That’s the title of a paper published recently in the The Journal of Applied Public Economics. Here is the abstract:
Economics is permeated with value judgements, and removing them would be neither possible nor desirable. They are consequential, in the sense that they have a sizeable impact on economists’ output. Yet many economists may not even realise they are there. This paper surveys ways in which values influence economic theory and practice and explores some implications for the manner in which economics – especially welfare economics – is taught, practised and communicated. Explicit attention to values needs to be embedded in the teaching of economics at all levels.
This really and truly is a paper that you should read in full, so rather than give you my notes about it, I’ll simply note ten points that were very important to me. But I’ll urge you once again to read the whole thing.
Hume’s law is worth noting: “You can’t derive an “ought” from an “is”.
Check the premises of your arguments. Always and everywhere. Students who have just finished reading Ayn Rand might remember a particular phrasing on the part of one of her characters, but the point goes much deeper than that. In this case, what Erik Angner (the author of the paper) is saying is that we should be aware of what values are entering our arguments. To give you just one example: should there be a market for kidneys (or organs in general)? I’m not judging you for your answer, and nor should you judge yourself. But whatever your answer to this question, you are telling yourself a fair bit about your values.
Disagreements can happen either because we fail to agree on what our understanding of reality is (which is relatively easy to correct), or because we have different value systems (which is much more difficult to correct). But begin by trying to understand where the disagreement comes from in the first place.
“Public policy must be responsive to the values of the population in whose name policymakers take action. This is an important lesson for students of economics who subsequently are engaged in policy decisions.” This is also why studying only economics isn’t enough to become a good policymaker. Knowing economics is a necessary, but not a sufficient condition for formulating policy. (Recommended reading: Where India Goes)
“Most importantly, and particularly when it comes to teaching future generations of economists, we will want to enquire: ‘What and whose values ought to inspire our work – and how?’” Answering this question is hard, in part because no single value system has “won”. Perhaps none ever will, and that makes answering this question hard, important, frustrating and rewarding – all at once.
“It is interesting to reflect on why economic pedagogy has become a surprisingly value-free zone. One reason may be that welfare economics itself (as discussed in the introductory paper in this symposium) has not been a prominent area of research for decades, with the publication of key texts dating to the early 1970s. Another is the lasting influence of positivism on economics as a social science committed to a particular conception of the scientific method, from Robbins (1932) through to recent continued insistence on the objectivity of economic analysis. Economists teach as we aim to practise our discipline, with courses – particularly at masters level and beyond – geared to the production of future academic economists rather than students who will work in policy or other domains of economic practice” Our job is not to produce more academic economists alone. Our job is also to produce economists who are employable in the world outside of academia. That is actually around eighty percent of our job!You’d be surprised at the number of academicians who do not et this point. At all.
Question number three in macroeconomics is “What can we do to make the world a better place?” The word “better” is inherently subjective, and it is a value judgment. You can’t teach or study economics independent of thinking about, talking about, and explicitly incorporating values into your work.
The work that we do, as economists, needs to be communicated. How we communicate it, through which medium, whether we communicate it or not, how we phrase our communication, are all value judgments.
“Kuhn said a good scientific theory has five qualities, or cognitive virtues: empirical accuracy, consistency, scope, simplicity and fruitfulness.” What if you have two competing theories, one being very good in three of these, and another being good in two of these, but with no overlap? Which do you “choose”? How is this not a value judgment?
Erik ends with an excellent list of suggestions that teachers could consider when designing a curriculum designed to surface values: Provide historical context | Provide alternative economic perspectives | Articulate relevant values | Practise normative reflection | Use case studies | Encourage epistemic humility
The paper’s concluding paragraph is worth quoting in full:
Recognising that values play an ineliminable role in economic theory and practice does not mean that anything goes, or that economics pedagogy should be used as a vehicle for promoting specific, parochial values and ideologies. It does mean recognising the centrality of values as an input in serious reflection about economic things, as well as helping us develop the requisite sophistication to engage in normative reflection as appropriate – in economic theory, practice, communication and teaching.
Before we begin, interested readers should note that this blogpost (and the paper it covers) are a welcome violation of Betteridge’s law. In this case, the paper argues (and I agree), the answer is very much yes.
The paper in question is written by Diane Coyle, Mark Fabian, Eric Beinhocker, Tim Besley and Margaret Stevens. It was published about a week ago or so, and the abstract is below:
The contributions of economists have long included both positive explanations of how economic systems work and normative recommendations for how they could and should work better. In recent decades, economics has taken a strong empirical turn as well as having a greater appreciation of the importance of the complexities of real-world human behaviour, institutions, the strengths and failures of markets, and interlinkages with other systems, including politics, technology, culture and the environment. This shift has also brought greater relevance and pragmatism to normative economics. While this shift towards evidence and pragmatism has been welcome, it does not in itself answer the core question of what exactly constitutes ‘better’, and for whom, and how to manage inevitable conflicts and trade-offs in society. These have long been the core concerns of welfare economics. Yet, in the 1980s and 1990s, debates on welfare economics seemed to have become marginalised. The articles in this Fiscal Studies symposium engage with the question of how to revive normative questions as a central issue in economic scholarship.
Coyle, D., Fabian, M., Beinhocker, E., Besley, T. & Stevens, M. (2023), Is it time to reboot welfare economics? Overview. Fiscal Studies, 00 1–13. https://doi.org/10.1111/1475-5890.12334
Positive economics is describing the world as it is, and normative economics is describing the world as it ought to be. Or as I prefer to explain it in class, positive economics is me standing in front of a normal mirror, and normative economics is me standing in front of a mirror that makes me look thinner than I am.
This paper, the one we’re talking about today, focusses on welfare economics, which concerns itself with the normative side of things. Which fits just fine with question number three in macro – this paper is about answering the question that goes “what can we do to make the world a better place?”
The first section of the paper after the introduction explains why the authors think that revisiting the ideas of welfare economics is a good idea in 2023. The tweet version of this section is that in 2023, efficiency is overrated, and welfare economics is underrated. As a person who has explored themes related to maximizing soul, this is an idea that resonates. This section is worth lingering over for two other reasons.
One, it covers Jim Buchanan’s definition of economics:
“Buchanan (1964) defined economics as the study of exchange relations. He distinguished it from the study of power relations (politics) and moral relations (sociology and anthropology).”
It is worth quoting the relevant paragraph from the original paper:
Economics is the study of the whole system of exchange relationships. Politics is the study of the whole system of coercive or potentially coercive relationships. In almost any particular social institution, there are elements of both types of behavior, and it is appropriate that both the economist and the political scientist study such institutions. What I should stress is the potentiality of exchange in those socio-political institutions that we normally consider to embody primarily coercive or quasi-coercive elements. To the extent that man has available to him alternatives of action, he meets his associates as, in some sense, an “equal,” in other words, in a trading relationship. Only in those situations where pure rent is the sole element in return is the economic relationship wholly replaced by the political
To what extent do people today have “alternatives of action”? In other words, when person X meets person Y today in India, do they meet as equals? Might income have a role to play? Might language have a role to play? Might caste have a role to play? Might religion have a role to play? Might gender have a role to play? To what extent is trade then purely economic in India? Or does politics (not to mention sociology and anthropology) have a role to play too?
Second, this nice little line that hides a world of pain: “What discount rate to use is a normative question.” Ask ChatGPT to tell you more about it, with examples. But in general, if you are starting off on studying economics, think carefully about time, and what time-horizons you keep in mind when you evaluate policies. Most underrated thing to do, in my opinion.
The next section begins thus:
One area in which the normative shortcomings of traditional economics are readily apparent is the way we measure progress. Businesses are freely depleting or damaging natural resources, the financial sector enriches the top 1 per cent, the food system is contributing to obesity and promoting antibiotic resistance, pharmaceutical firms rely on people being unwell for the pursuit of profit, and new AI technologies create value for a few technology firms mostly by learning from existing creators without compensation. It is, not surprisingly, widely perceived by citizens that the economic model encourages extraction and exploitation. Yet conventional economic statistics say that society is doing better than ever. The measurement focus on unidimensional metrics of ‘the domain of socially organised production’ calculated using exchange values or market prices is under sustained challenge from a demand to go ‘Beyond GDP’.
Coyle, D., Fabian, M., Beinhocker, E., Besley, T. & Stevens, M. (2023), Is it time to reboot welfare economics? Overview. Fiscal Studies, 00 1–13. https://doi.org/10.1111/1475-5890.12334
You might say this is getting into the weeds a little bit, but please do read the whole section carefully. How we measure progress, why current methods are limited, and why willingness-to-pay methodologies are today overrated are topics that more young students of economics should be reading about.
“The desire to trade away realism for tractability in service to cost–benefit analyse is one of the most common critiques of ‘neo-liberal’ public administration.” And there is some merit in these critiques. How much merit is a question that will never see full agreement, and that is just fine. But I begin to worry when extreme solutions are favored! Too much realism with next to no tractability is as bad as too much tractability with next to no realism. The truth always lies somewhere in the middle.
When I say that I will skip the next two sections, it is not because they’re unimportant. On the contrary, they’re important enough to merit separate blog posts in their own right. These sections are behavioral economics, and inequality and power. I’ll write more about them tomorrow and day after.
But I would like to end this blogpost with a paragraph that resonates a lot with me:
As Erik Angner argues in his paper, our students need better guidance than this if they are to make practical judgements, as citizens, policymakers, employers and employees, about the economic challenges facing society. Those teaching economics to decision-makers of the future should provide a framework that encompasses both normative and positive aspects of economic decisions. If we focus only on those where we feel comfortable, we convey the message that other considerations do not matter to us.
Coyle, D., Fabian, M., Beinhocker, E., Besley, T. & Stevens, M. (2023), Is it time to reboot welfare economics? Overview. Fiscal Studies, 00 1–13. https://doi.org/10.1111/1475-5890.12334
It is something that I need to keep in mind when I teach, and I don’t think I’ve always succeeded. Onwards!
We don’t argue enough in our classes here in India.
That is obviously a blanket statement, not backed by data, and I’m sure that there are exceptions to what I have stated is the norm. But all that being said, I am very much willing to defend the idea that our classes are more about listening than they are about conversing, let along arguing.
Which is a pity, because nothing helps you learn better than arguing. Not arguing for the sake of arguing, but arguing in order for all parties involved in the argument to walk away with a better understanding of the issue at hand. If your side of the argument “wins”, good for you. But don’t enter into debates in order to win them – enter into debates in order to sharpen your thinking, and in order to build better defenses for your claims. Also enter into debates to appreciate better the opinions of “the other side”, and learn what is best about their arguments.
When this process works well, much learning can ensue.
One limitation of my classes at the Gokhale Institute this year is the fact that I’m teaching one hundred and fifty (give or take) students at the same time. As with everything else in life, this comes with pros and cons.
I save on time, because I don’t have to teach two divisions (or sections, if you prefer) separately.
I don’t have to teach the same thing again, so I get bored lesser.
I don’t get to teach the same thing again, so I don’t get to practice more as a teacher
But by far and the most important factor: students don’t get as much time to ask questions.
A “lecture” to a hundred and fifty students isn’t a lecture. It is a speech. That’s the only way a one hour session with an audience that large will ever work. You can answer the odd question here and there, but a detailed back and forth between any one student and the professor leaves the other hundred and forty nine students twiddling their thumbs, and so in-depth back-and-forth dialog is pretty much out of the question. I hate myself for it, but I often have to cut off students from asking a follow-up question, or ask them to make their questions shorter. Whatay tragedy, if you ask me.
I can understand why colleges would want to do this from the point of view of finance, sure. When colleges choose to combine divisions, they’re giving a very clear answer to the question “What are you optimizing for?” They’re minimizing expenditure, instead of maximizing learning. Smaller classes work better for learning, larger classes work better for minimizing expenditure.
And if that is what they’re optimizing for, they should follow through on their chosen path and outsource the learning to the internet altogether. But there are elements of such an equilibrium that are worrisome for a college to think about, and so we will continue to have ever larger classes, more’s the pity.
But students can outsource the having an argument bit to the internet if the college can’t oblige! We live in the age of ChatGPT, and whatever topic you would like to have an argument about, ChatGPT will happily play along.
How about an argument about the usefulness of supply and demand diagrams, for example? If your professor cannot spare the time for an argument in class about this, ring up your always available arguer online, and have some fun:
You can read the rest of this debate here, if you’re interested. But please figure out how to put me out of a job, by getting ChatGPT to argue with you more often about issues in economics (and other subjects, naturally).
Arguments really and truly are a great way to learn, and have fun going up against ChatGPT. I wish you all the very best 🙂
Google Keep. Microsoft OneNote. Roam. Obsidian. Notion. Readwise.
There are other apps with whom I’ve had, so to speak, even shorter relationships, but the ones above are the ones that I have really and truly tried to use on an extensive basis. Google Keep, as with so many other things Google, is excellent in some ways, but utterly hopeless in others. You’ll never guess what their latest enhancement is, for example. OneNote was very promising, but Microsoft went through a bit of a phase where they had a OneNote app for Windows, and a separate one for Office365, and it just got too confusing for words. Roam was too expensive at 15USD per month, and Obsidian had too steep a learning curve for me. And if you want to talk about steep learning curves, you should try out Notion. Gah.
The latest one that I’m trying out is Readwise, and well, it’s going… ok, I guess. And we all know what that really means, don’t we?
Long story short, none of these have really worked out for me. And that, I suspect, is the case for most of you reading this. There will be some who are true converts and zealots of any one of these, and I envy you. I really do, good for you, really! But whichever one of these you’re selling, I’m not really on the market. And no, that other newnew one ain’t for me either, whichever one it is.
And that’s why this article in The Verge really resonated with me:
Note-taking, after all, does not take place in a vacuum. It takes place on your computer, next to email, and Slack, and Discord, and iMessage, and the text-based social network of your choosing. In the era of alt-tabbing between these and other apps, our ability to build knowledge and draw connections is permanently challenged by what might be our ultimately futile efforts to multitask.
As always, do go through the whole thing. It is full of fascinating snippets, including the somewhat surprising, somewhat entirely predictable finding that the average time we spend on a single screen before shifting our attention elsewhere was 2.5 minutes. If that seems too long for you, you’re right. That was in 2004. Today’s stats? 47 seconds.
The author of the article goes on to hope (as do some of us, while others are repulsed by the thought) that AI will help us make sense of all of these links that we have been squirrelling away for years. I’m on Team Maybe about this myself. But I really do agree with this bit:
In short: it is probably a mistake, in the end, to ask software to improve our thinking. Even if you can rescue your attention from the acid bath of the internet; even if you can gather the most interesting data and observations into the app of your choosing; even if you revisit that data from time to time — this will not be enough. It might not even be worth trying. The reason, sadly, is that thinking takes place in your brain. And thinking is an active pursuit — one that often happens when you are spending long stretches of time staring into space, then writing a bit, and then staring into space a bit more. It’s here here that the connections are made and the insights are formed. And it is a process that stubbornly resists automation.
And that is, in a way, comforting and reassuring. I haven’t failed all these awesome note-taking apps, and they haven’t failed me either. In each of these cases, it just wasn’t meant to be.
The article refers to the works of Andy Matuschak (Google him if you don’t know who he is), who says that the ultimate goal is to think effectively (amen!), and that all of us should really be thinking about two questions.
What practices can help me reliably develop insights over time?
How can I shepherd my attention effectively?
Don’t look to me for the answer to the second of these questions, I have no idea. If you know the answer, help a guy out, will ya? But I do have my own personal answer regarding the first of these questions.
I read a lot. Not as much as some others that I know, and I wish I read more, but I do think I read more than the average person. Some of what I read I find interesting enough to talk about with some people whose opinions I truly value. Some of these conversations end up being friendly arguments, where they challenge my view, and I challenge theirs. Then I have a cup of coffee and think about some of these arguments.
Then I write about it. And after I write about it, I send a draft of what I’ve written to them. Then, if I’m really lucky, we have another argument about the draft I’ve sent them. I think more about this second argument, and refine the draft.
How I would like to tell you that this is how every single post on EFE gets written.
The reality is that all of what I’ve described above happens for maybe one post every month. Those posts, and those arguments stay with me then for a very long time. But the vast majority of the posts you read over here are me reading something, finding it interesting enough to write about it, and well, I write it and you read it.
When the whole process described above works the way it should – that is utopia.
But between living in utopia and not writing about it at all lies a happy medium. Happy not because it is perfect, but because it is attainable. It involves at least one of all those things happening – me reading about something and then writing about it.
So my favorite note-taking app?
It happens to be a blog called EFE. The posts over here are me taking notes on something I’ve read – and that, more than anything else, helps me remember stuff better.
I’ve said this before, but I’ll say it again.
Write.
Write and put it out in the public domain for all to read. Best way to remember something, anything and most everything.
And if you can figure out a way for me to do achieve my utopian process for all the posts that I write, please do tell!
C.R. Rao passed away earlier this week, and this is a name that is familiar to anybody who has completed a course in statistics at the Masters level. Well, ought to be familiar, at any rate. And if you ask me, even undergraduate students ought to be familiar with both the name, and the many achievements of India’s best statistician.
Yes, that is a tall claim, but even folks who might disagree with me will admit that C.R. Rao makes for a very worthy contender. (And if you do disagree, please do tell me who your candidate would be.)
Here’s a lovely write-up about C.R. Rao from earlier on this year:
Professor C R Rao, the ageless maestro in mathematical statistics, was recently in the news because he received the 2023 International Prize in Statistics. The news made headlines because the Prize was called the ‘Nobel Prize in Statistics’. There’s no Nobel Prize in Statistics, but if there had indeed been one, Calyampudi Radhakrishna Rao would have got it long ago. Perhaps in 1960. C R Rao entered the field of statistics when it wasn’t sufficiently ‘mathematical’. Classical statistics, at that point, was about gathering data, obtaining counts and averages, and estimating data variability and associations. Think, for example, of the mammoth census exercise. Rao was among the first to bring serious mathematics into the mix. He asked questions like: When does a ‘best’ statistical estimate exist? If it does, how can we mathematically manoeuvre to make a given estimate the best? In situations where no best estimate exists, which among the candidate estimates is the most desirable?
By the way, the very last anecdote in this post was my favorite, so please make sure you read the whole thing.
You could argue for days about which of his many contributions were the most important, but there will be very little disagreement about which is the most famous: the Cramer-Rao Lower Bound.
In estimation theory and statistics, the Cramér–Rao bound (CRB) relates to estimation of a deterministic (fixed, though unknown) parameter. The result is named in honor of Harald Cramér and C. R. Rao.
Plow through the article if you like, but I would advise you against it if you are unfamiliar with statistical theory, and/or mathematical notation. You could try this on for size instead:
What is the Cramer-Rao Lower Bound? The Cramer-Rao Lower Bound (CRLB) gives a lower estimate for the variance of an unbiased estimator. Estimators that are close to the CLRB are more unbiased (i.e. more preferable to use) than estimators further away. The Cramer-Rao Lower bound is theoretical; Sometimes a perfectly unbiased estimator (i.e. one that meets the CRLB) doesn’t exist. Additionally, the CRLB is difficult to calculate unless you have a very simple scenario. Easier, general, alternatives for finding the best estimator do exist. You may want to consider running a more practical alternative for point estimation, like the Method of Moments.
But even this, I would say, isn’t a great way to make oneself familiar with the subject. Try your luck with YouTube, maybe? Lots of very good videos in there, but none that I would call simple enough.
Which, of course, brings us to ChatGPT.
Here’s what I started with:
“Give me the simplest possible explanation of what the cramer-rao lower bound is, why it is important, and one example of a simple application. Thank you!”
Your mileage may will vary, because you might end up using ChatGPT 3.5. Even if you were to use ChatGPT4, there’s no guarantee that the answer will be the same. It will, in fact, almost certainly be different. Bu that’s fine! Copy this prompt and run it.
This was my follow-up question:
“Lovely, this was helpful. Can you walk me through its theoretical derivation? Keep the explanation as simple as possible, and note that I am not very familiar with matrix algebra.”
I wanted as simple an explanation as possible from ChatGPT, which is why I added the bit about not being familiar with matrix algebra. You could say you’re not at all familiar with it. You could say you’re not familiar with statistics, or mathematical notations, or any other qualifiers you think are necessary. Don’t be shy about telling ChatGPT what you don’t know – this is important because it will tailor its answers accordingly.
This is what I went with next:
“Now imagine I have to explain this to, say, a very motivated 12 year old. This student is very willing to learn, but is unfamiliar with statistical concepts. She has, in fact, had no classes in statistics at all, but has learnt the basic concepts in statistics, and wants to run a real life experiment. In my conversations with her, the CRLB came up, and she wanted to know more about it. How would you explain the derivation of the CRLB to her?”
No twelve year old student asked me this question, to be clear. But this is just one of many, many ways in which you can try and get ChatGPT to simplify stuff for you. This answer is worth pasting in full:
“Alright, let’s use a more intuitive approach!
Setting the Scene: Imagine you’re trying to guess the number of candies in a jar. Each time you guess, you might be a little too high or a little too low, but on average, you’re pretty close. The CRLB is like a magic number that tells you the smallest amount you can be off by, on average, no matter how good your guessing strategy is.Step-by-Step Explanation:
Making a Guess: Every time you make a guess about the number of candies, you’re using some clues or information. Maybe you’re looking at the size of the jar, the size of the candies, or how full the jar is. All these clues help you make a better guess.
Score Function – The Clue Meter: Imagine you have a “clue meter” that measures how good each clue is. If the needle on the meter moves a lot when you change your guess a little, that means the clue is really helpful. If the needle barely moves, the clue isn’t very useful.
Expected Value – Average Clue Power: Now, if you average the readings of the “clue meter” over many guesses, it should point to zero. This means that sometimes the clues tell you to guess higher and sometimes lower, but on average, they don’t favor any particular direction.
Information Matrix – Clue Strength: The strength of your clues is like how much the needle on the “clue meter” wiggles around its average (zero). If it wiggles a lot, your clues are strong. If it barely wiggles, your clues are weak.
The Magic Number – CRLB: Now, the CRLB is like a magic number that tells you the smallest amount you can be off by, on average, based on how strong your clues are. If your clues are super strong (the needle wiggles a lot), then the magic number is small, and you can guess really accurately. If your clues are weak (the needle barely wiggles), then the magic number is big, and your guesses might be off by a bit more.
Conclusion: So, when you’re trying to guess the number of candies in the jar, the CRLB is like a challenge. It’s the universe saying, “Bet you can’t guess better than this!” And if you can guess with an error smaller than that magic number, then you’re doing an amazing job! If not, maybe there’s a better way to use your clues.”
Much better. But I had questions!
“Is it possible for the guess to be lower than the CRLB? If yes, I’m confused about why it should be called the “lower bound””
Here is its answer:
“Great question! Let’s clarify this.The Cramér-Rao Lower Bound (CRLB) is a theoretical lower bound on the variance (a measure of how spread out the estimates are) of any unbiased estimator. It doesn’t directly bound the error of a single guess or measurement. Instead, it bounds the average squared error (variance) of an estimator over many, many guesses or measurements.In our candy jar example, the CRLB is used in a slightly simplified and illustrative manner. Here’s what it means:
Single Guess: In any single guess, your error (the difference between your guess and the actual number of candies) can certainly be less than the CRLB. For instance, you might even guess the exact number of candies and have an error of zero!
Average Error Over Many Guesses: If you were to make many guesses (or if many people were to guess), and we calculated the average of the squared differences between all those guesses and the actual number, that average would typically be above the CRLB. The CRLB tells us that we can’t consistently get an average squared error below this bound with any guessing strategy.
So, when we say “Try to get within 5 candies of the actual number” in the game, it’s a simplification for illustration. In a real-world application of the CRLB, it’s about the average performance of an estimator, not the performance on a single estimate.In essence, while individual errors can be below the CRLB, the average squared error of a good estimator shouldn’t be below the CRLB. If it is, either the estimator is biased, or there’s some other issue with the assumptions or calculations.”
Next obvious (to me, at any rate) step is to ask it to come up with a working demo:
“Great! Can you help me build a very small demo of this experiment you just described in javascript that I can load as an HTML page?”
What a time to be alive! If you are learning statistics for the very first time, and especially if you have (in your opinion) a not-so-great stats prof, you can now make the world’s best lemonade from the lemon you’ve been handed! Here is its answer:
“Of course! Let’s create a simple demo where:
A random number of candies (between 1 and 100) is placed in a virtual jar.
The user tries to guess the number of candies.
After guessing, the user is told how close their guess was to the actual number.
We’ll also display the CRLB (for simplicity, we’ll just use a fixed value as our CRLB).”
Here’s a basic HTML page with embedded JavaScript for the demo it came up with:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Candy Guessing Game</title>
</head>
<body>
<h2>Candy Guessing Game</h2>
<p>Guess the number of candies in the jar (between 1 and 100):</p>
<input type="number" id="guess" min="1" max="100">
<button onclick="checkGuess()">Submit Guess</button>
<p id="feedback"></p>
<p id="crlb">Cramér-Rao Lower Bound (CRLB): 5 (This is our magic number! Try to get within 5 candies of the actual number.)</p>
<script>
// Randomly determine the number of candies in the jar
let candies = Math.floor(Math.random() * 100) + 1;
function checkGuess() {
let guess = document.getElementById("guess").value;
let difference = Math.abs(guess - candies);
if (difference === 0) {
document.getElementById("feedback").innerText = "Amazing! You guessed it exactly right!";
} else if (difference <= 5) { // Using 5 as our CRLB for simplicity
document.getElementById("feedback").innerText = "Great job! You're within the magic number! The jar has " + candies + " candies.";
} else {
document.getElementById("feedback").innerText = "Keep trying! The jar has " + candies + " candies. You were off by " + difference + ".";
}
}
</script>
</body>
</html>
What do you do with this code? Here’s ChatGPT again:
“You can save the above code as an .html file and open it in a web browser. The user can input their guess, and upon submission, they’ll receive feedback on how close their guess was to the actual number of candies. The CRLB is set to 5 for simplicity, so if the user’s guess is within 5 candies of the actual number, they’re doing great!”
What’s the point of having learnt an idea if you can’t discuss it in class or with like-minded friends, batchmates and peers? And so I had one final question for the best research assistant I’ve ever had:
“Thank you! One last question. Can you please give me five good questions regarding the CRLB that I can either ask in class, or use as a starting point for discussions with my batchmates or seniors. Please optimize the questions for conceptual clarity. That is, our attempts to answer these questions should make the concept, its applicability and its importance clearer to us.”
“Certainly! Here are five thought-provoking questions regarding the Cramér-Rao Lower Bound (CRLB) that can stimulate discussion and deepen understanding:
Foundational Understanding:
“Why is the CRLB considered a ‘lower bound’ on the variance of an unbiased estimator? What does it imply about the efficiency of other estimators?”
Practical Implications:
“In what real-world scenarios might the CRLB be particularly crucial for ensuring the accuracy of measurements or predictions? Can you think of any industries or fields where a slight improvement in estimation accuracy could have significant consequences?”
Assumptions and Limitations:
“The CRLB is derived under certain assumptions, such as the estimator being unbiased. How might the CRLB change if some of these assumptions are relaxed or not met? Are there situations where the CRLB might not be applicable or might be misleading?”
Comparison with Other Bounds:
“How does the CRLB compare to other bounds or benchmarks in statistics? Are there scenarios where another bound might be more appropriate or informative than the CRLB?”
Deepening Conceptual Understanding:
“If the CRLB provides a lower limit on the variance of an unbiased estimator, what would it mean if an estimator consistently has a variance below the CRLB? What might this indicate about the estimator or the data it’s working with?”
These questions are designed to encourage exploration of the foundational concepts behind the CRLB, its practical applications, and its relationship with other statistical tools and concepts. Discussing them should provide a more comprehensive and nuanced understanding of the CRLB and its significance in the field of statistics.”
There is always at least one student who says something along the lines of “No way can my college prof answer these, lol”, or “No way are my friends going to want to talk about this”, or “<Insert variant of choice here>”
Well, what about feeding these back to ChatGPT?
I’ve waited for years to write this sentence, and fellow students of econ will allow me to savor my moment of sweet, sweet revenge.
This is left as an exercise for the reader.
Honor the great man’s work by learning about it, and with ChatGPT around, you have no excuses left. Get to it! Oh, and by the way, the meta lesson, of course, is that you can do this with all of statistics – and other subjects besides.
That is an email I had sent to two of my friends, back in February of 2006. I’m sure Marginal Revolution must have been called plenty of things over the last twenty years, but “web resource”? Surely a record of sorts.
How I would like to tell you that I have read Marginal Revolution every single day since then. But even in the post truth era, that would be stretching things a bit. The remarkable bit, of course, is that it has been updated every single day since then – and for roughly three years before then.
I have no recollection of what post I read that day that made me want to share the URL with my friends. But I did go back and take a look at posts written on that day, and this delightful nugget cropped up:
“I am engaged and we are in the process of planning our wedding. There is a huge debate over what is OK to put in the invitations and what is not. My fiance and I have been living together for a little over a year and we aren’t planning on registering because we already have so much. So, monetary gifts would be great for us! Now, how do you put this in your invitation? A few suggestions have come up but we don’t want to seem rude or crass. Please help!” Tyler: Oh, what a softball. We have already blogged on the deadweight loss of gift-giving, here and here. So my major advice is simply to read MarginalRevolution on a regular basis. I can add only that if you are going to ask for money, set up a college fund. Your kids-to-be are not yet experiencing the impatience of waiting for the money, which implies an arbitrage opportunity with g > r, or the growth rate of the funds greater than the rate of time discount. Nor do I think that the mechanisms of Ricardian Equivalence will fully offset this transfer. Got that?
But the one thing that has remained constant is the fact that every single time I’ve visited the blog, I’ve come away with something I didn’t know earlier. And that’s been true for the last seventeen years in my case, and twenty for those lucky enough to have discovered the blog before I did.
I don’t claim to understand everything that I’ve read on MR, and I certainly don’t agree with everything written on it (what do you mean, give cash instead of gifts. Who does that?!). But I do claim, and with a lot of passion, that I have become a better student of economics for having read the blog for as long as I have.
Part of my motivation for starting EFE was to help other people fall in love with economics much the way I had over the years. And while there is a professor in Pune who is a major chunk of the reason I fell in love with economics, the other two reasons happen to be the co-authors of this blog. And certainly the inspiration to try and write daily comes from the fact that Tyler has written on MR every single day from August 2003 onwards.
2003. The year in which Federer won his first Wimbledon, and the year of the World Cup final That Never Happened. Hell, I was an undergraduate student in Fergusson College. And here I am now, father to a ten year old, with a blog of my own to try and post on daily – and MR continues on its own merry way, making the world a much better place, one small step at a time.
It is not for me to say whether the world has become a better place since then. But I can assure you that I have learnt a little about economics over the years, both because I’ve tried to read every single post written on MR, and because I’ve tried to write on EFE every single day. I’m less than perfect in both regards, and the failure is mine alone. But to the extent that I’m a better teacher today – be it ever so slightly – than in the year 2006, it is for the most part because of the inspiration that MR has provided over the years.
Two posts commemorating the twenty year anniversary on MR: here, and here.
Thank you for all that you’ve done, and here’s to the next twenty years. Cheers!
The IIT JEE (Indian Institute of Technology joint entrance exam) is revered as the arbiter of merit. With industrialised coaching classes, it is less clear how the JEE selects the right people to attend an IIT. Simplistic measurement of marks in an exam is not how the entry barriers into most sensible institutions work. The high-powered incentive — attending an IIT — is damaging the learning process. We propose a two-part mechanism: A broad exam that filters for sound capability, and then randomised allocation. The overall impact of such a mechanism would be positive. Test preparation has corroded Indian education. Across India, children no longer attend just high school. They are enrolled in coaching classes. Here, it is not necessary to study the subject and understand concepts. All they need to learn is the finite list of multiple-choice questions (MCQs) that are likely to be asked in entrance examinations.
Two of my favorite columnists writing about a topic that I am most passionate about – the conduct of examinations in India. What’s not to like, and how can I possibly not write about it?
As Nitin and Ajay mention, “test prep is not education”. Indeed. Test prep is just that: test prep. You can get very good at test prep, but that doesn’t mean that you will be educated.
They have their own definition of education, and while I don’t disagree with it one bit, I have a shorter one. Education is about learning to ask (and then answer) really good questions. My problem with our education system, and with exam test prep, is that we simply don’t teach our students the art of asking really good questions.
“The tendrils of curiosity, dissent, imagination, creativity, and risk-taking are likely to be crushed in these years. We are creating followers, not leaders.” If I nodded any harder, I could probably power a wind turbine all by myself.
“Upgrading high-school syllabi and implementing the National Education Policy 2020 are sometimes proposed as the answer. This is insufficient because they do not fundamentally change students’ and their parents’ incentives. Real change will come only if a seat in an elite academic institution is no longer seen as the sole objective of going to school.” Two first-pass responses to this issue would be to either increase supply or reduce demand. That is, increase the supply of high quality education seats (easier said than done), or reduce the demand for them (not gonna happen). Therefore their solution: lottery system. “The price of an IIT lottery ticket can be reduced to zero. Seats can be randomly allocated to applicants who meet basic requirements. Specifically, we could envision a first-level exam, which is not about the things that Google knows. Out of that the top 200,000 ranks are shortlisted. At the second stage, a random list of 20,000 would be chosen to attend the IITs. Such an approach, we contend, outperforms the current method on several important dimensions.”
It takes away the incentive of the mad entrance test world that we live in, sure. But I worry that “universities and engineering colleges around the country will feel customer pressure to upgrade their standards because they will now encounter candidates with higher expectations and ambitions” won’t necessarily work out in practice. Students enrolled in an institute have *massive* switching costs, and colleges know this all too well. Trust me on this one: they don’t feel no customer pressure.
My biggest problem with their solution isn’t with their solution per se, but with the fact that it ultimately boils down to whether we can scale up the supply of high quality higher education in our country quickly enough. I happen to think the answer is no, and I hope to god I’m wrong.
…the idea of attracting large manufacturers in ecosystem creating industries might be a promising strategy to adopt. An example is the Indian government’s push for Apple.
Industrial policy – what it is, what its benefits are, and what its limitations are – has been the focus of many an op-ed in the recent past. That, to me, is a signal to avoid reading most of them. But not because the topic itself isn’t important! On the contrary, industrial policy is the topic to learn more about if you are a student of the manufacturing sector in the Indian economy.
Why do I say so? Many reasons, but Gulzar Natarajan offers as good a summary as any I’ve read in the lead-up to the excerpt I’ve pasted above.
But in this post, Gulzar Natarajan points to a specific aspect of industrial policy:
Conventional wisdom would have it governments should not pick winners. India’s courting of Apple and mobile phones success is a good example that questions this wisdom. Mobile phones and Apple/Foxconn (and Samsung) are winners. Just as electric vehicles and Tesla, or semiconductor chips and Samsung/TSMC could be. Solar and wind power generation equipment manufacturers and defense manufacturers are another two examples. The same can be said of contract manufacturers Pou Chen, Feng Tay, Hong Fu, Apache, etc in footwear, and Toray, etc in apparel. The facilities of these companies will be large enough to create a manufacturing ecosystem that has transformational impacts in its town or region. In fact, there’s a strong case that instead of spreading resources thin by targeting economy-wide measures like concessions and input subsidies, an outcomes-focused industrial policy for a government would be to identify a few winners (sectors and large brands or contract manufacturers) and court them. Success would be measured by the ability to get one of them to actually make a meaningful enough investment.
But what of the risks with such a strategy? He identifies four of them:
You need to pick the “right” kind of winner, which is easier said than done.
It could well lead to crony capitalism.
This can be countered with effective state capacity, and we don’t have it.
It could crowd out the focus on small and medium enterprises.
I would add a fifth, and it is my biggest worry with such a policy: what if the winner ends up being a dud? Do we have the capacity to be ruthless and play hardball? To me, it is this that was, and remains, the key differentiator between East Asia of the 60’s and India today.
