Arun Chandrasekhar
arunc@mit.edu
E52-201
Office Hours:

Outline:
  - Perspectives
  - Basic statistics
  - PPP Adjustment
  - Misc.

=Perspectives=
"The difference between microeconomics and macroecnomics is that macroeconomics matters"
  - X S-M (Xhavier Sale-Martin at Columbia)
That's an old developmental economics opinion.  We're going to be covering a
  lot of micro topics like microlending, food, health, etc.

Along these lines, there's:
  - Banerjee (2008)---growth is all you need (e.g. China).  So development
    economists should just study growth (GDP per head).
     -> So study growth for development
     -> Meaning study macro

Counterarguments
  - correlation of growth to development is not causation
  - nigeria is different from china in a particular way.  averaging the two
    countries together might swallow nigeria's backward growth for the poor
    into china's general shift of the poor upward.

Microeconomics helps us study what happens with every marginal dollar
  spent, and what the output of various inputs is.

=Statistics=
Say we want to know if there is a meaningful economic effect of some policy

ITN---insecticide-treated bednets.
Say we give nets to half of families in a village.  Possible outcomes:
  - % infected with malaria
  - % people using nets
  - % people who are healthy and working
  - productivity levels
  - histogram of what age groups live/die

These are compared to some baseline or a similar village
Say we go with % infected.  Compare it to baseline.
  - baseline was 27%
  - measured (27 - \alpha)%
At what alpha are we significant?

Probability:
  Sample space---all possible events---\Omega
  P[A] >= 0
  P[\Omega] = 1
  P[Union of all disjoint A_i] = Sum(P[A_i])
  Probability Mass Function---discrete version of function that takes events and
    outputs probability
  Probability Density Function---continuous version of this
  Cumulative Density Function---F(x) = P[X<=x]
    -> That's the integral of the PDF
For the flipping of a fair coin twice, if X is a random variable for number of
  heads, then the CDF is:
   F(x) = 0 if x < 0
          .25 if x\in[0,1) (x=0)
          .75 if x\in[1,2) (x=1)
          1 if x\in[2,\infinity] (x=2)
Note: CDF at the median is .5, since half of the sample space is to the
  left of it.
So if the CDF of purchasing power shifts to the right over time, then you could
  argue that "the world got richer."  But that's not the only possibility.
  It's possible that more of the world got richer, but one country leapfrogged
  another, and the other got poorer, and at the macro level, it would seem
  that _everyone_ is doing better!

Expectation
  \mu = E[X] = integral(xf(x))dx -> value times its probability, summed
  Var(X) = integral(((x-E[x])^2)f(x))dx
  \sigma(x) = sqrt(Var(x)) -> standard deviation

Central Limit Theorem/Law of Large Numbers
  - Xbar = (1/n) (Sum X_i) -> average
  - E[Xbar] = E[X] (the expectation of the average is the expectation of the variable)
     E[aX+b] = aE[X] + b, so by linearity, E[Xbar] = E[X]
  - Var[Xbar] = ?

Law of large numbers
  -> If you keep taking samples, Xbar (the average) approached E[X] (the true mean)
  -> Central Limit Theorem
      (Xbar - E[X])/(\sigma/sqrt(n)) -> N(0,1) (normal with mean 0 and stddev 1)

So significance is how likely your change was to not just be caused by a mistake.

Read, Donald and Grey, look for email on purchasing power parity