Logic & Circuits

For example, low class sizes may be correlated with school wealth (e.g. richer schools can afford lower student-classroom ratios) which also affects test scores through other ways (e.g. better textbooks and non-classroom facilities). No – it may simply be that schools with more textbooks also have lower student-teacher-ratios (STRs), better classrooms and more engaged teachers – all of which could also improve exam performance. New ego e cig are now developed to lower such problems. With this being said, instrumental variables are not completely defunct. While the schools are being repaired, affected students are temporarily transferred to undamaged nearby schools, causing a sudden increase in class sizes. As a real-world example of how AI can influence B2C ecosystems, the chatbot implementation is destined to increase in the coming years, to address customer queries in real-time, to automate customer interactions, and then some. Assuming this argument is correct, we are left with a nice natural experiment: we have a random, isolated increase in class sizes (X) that allows us to identify its independent contribution to test scores (Y). We then test to see if there is a ‘difference-in-difference’ between the two groups, which effectively nets out any ex ante differences between the two.

We can add twists to this basic framework: for example, if we are worried about baseline imbalance, we can examine both groups before the intervention and then again at the end of the treatment window. For example, consider the claim that education causes people to earn higher wages. It’s not something people like to discuss constipation when it carries on for too long can be incredibly uncomfortable and in some cases even debilitating. In places like California, schools sometimes shut down due to infrastructure damage caused by periodic earthquakes. Correlation ≠ causation. To see this, suppose I collect data on textbooks per classroom and mean exam scores for 30 schools. To get around this, we can use the fact that judges are randomly assigned to cases, and that some judges appear systematically harsher at sentencing than others. If we conduct the same RCT in a variety of contexts and get the same result each time, this, I think, is the closest we can get to objective scientific knowledge about the social world. While the first published RCT in medicine took place in 1948, it took until the 1990s for RCTs to become popular in Economics.

Also, as my friend Hannah comments on my first post, there have been difficulties in scaling up the findings from RCTs to meaningful policy change – an issue I discuss further in my next post. Also, William Zinsser’s On Writing Well. We can theorise many potential effects of earthquakes on test scores besides its impact on class sizes: for instance, earthquakes can have localised income effects as well as psychological effects on affected students, both of which effect test results. For example, in the context of class sizes and test scores, a candidate instrument could be the occurrence of earthquakes. In my previous example, the exogeneity requirement is almost certainly not met. Hence, the relevance requirement is met: Z (settler mortality rates) affect X (modern institutions). Then comes the leap of faith: the authors claim that historic settler mortality rates (Z) have not affected modern day growth (Y) except via their effect on the institution’s they brought about (X).

For instance, settler mortality rates (Z) seem correlated with historic disease environment which is itself correlated with modern day growth (Y). In this instance, a treatment may be to provide schools with free textbooks for each child. When testing a new drug, pharmaceutical companies compare the outcomes of a treatment vs. Deval Abrasion Testing machine, Reciprocal theorem apparatus, Advance Microprocessor, etc. which provides excellent opportunities for students to practically experiment their theoretical knowledge. The goal is to prepare the students for using logic as a formal tool in computer science. Most importantly, by controlling for confounding factors at the outset, we get arguably the ‘cleanest’ identification of a causal relationship between X and Y. For me, this is where Economics most lives up to its social science moniker. We defeat ourselves by the way we force ourselves to get moving. These criticisms appear unanswerable: I remember a senior faculty member at Oxford once telling me that the IV would probably not get published today. As before, there may be ‘confounding’ variables that influence both X and Y, obscuring the true relationship between the two. The graph below gives a nice illustration of these new econometric techniques: some of which I may discuss in future posts.

We split the groups randomly to help ensure they are ‘balanced’, meaning the treatment and control group are as similar as possible in terms of STRS, desks, and any other confounding variables we can observe. The outcome of interest is the difference in exam score between groups: since the two groups were as similar as possible ex ante, we can assume any difference in exam performance post-treatment is caused by the treatment itself. After giving the treatment time to take effect, we then examine children in both groups to test for a ‘treatment effect’. Suppose I hope to estimate the causal effect of class sizes on student test scores. We could also argue that earthquakes do not affect test scores (Y) in any other way apart from via their effect on class sizes (X). Another way to solve this is to know yourself. Therefore, they pull one end of the cell membrane in the way they want, but there is no reaction at the other end of the cell membrane. Perhaps the simplest way to do this is to conduct a Randomised Controlled Trial (RCT). This is an RCT in its simplest form. When ethanol and water are mixed, there is a reduction in volume because the water molecules form close hydrogen-bonds with ethanol molecules and squeeze into spaces between ethanol molecules very closely.

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