|
Econ 615 Assignments
Georgetown University
Fall 2013
John Rust,
Georgetown University
Assignment 2 (due Tuesday Dec 3rd)
Write a short essay comparing and contrasting and offering your views on the pros and cons
to the different philosophies toward econometrics as reflected in the following two new books
Kenneth I. Wolpin (2013) The Limits of Inference without Theory
MIT Press
Password protected temporary version here
Charles F. Manski (2013 Public Policy in an Uncertain World
Harvard University Press
Password protected temporary version here
My own comments on Manski and Wolpin's book (I was asked to do a review of Wolpin's
book for the June, 2014 issue of the Journal of Economic Literature. I have a 5000-7000 word limit so that these comments will have
to be dramatically edited down, but I wanted to provide an unabridged version for the students in Econ 615 to see).
Assignment 3 (due Tuesday Dec 3rd)
Use the Matlab/C code and data files in the distribu.zip file below to
structurally estimate (using full or partial maximum likelihood estimate) the utility function parameters, and the paramters
of the wage equation, probability of dying, probability of finding a job if not working and the probability of becoming
unemployed. Using the estimated model and parameters, forecast the behavior and impact on individual welfare
(measured as the aggregate willingness of a 20 year old, 50 year old and 60 year old to avoid (or adopt, if the change improves
welfare) any of the following policy changes)
the response to the following three policy changes:
Increasing the age of retirement from 62 to 70
Increasing the unemployment benefits replacement rate from 20% to 30% and the retirement benefits
replacement rate from 40% to 50% but at the same time increasing the payroll tax rate from
25% to 35%
Abolishing unemployment benefits
I have created Matlab code with artificial data resulting from a
simulation program simulate_data.m
that simulates observations
from 500 hypothetical people followed from age 20 to their deaths at age
80 (I did not worry about modelling mortality and assumed everyone survives
with probability 1 to age 80 but die with probability 1 at age 81).
The decision problem is an discrete employment decision: work versus no work,
that implements a simple static problem of optimal retirement behavior that I discussed in
class. These consumers behave myopically and each period either work or retire depending
on which decision gives them higher utility. There is a matlab function
uf.m that encodes the utility function
I have assumed, which has a square root function representing the utility of money income
(or unemployment benefits if unemployed or pension/retirement benefits if retired) less
an additive disutility of work for individuals who are working. There is also an additive
disutility of searching for a job for those who are not working but decide to search for
a job and return to work. I assume that if a person searches, they will be 100% successful
in finding a job but they do incur the disutility of finding the job. I assume that both
work disutility and the disutility of searching for a job are quadratic functions of the
person's age so that there is a coefficient work_disutility_age and another
coefficient search_cost_age that are key determinants of a) when someone decides
to retire, and b) if someone gets unemployed, whether or not they will try to go back to
work, or decide to remain on unemployment benefits (if age 55 or younger), or retire and
collect their pension (if older than 55, with 55 being the retirement age, i.e. the earliest
age at which the person can collect their pension benefits. I assume that there is a 5 percent
chance that a person can be involuntarily unemployed and this probability is IID over time.
AT the start of each year a person makes a binary work/no work choice (with d=0 representing
the decision not to work and d=1 representing the decision to work), conditional on some
state variables (y,aw,e,age) where y is their wage offer they expect (and get) if they
choose to work, aw is their average wage, e is their employment state, and of courage age is their
age. The simulation program
simulate_data.m produces the matlab
data file data.dat which stores the results
of simulating 500 people over their employment choices between age 20 and 80. The columns
of this matrix are defined by line 87 of simulate_data.m which specifies the recursive
formula for building the data.dat matrix
data=[data; [i working work_state t income pension laid_off]];
so that the binary choice variable d is the Matlab variable working. the variable
i is the sequence/ID number of a particular consumer, work_state is the employment
status at the previous period, the e state variable above, t is the person's
age, income is the state variable y and pension is the calculated
pension benefit a person could receive (if older than 55), or the unemployment benefit a person
would receive if age 55 or younger. Finally the laid_off variable is 1 if the person
is laid off during the year, or 0 otherwise. We assume that a person makes an employment
decision or intention at the start of each year, but due to unexpected events, may
be laid off ex post later in that year due to unplanned bad outcomes. The probability
of beinf laid off is unemp_prob and is assumed to equal 5% in this problem.
Your first task is to try to struturally estimate the three parameters of the utility
function theta that are set in the file setup.m.
I have written a Matlab program estimate.m that estimates
these parameters by Maximum likelihood using the log-likeihood function programmed in the
file lfeval.m. Below is the results of running
estimate.m using as starting values the true parameter values that I used to generate the data.
You can see that the estimated parameters are close to the true values.
Local minimum possible. Constraints satisfied.
fmincon stopped because the size of the current search direction is less than
twice the default value of the step size tolerance and constraints are
satisfied to within the default value of the constraint tolerance.
No active inequalities.
Estimation converged, initial likelihood: -417.41 final likelihood: -417.202
estimated vs true parameters
ans =
0.0020224 0.002
0.010182 0.01
0.5015 0.5
HINTS: I have updated the code and included the calculation of the gradient
of the log-likelihood function in lfeval.m
and I have added a new file that calculates the information matrix, information_matrix.m
and I have added code in estimate.m that conducts a Wald test of the
hypothesis that the estimated theta parameters equals the true values used to generate the artificial data.
Note that the test rejects the null hypothesis very strongly! Your job (if you choose to accept it) is to find out why and
correct any bugs in my code that may be causing the problem. Of you can ignore my code and write your own,
and not worry about what bugs there may be in my code.
If you are programming in Matlab, use the function interp2 to do 2-dimensional interpolation
that is needed to interpolate the value functions over (y,aw) values as per my other hints in lectures. Also I have
posted qgausl.m a Matlab program that generates Gaussian quadrature
weights and abscissae to numerically integrate a function of one variable over a finite interval [a,b]. Finally
note that Matlab has functions cdf to compute the cumulative distribution of various functions and
icdf to compute the inverse CDF of various functions. These functions together with the hints I provided
in lecture should enable you to write Matlab code that can calculate the dynamic labor supply/retirement
problem by backward induction.
Assignment 4
This assignment is optional, not for a grade. The purpose is to illustrate the structural
estimation of a static game via a nested fixed point, maximum likelihood approach. I have the question and
the full answer here. For the Gauss code that produced these answers
and can be used to estimate static game models using this approach, see here.
Assignment 5
Though I said it was hard to give a precise defintion of what we mean
by a model and what the difference is between a structural model
and a reduced-form model in econometrics, the best way to understand is
to read empirical work and compare and constrast methologies employed, questions
asked, and conclusions reached. In assignment one I would like you to read either
the two labor papers by Angrist and coauthors and Robin and coauthors that were presented
in the Labor Week conference here at Georgetown on Monday and Tuesday, or the two
development papers, one by Townsend and coauthor (which won the Frisch Medal of the
Econometric Society this year), and the other by Duflo and coauthor. All 4 papers are
by leading people in the profession and represent some of the very best empirical work done
in either the reduced form or the more structural econometric methodologies. However opinions
may still differ about the pros and cons of different approaches and methodologies, and
I want you to read one or the other pair of papers critically and write a several page
analysis comparing and contrasting the papers, the methodologies and what you learned
from them. There is no right or wrong answer here: just an attempt to get you into this
literature and to start to encourage you to think independently about important economic
research questions and how to analyze them empirically, and to what extent it is necessary
or desirable or valuable to have a more or less explicit model in order to
reach meaningful conclusions from data, or to make predictions or policy recommendations.
I would like you to hand in this assignment by next Tuesday, at the make up class at
10am at a location to be announced.
Readings: choose two read and write on the development papers or the labor papers, but not on both
Answers by students
|