1. Joshua Klick, Economist, Bureau of Labor Statistics
Measuring Consumer Substitution with JMP®
Joshua Klick, Economist, Bureau of Labor Statistics
Contact:
Abstract
Agenda
End result of multi-year pooled regression analysis of CPI annual average index and weight data.
JMP® Version 10 introduced Local Data Filter for the report window.
A user can conduct an interactive pooled regression analysis using the Check Box Display option.
In this presentation I use JMP® Fit Y by X platform to evaluate a Feenstra-Reinsdorf model.
The β results estimate the elasticity of substitution parameter (referred to as σ) used in a Constant Elasticity of Substitution (CES) price index.
This presentation reviews setting up the index data with JMP® script to conduct multi-year pooled regression analysis to estimate σ.
Purpose: Estimate elasticity of substitution parameter (σ).
Review price index theory and set up data using JMP® script.
Show Check Box Display option - Local Data Filter within Fit Y by X platform.
Show regression results of data pooled across years.
Summary and Conclusions
Q & A

2. Price change measurement is dependent on price index formulas.
Review price index theory
Price index formulas are dependent on theories about how consumers change their consumption patterns in response to price change. Substitution Elasticity is a measure of substitution in response to price change.
σ is calculated using the Feenstra-Reinsdorf regression model, where it is measured as the change in relative expenditure shares in response to the change in relative prices. σ is equal to 1 minus the resulting β of the Feenstra-Reinsdorf regression.
Where:
s = Basic level annualized expenditure weight share.
p = Basic level annual average price index.
w = Basic level normalized weights sum to unity over periods.
k = CPI Item-Area Category (211 Items * 38 Areas).
y = Current Period; Y-1 = Previous Period.

3. Set up Interactive Pooled Regression Analysis Data Set up with JSL:
1. Connecting to SAS- in my case a local connection (see JMP.com for details)
1. Use JMP® Fit Y by X platform
2. Select Fit Line
2. Process SAS Code using
SAS SUBMIT(“”).
SAS Submit("
libname SAVE 'C:\Users\klick_j\Desktop\Temp\JMP CES';
DATA CES_PREP_JG2; SET SAVE.CES_PREP_JG;
ARRAY X (4) AIX_1999-AIX_2002;
ARRAY S (4) SH1999-SH2002;
ARRAY DLRX (3) DLRX2000-DLRX2002;
ARRAY DLRS (3) DLRS2000-DLRS2002;
ARRAY W (3) W2000-W2002;
DO Y = 1 TO 3;
DLRX(Y) = log(X(Y+1) / X(Y));
DLRS(Y) = log(S(Y+1) / S(Y));
W(Y) = (S(Y+1) - S(Y)) / (log (S(Y+1)/S(Y)));
END;
if area='A427' and item='SETG03' then DO;
DLRX2000=0; END;
if area='A111' and item='SEEE03' then DO;
if area='A429' and item='SEFV03' then DO;
RUN;
PROC SQL;
CREATE TABLE SAVE.CES_PREP_JG_V2 AS
SELECT '2000' AS Y, ITEM, AREA, DLRX2000 AS DLRX, DLRS2000 AS DLRS,
W2000/sum(W2000) AS W
FROM CES_PREP_JG2
outer union corr
SELECT '2001' AS Y, ITEM, AREA, DLRX2001 AS DLRX, DLRS2001 AS DLRS,
W2001/sum(W2001) AS W
SELECT '2002' AS Y, ITEM, AREA, DLRX2002 AS DLRX, DLRS2002 AS DLRS,
W2002/sum(W2002) AS W
FROM CES_PREP_JG2;
QUIT;
; run;");
Open(
"C:\Users\klick_j\Desktop\Temp\JMP CES\ces_prep_jg_V2.sas7bdat",
Use Labels For Var Names( 0 ) )
Set up data using JMP Script and set for Interactive Pooled Regression Analysis
The ARRAY statements create index and weight natural log relatives across years. Note that this model is sensitive to large changes. Data edits are used to mitigate the impact of outliers.
3. Under Script Select Local Data Filter; Select Y to add year as filter.
4. Under the Hot Spot select Display Options and Check Box Display
3. Import new data set using Open()

4. Conclusions References
Evaluate using the Filter Check Box options to pool across years.
JSL to set up pooled regression analysis is displayed below. Don’t forget the “;” if you want to glue the JSL SAS code to the Fit Y by X code below.
Bivariate(
Y( :DLRS ),
X( :DLRX ),
Weight( :W ),
Automatic Recalc( 1 ),
Fit Line( {Line Color( {213, 72, 87} )} ),
Local Data Filter(
Location( {0, 0} ),
Mode( Select( 0 ), Show( 1 ), Include( 1 ) ),
Add Filter(
columns( :Y ),
Where( :Y == {"2000", "2001"} ),
Display( :Y, Size( 105, 83 ), Check Box Display )))))
Evaluate. JSL script. Conclusions. Refs. Disclaimer.
Conclusions
The Filtering Check Box options for the Fit Y by X platform allow a user to efficiently pool data across years to conduct an interactive regression analysis. Future research will consist of evaluating pooled regressions with a base period versus a rolling approach to minimize the impact of historically less relevant data.
References
Greenlees, J. JSM (2010) and BLS website, “Improving the Preliminary Values of the Chained CPI-U”.
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Disclaimer: The views expressed in this presentation are those of the presenters and do not necessarily represent the views of the US Bureau of Labor Statistics, or SAS Institute, Inc.