PROBLEM SET 3 - EC551 (A1)
Spring 2021 – Daniele Paserman

Due: no later than Thursday, 4/8/2021 at 11:59pm Eastern time
Problem Set must be uploaded on Blackboard in the appropriate section.

Please submit your problem set as a single PDF file titled PS3_[LastName][Firstname].pdf.
Example: PS3_PasermanDaniele.pdf.


Remarks:
All work handed must be your own, with the exception that you are encouraged to discuss your
papers with each other but must turn in separate work demonstrating independent thought and
investigation.
Answers must not be poems, so try to keep your answers short. But don’t forget to explain your
results, because a single number without any explanation or the appropriate algebraic passages
will be graded lower.

Introduction
The file MinimumWage_ByState_2011-2019.dta (also available in .csv format)
contains information on the minimum wage in each US state and the District of Columbia
between 2011 and 2019. The data is taken from:
https://www.dol.gov/agencies/whd/state/minimum-wage/history. In cases in which there is more
than one minimum wage in a state, the value in the table is the highest possible value.
The file ps3_cps2011-2019.dta is a Stata file with a raw extract of the CPS for the months
of February, May, August and November between 2011 and 2019. Notice that the data is raw.
For the analysis, you will have to make sure that you clean the data (identify missing values
and categorical variables and eventually transform the data in a way that is amenable to
regression analysis).
I have also made available two additional data sets:
- cb_2018_us_state_5m.shp. This is called a shape file, and contains information
on the geographic coordinates of US states, which can then be used to draw maps in
Stata.
- cb_2018_us_state_crosswalk.dta. This is a Stata file with a crosswalk
between the state codes used in the shape file and the states codes used in the minimum
wage data set and in the CPS.

In the Problem Set, you will be asked to perform a number of analyses to describe the evolution
of minimum wage laws across states, and its impact on employment, wages, and family
outcomes.
Part A: Mapping the Minimum Wage (15 points)
In this part, you are asked to graph the data on minimum wages into a map. To create maps, you
will need to install the user-written commands spmap, shp2dta and mif2dta. See here for a starter
on how to create maps in Stata: https://www.stata.com/support/faqs/graphics/spmap-and-maps/
[The default maps created by Stata tend look a bit distorted relative to maps that you may be
familiar with. This has to do with the well-known problem of rendering in two dimensions maps
of the surface of the Earth, an ellipsoid. To make more familiar maps, you can also download the
user written command geo2xy]
1) Using the MinimumWage_ByState_2015-2019.dta file, create in Stata a
cloropleth map of minimum wages by state in 2011, 2015 and 2019, for the 48
contiguous US states (excluding Alaska and Hawaii). Comment on the results. Which
states tend to have high minimum wages? Which states tend to have low minimum
wages?
2) Create a new variable equal to the change in the minimum wage by state between 2011
and 2019 (you will probably have to use the egen command in Stata). Map this variable
and comment on the results. Which states had the largest absolute increase in the
minimum wage? Which ones had the lowest?
3) Run a regression of the absolute change in the minimum wage on the minimum wage in
2011. Comment on the results. How do these results relate to the maps you drew in
questions 1 and 2?

Part B: The effect of the minimum wage on employment (36 points)
For this part of the problem set, load the CPS data, and merge it by state and year with the
minimum wage data using the merge command. Define the effective minimum wage in a state
as the maximum between the state minimum wage and the federal minimum wage, which was
$7.25 throughout this period. Create a variable equal to ln(effective minimum wage). We will
call this lnܯܹ݅݊ܽ݃݁௦௧.
4) (6 points) Consider the following model:
ܧ݉݌݈݋ݕ݁݀௜௦௧ = ߚ଴ + ߚଵ lnܯܹ݅݊ܽ݃ ௦݁௧ + ݑ௜௦௧ (1)
Under what assumptions does this model yield a consistent estimate of the causal effect
of the minimum wage on employment? Do you think these assumptions are likely to be
satisfied in this context?
5) (6 points) Consider instead the alternative model:
ܧ݉݌݈݋ݕ݁݀௜௦௧ = ߚ଴ + ߚଵ lnܯܹ݅݊ܽ݃ ௦݁௧ + ߜ௦ + ߛ௧ + ݑ௜௦௧ (2)
where ߜ௦ represents state fixed effects and ߛ௧ represents time fixed effects. Under what
assumptions does this model yield a consistent estimate of the causal effect of the
minimum wage on employment? Do you think these assumptions are likely to be
satisfied in this context? Give an example
6) (6 points) Estimate the models in parts 4) and 5), using the sample of all individuals
between 15 and 64 year old, and report the results in a table that looks like Table 1 below.
(Make sure to also report the number of observations and the mean of the dependent
variable). Comment on the results. Are the results consistent with the textbook model of
the minimum wage?
Table 1: Baseline Model

Part (4): without fixed effects Part (5): with fixed effects lnܯܹ݅݊ܽ݃ ௦݁௧ Coefficient
(standard error)
Coefficient
(standard error)

Number of
observations

Mean of the
dependent variable

State fixed effects No Yes
Time fixed effects No Yes

7) (6 points) Estimate the model in part (5) for:
a) Only individuals with less than a high school degree.
b) Only individuals with at most a high school degree.
c) Teenagers (ages 15-19).
d) Blacks or Hispanics.
Report the results in Table 2 below. Comment on the results. Why are we interested in
these subgroups? Are the results for the different subgroups consistent with the textbook
model?
Table 2: Minimum wage and employment – Different Samples

Full sample
(same as
column 2,
part 6)
High school
dropouts
High school
or less
Teenagers Black or
Hispanic
lnܯܹ݅݊ܽ݃ ௦݁௧ Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)

Number of
observations

Mean dependent
variable

State fixed
effects
Yes Yes Yes Yes Yes
Time fixed
effects
Yes Yes Yes Yes Yes

8) (12 points) An economist thinks that equation (2) (from part 5) does not yield consistent
estimates of the effect of the minimum wage on employment because there may be other
variables that affect employment rates and are correlated with the minimum wage. She
therefore suggests that you estimate the following model:
ܧ݉݌݈݋ݕ݁݀௜௦௧ = ߚ଴ + ߚଵ lnܯܹ݅݊ܽ݃ ௦݁௧ + ߚଶԢ ௜ܺ௦௧ + ߚଷᇱܼ௦௧ + ߜ௦ + ߛ௧ + ݑ௜௦௧,
where ܺ௜௦௧ is a vector of individual characteristics and ܼ௦௧ is a vector of time-varying state
characteristics. Estimate the model above, report the results in Table 3 below, and comment
on what you find. but make sure to follow the following guidelines:
- You are free to choose any variables you want in ܺ௜௦௧ and ܼ௦௧, but remember that
you want to include variables that will plausibly address your economist friend’s
concerns: variables that are likely to affect the employment rate, but also may be
correlated with the minimum wage. Explain your rationale for including these
variables.
- You should have at least one variable in the ܺ௜௦௧ vector and one variable in the ܼ௦௧
vector. For variables in ܺ௜௦௧, you will have to simply choose variables in the CPS
sample. For variables in ܼ௦௧, you can either construct them from the CPS sample, or
merge them into the data set from other sources (but state clearly what the sources are).
These can be demographic characteristics (e.g., the share of the population with a
certain characteristic), economic characteristics (e.g., the share of workers employed
in the hospitality industry), political characteristics (the share of votes for the
Democratic candidate in the previous presidential election), etc.
- Make sure to include the variables correctly in the regression equation (make sure
that you drop missing values; transform discrete variables into a series of dummy
variables; make any non-linear transformations if necessary, etc.).

Table 3: Minimum wage and employment – Different Samples, With Controls

Full sample High school
dropouts
High school
or less
Teenagers Black or
Hispanic lnܯܹ݅݊ܽ݃ ௦݁௧ Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)

Number of
observations

Mean dependent
variable

Control variables Yes Yes Yes Yes Yes
State fixed
effects
Yes Yes Yes Yes Yes
Time fixed
effects
Yes Yes Yes Yes Yes


Part C: The effect of the minimum wage on hourly wages (12 points)
For this part, you will work with the sample of workers who are paid by the hour. Replace the
hourly wage variable (hourwage) to be equal to missing if the hourly wage is equal to 999.99 or
if the hourly wage has been allocated (based on the qhourwag variable).
9) Estimate regressions similar to those of part 8), but using ln(hourwage) as the dependent
variable. Report the results in Table 4 below and comment on what you find.
10) Some economists suggest that one can calculate the elasticity as labor demand as:
߲݈݊ܮ
߲݈݊ݓ
= ߲ ln ܮ߲ lnܯܹ
߲ lnݓ
߲ lnܯܹ .
Use the estimates in parts 8 and 9 and the margins command in Stata (see also Problem
Set 1) to estimate the elasticity of labor demand using this formula, for the 5 different
samples. What do these elasticity estimates imply for the effect of a minimum wage
increase on the earnings of these different groups (earnings = employment×wages)?

Table 4: Minimum wage and ln (wages) – Different Samples, With Controls

Full sample High school
dropouts
High school
or less
Teenagers Black or
Hispanic lnܯܹ݅݊ܽ݃ ௦݁௧ Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)
Coefficient
(std. error)

Number of
observations

Mean dependent
variable

Control variables Yes Yes Yes Yes Yes
State fixed
effects
Yes Yes Yes Yes Yes
Time fixed
effects
Yes Yes Yes Yes Yes


Part D: The effect of the minimum wage on the distribution of wages (10 points)
We will now study how the minimum wage affects the whole distribution of wages. Create a
new variable equal to the difference between the hourly wage of individual ݅ in state ݏ at time ݐ
and the 2019 effective minimum wage. Call this variable diff2019.
݂݂݀݅2019௜,௦,௧ = ݓ௜௦௧ െ ܯܹ݅݊ܽ݃݁௦,ଶ଴ଵଽ .
Split the sample into two: states in which the effective minimum wage did not increase between
2011 and 2019 (including the states in which there is no minimum wage); and states in which the
minimum wage did increase between 2011 and 2019.
11)
a. Draw a histogram of diff2019 in years 2011-2013 in states that did not
increase the minimum wage. Restrict the sample to values of diff2019 between
-11 and +15. Use the width and start options of the histogram command
to have bins of width equal to $1 and starting at whole dollar values. Use the
xline option to superimpose a vertical line at 0.
b. Repeat part a), but now for the year 2019.
c. Repeat parts a) and b), but now for the sample of states that did increase the
minimum wage between 2011 and 2019.
Comment on the four histograms. How did the entire distribution of wages change in
states that increased the minimum wage between 2011 and 2019? What about states that
did not increase the minimum wage? Would you say that today the minimum wage is
binding in states that have not increased the minimum wage since 2011?

Part E: Who gets paid the minimum wage? (12 points)
In this part, we will split the sample on the basis of the variable relate, the relationship with
the head of the household. Divide the sample into five groups:
a) Heads of household with dependents. Heads of households (relate==101), spouses
(relate ==201) or unmarried partners (relate==1114) in households in which there are any
dependent children, foster children, or other relatives.
b) Heads of household without dependents. Heads of household, spouses or unmarried
partners in households in which there are no dependent children, foster children, or other
relatives.
c) Children. Children (relate==301) or foster children (relate==1242) of the head of
household.
d) Other relatives. Other relatives of the head of household (parents, siblings,
grandparents, other relatives)
e) Other nonrelatives. Other nonrelatives of the head of household, including
housemates, roomers/boarders and other nonrelatives.
[Hint: you can uniquely identify every household in the sample by the combination of year,
month and the variable serial. Then, use the egen command in the Stata to identify households
with and without dependents.]
Define a person as a minimum wage recipient if their wage is at most $0.99 higher than the
effective minimum wage in the state.
12) For the whole population of 15-64 years olds, what fraction of minimum wage recipients
are heads with dependents, heads without dependents, children, other relatives and other
nonrelatives?
13) Repeat part 12, but now do it separately for a) states that did not increase the minimum
wage, for the years 2011-2013; b) states that did not increase the minimum wage, for
2019; c) states that did increase the minimum wage, for the years 2011-2013; d) states
that did increase the minimum wage, for 2019. Comment on the results. Is it correct to
say that the minimum wage is an ineffective tool for combating poverty, because the
beneficiaries of the minimum wage are mostly teenagers, many of which are potentially
in relatively affluent households?

Part F: Final thoughts
14) Summarize briefly (no more than half a page!) what you have learned from this problem
set about the minimum wage. Has the evidence in this problem set made you more or less
likely (or no change) to support a gradual increase in the federal minimum wage to $15
per hour?





















































































































































































































































































































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