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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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One can model anything, that's why it is a model. The real question is what the value of such a model would be. More to the point, I think this would be a very hard thing to do sensibly because how are we going to measure well-being? It encompasses way more factors than our economic models typically capture, such as social relations, health and mental state....


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New technology makes past technology obsolete. How many people know these days how to light a fire by rubbing wood together? How many people know the nuts and bolts of tending to the engine of a train powered by coal? Heck, how many coal-trains are still operational? So yes, we do forget our past discoveries and technologies, as they are replaced by new ...


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As Dave Harris commented it depends a bit on the context. I know the guess and verify solution method mainly from solving value functions in differential resource games (more specifically the papers on fish wars), although I have also seen it used for value functions when there is no strategic interaction. In such problems one is typically looking for a ...


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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 ...


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If possible, clarifying what exactly you're most interested in might help answers be more on point and useful. Are you interested in the mechanisms that cause a one-period shock to last (and not just immediately dissipate)? Or are you interested in understanding some of the reasons that a shock to one variable (say technological progress) leads to changes in ...


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$n_{t-1}$ is exogenous at time $t$. Since you must be working in a dynamic setting, $n_t$ will also show up in the utility function at time $t+1$.


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I believe $n_{t-1}$ is a quantity from the past, so you should be able to treat it as an exogenous variable


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I guess you already went trough the algebra below, but just for context, the problem you're trying to solve is $$ \max_{c}\sum_{t=0}^{+\infty}\beta^t u(c_t) \\ \text{s.t.}~~ f(k_t) + (1- \delta)k_t = c_t + k_{t+1} \tag{1} $$ where $f(k_t) = k_t^\alpha$ and $$ u(c_t) = \frac{c_t^{1-\gamma}}{1-\gamma} - 1 \tag{2} $$ The problem in (1) can be cast into the ...


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By re-indexing all investment projects in the form of $s_{J,t}$, I get the following two equivalent constraints \begin{align} c_t+y_{t+1}-y_t&\leq f(k_t)-\sum_{i=1}^\infty\varphi_j s_{J,t-(J-j)} % Resource Constraint \\ k_{t+1}&=(1-\delta)k_t+S_{J,t-(J-1)} %Law of motion for capital formation \end{align} Hence, the Lagrangian for the maximization ...


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