Hi Johannes,
While we’re waiting for the guidance on the SMM, I started looking into the ways in which this mini model can be estimated using the particle filter (I found this helpful: [Particle filter dynare)). First things first, I am thinking of applying this to the UK, since CPI is particularly positively-skewed in many OECD economies (but not the US). Here are some questions in terms of specifying the observation equations in a non-linear setting (I have also read your handout ‘A Guide to Specifying Observation Equations for the Estimation of DSGE Models’ in great detail).
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There is no government expenditure or trade balance in this stylised model. So to specify the observation equation that links the model output to data GDP, firstly one must subtract the gross fixed capital formation, government expenditure and net exports from the time series of GDP to get the series of interest (i.e. Y_t=GDP_t-GOV_EXP_t-NX_t-I_t) ? I’m not sure if people usually subract NX_t in closed economy settings though (e.g. SW(2007) or SGU(2012)). If not, how so?
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Output in the model is stationary, but in the data of GDP is non-stationary. Specifically, data GDP grows over time due to population growth and technological innovation. So Y_t needs to be divided by some measure of Population or Labour Force (say N_t) in order to translate the data in per capita terms. Also, while the theoretical model incorporates non-stationary technological innovations, the code is expressed in ‘per effective worker’ terms (i.e. de-trended by productivity growth), so the time series from the data Y_t needs to be de-trended in some way to produce an accurate mapping. As far as I understand, simple HP filter or polynomial de-trending will not do, because these methods are typically scale-dependent (i.e. you log them first and then de-trend them, but that defeats the purpose of this non-linear model). So the observation equation I intend to use incorporates a gross de-meaned growth rate (i.e. Y_t/Y_{t-1}-mu_y) . Is this a legitimate approach? What are the potential caveats or other suggestions?
As for Inflation, it is also a gross growth rate, only I it is not de-meaned. Rather, the long-run trend is calibrated to a parameter equivalent to the quarterly inflation target. Nominal rate of interest is the annualised interest rate divided by 400 (as in the guide).
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If there are 2 shocks in the model, but I want to have 3 observable variables (GDP, CPI Inflation and Nominal Interest Rate), I should introduce 1 measurement error (e.g. in the observation equation for output) in order to avoid stochastic singularity, right? The reason I ask, is because there are examples in the guide (e.g. Listing 2 on page 16), where there are 3 observables, 1 shock and 1 measurement error. It doesn’t seem to add up.
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Is there any downside to including additional observables (say 2-3 more) using this measurement error approach?
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If I specify the observation equations in the above way, but decide to choose order=1 in stoch_simul, will there be any hurdles for dynare to estimate the linear version of the model? Since it is simple to nest the model in a linear setting, I’m thinking of using it as a cross-check, only I expect parameters phi and zeta not to be uniquely identified up to a first order (instead people often use the slope of the Phillips curve for such purposes). I could also just use a quadratic functional form to start with.
I’ll upload the code with particle filter estimation + data once I get the green light for the above specifications of observation equations.
Thanks in advance