options pagesize=60 linesize=74 nodate; /* lhur = unemployment rate, all workers (in percent) puxx = cpi-u: all items less food & energy Data obtained from Citibase. */ data c; input date yymmdd8. lhur puxx; format date monyy5.; cards; 19570101 4.2 28.5 19570201 3.9 28.6 19570301 3.7 28.7 19570401 3.9 28.8 19570501 4.1 28.8 19570601 4.3 28.9 19570701 4.2 29 19570801 4.1 29 19570901 4.4 29.1 19571001 4.5 29.2 19571101 5.1 29.3 19571201 5.2 29.3 19580101 5.8 29.3 19580201 6.4 29.4 19580301 6.7 29.5 19580401 7.4 29.5 19580501 7.4 29.5 19580601 7.3 29.6 19580701 7.5 29.6 19580801 7.4 29.6 19580901 7.1 29.7 19581001 6.7 29.7 19581101 6.2 29.8 19581201 6.2 29.9 19590101 6 29.9 19590201 5.9 29.9 19590301 5.6 30 19590401 5.2 30 19590501 5.1 30.1 19590601 5 30.2 19590701 5.1 30.2 19590801 5.2 30.2 19590901 5.5 30.3 19591001 5.7 30.4 19591101 5.8 30.4 19591201 5.3 30.5 19600101 5.2 30.5 19600201 4.8 30.6 19600301 5.4 30.6 19600401 5.2 30.6 19600501 5.1 30.6 19600601 5.4 30.7 19600701 5.5 30.6 19600801 5.6 30.6 19600901 5.5 30.6 19601001 6.1 30.8 19601101 6.1 30.8 19601201 6.6 30.7 19610101 6.6 30.8 19610201 6.9 30.8 19610301 6.9 30.9 19610401 7 30.9 19610501 7.1 30.9 19610601 6.9 31 19610701 7 31 19610801 6.6 31.1 19610901 6.7 31.1 19611001 6.5 31.1 19611101 6.1 31.2 19611201 6 31.2 19620101 5.8 31.2 19620201 5.5 31.2 19620301 5.6 31.3 19620401 5.6 31.3 19620501 5.5 31.4 19620601 5.5 31.4 19620701 5.4 31.4 19620801 5.7 31.5 19620901 5.6 31.5 19621001 5.4 31.5 19621101 5.7 31.5 19621201 5.5 31.6 19630101 5.7 31.5 19630201 5.9 31.6 19630301 5.7 31.7 19630401 5.7 31.7 19630501 5.9 31.7 19630601 5.6 31.8 19630701 5.6 31.8 19630801 5.4 31.9 19630901 5.5 31.9 19631001 5.5 32 19631101 5.7 32 19631201 5.5 32.1 19640101 5.6 32.2 19640201 5.4 32.2 19640301 5.4 32.2 19640401 5.3 32.2 19640501 5.1 32.2 19640601 5.2 32.3 19640701 4.9 32.3 19640801 5 32.3 19640901 5.1 32.3 19641001 5.1 32.4 19641101 4.8 32.5 19641201 5 32.5 19650101 4.9 32.6 19650201 5.1 32.6 19650301 4.7 32.6 19650401 4.8 32.7 19650501 4.6 32.7 19650601 4.6 32.7 19650701 4.4 32.7 19650801 4.4 32.7 19650901 4.3 32.8 19651001 4.2 32.8 19651101 4.1 32.9 19651201 4 33 19660101 4 33 19660201 3.8 33.1 19660301 3.8 33.1 19660401 3.8 33.3 19660501 3.9 33.4 19660601 3.8 33.5 19660701 3.8 33.6 19660801 3.8 33.7 19660901 3.7 33.8 19661001 3.7 34 19661101 3.6 34 19661201 3.8 34.1 19670101 3.9 34.2 19670201 3.8 34.2 19670301 3.8 34.3 19670401 3.8 34.4 19670501 3.8 34.5 19670601 3.9 34.6 19670701 3.8 34.7 19670801 3.8 34.9 19670901 3.8 35 19671001 4 35.1 19671101 3.9 35.2 19671201 3.8 35.4 19680101 3.7 35.5 19680201 3.8 35.7 19680301 3.7 35.8 19680401 3.5 35.9 19680501 3.5 36 19680601 3.7 36.2 19680701 3.7 36.4 19680801 3.5 36.5 19680901 3.4 36.7 19681001 3.4 36.9 19681101 3.4 37.1 19681201 3.4 37.2 19690101 3.4 37.3 19690201 3.4 37.6 19690301 3.4 37.8 19690401 3.4 38.1 19690501 3.4 38.1 19690601 3.5 38.3 19690701 3.5 38.5 19690801 3.5 38.7 19690901 3.7 38.9 19691001 3.7 39.1 19691101 3.5 39.2 19691201 3.5 39.4 19700101 3.9 39.6 19700201 4.2 39.8 19700301 4.4 40.1 19700401 4.6 40.4 19700501 4.8 40.5 19700601 4.9 40.8 19700701 5 40.9 19700801 5.1 41.1 19700901 5.4 41.3 19701001 5.5 41.5 19701101 5.9 41.8 19701201 6.1 42 19710101 5.9 42.1 19710201 5.9 42.2 19710301 6 42.2 19710401 5.9 42.4 19710501 5.9 42.6 19710601 5.9 42.8 19710701 6 42.9 19710801 6.1 43 19710901 6 43 19711001 5.8 43.1 19711101 6 43.2 19711201 6 43.3 19720101 5.8 43.5 19720201 5.7 43.6 19720301 5.8 43.6 19720401 5.7 43.8 19720501 5.7 43.9 19720601 5.7 44 19720701 5.6 44.1 19720801 5.6 44.3 19720901 5.5 44.3 19721001 5.6 44.4 19721101 5.3 44.4 19721201 5.2 44.6 19730101 4.9 44.6 19730201 5 44.8 19730301 4.9 45 19730401 5 45.1 19730501 4.9 45.3 19730601 4.9 45.4 19730701 4.8 45.5 19730801 4.8 45.7 19730901 4.8 46 19731001 4.6 46.3 19731101 4.8 46.5 19731201 4.9 46.7 19740101 5.1 46.9 19740201 5.2 47.2 19740301 5.1 47.6 19740401 5.1 47.9 19740501 5.1 48.5 19740601 5.4 49 19740701 5.5 49.5 19740801 5.5 50.2 19740901 5.9 50.7 19741001 6 51.2 19741101 6.6 51.6 19741201 7.2 52 19750101 8.1 52.3 19750201 8.1 52.8 19750301 8.6 53 19750401 8.8 53.3 19750501 9 53.5 19750601 8.8 53.8 19750701 8.6 54 19750801 8.4 54.2 19750901 8.4 54.5 19751001 8.4 54.8 19751101 8.3 55.2 19751201 8.2 55.5 19760101 7.9 55.9 19760201 7.7 56.2 19760301 7.6 56.5 19760401 7.7 56.7 19760501 7.4 57 19760601 7.6 57.2 19760701 7.8 57.6 19760801 7.8 57.9 19760901 7.6 58.2 19761001 7.7 58.5 19761101 7.8 58.7 19761201 7.8 58.9 19770101 7.5 59.3 19770201 7.6 59.7 19770301 7.4 60 19770401 7.2 60.3 19770501 7 60.6 19770601 7.2 61 19770701 6.9 61.2 19770801 7 61.5 19770901 6.8 61.8 19771001 6.8 62 19771101 6.8 62.3 19771201 6.4 62.7 19780101 6.4 63.1 19780201 6.3 63.4 19780301 6.3 63.8 19780401 6.1 64.3 19780501 6 64.7 19780601 5.9 65.2 19780701 6.2 65.6 19780801 5.9 66.1 19780901 6 66.7 19781001 5.8 67.2 19781101 5.9 67.6 19781201 6 68 19790101 5.9 68.5 19790201 5.9 69.2 19790301 5.8 69.8 19790401 5.8 70.3 19790501 5.6 70.8 19790601 5.7 71.3 19790701 5.7 71.9 19790801 6 72.7 19790901 5.9 73.3 19791001 6 74 19791101 5.9 74.8 19791201 6 75.7 19800101 6.3 76.7 19800201 6.3 77.5 19800301 6.3 78.6 19800401 6.9 79.5 19800501 7.5 80.1 19800601 7.6 81 19800701 7.8 80.8 19800801 7.7 81.3 19800901 7.5 82.1 19801001 7.5 83 19801101 7.5 83.9 19801201 7.2 84.9 19810101 7.5 85.4 19810201 7.4 85.9 19810301 7.4 86.4 19810401 7.2 87 19810501 7.5 87.8 19810601 7.5 88.6 19810701 7.2 89.8 19810801 7.4 90.7 19810901 7.6 91.8 19811001 7.9 92.1 19811101 8.3 92.5 19811201 8.5 93 19820101 8.6 93.3 19820201 8.9 93.8 19820301 9 93.9 19820401 9.3 94.7 19820501 9.4 95.4 19820601 9.6 96.1 19820701 9.8 96.7 19820801 9.8 97.1 19820901 10.1 97.2 19821001 10.4 97.5 19821101 10.8 97.3 19821201 10.8 97.2 19830101 10.4 97.6 19830201 10.4 98 19830301 10.3 98.2 19830401 10.2 98.6 19830501 10.1 98.9 19830601 10.1 99.2 19830701 9.4 99.8 19830801 9.5 100.1 19830901 9.2 100.5 19831001 8.8 101 19831101 8.5 101.5 19831201 8.3 101.8 19840101 8 102.5 19840201 7.8 102.8 19840301 7.8 103.2 19840401 7.7 103.7 19840501 7.4 104.1 19840601 7.2 104.5 19840701 7.5 105 19840801 7.5 105.4 19840901 7.3 105.8 19841001 7.4 106.2 19841101 7.2 106.4 19841201 7.3 106.8 19850101 7.3 107.1 19850201 7.2 107.7 19850301 7.2 108.1 19850401 7.3 108.4 19850501 7.2 108.8 19850601 7.4 109.1 19850701 7.4 109.4 19850801 7.1 109.8 19850901 7.1 110 19851001 7.1 110.5 19851101 7 111.1 19851201 7 111.4 19860101 6.7 111.9 19860201 7.2 112.2 19860301 7.2 112.5 19860401 7.1 112.9 19860501 7.2 113.1 19860601 7.2 113.4 19860701 7 113.8 19860801 6.9 114.2 19860901 7 114.6 19861001 7 115 19861101 6.9 115.3 19861201 6.6 115.6 19870101 6.6 116.1 19870201 6.6 116.4 19870301 6.6 116.8 19870401 6.3 117.5 19870501 6.3 117.9 19870601 6.2 118.1 19870701 6.1 118.5 19870801 6 118.9 19870901 5.9 119.4 19871001 6 120 19871101 5.8 120.3 19871201 5.7 120.6 19880101 5.7 121.1 19880201 5.7 121.3 19880301 5.7 121.9 19880401 5.4 122.5 19880501 5.6 122.9 19880601 5.4 123.4 19880701 5.4 123.8 19880801 5.6 124.1 19880901 5.4 124.8 19881001 5.4 125.3 19881101 5.3 125.8 19881201 5.3 126.2 19890101 5.4 126.7 19890201 5.2 127 19890301 5 127.5 19890401 5.2 128 19890501 5.2 128.5 19890601 5.3 128.9 19890701 5.2 129.4 19890801 5.2 129.7 19890901 5.3 130.1 19891001 5.3 130.8 19891101 5.4 131.3 19891201 5.4 131.8 19900101 5.3 132.3 19900201 5.3 132.9 19900301 5.2 133.7 19900401 5.4 134.2 19900501 5.3 134.6 19900601 5.1 135.3 19900701 5.4 136 19900801 5.6 136.8 19900901 5.7 137.3 19901001 5.8 137.8 19901101 6 138.2 19901201 6.2 138.8 19910101 6.3 139.8 19910201 6.5 140.4 19910301 6.8 140.7 19910401 6.6 141.1 19910501 6.8 141.5 19910601 6.8 141.9 19910701 6.7 142.5 19910801 6.8 143.1 19910901 6.7 143.6 19911001 6.8 143.9 19911101 6.9 144.4 19911201 7.2 144.8 19920101 7.1 145.3 19920201 7.4 145.6 19920301 7.3 146.2 19920401 7.3 146.6 19920501 7.5 146.9 19920601 7.7 147.3 19920701 7.5 147.8 19920801 7.5 148.1 19920901 7.5 148.3 19921001 7.3 149 19921101 7.3 149.4 19921201 7.3 149.8 19930101 7.1 150.3 19930201 7 150.8 19930301 7 151.1 19930401 7 151.6 19930501 6.9 152 19930601 6.9 152.3 19930701 6.8 152.6 19930801 6.7 153 19930901 6.7 153.1 19931001 6.7 153.5 19931101 6.5 154 19931201 6.4 154.4 19940101 6.7 154.7 19940201 6.6 155 19940301 6.5 155.5 19940401 6.4 155.8 19940501 6.1 156.2 19940601 6.1 156.7 19940701 6.1 157 19940801 6 157.4 19940901 5.8 157.7 19941001 5.7 158 19941101 5.6 158.3 19941201 5.4 158.5 19950101 5.7 159.2 19950201 5.4 159.6 19950301 5.5 160.1 19950401 5.8 160.7 19950501 5.7 161 19950601 5.6 161.3 19950701 5.7 161.7 19950801 5.6 162 19950901 5.6 162.4 ; /* Convert the monthly data above to quarterly averages. */ data qtrconv; set c; flag = mod(_n_,3); lhurq = (lhur + lag1(lhur) + lag2(lhur))/3; puxxq = (puxx + lag1(puxx) + lag2(puxx))/3; data qtr; set qtrconv; if flag > 0 then delete; keep date lhurq puxxq; /* Now that you have quarterly data, calculate the annual rate of inflation for each quarter (in percent). Also create the indicator dependent variable (y) as described in THE ECONOMIC REPORT OF THE PRESIDENT, 1997. */ data inflat; set qtr; lhurq4 = lag4(lhurq); inflat = ((1 + (puxxq - lag(puxxq))/lag(puxxq))**4 - 1.0)*100; index = inflat - lag4(inflat); if index <= 0 then y = 0; if index > 0 then y = 1; *proc print data=inflat; /* Eliminate the missing observations and relabel the variable name lhurq4 as unemp (unemployment rate). */ data inflat2; set inflat; if _n_ < 6 then delete; unemp = lhurq4; keep date unemp y; proc print data=inflat2; /* Logit Analysis of NAIRU using all of the data: In order to get proc logistic to model prob(y=1) instead of prob(y=0), we have to use the "descending" option. (Note: The Logit option in EASYREG models prob(y=1).) */ proc logistic data=inflat2 descending; model y = unemp/covb; /* Probit Analysis of NAIRU using all of the data: Proc Probit has to know which variable is the classificatory variable. Therefore the "class" statement is used to declare y as the classificatory variable. Proc Probit models the prob(y=0). Evidently, there is no option (as there is in Proc Logistic) that allows us instead to model prob(y=1). Therefore, we need to interpret the following proc probit output as modelling prob(y=0). However, it is easy to turn this output into the output that would be derived when modelling prob(y=1). All we have to do is to REVERSE THE SIGNS of the coefficient estimates. This follows because F(u) = Pr(y=0) and Pr(y=1) = 1 - F(u). But F(u) = 1 - F(-u) when F(u) = cdf(N(0,1)) as in the probit case. Therefore, Pr(y=1) = 1 - F(u) = 1 - (1 - F(-u)) = F(-u), where u = a + bx is the index for modelling Pr(y=0). (Note: The Probit option in EASYREG models prob(y=1).) */ proc probit data=inflat2 c=0; class y; model y = unemp/covb; proc means data = inflat2; var unemp; run;