Archive for April, 2006

Sorry for the lack of updates..

April 28, 2006

And to compensate for it, I will recite to you a ditty I learnt when I was a leeeetil kid.

Sorry Sorry, Gadhey Ki Lorry,
uspar baithi Meena Kumari,
Meena Kumari ka laal dupatta,
us-se nikala ullu ka paththa,
ullu ke paththe ne khaayi amrood,
us-se nikale Mr. Mehmood,
Mr. Mehmood ne lagaayi aawaaz,
Mahatma Gandhi Zindabaad!

* Apologies to the non-Hindi Speakers amongst my (mostly hypothetical) readers.

The problem, my dear readers, is that the wells of negativity that usually supply me with material for this blog have run dry. Not that I am *happy* or anything like that – it’s just an annoying little phase of positivity that I am sure will pass.

I could rant about feeling positive because it makes me hate the world even more and cramps my style, but such ranting takes effort, and I am too lazy to do that. Meanwhile, it is every intention of mine to pile on drivel like this.

Happy Easter from mentaldeviation!

April 17, 2006

*Inspired by cheery “Happy Easter” posts like these.

My reservations post

April 14, 2006

Since every self respecting blogger has made their voice heard in this brouhaha about reservations, I thought I would chip in too, being a self-respecting individual myself. 🙂 The point I make might appear pedantic. Nevertheless, do hear me out. (Hello. Is there anybody out there?)

There is an important assumption made by proponents of reservations (and occasionally, this is a point conceded by those who oppose it). It sounds like the following:

The Backward Classes are disadvantaged. Hence they are unable to develop skills (that are required for competing). This is due to lower intelligence due to poor childhood nutrition, an environment that is not conducive to skill development, and other such factors. By enforcing quotas so that lower skill candidates get access to centres of excellence, the next generation is more likely to possess the skills required to compete, and society, as such, will benefit through access to more productive human resources (within multiple, if not within one generation)

Although it appears very plausible first hand, let us analyse the implications in terms of cost to society and productivity. Let us also (in a sense) bring in the notion of comparative advantage amongst groups, in a setting where the education of parents affects the skill sets of children. I will not address the issue of “social justice”, for it is not clear to me what that means. I will make the following assumptions.

1. There are two groups in society – The advantaged/high skilled group (H) and the disadvantaged/low skilled group (L). Time proceeds in discrete steps, each step corresponding to a generation.

2. There are two kinds of educational resources – Good (G) and Bad (B) with a fixed number of seats each.

3. Good educational resources are costlier to society.

4. Each agent, when she dies, produces a child. The child could be advantaged or disadvantaged with probabilities that depend on the kind of agent that she is, and the level of education she received.

5. The probabilities are such that if an agent has received good schooling, whether they were advantaged or not does not matter, they are equally likely to produce an advantaged child, and this likelihood is significantly greater than 1/2. On the other hand, disadvantaged agents that get poor schooling are very unlikely to produce advantaged children. This is the standard argument used in support of reservations.

6. Advantaged agents that are “forced” to go to a bad school have a lower likelihood of producing an advantaged child than if they had got a good education. These likelihoods are indicators of social mobility, and will have a large role to play in our subsequent analysis.

Ok, so I hope you are with me. Go back to my assumptions and check them. Note down any disagreements. Especially look at number 5. It implies that regardless of what you do, in the “steady state” there will always be disadvantaged agents in the society (and also, somewhat trivially, that the population is constant, which is not so serious, because I have never heard any arguments in support of reservations that appeal to population growth).

Now, coming to the productivity of the agents.

7. Before dying, agents produce an amount of goods that is defined by their productivity, and is more than the cost incurred for their education. The productivity of disdvantaged agents is lower than that of the advantaged agents (owing to lower skill-sets). The difference does not matter, it can be arbitrarily small. All that matters is that there is a difference. In my setting I use the following assumption: Productivity (H,G) > Productivity(L, G) > Productivity(H,B) > Productivity(L,B).

8. The total number of seats is the same as the number of agents. This is not such a serious assumption, because in the sense of our stylized setting, “no education” can be defined as a very weak form of educational resource (with zero cost).

9. “Good” seats are always scarce resources even for the advantaged group and even in the absence of reservations, in the sense that the number of good seats is less than the number of advantaged agents. Another very crucial assumption that is often ignored by those who advocate reservations.

10. The person who allocates seats to groups is a social planner who is looking to maximise the overall gain to society (production – cost of education). This is the same as the “society as a whole will gain” argument made by those who advocate reservations. The social planner also gives greater weight to gains in the near future than to those in the far future. (Discount factor less than 1)

Right then, so now let us look at what our social planner does. It is easy enough to analyze the “steady state” that society reaches with these probabilities, with these
assumptions. Solving our little model mathematically , we can establish the following little factoid: For each constant reservation policy (defined as the proportion of good seats allocated to disadvantaged agents), there is a unique steady state. For a given value of parameters, the utility of the planner is monotonic (either increasing or decreasing) in the reservation policy.

That is, depending on the value of costs/productivities/progeny assumed, the “best” reservation policy is either 100% or 0, but nowhere in between.

I am not going to go into the model, but i will intuitively explain it. What constrains the level of skill in society is the number of good seats. As long as good seats are scarce resources, society is always better of giving off all the good seats to the greater productivity agents. However, for some values of the probability of producing productive offspring and their relative productivities, it is always better for society to allocate all the good seats to the disadvantaged agents. The policy takes an “all or nothing” form depending the values of parameters.

What the model is very sensitive to is this: If the progeny of an advantaged agent who was forced to get a poor education still has a decent likelihood of being advantaged, and at the same time the progeny of a disadvantaged agent who was forced to get a poor education is very unlikely to be advantaged, then a policy of 100% reservations works. If the difference between these likelihoods is not as stark, then a policy of no reservations at all is the best policy.

I will show you some pictures now. I have fixed the values of other parameters, and considered a population of 100 with 20 good seats available. The first picture is the effect the social mobility for poorly educated people has on the optimal reservation policy. The knife edge is clearly visible. The second is the gain to society depending on the mobility. It shows that society gains with greater social mobility. The third is the number of advantaged people in the society. You will see a cliff in this picture, and it corresponds to the knife edge where it suddenly become more optimal to have no reservations at all, and suffer a lack of advantaged workers.

The interesting point to be noted around this cliff that for the same level of utility to the planner, reservations increase the number of advantaged workers in society. I am unwilling, however, to attach any social justice implications to this. Have fun with these pictures. With such a simplistic model, it is amazing the level of complexity you can get. And I have not even talked about relative productivity effects!!

This is admittedly a rather shallow analysis, and I am sure alternate settings could be imagined, which could, perhaps lead to completely different conclusions. But it is very interesting indeed.

(This work is preliminary and incomplete and may not be cited.)

Eulogy for a friend

April 6, 2006

My first encounter with Chris was on a hurried monday morning. I had picked up a bagel (cinnamon-raisin, toasted, with butter) at the bagel shop near the subway, and was on my way out, when I ran into an old gentleman slowly shuffling his way in. I excused myself, only to be greeted with a cheerful, “How are you doing today?” When I muttered the expected grumpy New York response (“Good. You?”), he responded with a “Cheer up. Its a great day”, which only annoyed be further.

I ran into Chris several times after that incident. Over time I came to take his cheerfulness for granted. It was one of the few constants in a bipolar world. It was good to chat with him over a bagel or a sandwich, and occasionally, as old men are wont to do, he would tell me the story of his life. I got to know, for instance, that he lived with his daughter and her children in a house nearby. He was born and raised in the Brooklyn of the early 20th century – when it was rough neighborhood in the process of being gentrified. I knew that he was ninety and had fought in the second world war – he claimed that he had a bullet lodged in his thigh (which gave him his limp) and that he had killed nine germans on D-day, and had been decorated for it.

In some ways, he reminded me of a grandfather I lost seven years ago – someone I grew up with, and who was responsible, to a great extent, for many of the values that I cherish. There were a lot of physical similarities between them. And they would have been roughly the same age.

Chris died a few days ago – it came to my knowledge only today. He was a stranger in many ways -I never got to know his last name – and yet, he was a reminder of how connected humanity is, and an example of how nostalgia can strike you in places where you least expect it to. I do not grieve for him – his death does not make a significant difference to my life. But, at the least, it deserves this post.


April 4, 2006