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Question

Are there any simulated datasets that have been designed specifically to represent macroeconomic data? In particular, are there any such datasets that can be used in benchmark studies?

Background

To give an analogy, in optimization, one may be interested in assessing the quality of a given algorithm. To do this, there are a number of test functions for optimization, such as the well-known banana function, that can be used to evaluate the performance of an algorithm; for example, by analysing if and how fast the algorithm can find a global minimum.

I am interested in working in this controlled experimental setting using simulated data that has a macroeconomic interpretation. With data simulated from a known data generating process (this would be my control), it would be possible to investigate, say, the performance of algorithms designed to detect structural breaks and to assess techniques/models used for forecasting.

I would greatly appreciate if someone could help: either by pointing me to some simulated datasets that can be used for the above purposes or by providing some guidance on how to simulate data that carries a macroeconomic interpretation.

It's possible for me to simulate a variety of ARMA processes (or VARMA model), but I am really interested in something that goes beyond that; the simulated data ought to have similar properties to observed macroeconomic data. Obviously, I am trying to avoid using actual data because my control (of knowing the data generating process) would be lost.

Update

For one of the purposes I had in mind, a quick read of Castle, Doornik, and Hendry (2013) suggests that it is, perhaps, not that difficult. Their "experimental design" is based on the following equations $$ y_{t} = \beta_{0} + \gamma y_{t-1} + \beta_{1}x_{1,t} + \cdots + \beta_{10} x_{10,t} + \epsilon_{t}\\ x_{i,t} = \rho x_{i,t-1} + v_{i,t}, v_{i,t} \sim IN[0,1], i=1,\ldots,10,\\ \epsilon_{t} \sim IN[0,1], t=1,\ldots ,10. $$ along with some further qualifications. So, it would appear that for one of my examples (the case of evaluating structural break algorithms), relatively simple (although by no means, "not tricky") DGPs are all that's required.

Reference: Castle, Doornik, and Hendry (2013) Model Selection when there are Multiple Breaks

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I think yes. Macroeconomists usually build DSGE models to predict short-run fluctuations. Calibrating the data is the part of the process. After using numerical methods to run the models, researchers check the moments of the simulated values. This is a way to examine whether the simulated data represents real life outcomes.

However, every economic situation differs so you have to choose wisely the simulated data depending on your research every time. I mean the growth was huge in the 1950s in the US, but today the main objective is to kill the deflation monster.

Here's the benchmark model by Hansen and Wright (1992):

enter image description here

$\sigma$ denotes standard deviation, $Y,C,I$ and $L$ are macroeconomic variables.

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