Estimating Okun's Law using data from Economic Report of the President 2020

[Jo Shekar]

Hi,

I am a beginner in stata, trying to estimate Okun's law using data from Economic Report of the President for years between 1959-2019. My variables are pcrgdp (percentage change in real GDP), unem (civilian unemployment rate), cunem (unem – unem[n-1]). I am referring to the paper “Okun’s Law: Fit at Fifty?” (Ball et al., 2013). Link to the paper-https://www.imf.org/en/Publications/...it-at-50-40236. In this paper, they use the following equations-

1. Ut – Ut* = β (Yt – Yt*) + εt, β < 0,

Where, Yt is the log of output, Ut is the unemployment rate, and *indicates a long-run level and β = γδ and εt = μt + δ ηt . Equation 1 is derived from-

Et – Et* = γ (Yt – Yt*) + ηt, γ > 0;
Ut – Ut* = δ (Et – Et*) + μt, δ < 0;

1. ΔUt = α + β ΔYt + ωt,

Where Δ is the change from the previous period. In this case, differencing the levels equation (1) yields equation (2) with α= –β ΔY*, where ΔY* is the constant growth rate of potential and ωt = Δ εt

I wanted to confirm if the following stata command is equivalent to equation 1?

regress cunem lnpcrgdp

I also tried using an HP filter as used in the paper with smoothing parameters of λ= 100 and λ = 1,000, however, the command for pcrgdp did not provide any results.

tsfilter hp pcrgdp_hp = pcrgdp

Can someone confirm if the stata commands for equation 1 are correct? Furthermore, how should I estimate equation 2? Thanks for considering this!

[Jo Shekar]

Apologies, equation 2 -

2. ΔUt = α + β ΔYt + ωt

[Justin Niakamal]

I think it's best you use time-series operators. You can read about them here.

I also tried using an HP filter as used in the paper with smoothing parameters of λ= 100 and λ = 1,000, however, the command for pcrgdp did not provide any results.

You'll need to specify the smoothing parameter using the smooth(#) option and you'll want to generate the trend component -- see the help file for tsfilter. hp. So something like

tsfilter hp cyc_gdp = gdp, smooth(100) trend(tr_gdp)

As for equation 2, something like this is what's being done in table 3 equation 3 of the paper you referenced (note that the sample time frame isn't the same).

clear 
tempfile temp

* unemployment rate 
local v = "UNRATE"
import delimited using "https://fred.stlouisfed.org/series/`v'/downloaddata/`v'.csv", clear

gen quarter = qofd(date(date, "YMD"))
collapse (mean) value , by(quarter)
ren value un 
save `temp'

* real gdp 
local v = "GDPC1"
import delimited using "https://fred.stlouisfed.org/series/`v'/downloaddata/`v'.csv", clear

gen quarter = qofd(date(date, "YMD"))
ren value gdp 
gen gr_gdp = 100*(gdp/gdp[_n-1] - 1)

merge 1:1 quarter using `temp', keep(match) nogen


format quarter %tq
tsset quarter, quarterly 

reg D.un gr_gdp


      Source |       SS           df       MS      Number of obs   =       288
-------------+----------------------------------   F(1, 286)       =    243.02
       Model |  19.1718857         1  19.1718857   Prob > F        =    0.0000
    Residual |  22.5625276       286  .078889956   R-squared       =    0.4594
-------------+----------------------------------   Adj R-squared   =    0.4575
       Total |  41.7344132       287  .145416074   Root MSE        =    .28087

------------------------------------------------------------------------------
        D.un |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      gr_gdp |  -.2743288   .0175975   -15.59   0.000    -.3089658   -.2396919
       _cons |   .2127309   .0214367     9.92   0.000     .1705372    .2549246
------------------------------------------------------------------------------

Hope this helps.

[Jo Shekar]

Hi Justin,

Thanks so much for sharing this!

I tried to use time series filters and the code you specified for the dataset extracted from Economic Report of President 2020. However, I get the following output-

Code:
. tsset pcrgdp
time variable must contain only integer values
r(451);

. tsreport pcrgdp

Gap summary report

-Number of--
Variable Start End Obs. Gaps

pcrgdp 1959 2019 59 1


. tsfilter hp cyc_pcrgdp = pcrgdp, smooth(100) trend(tr_pcrgdp)

Number of gaps in sample: 1
sample may not contain gaps
r(498);

I am not sure as to why it is displaying this output for pcrgdp. Do I need to transform pcrgdp in some way?

[Nick Cox]

tsset needs a time variable, not a response or outcome -- or otherwise a panel identifier and a time variable. See the help.

Declare data to be time series

tsset timevar [, options]

tsset panelvar timevar [, options]

In #1 you stated (edited slightly)

My variables are pcrgdp (percentage change in real GDP), unem (civilian unemployment rate), cunem (unem – unem[n-1])

but for this to make sense you should have a time variable too, which may be called something like year.

So, it's a mystery how you got past that first problem, as tsfilter won't run at all without a successful tsset.

[Jo Shekar]

Hi Nick,

Thanks for your help.

Apologies, I do have a year variable. year (1959-2019). After setting, tsset year, the filters worked.


. tsset year
time variable: year, 1959 to 2019
delta: 1 unit

. drop tr_pcrgdp

. drop cyc_pcrgdp

. tsfilter hp cyc_pcrgdp = pcrgdp, smooth(100) trend(tr_pcrgdp)

. tsfilter hp cyc_cunem = cunem, smooth(100) trend(tr_cunem)

However, when I tried using the code tsset timevar [, options], I get the following results-

. tsset year [, options]
weights not allowed

[Nick Cox]

You are misunderstanding the nature of syntax diagrams. See e.g.

help language

for more.