What are "measurement equations"

Estimation ML/Bayesian estimation
1

Hi all!

Recently I took a quick glance over the C++ code for Liu, Wang, and Zha (2013 Econometrica). The code is available on Zha’s homepage: tzha.net.

They first inputted their model in Mathematica, then converted .nb files to .m files, and finally converted .m files to c files. Among these files, some named “Cinput_MeasureEqns_TAG.m”Cinput_MeasureEqns_modb_6v.m (2.09 KB) raise a question to me. What are “measurement equations”? In effect, I didn’t find any comment on this conception in their code, so I think it might be a technical term. In their file “Generate_gensysform_credit4housing.nb”Generate_gensysform_credit4housing.zip (23.8 KB), there is a block named “measurement equations” at the bottom, but it’s blank.

I searched dynare user’s guide, and also found the key word, but without any explanation. Are these equations related to Kalman filter and log-likelyhood functions? Or, are these equations related to the observable variables?

BTW, have anyone implemented their C++ code?

Thanks in advance for any help!
Fuyang

2

They are equivalently called observation equations. See Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” for details

3

Thank you Professor, for always quick reply! I’ll carefully study your work!

In LWZ’s measurment equations .m file, I couldn’t understand the following lines. I took a quick scan of your work and didn’t find the answer.

[code]a1st(1) = log(glambdastar);
a1st(2) = log(glambdaq);
a1st(3) = log(glambdastar);
a1st(4) = log(glambdastar);
a1st(5) = log(glambdastar);
a1st(6) = log(nbar);

%-- A few derived parameters.
InvdenTerm = 1.0/(1.0-(1.0-gphi)*galpha);
numTerm = (1.0-gphi)*galpha;
COY = CeOY + ChOY;
CeOC = CeOY/COY; % Ce/C
ChOC = ChOY/COY; % Ch/C

%—$$##
%— 1st measurement equation for land price.
H1st(1,1) = 1.0;
H1st(1,34) = -1.0;
H1st(1,18) = InvdenTerm;
H1st(1,19) = InvdenTerm;
H1st(1,39) = -InvdenTerm;
H1st(1,20) = numTermInvdenTerm;
H1st(1,21) = numTermInvdenTerm;
H1st(1,40) = -numTermInvdenTerm;
%— 2nd measurement equation for biased technology.
H1st(2,20) = 1.0;
H1st(2,21) = 1.0;
H1st(2,40) = -1.0;
%— 3rd measurement equation for consumption.
H1st(3,2) = ChOC;
H1st(3,35) = -ChOC;
H1st(3,3) = CeOC;
H1st(3,36) = -CeOC;
H1st(3,18) = InvdenTerm;
H1st(3,19) = InvdenTerm;
H1st(3,39) = -InvdenTerm;
H1st(3,20) = numTermInvdenTerm;
H1st(3,21) = numTermInvdenTerm;
H1st(3,40) = -numTermInvdenTerm;
%— 4th measurement equation for investment.
H1st(4,4) = 1.0;
H1st(4,37) = -1.0;
H1st(4,18) = InvdenTerm;
H1st(4,19) = InvdenTerm;
H1st(4,39) = -InvdenTerm;
H1st(4,20) = numTermInvdenTerm;
H1st(4,21) = numTermInvdenTerm;
H1st(4,40) = -numTermInvdenTerm;
%— 5th measurement equation for business debt.
H1st(5,12) = 1.0;
H1st(5,38) = -1.0;
H1st(5,18) = InvdenTerm;
H1st(5,19) = InvdenTerm;
H1st(5,39) = -InvdenTerm;
H1st(5,20) = numTermInvdenTerm;
H1st(5,21) = numTermInvdenTerm;
H1st(5,40) = -numTermInvdenTerm;
%— 6th measurement equation for hours.
H1st(6,5) = 1.0;

%—$$##
F1st(nzbase+1,1) = 1.0; %34
F1st(nzbase+2,2) = 1.0; %35
F1st(nzbase+3,3) = 1.0; %36
F1st(nzbase+4,4) = 1.0; %37
F1st(nzbase+5,12) = 1.0; %38
F1st(nzbase+6,19) = 1.0; %39
F1st(nzbase+7,21) = 1.0; %40[/code]

There were 6 observable variables. And it seems that they were dealing with them for the first 40 periods. Would it possible that you explain for me?
Thanks!
Fuyang