Statistics is a statement about the possible correlation between two facts and not a statement of causation or that one fact absolutely causes another. The relationship between two facts may vary in degree based on changing circumstances and the correlation may also be a function of time so that one fact may only significantly affect another many years after its impact.
The correlation between debt and economic growth intuitively and statistically seems to be valid. The more a nation is burdened by debt the less real growth it is capable of.
However, there are many other variables which affect growth such as an increase in the efficiency of infrastructure which promotes growth in the long duration.
Investment in useful technological education skills can also promote eventual greater productivity and economic growth in the long duration.
Decrease in taxes frees up more money to be invested in the economy more efficiently in the long duration because automatic decreases can increase the national debt which does not stimulate growth.
Laws which handicap the growth of small businesses which increase the net income of workers and expand GDP reverse economic growth. These same laws which promote the growth of big business reduces employment of workers thus decreasing net income and resulting in a lower GDP.
A growth in the size of government also decreases a growth in the GDP because government workers are not as productive as private business workers and make the economic growth pie smaller since it is a parasite on the economy.
Business cycles also affect economic growth and during times of recession or depression growth is either slowed down considerably or stopped or it is even reversed in a depression.
An increase in the rate of natural resource usage also increases GDP growth since more goods are produced and sold.
Cheaper energy also stimulates economic growth because more goods are produced more cheaply increasing the net amount of goods in circulation.
Free trade can decrease economic growth because of worldwide competition which causes many workers to go on unemployment or welfare and add to the burden of national debt.
Summarizing the 10 most important intuitive causes of national economic growth they are- laws which promote small businesses, less debt, decrease in government size, decrease in taxes, increase in the use of natural resources, cheaper energy, more efficient infrastructure, more useful technological education, business cycle high, and Fed and bank money investment in the economy from a lending high in the business cycle which unfortunately mostly causes inflation if it is not an investment in small businesses.
No amount of statistical data will verify the correlation of all these 10 variables to economic growth because these variables change and depend on the given point in time that you are talking about which is impossible to correlate accurately or statistically. Statistics just give you rather vague ballpark approximations and they are just a little better than smart intuitive thinking in economics which is still largely intuitive art and not a science which it will never be because there are too many impacting variables.
***Realistically it is debatable whether economic growth is desirable in a finite planet with finite natural resources, especially wilderness, and an ever increasing human population which is threatening the very survival of this precious endangered planet. The real emphasis should be on no inflation very efficient sustainable living and not trying to crazily try and grow indefinitely.
The true goal of all nations should be to function more efficiently with more sustainable living, no inflation or a constant value in money, balancing the budget, and conserving and even expanding wilderness throughout the world.
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