What are "measurement equations"

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!

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

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) = numTerm
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) = numTerm
H1st(3,21) = numTermInvdenTerm;
H1st(3,40) = -numTerm
%— 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) = numTerm
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) = numTerm
H1st(5,21) = numTermInvdenTerm;
H1st(5,40) = -numTerm
%— 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?