Explore the Advanced Macroeconomics An Easy Guide Appendix - B Simulating an RBC model study material pdf and utilize it for learning all the covered concepts as it always helps in improving the conceptual knowledge.
Simulating an model Chapter 14 outlined the basic building blocks of an model . This appendix will take you through the steps to estimate it and then compute the empirical counterpart to the business cycle data . The steps are quite simple . Imagine first that you were to do this by hand . Of course the starting point would be your model with its associated parameter values . The conditions that describe your model typically will be a combination of and budget constraints that determine the tion of variables through time . Plugging the parameter Values into the model , you could compute the steady state ofthe economy ( pretty much as we did in Chapter 14 ) We use the word could because this may be quite . 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 tem , that can be shocked to compute the trajectory of the variables in response . For an model , you shock it over and over again to get a series for the variables , from which you can compute the correlations that you will confront with the data . This is easy to say but involves computing the saddle path in which variables converge to the equilibrium . And to be able to do this we would also need to check first 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 daunting , 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 . 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 first using that . Before starting you need to download which is to run these models . Below we will Write the model , and , say , we call it . We will then run in . It is as easy as that , but 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 the folder . This means going to ( where means which version of you have in other words , you need to go to the folder in ) select that folder , and then 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 regular folder in your computer will do ) We will write the model ( see below ) and save it in this folder . It is important to save the model with the extension . So ifyou call the model you need to save it in this folder as . This will indicate to that it is a when you run . Then , you How to cite this book chapter , and , A . 2021 . Advanced An Easy Guide . Appendix . Simulating an model , London Press . DOI License .
372 SIMULATING AN MODEL have to specify to that you are currently working on the desired folder . You can do this by clicking the browse for folder button HOME ED New Open Save am FILE I I Users I Now to the model . The we will work with is the same as in Chapter 14 . You can more complex structures ( including versions ) within the framework of . For our purposes of taking a 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 . parameters parameters BETA PHI ALPHA DELTA The var command sets all the variables of the model , both exogenous and endogenous . In this case , we have output ( consumption ( labour ( investment ( ii ) the shadow price of consumption ( lambda ) the stock of capital ( the nominal interest rate ( productivity ( and wages ( The command shocks . indicates the exogenous shock that will hit the variable . The command parameters is used to the parameters of the model . Also , some values will remain free for our model to match certain moments of the variables . 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 the chapter . Once you ve out what values you want to use , setting the values in the model is forward , and is the next step . You can later play around by considering the response of the model to different values of these parameters . Here we assume , for example ALPHA
SIMULATING AN MODEL 373 . 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 . We also a process for the shock , that here will be an process . Lagged and forward variables are indicated by a or respectively , between parentheses , after the variable name , and can be added without any problem . will work with a version , so we need to our variables as the log version of the original variables . But this is no problem , it just means that where we had we write ( This change of variables can only be done with variables that always take positive values , though , so watch out ! So the model is a series of and budget constraints . For example , our equation below is the resource constraint , the second and third are the optimal choice of consumption and labour , the fourth is the relative to capital , and the is the of the interest rate . The last equations are the production function , the law of motion of capital , the of the real wage as the marginal productivity of labour , and the process for productivity . model Aggregate Demand ( ii ) for consumption ( lambda ) for labour ( lambda ) for capital ( lambda ) BETA ( lambda ( ALPHA ( The interest rate equation ( ALPHA ( Production Function
374 SIMULATING AN MODEL ( Law of movement of capital ( ii ) Wage equation ( ALPHA ( Productivity process log ( log ( end Now we need to compute the steady state , by hand ( endogenous variables as a function of exogenous variables ) needs to work with a steady state , so if you don write it down , will try to compute it directly . However , doing so in a model ( like this model ) generally will not work . For that reason , it is advisable to provide it manually To do that , we have to introduce the command as shown below . This is not as as it sounds , and ing the steady state properties of the model is always useful to do . Finally , we need to establish that the initial values for the model are those for the steady state ( in logs ) BETA ALPHA ) DELTA ( ALPHA ) log ( log ( log ( log (
SIMULATING AN MODEL 375 log ( ii log ( log ( lambda log ( log ( end Then we have to check if the steady state is well . For that we use the steady and check commands , these will compute the of the model around the steady state , to verify that the dynamic properties are the desired ones . steady check Next , we have to set the shocks that we want to study . In this model , we want to analyse the effect of a productivity shock . We use the shocks command for that . For example , a shock of 10 can be coded as shocks var end Finally , we set the simulation to allow to show us the functions . We use for that ( 100 , order ) This completes the script for the model . It has to look something like this . Defining variables . Endogenous variables ( Exogenous variables ( Parameters parameters BETA PHI ALPHA DELTA parameters
376 SIMULATING AN MODEL . Calibration . 95 Targeted steady state values . Model model Demand ( ii ) for the consumption ( lambda ) lambda ) lambda ( ALPHA ( Function ( ALPHA ) rate equation ( ALPHA ( of movement of capital ( ii ) equation ( ALPHA ( end SIMULATING AN MODEL 377 . Steady State Computing the steady state and calibrated parameters ( ALPHA ( end . Computation steady check shocks var end ( 100 , order ) 378 SIMULATING AN MODEL Now we run , and voila ! The output will be like thi 11 lambda Modulus . 0505 . 3503 . 35 . 35 mete are ) 1129 than modulus tax to ) The . II The . MODEL at oz shocks ! oz ez oz or or POLICY 11211115111011 FUNCTIONS 11 Constant ( SIMULATING AN MODEL or VARIABLE . DEV . VARIANCE ) OP VARIABLE 11 lambda I 11 . OF mum . 11 lambda I vi Tonal um 011001037 ( an code I ! I El Em lack adv Luau ' as nA 015 . an . Note 379