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  • Reply to: How Significant is a 1 Percent Difference in Growth Under Debt?   5 years 10 months ago
    I agree with your comment that overlapping error bars generated from confidence intervals do not, in and of themselves, necessarily imply statistically insignificant differences. This is precisely why, in the postscript, I had provided the same figure with error bars generated from standard errors, of which overlap definitively indicates the absence of statistical significance. And as clarified in the postscript, there is no statistically significant difference in the 30/60 and 60/90 bins, and between the 60/90 and >90 bins, which can be formally verified with two-tailed t-tests (which for the record yield T = 0.83, p = 0.25 and 1.18, p = 0.25, respectively). This is the point of the post: that R-R have overstated their case of how >90 percent debt/GDP ratio actually represents some kind of (statistically significant) threshold (based on their data). Of course, there is always a tradeoff between clarity and ease of interpretation in conveying statistical results in the form of a graph, and I regret that I was not clearer in my original post.
  • Reply to: How Significant is a 1 Percent Difference in Growth Under Debt?   5 years 10 months ago
    Hi Carlos, Thanks for your comment. As I understand it, you believe that the comparison made in the post is incorrect, because the relationship between growth and debt is endogenous. This is entirely true, and why in the first paragraph of the post, I pointed out that the causality problem, which poses a problem for inference. But since the non-independence of growth and debt (as you call it) is an issue that has already been repeatedly discussed (even by Reinhart and Rogoff themselves), I wanted to focus on an alternative aspect of the R-R paper, that of statistical inference. My point of the post, which hopefully came across, is that the difference in means---a fairly standard statistical test---turns out not to be statistically significant between the 30/60 and 60/90 bins, nor between the 60/90 and >90 bins. The graph was chosen to replicate the graph in R-R's original paper, with the data edits mentioned in the footnote to the table. So if the comparison rubs you the wrong way, it is an issue with how R-R make their comparisons (and inferences).
  • Reply to: How Significant is a 1 Percent Difference in Growth Under Debt?   5 years 10 months ago
    Hi, Jamus These are not adequate comparisons. See, first, the pure "statistical significance" of the differences is not the important thing here, this is an estimation problem, not a test problem. But, even if statistical significance were the most important thing, both comparisons are wrong. For example, do you think that growth rates and debts between countries are independent? If they aren't, then the relationship between individual CI's and differences CI's can be very odd, not only in the way mentioned in the paper you have linked. So, all these "eyeballing" tests are misleading. Best Regards! Carlos
  • Reply to: How Significant is a 1 Percent Difference in Growth Under Debt?   5 years 10 months ago
    Maybe you guys are misssing some point... [EDITORIAL NOTE: THIS COMMENT WAS ORIGINALLY POSTED ANONYMOUSLY IN PORTUGUESE, AND REPLICATED IN ENGLISH HERE TO EASE DICUSSION.] Teach the World Bank statistics. Cult of statistical significance or IV. (Teach the World Bank statistics. Cult of statistical significance or IV.) by Carlos Cinelli Consider two random samples with 10 observations, drawn from a normal distribution with different means and the same variance unknown. To use a concrete example, R simulates the two samples, one from a normal with mean 5 and standard deviation 1 and the other a normal with mean 2 and standard deviation 1. The samples resulted in the following statistics: *** Sample 1 Sample mean: 5 Sample standard deviation: 0.8 The 95% confidence interval: 3.4 to 6.6 *** Sample 2 Sample mean: 2.6 Sample standard deviation: 0.7 The 95% confidence interval: 2.6 to 4.0 *** Note that the confidence intervals intersect. The lower limit of sample 1 is 3.4 and the upper limit of sample 2 is 4.0. This means that the difference between the sample means is not statistically significant at 5%? Not by far! Making a t test for the difference between the two means you get a statistically significant result. Even if you did not know that the variances were equal, the Welch t test gives us a range of 95% confidence interval for the difference between the averages between 1.8 and 3.2. Now imagine that these data were GDP growth, ie, a group has sample average growth of 5% and others 2.6%. If you compare the confidence intervals, you might tend to say that the two groups have no growth "different" ... when, in fact, a proper test classic differences between means indicates a difference between 1.8 and 3.2 points percentage, very important in terms of economic growth! But this error happens? Yes, the World Bank. On Econbrowser on the controversy Heinhart and Rogoff, Chinn released this graph relating the average growth and percentage of public debt to GDP ratio. The bars are the mean and the black line represents the 95% confidence level. debtgdpgrowth.pngNote that although the average growth of countries with high debt (over 90% of GDP) to be much lower than the average of the other, the confidence intervals intersect. This led the staff blog of the World Bank said that "[...] the confidence intervals of all three bins above the 30 percent debt / GDP threshold Also overlap. On this (admittedly crude) basis, then, any claim que a 1 percent growth differential over a decade compounds is simply overstating the case made by the date. " This is wrong, the simple fact of the ranges of 95% confidence cross does not mean anything, even if you thought that statistical significance was the relevant point here. As we saw in the previous example, with a super simple example, the confidence intervals can intersect and yet the difference is "statistically significant" and, more importantly, economically relevant! Aware of the error, the authors did a PS warning for apparel and reducing the confidence interval for standard deviation, instead of two ... Despite the play's title, it was not a "stupidity" of the World Bank. One problem I have encountered when discussing this is that, in general, people think that only "dumb" make this kind of mistake, or just "journals" crappy publish things like this. Ledo mistake ... misunderstanding about confidence intervals, statistical significance, p-values ​​are pervasive in the social sciences, including applied work in the best journals and with the best researchers. Be in the USA, Brazil or Germany, this happens a lot and it's something we have to change. source: source:
  • Reply to: Commodity Market Outlook   6 years 2 weeks ago
    A major oil supply cutoff will drive oil price high. While oil price has relative effect on prices of other commodities, it will have certain implications for oil driven economies. A rise in the price of oil will cause a relative increase in the price of other commodities, including price of food (both for oil producing and consuming states). Oil producing states will benefit from this increase in oil price as more money will run into their coffers. An oil producing country whose GDP is largely dependent on oil will have increased stock of money and in turn inflation (if consumption policy is not effective). Nigeria has been in this situation, where increase in oil price caused a boom and inflation increased alongside expenditure. When supply was restored and oil price reduced, prices of other commodities did not drop immediately and consumption pattern of the people was hard to reverse. The impact on the people was painful and more was driven back to poverty. Also, while the boom lasted, GDP and money stock increased, government and policy authorities were dissuaded from other sources of income and focused largely on oil, making the economy one sector driven. Oil consuming states like USA will also notice a relative increase in prices of other commodities, including food. However, this will not be due to inflation but as a result of scarcity of oil (increase of demand over supply) and while oil price drive the economy, market forces that push oil price will have relative effect on the prices of other commodities. This could give a painful experience to the middle and low income earners period when supply is cutoff. Once supply is restored, business becomes as usual. However, this will be true mainly for economies without alternative and those who do not have precautionary plan. Furthermore, oil is a commodity on the world market and increase in oil price will relatively cause an increase in prices of other commodities on international market that depend on it. Major car companies, air lines, heavy machine producers and others will be affected. I suggest that oil producing states try to foresee the impact of oil price movement and plan for a sustained growth in the economy. While oil price have relative effect on the price of other commodities, its effect on the price of food will be felt more by the low income earners. Therefore, prudent governments should plan to improve agriculture and increase supply of food to its populace. Increase in the supply of food will check the relative effect of oil price increase on food price. Furthermore, middle east countries should be encouraged to seek peace. Organizations like the UN, World bank, and neighboring countries should intervene and calm the unrest in the region. The unrest in the middle east could cutoff oil supply, drive its price high and in turn the price of food. This will worsen the world food security issue and increase hunger, malnutrition and death.