Advanced Macroeconomics An Easy Guide Appendix - C Simulating a DSGE model

Simulating a model Chapter 15 outlined the basic building blocks ofa New model . How do We estimate it ?

We laid out the framework in Appendix , so you may want to check out the setup section there . At any rate , we will repeat most of it here , for convenience . The starting point would be your model with its associated parameter values . Again , the conditions that describe your model will typically be a combination of and budget constraints that determine the evolution of variables through time . Plugging the parameter values in the model , you could compute the steady state of the economy ( pretty much as we did in the case ) Once you know the steady state , you could the model around that steady state ( pretty much as we did for example in Chapter ) Now you have a linear dynamic system , that can be shocked to compute the trajectory of the variables in response . This is easy to say but involves computing the saddle path in which variables converge to equilibrium . And to be able to do this you would also need to check that that dynamic properties are those required for convergence ( also see Chapter and the Mathematical Appendix for a discussion ofthis ) Well , if all that looked a bit , you are lucky that most of this work will be done by the computer itself . What remains of this appendix shows you how to go about it . These are all quite mechanical steps , so most of the work has already been done for us . First of all , you will need to have , and we will assume you are minimally knowledgeable . offers a free trial , so you may want to practice using that . Before doing this we will to download which is to run these els . Below we will write the mode , say you call it . We will eventually run in . It is as easy as that , we have to do some setting up before . In , go to the HOME tab , and look for the Set Path button . In the new window , go to the Add Folder command and search in the download for the folder . This means going to ( you to go to the folder in ) select that folder and select to add this . It typically places it , but if it does not , make sure to use the left buttons to place it first . Then save . Now We need to open a folder to save the results . Any folder will do . You can do this by clicking the browse for folder button How to cite this book chapter , and , A . 2021 . Advanced An Easy Guide . Appendix Simulating a model , London Press . DOI License .

382 SIMULATING A MODEL co New Open save ' FILE Users ) We will write the model ( see below ) and then we will save this model in this folder . It is important to save the model with the extension . So if you call the model you need to save it in this folder as This will indicate to it is a when you run . Now to the model . The we will work with here replicates the framework of Chapter 15 , but you can more complex structures ( including versions ) within the framework of . For our purposes of taking a first step in modelling , this simple will do . In what follows we will take you through the steps to run this simple model . First , we need to the variables . You need to start your code in the editor . Type the following var pi i parameters beta sigma phi alpha The var command sets all the variables of the model both exogenous and endogenous . In this case , we have ( pi ) output ( nominal interest rate ( i ) the exogenous shock ( and the real interest rate ( The command shocks . indicates the exogenous shock that will hit the variable The command parameters is used to the parameters of the model . Our model will implement versions of the equations ( 1562 ) and ( The parameters then correspond to those in those equations . We add , which will be the parameter for the shock process ( explained below ) Next we need to provide a numerical value for these parameters . For this you will typically rely on previous literature , or use the calibration exercises that we saw in Chapter 14 . Setting the values is straightforward and is the next step . You can later play by changing the response of the model to a different value of these parameters ) Here we assume , for example alpha beta

SIMULATING A MODEL 383 sigma phi 05 With the variables and the parameter values established , we next have to specify the model . We use the command model for that . We will conclude the section with the end command The model is written in a fashion below , which , in this case , as said , replicates equations ( and ( We also a process for the shock , here we it as an process . Lagged and forward variables are indicated by a or respectively and can be added without any problem . model ( linear ) i ( Phillips Curve pi ( phi pi ( Error ( Real rate ( end To check if the steady state is well we use the check command It computes the of the model Generally , the are only meaningful if the is done around a steady state of the model . It is a device for local analysis in the neighbourhood of this steady states check

384 SIMULATING A MODEL This will show something like this Command Window Processing output done completed . Modulus Real Imaginary There are ) larger than in modulus for variable ( The rank condition is verified . fa Next , we have to set the shocks that we want to study . In this model , we want to analyse the effect of an interest rate policy shock We use the shocks command for that . For example , a shock of shocks var end . Finally , we set the simulation to allow to show us the functions We use for that ( periods ,

SIMULATING A MODEL 385 This completes the script for the model . It has to look something like this Preamble vat Parameter beta sigma beca model . linear ) A ' 25 ) so ' 13 ( 22 ) co A ! there axe only shack ) gap ( 22 ) equal output ! are only shocks Curve pi ( a ' a ( 21 ) shock to ( bottom so ) Real race ) end Steady State Snacks shocks vu ep , end Computation ( pe ,

386 Now we run . The output will be like this SIMULATING A MODEL An interest rate shock reduces transitorily output and . Notes ( in an um Help . iH . It DE ID I 42 4306 A a 12 to 12 I on oz as an 41 A 12 10 12 on on om 12 If you are using MAC , maybe will be unable to save it with the extension . If that were the case you could write the whole model in a outside of and then save it in the appropriate folder .