********************************************************************
** THIS FILE CONTAINS THE PROGRAMS USED TO COMPUTE THE TABLES AND **
** CERTAIN FIGURES FOR THE MILLS & WOOD JULY/AUGUST 1993 REVIEW   **
** ARTICLE "DOES THE EXCHANGE RATE REGIME AFFECT THE ECONOMY?"    **
** -------------------------------------------------------------- **
** THIS PROGRAM IS WRITTEN IN MAINFRAME SAS, VERSION 6.07         **
** THE HODRICK-PRESCOTT FILTER IS WRITTEN IN "IML" (MATRIX CODE)  **
** AND IS ENCLOSED IN A "MACRO" (SUBROUTINE)                      **
********************************************************************
;


************************************************************************
** THE FOLLOWING CODE ESTIMATES THE OUTPUT MODEL ON PAGE 6, GENERATES **
** THE DATA TO BE USED IN FIGURE 1 (THE TREND LINE) AND COMPUTES THE  **
** TREND GROWTH RATES USED ON PAGE 6.                                 **
************************************************************************
;

FILENAME ON 'H1KMW00.WOOD.CNTL';

DATA OUTPUT;
 INFILE ON(OUTPUT) FIRSTOBS=9;
 INPUT YEAR OUTPUT;
 T +1;
 y = LOG(OUTPUT);
 IF T > 64 THEN DUMMY1=T-64;
  ELSE DUMMY1=0;
 IF T > 67 THEN DUMMY2=T-67;
  ELSE DUMMY2=0;
 int = 1;

************************************************
** output model from page 6                   **
** trend from this model is used for figure 1 **
************************************************;

PROC MODEL DATA=OUTPUT;
 PARMS ALPHA BETA LAMBDA1 LAMBDA2 THETA1 THETA2;

      Y = (ALPHA*INT + BETA*T + LAMBDA1*DUMMY1 + LAMBDA2*DUMMY2) +

         THETA1*(LAG1(Y) - (ALPHA*INT + BETA*LAG1(T) +
         LAMBDA1*LAG1(DUMMY1) + LAMBDA2*LAG1(DUMMY2))) +

         THETA2*(LAG2(Y) - (ALPHA*INT + BETA*LAG2(T) +
         LAMBDA1*LAG2(DUMMY1) + LAMBDA2*LAG2(DUMMY2)));

 FIT Y / OUTEST=PARMS;

DATA BOTH;
 if _n_=1 then set parms(drop=_name_ _type_ _nused_);
 set OUTPUT;

 TREND = ALPHA + BETA*T + LAMBDA1*DUMMY1 + LAMBDA2*DUMMY2;
 TRENDGRO = DIF(TREND);
 CYCLE = Y - TREND;

 **************************************
 ** trend growth mentioned on page 6 **
 **************************************;

 PROC PRINT DATA=BOTH;

 ****************************
 ** STATISTICS FOR TABLE 1 **
 ****************************;

 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1855<=YEAR<=1913));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1855<=YEAR<=1931));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1855<=YEAR<=1913 ³ 1922<=YEAR<=1931));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1922<=YEAR<=1931));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1922<=YEAR<=1939));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1932<=YEAR<=1939));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1932<=YEAR<=1990));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1932<=YEAR<=1939 ³ 1946<=YEAR<=1990));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1946<=YEAR<=1990));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1946<=YEAR<=1972));
  VAR CYCLE;
 PROC MEANS DATA=BOTH(KEEP=YEAR CYCLE
                       WHERE=(1973<=YEAR<=1990));
  VAR CYCLE;

****************************************************************
** the following are programs for tables 2-5, with each table **
** using the Hodrick-Prescott filter, for which the code      **
** immediately follows this note                              **
****************************************************************;

%MACRO HPFILTER(VAR=,DATASET=);

PROC IML;
USE &DATASET;

READ ALL VAR{&VAR} INTO XDATA;

S    = 1600;     ******** SMOOTHING PARAMETER;
N = NROW(XDATA);
IOPT = 0;
SS = 0;
NN = 0;

T = J(N,1,0);
D = J(N,1,0);
V = J(N,3,0);

IF ( (NN <> N) ³ (S <> SS) ³ (IOPT <> 1) )   THEN DO;
   SS  = S;
   NN  = N;
   V11 = 1;
   V22 = 1;
   V12 = 0;

   DO I = 3 TO N;
      X = V11;
      Z = V12;
      V11 = (1 / S) + (4 * (X - Z)) + V22;
      V12 = (2 * X) - Z;
      V22 = X;
      DET = (V11 * V22) - (V12 * V12);
      V(³I,1³) = (V22 / DET);
      V(³I,3³) = (V11 / DET);
      V(³I,2³) = -(V12 / DET);
      X = (V11 + 1);
      Z = V11;
      V11 = V11 - ((V11 * V11) / X);
      V22 = V22 - ((V12 * V12) / X);
      V12 = V12 - ((Z * V12) / X);
   END;
END;

M1 = XDATA(³2,1³);
M2 = XDATA(³1,1³);

DO I = 3 TO N;
   X = M1;
   M1 = (2 * M1) - M2;
   M2 = X;
   T(³I-1,1³) = (V(³I,1³) * M1) + (V(³I,2³) * M2);
   D(³I-1,1³) = (V(³I,2³) * M1) + (V(³I,3³) * M2);
   DET = (V(³I,1³) * V(³I,3³)) - (V(³I,2³) * V(³I,2³));
   V11 = V(³I,3³) / DET;
   V12 = -(V(³I,2³) / DET);
   Z = (XDATA(³I,1³) - M1) / (V11 + 1);
   M1 = M1 + (V11 * Z);
   M2 = M2 + (V12 * Z);
END;

T(³N,1³) = M1;
T(³N-1,1³) = M2;
M1 = XDATA(³N-1,1³);
M2 = XDATA(³N,1³);

DO I = (N-2) TO 1 BY -1;
   I1 = I + 1;
   IB = N - I + 1;
   X = M1;
   M1 = (2* M1) - M2;
   M2 = X;

   IF (I > 2) THEN DO;
      E1 = (V(³IB,3³) * M2) + (V(³IB,2³) * M1) + T(³I,1³);
      E2 = (V(³IB,2³) * M2) + (V(³IB,1³) * M1) + D(³I,1³);
      B11 = V(³IB,3³) + V(³I1,1³);
      B12 = V(³IB,2³) + V(³I1,2³);
      B22 = V(³IB,1³) + V(³I1,3³);
      DET = (B11 * B22) - (B12 * B12);
      T(³I,1³) = ( (-B12 * E1) + (B11 * E2) ) / DET;
   END;

   DET = (V(³IB,1³) * V(³IB,3³)) - (V(³IB,2³) * V(³IB,2³));
   V11 = V(³IB,3³) / DET;
   V12 = -(V(³IB,2³)) / DET;
   Z = (XDATA(³I,1³) - M1) / (V11 + 1);
   M1 = M1 + (V11 * Z);
   M2 = M2 + (V12 * Z);
END;

T(³1,1³) = M1;
T(³2,1³) = M2;

DO I = 1 TO N;
   D(³I,1³) = XDATA(³I,1³) - T(³I,1³);
END;

ALL = XDATA³³T³³D;

CREATE OUTDAT FROM ALL;
APPEND FROM ALL;

%MEND;
**********   MACRO ENDS HERE   ***************;

**********************
** code for table 2 **
**********************;

FILENAME ON 'H1KMW00.wood.CNTL';

DATA RPI;
 INFILE ON(RPI);
 INPUT RPI;
 sasdate = mdy(month,1,year);
 rpi = log(rpi);
 IF '01jan22'd <= sasdate <= '01apr92'd;
 FORMAT SASDATE YYMMP7.;


%HPFILTER(VAR=rpi,DATASET=rpi);
 data trend;merge outdat(rename=(col1=rpi col2=trend col3=cycle))
                  rpi(keep=sasdate);

** THE "OUTDAT" DATA SET IS CREATED IN THE MACRO HPFILTER **;

proc means data=trend(where=('01jan22'd<=sasdate<='31dec39'd));
 var rpi trend cycle;
 title1 '1922.01 to 1939.12';
proc means data=trend(where=('01jan46'd<=sasdate<='01apr92'd));
 var rpi trend cycle;
 title1 '1946.01 to 1992.04';
proc means data=trend(where=('01jan46'd<=sasdate<='31dec72'd));
 var rpi trend cycle;
 title1 '1946.01 to 1972.12';
proc means data=trend(where=('01jan73'd<=sasdate<='01apr92'd));
 var rpi trend cycle;
 title1 '1973.01 to 1992.04';



**********************
** code for table 3 **
**********************;

DATA M3;
 INFILE ON(M3);
 INPUT M3;
 m3 = log(m3);
 sasdate = mdy(month,1,year);
 IF '01JAN22'D <= SASDATE <= '01JUN89'D;
 FORMAT SASDATE YYMMP7.;

%HPFILTER(VAR=m3,DATASET=m3);
 data trend;merge outdat(rename=(col1=m3 col2=trend col3=cycle))
                  m3(keep=sasdate);

proc means data=trend(where=('01jan1922'd<=sasdate<='31dec1939'd));
 var m3 trend cycle;
 title1 '1922.01 to 1939.12';

proc means data=trend(where=('01jan1946'd<=sasdate<='01jun1989'd));
 var m3 trend cycle;
 title1 '1946.01 to 1989.06';

proc means data=trend(where=('01jan1946'd<=sasdate<='31dec1972'd));
 var m3 trend cycle;
 title1 '1946.01 to 1972.12';

proc means data=trend(where=('01jan1973'd<=sasdate<='01jun1989'd));
 var m3 trend cycle;
 title1 '1973.01 to 1989.06';


**********************
** code for table 4 **
**********************;

DATA PRIME;
 INFILE ON(PRIME);
 INPUT PRIME;
 sasdate = mdy(month,1,year);
 FORMAT SASDATE YYMMP7.;


%HPFILTER(VAR=prime,DATASET=prime);
data trend;
 merge outdat(rename=(col1=prime col2=trend col3=cycle))
       prime(keep=sasdate);

proc means data=trend(where=('01jan1870'd<=sasdate<='31dec1913'd));
 var prime trend cycle;
 title1 '1870.01 to 1913.12';
proc means data=trend(where=('01jan1922'd<=sasdate<='31dec1931'd));
 var prime trend cycle;
 title1 '1922.01 to 1931.12';
proc means data=trend(where=('01jan1932'd<=sasdate<='31dec1939'd));
 var prime trend cycle;
 title1 '1932.01 to 1939.12';
proc means data=trend(where=('01jan1954'd<=sasdate<='31dec1972'd));
 var prime trend cycle;
 title1 '1954.01 to 1972.12';
proc means data=trend(where=('01jan1973'd<=sasdate<='01apr1992'd));
 var prime trend cycle;
 title1 '1973.01 to 1992.04';



**********************
** code for table 5 **
**********************;

DATA CONSOL;
 INFILE ON(CONSOL);
 INPUT CONSOL;
 sasdate = mdy(month,1,year);
 FORMAT SASDATE YYMMP7.;
 if 537<=_n_<=540 then delete;

%HPFILTER(VAR=consol,DATASET=consol);
 data trend;
  merge outdat(rename=(col1=consol col2=trend col3=cycle))
        consol(keep=sasdate);


proc means data=trend(where=('01jan1870'd<=sasdate<='31dec1913'd));
 var consol trend cycle;
 title1 '1870.01 to 1913.12';

proc means data=trend(where=('01jan1922'd<=sasdate<='31dec1931'd));
 var consol trend cycle;
 title1 '1922.01 to 1931.12';

proc means data=trend(where=('01jan1932'd<=sasdate<='31dec1939'd));
 var consol trend cycle;
 title1 '1932.01 to 1939.12';

proc means data=trend(where=('01jan1954'd<=sasdate<='31dec1972'd));
 var consol trend cycle;
 title1 '1954.01 to 1972.12';

proc means data=trend(where=('01jan1973'd<=sasdate<='01apr1992'd));
 var consol trend cycle;
 title1 '1973.01 to 1992.04';


**********************************************************
** THE FOLLOWING IS THE CODE USED TO PRODUCE THE CHARTS **
** IN FIGURES 9 THROUGH 12                              **
**********************************************************;

***********************
** CODE FOR FIGURE 9 **
***********************;

DATA RPI;
 INFILE ON(RPI);
 INPUT RPI;
 sasdate = mdy(month,1,year);
 rpi = log(rpi);
 IF '01JAN22'D <= SASDATE <= '01APR92'D;
 FORMAT SASDATE YYMMP7.;

%HPFILTER(VAR=rpi,DATASET=rpi);
 data rpi_t;MERGE outdat(rename=(col1=rpi col2=TREND col3=CYCLE))
                  RPI(KEEP=SASDATE);

 file 'wood.cntl(figure9)';
 put sasdate yymmp7. @12 rpit1 @26 rpid1;


************************
** CODE FOR FIGURE 10 **
************************;

DATA M3;
 INFILE ON(M3);
 INPUT M3;
 sasdate = mdy(month,1,year);
 M3 = log(M3);
 IF '01JAN22'D <= SASDATE <= '01JUN89'D;
 FORMAT SASDATE YYMMP7.;

%HPFILTER(VAR=M3,DATASET=M3);
 data M3_t;MERGE outdat(rename=(col1=M3 col2=TREND col3=CYCLE))
                     M3(KEEP=SASDATE);

 file 'wood.cntl(figure10)';
 put sasdate yymmp7. @12 TREND @26 CYCLE;


************************
** CODE FOR FIGURE 11 **
************************;

DATA PRIME;
 INFILE ON(PRIME);
 INPUT PRIME;
 sasdate = mdy(month,1,year);
 PRIME = log(PRIME);
 FORMAT SASDATE YYMMP7.;

%HPFILTER(VAR=PRIME,DATASET=PRIME);
 data PRIME_t;MERGE outdat(rename=(col1=PRIME col2=TREND col3=CYCLE))
                    PRIME(KEEP=SASDATE);

 file 'wood.cntl(figure11)';
 put sasdate yymmp7. @12 TREND @26 CYCLE;


************************
** CODE FOR FIGURE 12 **
************************;

DATA CONSOL;
 INFILE ON(CONSOL);
 INPUT CONSOL;
 CONSOL = log(CONSOL);
 IF 537 <= _N_ <= 540 THEN DELETE;
 FORMAT SASDATE YYMMP7.;

%HPFILTER(VAR=CONSOL,DATASET=CONSOL);
 data CONSOL_t;MERGE outdat(rename=(col1=CONSOL col2=TREND col3=CYCLE))
                     CONSOL(KEEP=SASDATE);

 file 'wood.cntl(figure12)';
 put sasdate yymmp7. @12 TREND @26 CYCLE;



********************************************************************;
** THE FOLLOWING CODE DETAILS HOW THE ANNUAL PRICE LEVEL DATA WAS **
** COMPUTED FOR USE IN FIGURE 2.                                  **
** THE "OLD" SERIES WAS TAKEN FROM CAPIE & WEBBER(1985) AND RUNS  **
** THROUGH 1948.  THE "NEW" SERIES WAS TAKEN FROM THE 1991 ANNUAL **
** SUPPLEMENT TO ECONOMIC TRENDS, TABLE 25, THE "ALL ITEMS" INDEX **
** AND THE RATIO THE "OLD" 1948 VALUE AND THE "NEW" 1948 VALUE    **
** WAS USED TO LINK THE TWO SERIES.                               **
********************************************************************;

DATA OLD;
 INFILE ON(RPI1) FIRSTOBS=5;
 INPUT YEAR RPI;

DATA NEW;
 INFILE ON(RPI2) FIRSTOBS=8; ** FIRST YEAR IS 1949 **;
 INPUT YEAR RPI;
 RPI = RPI * (268/8.3);  ** RATIO OF OLD TO NEW AT COMMON YR OF 1948 **;

DATA BOTH;
 SET OLD NEW;   ** STACK TWO SERIES INTO ONE **;
 RPI = LOG(RPI);
 PROC PRINT;

 DATA _NULL_;SET BOTH;
  FILE ON(FIGURE2A);     ** CREATE TWO OUTPUT FILES FOR CHARTS **;
  PUT YEAR @10 RPI;
 DATA _NULL_;SET BOTH;
  FILE ON(FIGURE2B);
  PUT YEAR @10 RPI;


******************************************************************;
** THE FOLLOWING CODE DETAILS HOW THE OUTPUT SERIES WAS CREATED **
** THE "OLD" DATA RUNS THROUGH 1948 AND IS FROM FEINSTEIN, THE  **
** "NEW" DATA STARTS IN 1948, BUT 1948'S VALUE IS ONLY USED TO  **
** COMPUTE THE RATIO OF THE TWO SERIES IN THAT YEAR.  THEN THE  **
** NEW DATA IS MULTIPLIED BY THE RATIO AND THE TWO SERIES ARE   **
** LINKED, TAKING 1949 AS THE FIRST "NEW" DATA SERIES POINT.    **
******************************************************************;

DATA OLD;
 INFILE ON(OUTPUT1) FIRSTOBS=7;
 INPUT YEAR OUTPUT;

DATA NEW;
 INFILE ON(OUTPUT2) FIRSTOBS=9; ** OBS 9 IS YEAR 1949 **;
 INPUT YEAR OUTPUT;
 OUTPUT = OUTPUT * (144.7/40.3); ** RATIO OF OLD/NEW AT COMMON 1948 **;
 PROC PRINT;

DATA BOTH;
 SET OLD NEW;  ** STACK THE TWO SERIES TO CREATE NEW LINKED SERIES **;

 DATA _NULL_;SET BOTH; ** SET UP LINKED DATA FILE TO BE USED IN PGMS **;
  FILE ON(OUTPUT);
  PUT YEAR @10 OUTPUT;