Dear Statalist community,
I have an elementary question on impulse response functions generated through local projections, a methodology proposed by Jordà (2005). Estimation and inference of impulse responses by local projections. American economic review, 95(1), 161-182. When I speak of "local projections" I refer to this paper.
Specifically, I have time series of identified shocks to global crude oil supply and monetary policy and I am interested in the impact these shocks have on cumulative inflation. I provide my code and an example of my data below, but basically my question is if and how statisticians differentiate between positive and negative shocks in local projections. Now, I know that impulse responses generated by VARs underly a symmetry assumption but I don't believe that this extends to local projections. Moreover, since I rely on shocks identified based on data, these shocks may be negative or positive depending on the time period and in the impulse response function I cannot see the nature of the shock (in contrast to unit root and orthogonal impulse responses generated by VARs). In other words, if I see that my impulse response function suggests a negative reaction of my dependent variable over the time horizon, I don't know how to interpret that since I'm not sure whether the initial monetary policy or oil supply shock was positive or negative. I hope this makes sense, I would appreciate your input.
This is the code that produces an impulse response function over a time horizon of 5 years.
And here is an example of my code: t denotes time in moths; months are the calendar months from January to December; categ are product categories so these could be food, services, raw materials etc., inf is inflation (rate of change in the consumer price index), cuminf is cumulative inflation in each product category, mpshock are monetary policy shocks, and oilshock are shocks to the global oil supply.
I am using Stata 16.1 on windows 10
Thank you in advance,
Moritz
I have an elementary question on impulse response functions generated through local projections, a methodology proposed by Jordà (2005). Estimation and inference of impulse responses by local projections. American economic review, 95(1), 161-182. When I speak of "local projections" I refer to this paper.
Specifically, I have time series of identified shocks to global crude oil supply and monetary policy and I am interested in the impact these shocks have on cumulative inflation. I provide my code and an example of my data below, but basically my question is if and how statisticians differentiate between positive and negative shocks in local projections. Now, I know that impulse responses generated by VARs underly a symmetry assumption but I don't believe that this extends to local projections. Moreover, since I rely on shocks identified based on data, these shocks may be negative or positive depending on the time period and in the impulse response function I cannot see the nature of the shock (in contrast to unit root and orthogonal impulse responses generated by VARs). In other words, if I see that my impulse response function suggests a negative reaction of my dependent variable over the time horizon, I don't know how to interpret that since I'm not sure whether the initial monetary policy or oil supply shock was positive or negative. I hope this makes sense, I would appreciate your input.
This is the code that produces an impulse response function over a time horizon of 5 years.
Code:
xtset categ t
forv i = 0/5 {
gen cuminf`i' = f`i'.cuminf
}
eststo clear
capture drop time_periods zero upper lower coeff
gen time_periods = _n-1 if _n<=6
gen zero = 0 if _n<=6
gen upper=0
gen coeff=0
gen lower=0
forv i = 0/5 {
xtreg cuminf`i' l(1/6).cuminf l(1/6).mpshock l(1/6).oilshock, fe
replace coeff = _b[l.oilshock] if _n == `i'+2
replace upper = _b[l.oilshock] + 1.645 * _se[l.oilshock] if _n == `i'+2
replace lower = _b[l.oilshock] - 1.645 * _se[l.oilshock] if _n == `i'+2
eststo
}
nois esttab , se nocons keep(L.oilshock)
twoway (rarea upper lower time_periods, fcolor(gs13) lcolor(gs13) lw(none) lpattern(solid)) (line coeff time_periods, lcolor(blue) lpattern(solid) lwidth(thick)) (line zero time_periods, lcolor(black)), legend(off)
Code:
* Example generated by -dataex-. For more info, type help dataex clear input int t byte months double(inf cuminf mpshock oilshock) byte categ 1 1 -.11845064795433258 -.11845064795433258 -.00758481 -.859742491011577 1 2 2 3.73680444736101 3.6183537994066772 .000499964 -.101416699380897 1 3 3 .8782394618848723 4.496593261291549 -.00699997 -.492805740344123 1 4 4 -.5206729239800625 3.9759203373114866 -.002499819 .980696608288988 1 5 5 1.9740103861530125 5.949930723464499 -.00399971 .337822957357602 1 6 6 1.5663765854519665 7.516307308916465 .012999773 -.716288861569563 1 7 7 3.7934459622464116 11.309753271162876 .006499767 -.656788112207912 1 8 8 .17361882868427636 11.483372099847152 .004000187 -.932861389640944 1 9 9 1.2234958983321458 12.706867998179298 -.001000166 -.540237430452909 1 10 10 1.2050785198386418 13.91194651801794 -.00425005 -.24950891877466 1 11 11 3.0777952024957322 16.98974172051367 -.007500172 1.05654907359192 1 12 12 1.7720735640081347 18.761815284521806 -.019999981 -.972344761867327 1 13 1 .6829108476388799 .6829108476388799 -.016000032 -1.53019295478818 2 14 2 3.6472577944176283 4.330168642056508 -.003000021 .261949916668666 2 15 3 2.616046556179537 6.946215198236045 .001499891 -1.53442303102815 2 16 4 2.5911409340867744 9.53735613232282 -.07249999 -.878253629601385 2 17 5 2.139569384628219 11.676925516951039 .003999949 .0676936992534705 2 18 6 3.356821503518627 15.033747020469665 -.032500029 -.478871462577872 2 19 7 1.5651029254798159 16.598849945949482 .021999836 .122494535706305 2 20 8 3.160276256214252 19.759126202163735 .013499737 -.1448226842424 2 21 9 3.5908702503789813 23.349996452542715 0 -.264171047780807 2 22 10 3.0909967348648166 26.440993187407532 .000500202 -.0105628666379299 2 23 11 -.7388615245770216 25.70213166283051 -.003499985 -1.09344326431085 2 24 12 2.987983662748136 28.690115325578645 .004999876 -.902791280373235 2 25 1 2.313689331416414 31.003804656995058 -.02850008 -.481625400302437 2 26 2 2.9158830464484873 33.91968770344354 .000999928 -1.39277329530944 2 27 3 3.0961174829346065 37.01580518637815 .005000114 -.200793386615026 2 28 4 .7091781325226407 37.72498331890079 -.00699997 -.491697752622017 2 29 5 2.759039679432199 40.48402299833299 .004499912 -.62989277850946 2 30 6 -.5236487258058644 39.960374272527126 .001999855 -1.67440963492294 2 31 7 3.139851472718094 43.10022574524522 .000500202 .347850747448338 2 32 8 2.4878499581636713 45.58807570340889 .01099968 -.694719420182538 2 33 9 1.8057170042738218 47.393792707682714 -.029500484 -.883736484500096 2 34 10 3.521459811213914 50.91525251889663 .006500244 .0732174268043659 2 35 11 -.8923436375089024 50.02290888138773 -.008499622 -1.57601827132714 2 36 12 1.8887699667510756 51.911678848138806 -.00150013 .165092151038313 2 37 1 .10566126153163591 52.01734010967044 -.005000114 -.84434983562608 2 38 2 3.2900612173327985 55.30740132700324 -.031499863 -.723533112352136 2 39 3 3.3442644629463976 58.65166578994964 .003499746 .00890008743666448 2 40 4 1.1204844100974212 59.77215020004706 .00549984 -.417928972870517 2 41 5 .4996964960043164 60.27184669605138 -.00399971 -.38372568538378 2 42 6 3.2600512475923322 3.2600512475923322 .10449982 .436421624709618 3 43 7 -.7460230305376511 2.514028217054681 -.039999962 .668184108075028 3 44 8 2.377146565459239 4.89117478251392 -.024000168 -.404346971411131 3 45 9 .0781369673755481 4.969311749889468 -.020999432 -.374199401411589 3 46 10 1.8765272933215091 6.845839043210978 -.13350034 3.41553476749646 3 47 11 1.4977998611864924 8.34363890439747 .16450024 1.93531773287233 3 48 12 -.979364181010778 7.364274723386691 .027499795 1.90089476223377 3 49 1 -.17270145238236245 -.17270145238236245 -.014999986 .0375167959371395 3 50 2 3.54040030827162 3.367698855889257 -.056249976 2.74642390450234 3 51 3 .2647757351711557 3.632474591060413 .016250014 -.633870763868911 3 52 4 2.646778537021211 6.279253128081624 .04399997 1.40191669330257 3 53 5 1.6772398444991286 7.956492972580753 -.028000057 -.0139604151889791 3 54 6 1.560212125330223 9.516705097910975 .032999992 -.579901457470845 3 55 7 1.0397500130738475 10.556455110984823 -.055500031 .826590004050571 3 56 8 -.24683897658105325 10.30961613440377 -.009500027 -2.10463209930525 3 57 9 2.9145714892446866 13.224187623648456 -.015500039 .504474637681826 3 58 10 2.910563179187554 16.13475080283601 -.010499954 -.336173494745439 3 59 11 2.9768585212370846 19.111609324073093 -.011500031 -.0679165845191818 3 60 12 2.719175455356316 21.830784779429408 -.032000005 -1.15360992579724 3 61 1 -.19187861560984754 21.63890616381956 -.011500031 -.28422127543813 3 62 2 -.29493299755451696 21.34397316626504 .000999987 .0657435623105083 3 63 3 -.8884545467803808 20.45551861948466 -.002000004 .29837170747966 3 64 4 1.4234101599108153 21.878928779395476 .001500011 -.417664523854986 3 65 5 .0375144572485806 21.916443236644056 .013999999 .679517756726244 3 66 6 2.47993217986019 24.396375416504245 -.005499959 -.858314483422081 3 67 7 1.1717252191354222 25.568100635639667 .029500067 -.0345118625333262 3 68 8 3.8277995733823413 29.39590020902201 -.004499972 -.582247543755428 3 69 9 2.4000247424738435 31.795924951495852 -.008000016 -.262630526212548 3 70 10 3.1119864776618202 34.90791142915767 .006500006 -1.53498902914088 3 71 11 2.8239015809870636 37.731813010144734 -.008000076 .0605488216633381 3 72 12 2.408776902218519 40.140589912363254 -.03549999 -.999236937648101 3 73 1 .6675469476276605 40.80813685999092 .009999991 -.382847477103011 3 74 2 1.9177885720213497 42.72592543201227 -.022499979 -2.35860315614424 3 75 3 3.554972107247357 46.28089753925963 .10700005 -2.36331459929281 3 76 4 2.509065680284042 48.789963219543665 .016000032 -.294080919600528 3 77 5 -.11358664278085984 48.676376576762806 -.07099998 -.757582637251801 3 78 6 1.7726667069672573 50.44904328373006 .001000047 .150946057230369 3 79 7 3.844458708991974 54.293501992722035 .010999918 .10765195297158 3 80 8 1.3858156662862773 55.67931765900831 -.10900003 .882701643166809 3 81 9 2.2552189982784148 57.93453665728673 .014499962 -2.19721605891552 3 82 10 .6336861485931797 58.568222805879905 .11750007 -.628571197144074 3 83 11 2.1112516341932634 60.67947444007317 -.084999979 .160098742251459 3 84 12 -.2974578681573755 60.3820165719158 .000500023 .301078592113367 3 85 1 -.4045178223102327 59.977498749605566 .003499955 -.183773274892422 3 86 2 1.9963202669798852 61.97381901658545 -.001500011 -.0698330518013632 3 87 3 3.853433674742252 65.8272526913277 .000499964 -.208817774902146 3 88 4 2.642312696741143 68.46956538806884 .002499968 1.71804809725079 3 89 5 1.5865337681496117 70.05609915621845 .009499997 .207456843269754 3 90 6 1.1549046468184403 71.21100380303689 .015000015 .497050554270771 3 91 7 2.8816227455082526 74.09262654854514 -.089500025 .322455620784582 3 92 8 2.326108730536225 76.41873527908136 .019000001 -.0602070944459031 3 93 9 3.89941273992231 80.31814801900367 .002500005 -.852643027926585 3 94 10 -.9340730290554508 79.38407498994822 .002999991 .768113023363957 3 95 11 -.3688127313819214 79.0152622585663 .00850001 .00706280310713803 3 96 12 .4592071000445612 79.47446935861086 -.004499998 -.0341704852251901 3 97 1 1.8009134195349352 81.2753827781458 .005999997 -1.4003106989097 3 98 2 3.528333719128667 84.80371649727446 -.00850001 -.716843226680226 3 99 3 3.9952576042387324 88.7989741015132 .001000002 .388047278660598 3 100 4 .028617238773442688 88.82759134028665 0 1.12608926975935 3 end
I am using Stata 16.1 on windows 10
Thank you in advance,
Moritz
