Recitation 2

Part 1

Review the code and solution method for the search model.

Part 2

Review the code and solution method for the entry/exit model.

Part 3: CPS data

Reading the data

Let’s take a look at data from the CPS on wages, employment status, and labor market transitions. Here is code to read in the data:

using CSV, DataFrames, DataFramesMeta, Statistics

data = CSV.read("../data/cps_00019.csv",DataFrame)

183277×22 DataFrame

183252 rows omitted

Row	YEAR	SERIAL	MONTH	HWTFINL	CPSID	ASECFLAG	PERNUM	WTFINL	CPSIDP	AGE	SEX	RACE	MARST	EMPSTAT	LABFORCE	UHRSWORKT	DURUNEMP	EDUC	HOURWAGE	PAIDHOUR	EARNWEEK	UHRSWORKORG
	Int64	Int64	Int64	Float64	Int64	Int64?	Int64	Float64	Int64	Int64	Int64	Int64	Int64	Int64	Int64	Int64	Int64	Int64	Float64	Int64	Float64	Int64
1	2018	2	1	1609.49	20161200000200	missing	1	1420.75	20161200000201	72	1	100	1	10	2	55	999	81	99.99	0	9999.99	999
2	2018	3	1	1797.04	20180100000300	missing	1	2053.27	20180100000301	66	1	100	1	10	2	997	999	111	99.99	0	9999.99	999
3	2018	3	1	1797.04	20180100000300	missing	2	1797.04	20180100000302	61	2	100	1	10	2	997	999	111	99.99	0	9999.99	999
4	2018	9	1	1735.76	20171000000400	missing	1	1735.76	20171000000401	52	2	200	4	10	2	40	999	73	20.84	2	903.0	999
5	2018	9	1	1735.76	20171000000400	missing	4	3069.4	20171000000404	19	2	200	6	10	2	40	999	73	10.0	2	400.0	40
6	2018	10	1	1582.77	20171000000600	missing	1	1582.77	20171000000601	56	2	200	4	10	2	40	999	111	25.0	2	1250.0	999
7	2018	10	1	1582.77	20171000000600	missing	2	2409.42	20171000000602	22	2	200	6	10	2	30	999	81	9.5	2	70.0	999
8	2018	11	1	1795.64	20170100000900	missing	1	1795.64	20170100000901	23	2	100	6	10	2	40	999	124	99.99	0	9999.99	999
9	2018	11	1	1795.64	20170100000900	missing	2	1795.64	20170100000902	24	2	100	6	10	2	40	999	124	99.99	0	9999.99	999
10	2018	12	1	1927.69	20170100001000	missing	1	1927.69	20170100001001	59	2	200	1	10	2	55	999	111	99.99	0	9999.99	999
11	2018	12	1	1927.69	20170100001000	missing	2	2151.5	20170100001002	53	1	200	1	10	2	58	999	81	99.99	0	9999.99	999
12	2018	14	1	2926.96	20171200001200	missing	1	2926.96	20171200001201	24	2	200	6	10	2	40	999	73	99.99	0	9999.99	999
13	2018	15	1	1861.24	20161200000800	missing	1	1557.36	20161200000801	60	1	100	1	10	2	40	999	124	99.99	0	9999.99	999
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
183266	2018	72283	3	275.748	20170107444500	2	3	280.118	20170107444503	33	1	100	6	21	2	999	61	73	99.99	0	9999.99	999
183267	2018	72286	3	332.029	20170307448900	2	1	332.029	20170307448901	44	2	100	1	10	2	30	999	111	99.99	0	9999.99	999
183268	2018	72286	3	332.029	20170307448900	2	2	334.955	20170307448902	46	1	100	1	10	2	45	999	91	99.99	0	9999.99	999
183269	2018	72288	3	341.227	20171207232200	2	1	341.227	20171207232201	42	1	100	6	10	2	40	999	111	99.99	1	365.0	999
183270	2018	72288	3	341.227	20171207232200	2	2	281.741	20171207232202	41	2	100	4	10	2	40	999	73	14.0	2	560.0	40
183271	2018	72289	3	256.804	20170107445500	2	1	256.804	20170107445501	42	1	100	4	10	2	45	999	73	99.99	0	9999.99	999
183272	2018	72291	3	281.741	20171207232600	2	1	507.056	20171207232601	42	1	100	1	10	2	40	999	111	99.99	1	519.23	999
183273	2018	72291	3	281.741	20171207232600	2	2	281.741	20171207232602	43	2	100	1	10	2	50	999	123	99.99	1	1442.3	999
183274	2018	72291	3	281.741	20171207232600	2	4	377.923	20171207232604	18	1	100	6	10	2	15	999	60	9.0	2	108.0	12
183275	2018	72292	3	288.99	20171207232700	2	1	288.99	20171207232701	32	2	100	6	10	2	40	999	81	25.0	2	1000.0	40
183276	2018	72292	3	288.99	20171207232700	2	2	288.99	20171207232702	30	2	100	1	10	2	20	999	81	99.99	0	9999.99	999
183277	2018	72292	3	288.99	20171207232700	2	3	336.057	20171207232703	31	1	100	1	10	2	997	999	91	99.99	1	1346.0	999

As you can see from the preview of the data, the data is taken from January-March 2018. Here is a quick snippet of code to see how many observations we have on average per person:

@chain data begin
    groupby(:CPSIDP)
    @combine :T = length(:EMPSTAT)
    @combine :average = mean(:T) :frac_panel = mean(:T.>1)
end

1×2 DataFrame

Row	average	frac_panel
	Float64	Float64
1	1.83191	0.582806

So we see that more than half of the individuals in this sample can be found in more than one month of the data.

The @chain macro comes from the package DataFramesMeta and is a convenient syntax for composing operations into one block. For example:

@chain x begin
    func1(y1)
    func2(y2)
    func3(y3)
end

is equivalent to

func3(func2(func1(x,y1),y2),y3)

Calculating some moments

You may find the codebook useful for understanding particular variables. We have already limited the data to individuals who are working (EMPSTAT=10), have a job but did not work last week (EMPSTAT==12), or are unemployed (EMPSTAT==21).

Suppose we wanted to use the panel dimension to measure transition rates. Here is a simple way to do that by simply measuring transitions between January and Feburary.

data[!,:E] .= data.EMPSTAT.<21 #<- code the employment variable

data_jan = @chain data begin
    @subset :MONTH.==1
    @select :CPSIDP :AGE :SEX :EDUC :RACE :E
    @rename :E_lag = :E
end

data_merged = @chain data begin
    @subset :MONTH.==2
    @select :CPSIDP :E
    innerjoin(data_jan,on=:CPSIDP)
end

41262×7 DataFrame

41237 rows omitted

Row	CPSIDP	E	AGE	SEX	EDUC	RACE	E_lag
	Int64	Bool	Int64	Int64	Int64	Int64	Bool
1	20161200000201	true	72	1	81	100	true
2	20180100000301	true	66	1	111	100	true
3	20180100000302	true	61	2	111	100	true
4	20170100000901	true	23	2	124	100	true
5	20170100000902	true	24	2	124	100	true
6	20170100001001	true	59	2	111	200	true
7	20170100001002	true	53	1	81	200	true
8	20171200001201	true	24	2	73	200	true
9	20161200000801	true	60	1	124	100	true
10	20161200000802	true	57	2	123	100	true
11	20170100001401	false	50	2	73	200	false
12	20170100001403	true	18	1	81	200	true
13	20170100001405	true	29	1	50	200	true
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
41251	20161107451001	true	59	1	92	100	true
41252	20161107451901	true	59	1	91	100	true
41253	20171107237801	true	45	1	91	100	true
41254	20171107237802	true	37	2	123	100	true
41255	20171207232201	true	41	1	111	100	true
41256	20171207232202	true	41	2	73	100	true
41257	20161107452301	true	38	1	73	100	true
41258	20161107452302	true	29	2	73	100	true
41259	20170107445501	true	41	1	73	100	true
41260	20171207232601	true	42	1	111	100	true
41261	20171207232602	true	43	2	123	100	true
41262	20171207232604	true	17	1	60	100	true

So now we can calculate the overall transition rate out of unemployment:

@combine data_merged begin
    :EU =  1-mean(:E[:E_lag.==1])
    :UE = mean(:E[:E_lag.==0])
end 

1×2 DataFrame

Row	EU	UE
	Float64	Float64
1	0.00997824	0.377255

So here we’re estimating a very low separation rate and a pretty high hazard rate out of unemployment.

Observable heterogeneity

Next we’ll define a very simple education classification (Bachelor’s degree or not) and race classification (white vs non-white), and use groupby to calculate rates separately by demographics:

@chain data_merged begin
    @transform begin
        :bachelors = :EDUC.>=111
        :nonwhite = :RACE.!=100 
    end
    groupby([:bachelors,:nonwhite,:SEX])
    @combine begin
       :EU =  1-mean(:E[:E_lag.==1])
       :UE = mean(:E[:E_lag.==0])
    end 
end

8×5 DataFrame

Row	bachelors	nonwhite	SEX	EU	UE
	Bool	Bool	Int64	Float64	Float64
1	false	false	1	0.0131	0.40257
2	false	false	2	0.0110061	0.385417
3	false	true	1	0.0159176	0.338346
4	false	true	2	0.0150977	0.300885
5	true	false	1	0.00447284	0.315315
6	true	false	2	0.00601388	0.489362
7	true	true	1	0.00547303	0.342105
8	true	true	2	0.00836237	0.290323

What do these differences in transition rates tell you about how we should extend the simple model with homogenous parameters?

A Disclaimer for IPUMS CPS data

These data are a subsample of the IPUMS CPS data available from cps.ipums.org. Any use of these data should be cited as follows:

Sarah Flood, Miriam King, Renae Rodgers, Steven Ruggles, J. Robert Warren, Daniel Backman, Annie Chen, Grace Cooper, Stephanie Richards, Megan Schouweiler, and Michael Westberry. IPUMS CPS: Version 11.0 [dataset]. Minneapolis, MN: IPUMS, 2023. https://doi.org/10.18128/D030.V11.0

The CPS data file is intended only for exercises as part of ECON8208. Individuals are not to redistribute the data without permission. Contact ipums@umn.edu for redistribution requests. For all other uses of these data, please access data directly via cps.ipums.org.