The first-order approximation has the property of certainty equivalence. So, for those forward-looking equations, can I treat them as backward-looking, and will their variable changes be the same as those in the original model equations?
No. Certainty equivalence just means that future values are treated as if the expected value would happen with certainty. Those expected values still need to be computed, which would not be the case if you would make them backward looking.
1 Like
Thank you, I have two more questions:
-
I would like to ask, if a variable has subscripts t-1, t, and t+1, do we know both its end value (endval) and its initial value (initial) in a deterministic simulation?
-
Can a model assume that its corresponding three-period model is solved according to the deterministic simulation approach to study the general properties of the model, such as the direction of the IRF, the scale ratio of each variable, etc.?
- For t-1 variables, the initial condition can be freely chosen/set. The t+1 variables need a terminal condition (usually a steady state).
- I don’t understand the question.
General DSGE models are infinite-horizon models. If I linearize the model and modify it into a three-period model, meaning the model terminates at the third period, and given the terminal values of the forward-looking variables, can I solve this three-period model using the deterministic simulation approach and infer some characteristics of the infinite-horizon model, such as the impulse response changes of each variable?
No, typically you cannot do that. Future variables are a function of today’s choices, which still need to be computed. Setting the terminal condition is only an option if the model had sufficient time to actually converge to that state.
Thank you, Professor. My last question is, does the first-order approximation process in Dynare default to linearization by performing Taylor expansion around the steady-state values on both sides of the equations, or does it use log-linearization as represented by the Uhlig method?
Dynare by default conducts linearization, not a log-linearization.
I looked at Romer’s textbook on the three-equation New Keynesian model, which mentioned that if the exogenous shock only lasts for one period and its autoregressive coefficient is 0, the value of the variable at t+1 will be 0. Does this situation apply to general DSGE models? Is it not applicable when a set of equations appears with both the t-th value of a variable and the t-1 value of another variable?
No, that is model is special. See
Thank you, Professor. If I now have a linearized model, is there any method or approach to conduct a preliminary analysis of the transmission mechanism of model shocks? For example, I want to roughly understand which variables are first affected by interest rates, which then affect other variables, and ultimately affect the variables I care about. Additionally, I want to know the direction and sign of these effects.
That sounds like a case for a simple first order stochastic simulation.
But in stochastic simulations, it seems that changes in the model’s variables occur simultaneously, making it difficult to distinguish the order in which variables are affected. Is it possible to determine this from the symbolic equations of the linearized model? Or could we consider the linearized equations alongside the impulse response graphs to figure it out?
If you are talking about a general equilibrium model, of course everything happens simultaneously. Price and decision variables need to adjust to be consistent.
Thank you, Professor. I understand now. I have also found that the general equilibrium makes analysis very difficult during various transformations and summations of the model equations. So, it seems that predicting the possible signs of impulse responses, such as from the linearized model equations, is also not feasible in practice.
Yes, generally that is not feasible. General equilibrium effects can overrule partial equilibrium ones.