the movement or pattern of your variables’ standard deviation.

I will show you the example from my essay.. In this essay, I have the economic growth as its dependent variable and I also use independent variables such as economic openness, exchange rate, interest rate, inflation, the unemployment rate and export value.

Then, I will generate the Solow Swan flow thought of convergence to Indonesian level. And what the result? I succeed to identify whether the low economic growth provinces (low GDP) can catch up the high economic growth ones. For information, the time period of my research is from 2006(1st Q) to 2011 (4th Q).

Notice this is the fluctuation of economic growth (independent variable) standar deviation.

Keep attention for the dispersion. . It’s so fluctuative.. Okay, this information merely inform that the inter provinces economic growth is unstable yet. But, look, even its fluctuative movement, we can see that the pattern of standard deviation tends to decrease/diminish.. Can you get this phenomena?

Okay, this decreasing pattern describes that there is still a chance to achieve  the imbalance decrease. So, in the other words, we say that there is still a chance for being convergent; the low economic growth provinces (low GDP) will have a chance to chase the high economic growth ones. Can this explanation help you? I hope it can and let’s go on.

Now, we step to the next analysis, it’s beta convergence. The calculation will be based on Barro and Sala-i-Martin text books. The way to conduct, just regress the economic growth in the initial research time period or the former period (independent variable) with the economic growth in the research time period (dependent variable).

The first way we can do that we have to know what’s called “Absolute Convergence” then we can test the conditional convergence. So, this is the model spesification for absolute convergence:

a and b is the intercept and slope with 0 < b < 1. The higher value for b, the higher it tends to show convergence. (Barro and Martin, 2004).

In my essay, to analyze the absolute convergence, I regress the ecocomic growth of 33 provinces (all provinces in Indonesia until 2011) at –t quarter as the dependent variable and the former economic growth of 33 provinces (distributed lag) as the independent variable.

This is the the result from Eviews (aproximation by common effect panel regression)
From this model we can explain that: The coefficient of economic growth per province in Indonesia in the former quarter is 0,2362 and it means that the increase/decrease for one percent of former economic growth (33 provinces in Indonesia ) will increase/decrease the economic growth in Indonesia for 0,2362%.

So lucky we are,, the slope of independent variables (former economic growth) statistically is negative to effect the dependent one with p-value is 0,0000 or less than Alpha 0,05.
The R square value is 0,059 that means 5,9 percent variation of economic growth increase/decrease  can be explained by the former economic growth. It’s so small. Is not a problem??

Okay in this case, the small R square can be permitted because the objective of my research is not to make an estimation that really requires a high value of R square but I just want to make an identification whether the convergence will happen or not) based on the regression coefficient.  Heemm, the most important thing to understand that the independent variable has significant statistically.

A liitle bit more, we go to the way of how we can see the speed of convergence with given formula:

b can be gained from the coefficient of independent variable and T is time period of research.

Wow, we can get the speed of convergence, yeah it is 0,008835. This result indicates that the provincial economic growth, mainly for the provinces with low economic growth  must grow minimally 0,8 percent per period (in this case the period is quarter) for decreasing the dispersion of economic growth.
Finally, we can find what called “a half time”.. This term means the time that we need to cover a half of the imbalance of economic growth.
From Barro and Martin formula in their book “Economic Growth”, we use the formula:

What does it sound? Here it is : “to cover a half of economic growth imbalance, needed 78,4547 time period (quarter) that equals to 19,6137 years”. So, by overall, to cover the whole of imbalance of economic growth, it’s needed for about 39,2273 years in terms of condition, the provincial economic growth (mainly for provinces of which the economic growth is low) must grow at leasy 0,8 percent per quarter.
Okay, that’s what I can tell you about the convergence analysis hahaha.. Have a nice time.. Hope that this post can be useful for you.. Nice greeting..

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