Finite Sample Properties of GMM

In a comment on a post earlier today,  Stephen Gordon quite rightly questioned the use of GMM estimation with relatively small sample sizes. The GMM estimator is weakly consistent, the "t-test" statistics associated with the estimated parameters are asymptotically standard normal, and the J-test statistic is asymptotically chi-square distributed under the null. But what can be said in finite samples?

Of course, this question applies to almost all of the estimators that we use in practice - IV, MLE, GMM, etc. Indeed, lots of work has been done to explore the finite-sample properties of such estimators. For instance, consider my own work on bias corrections for MLEs (see here, here, and here). So, I'm more than sympathetic to the general point that Stephen made.

Estimating an Euler Equation Using GMM

In one of my grad. econometrics courses we cover Generalized Method of Moments (GMM) estimation. I thought that some readers might be interested in the material that I use for one of the associated lab. classes.

The lab. exercise involves estimating the Euler equation associated with the "Consumption-Based Asset-Pricing Model" (e.g., Campbell, 1993, 1996.) This is a great example for illustrating GMM estimation, because the Euler equation is a natural "moment equation".

The basic statement of the problem is given below, taken from the handout that accompanies the lab. class exercises:

Some Official Data Come With Standard Errors!

Without intending to, I seem to have been on a bit of a rant about data quality and reliability recently! For example, see here, here, and here.

This post is about a related topic that's bugged me for a long time. It's to do with the measures of uncertainty that some statistical agencies (e.g., Statistics Canada) correctly report with some of their survey-based statistics.

A good example of what I have in mind is the Labour Force Survey (LFS) from Statistics Canada.

What (Some of) My Colleagues Are Up To

There's plenty of empirical research going on in the Department of Economics at the University of Victoria, where I work. Readers of the blog get to read plenty about what I've been doing, but what about other empirical work by some of my colleagues?

The following is a small cross-section of some of the quantitative papers that have been produced recently in this department. I've limited myself to very papers that are readily available for downloading, so not all of my empirically oriented colleagues are represented here - sorry!.

Confidence Intervals for Impulse Response Functions

An impulse response function gives the time-path for a variable explained in a VAR model, when one of the variables in the model is "shocked". We get a "picture" of how the variable in question responds to the shock over several periods of time.

An impulse response function (IRF) is essentially a type of conditional forecast. It's a messy function of the estimated coefficients in the VAR model, and the data. So, it's really just a point estimate, period by period. There's some uncertainty associated with the IRF, of course - this comes from the uncertainty associated with the estimated coefficients in the model. So, we really need to report a confidence band, period by period, to go with the IRF.

More on the Quality of Economic Data

Yesterday I posted two pieces relating to the quality of economic data, in general terms, and with reference to China.

I'm firmly of the view that we need to be paying more attention to data quality than we currently do as economists. We also need to keep in mind that data are frequently revised, and this has implications for policy conclusions based on preliminary figures.

To help you with your reading on this topic, here's a small selection of papers that touch on different aspects of this topic:

Now That the Semester is Over....

Another teaching term is done, and the exams are all graded!

HT to my colleague, Emma Hutchinson, for this timely item:

Bias Reduction Paper Published

Another of our papers on bias reduction for Maximum Likelihood estimators has now been published. This one is titled, "On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution", and is co-authored with Ryan Godwin and Helen Feng. It's in Vol. 42 (11) of Communications in Statistics - Theory and Methods, and is available here.

This paper stems from an ongoing research program with Helen, Ryan, and others. Other posts relating to this program can be found here and here. There's more of this on the way!

© 2013, David E. Giles

The Reliability of China's Economic Data

There have long been concerns about the reliability of published macroeconomic data for China. About 3 months ago, the U.S. - China Economic and Security Review Commission published a timely report, titled, "The Reliability of China's Economic Data - An Analysis of National Output". The report certainly makes interesting reading.

In a post earlier today I warned about the importance of data quality. When the data relate to an economy that's size and importance as that of China, then it's time to sit up and take notice!

Data Quality is Paramount

Yesterday, in a post on the Worthwhile Canadian Initiative, Frances Woolley rightly drew attention to some rather disturbing issues associated with the upcoming release of the 2011 National Household Survey (NHS), by Statistics Canada. In a nutshell, she asks the question, "How can we be sure that the NHS information about the religious beliefs of Canadians is accuarate?"

Recently, I made the comment: Data - the econometrician's lifeblood! Can't function without it." I wish I'd been more specific, and said "reliable data."