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Short answer It doesn't seem like you've tried very hard to find estimation using Dynare (google results of "Dynare estimation"). Dynare is in fact capable of doing estimation and typically people use some sort of data to estimate the parameters that govern their model. Longer Answer What is a DSGE model? A DSGE model is a series of equations (and ...

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The mathematical theory behind DSGE models can be found in any textbook on stochastic dynamic optimisation. One common reference that economists use for this is Stokey, Lucas and Prescott. Of course, they focus exclusively on recursive methods, but (perhaps) the lion’s share of dynamic problems in economics are solved in this way. There is also a treatment ...

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I've just solved this problem. First of all, your solution does not make too much sense, as in a simple interest rate rule it must hold that the sum of all coefficients must be greater than one. In your case this means that $\phi>1$. Therefore, the series would converge not to zero. Second, an interest rate rule should try to offset fluctuations. This ...

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Heuristically, you can think of the integral as just a sum: $$\bar{C} = \left( \sum_{i=1}^n C_i^{1-\frac{1}{\epsilon}} \right)^{\frac{\epsilon}{\epsilon - 1}}$$ where $\bar{C}$ is an index of aggregate consumption, and utility is given by $u \left( \bar{C} \right)$. It's easy to check that the marginal rate of substitution between goods $j$ and $k$ is ...

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The "standard" New Keynesian model could be many things, but suppose that we're dealing with the basic log-linearized 3-equation model (intertemporal Euler equation, New Keynesian Phillips curve, and monetary policy rule) exhibited, for instance, in Gali's textbook. In most variants of this simple model, a temporary increase in government expenditure will ...

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Short answer: no. Dynare, and linearization/perturbation methods in general, are designed for solving smooth models approximated around a single point in state space (the steady state). A model with fixed cost is typically non-smooth, and its behavior away from the steady state may be very different, if e.g. the firm switches from investing to not ...

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As mentioned by Michael quantecon has good resources. Here is an example of very simple DSGE model from quantecon. I am not sure if you can get to as low as 3 equations but here is very simple example of real business cycle DSGE by Chad Fulton. I won't copy all the code from the site, you can just follow the link which has full code, but it is based on the ...

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Jordi Galís book "Monetary Policy, Inflation, and the Business Cycle" features the 3-equation "Simple New Keynesian" Model: \begin{align*} \pi_t &= \beta E_t[\pi_{t+1}] + \kappa\tilde{y_t}\\ \tilde{y}_t &= -\frac{1}{\sigma}\left(i_t-E_t[\pi_{t+1}]-r_t^n\right)+E_t[\tilde{y}_{t+1}]\\ i_t &= \rho + \phi_\pi\pi_t + \...

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There are certainly cases where the performance differences between Python and Julia matter, but solving a simple DSGE model is not one of them. There have been some formal comparison exercises (e.g., Aruoba and Fernández-Villaverde 2015 and 2018 update). Coleman et al. 2020 also consider a NK model (see Table 4). The real gains are only found when ...

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Yes, there are DSGE models that can be used for forecasting. These models typically have a particular kind of steady-state, which is, more precisely, called balanced growth path (BGP). On the BGP (in the absence of shocks), key indicators growth at the same constant rate. For example, GDP, household consumption, investment all grow at 2% a year. This is ...

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First, you can also have a state-space setup for a model which is not log-linearised. It is the combination of the solution of your model (that you get by using Sims, Klein, Binder-Pesaran, or Blanchard-Kahn solution methods for rational expectation models) - the transition equation, which gives the transition of your state variables depending on shocks - ...

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Intuitively, it means that the model has such characteristics that "the best we can say" about remaining uncertainty, is that it will be zero. From general experience, we know that it won't be zero, but the information we possess does not permit us to say anything else than that it will be zero. The even deeper assumption here is that the information and ...

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The condition that unstable eigenvalues equal in number the control/decision/non-predetermined variables is equivalent to the requirement that a model possess the "saddle point property". Of more interest is why economists generally want their models to possess such a property, something that holds for the DSGE models. In Economics we call models with ...

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It is generally not possible to make a sharp statement about the types of non-convex costs that Dynare can handle. Many different factors come into play about whether a model can be "solved" by Dynare or not. Is the steady-state correctly defined? Is the model stationary? Is the model differentiable everywhere in the ergodic set? Are the number of ...

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To understand why macroeconomists use DSGE as a tool, in general, it's a good idea to read up on the Lucas critique. More colloquially, DSGE models provide macroeconomists with a laboratory that allows quantitative comparison (and ranking) of different economic policies. Further, the process of writing a model disciplines thinking: if one cannot write down ...

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There's no correct method to do this. DSGE guys will estimate the model by doing something like this: plugging in priors for their parameters and then running an optimization that minimizes the distance between model and data moments while maximizing the log likelihood from the priors. The data moments for them will be well known values of variances and ...

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They consider a model with two islands: a Production island and a Leisure island. Every transition from a period $t$ to a period $t+1$ is split into two parts. People who are in the Production island at the end of period $t$, start on the Leisure island in the beginning of period $t+1$ with probability $\sigma$, and stay on the Production island with ...

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The shock process is already linear. any log linearisation will result in identical expression. The underlying non linear shock process can be something like this:$$$Z_t = Z^{(1-\rho)} Z_{t-1} e^{\epsilon_{t}}$$ This when you linearise, you obtain your linear shock processes. 2 I found the error in my derivation: I mistakenly supposet that the steady state of$p_t+1$equals$\bar{\rho}$. I did not recognize that p was different from$\rho$because of the poor quality of my printout. Reading the paper again on a screen I immediately spotted the mistake. 2 I can think of two big ways. Formal tests of model fit: If you are using SMM, GMM or indirect influence check out the J-stat. If you are using maximum likelihood you want a likelihood ratio. Bayesian model testing is similar to likelihood ratios, but more complicated. Many of the DSGE models were rejected on these bases (you can see Sargent discussing it ... 2 On the empirical side, there might be answers for you in the national accounts. I only know about the french case : the french statistical institute (INSEE) has different depreciation data for different types of capital (e.g. buildings, machines, patents) and for different sectors. These data are supposed to reflect both physical depreciation and "normal ... 2 Try to give a look at what happens to inflation's IRF. If it stays positive for the whole horizon of the IRF then simply prices have increased over time at the inflation rate. I guess that any non-degenerate price level (nominal!) is compatible with such model structure, as its system is written down in growth rates, as that's what loglinearised variables ... 2 While in GMM one uses theoretical analytical moments, in MSM one uses simulated theoretical moments instead. For GMM, [t]he method requires that a certain number of moment conditions were specified for the model. These moment conditions are functions of the model parameters and the data, such that their expectation is zero at the true values of the ... 2 Hi: I can't speak for DSGE models specifically but, in more standard "rational expectations" econometrics, the measurement equation usually comes from some assumed linear relation between the dependent variable and the expectation of some other variable. For example, one might have$y_t = \beta x^{*}_{t} + \epsilon_{t}$where$x^{*}_{t}$is the ... 2 It’s derived as follows. First start with original equation. $$(1+i_t)=(1+i^*_t)\frac{S_{t+1}}{S_t}$$ Take natural logs of both sides: $$\ln(1+i_t)=\ln(1+i^*_t)+\ln(S_{t+1}) -\ln(S_t)$$ Now you just use the following: $$s_t=\ln(S_t)$$ And use the well known fact that for small values of$i\$ the following approximation holds: $$\ln(1+i)\approx i$$ And ...

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Is there future for DSGE? Well, DSGE stands for dynamic stochastic general equilibrium models. You can’t really model time series appropriately without the dynamic stochastic part, and when it comes to general equilibrium there are economists who think that this approach does not really capture all interesting questions, as in many cases it might be more ...

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You can find OLG models that do not classify as DSGE (in particular, the model might not be stochastic) as well as DSGE with overlapping generations (contrary to those with infinitely lived agents). You can find more detail on this on this working paper by Assous and Duarte (2017), as they note In the early 1980s, when the real business cycle ...

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This is due to the famous Lucas critique. To make long story short, in the past in the heyday of Keynesian macroeconomics it was quite normal for macroeconomists to just postulate some relationships based on relatively casual empirical observations like for example the Philips curve which says that there is positive relationship between inflation and ...

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Minimum state variable (MSV) solution is a special technique used to find an unique equilibrium with desirable properties in DSGE models. Often DSGE models can have multiple paths that will satisfy the conditions given by the system you are modelling. Hence to provide some meaningful results you have to somehow choose between the all possible paths/...

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Business cycle fluctuations can be studied in many ways including also growth models. An example of using growth model to study business cycle would be this 1995 paper by Cho & Cooley. This being said growth models are not as common for examining business cycles as for example DSGE models so saying they are usually used for that purpose is correct. To my ...

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