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Using the public-debt dataset from lab 1 (available at https://ift.tt/2Aqvxqq.

Due Date
By midnight Wednesday, 1 August. Submit to kimbk@umich.edu. Please attach your solution and
the R/stata code.
1. Multicausality
Using the public-debt dataset from lab 1 (available at https://ift.tt/1kQRHPe
~franzese/debt_699.dta), do the following.
• model 1: regress debtx on growth, ue, cog and enop
• model 2: regress debtx on growth, ue and cog. Save the estimated residuals as Mdebtx.
• model 3: regress enop on growth, ue and cog. Save the estimated residuals as Menop.
• model 4: regress Mdebtx on Menop.
• Compare the coe!cients and the standard errors of enop in model 1 and that of Menop in
model 4.
• Explain any di↵erences
Omitted Variable Bias
Using the same dataset, answer the following.
• model 5: regress debtx on growth
• Compare the coe!cients of growth in model 2 and model 5.
• Explain the di↵erence using what we learned in the class
Measurement Error
• Create a variable m by drawing randomly from a standard normal distribution
• Add the measurement error m to growth, creating a mismeasured variable growth2
• Fit model 2 and model 5 again, using growth2 in place of growth
• Explain the di↵erences in the coe!cient estimates
1
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ICPSR 2018 Assignment 1 EMTI
Ubiquitous Endogeneity
We have the following relations between variables.
z = az + bz,xx + ✏z
x = ax + bx,zz + ✏x
We can write this system in matrix notation as follows.
“xz# = “aaxz# + “bx,z 0 bz,x 0 # “xz# + “✏✏xz# (1)
• Use the matrix notation to solve the system for its reduced form leaving only z and x on the
left side
• Set b
z,x = bx,z = 0.5. What is the matrix-inverse multiplier in this system?
• What does the matrix-inverse multiplier indicate about the full response of z to an exogenous
shock in x?
• In lab 1, ols estimate of bx was approximately 0.6. Using the same formula given in class for
simultaneity bias, calculate bx for this system.
2 of 2
apotheoses

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