Technology Shocks and Employment in Open Economies

A growing body of empirical evidence suggests that a positive technology shock leads to a temporary decline in employment. A two-country model is used to demonstrate that the open economy dimension can enhance the ability of sticky price models to account for the evidence. The reasoning is as follows. An improvement in technology appreciates the nominal exchange rate. Under producer-currency pricing, the exchange rate appreciation shifts global demand toward foreign goods away from domestic goods. This causes a temporary decline in domestic employment. If the expenditure-switching effect is sufficiently strong, a technology shock also has a negative effect on output in the short run.

This appendix provides background information as to how the Matlab …le (technologyshock.m) that solves the model is written and how to replicate Figure 1. First, I brie ‡y describe the method used for solving the model. Then, I attempt to provide guidance as to how to install the necessary …les for running the …le that solves the model. I also describe the …le's key part so readers can e.g. investigate how responsive the main results of the paper are to changes in key parameter values. In addition, the model and the …le can easily be used to analyse a number of questions related to the international transmission of technology shocks. In the …nal part, I lay out the log-linearised versions of the model's equations, to allow for an in-depth understanding of the model's foundations.

The File
The model is solved using the algorithm developed by Klein (2000) 1 and McCallum (2001) 2 . The equations of the model are written in matrix form AE t x t+1 = Bx t + Cz t , where E t x t+1 denotes the expectation of x t+1 formed in time t and x t is a vector of endogenous variables, x t = [y 0 t k 0 t ] 0 , where k t is predetermined and y t is non-predetermined. A and B are n n matrices, C is n 1 matrix and z t is a vector of exogenous variables determined by an AR(1) process.
The core …le that solves the model is called technologyshock.m. This …le uses software written by McCallum (2001). To be able to run the …le, the …rst step is to install the needed Matlab …les (See McCallum 2001, 1-2). The necessary …les, solvek.m, impo.m, sim33p.m, qzswitch.m, reorder.m, autocor.m, dlsim.m and dimpulse.m, are available for download from Bennett McCallum's web page.
The next step is to start Matlab and to copy/paste the …les to the speci…ed path. The …les should be installed as .m …les, not as .txt …les. Choose File and then Set Path from the menu bar. A new window opens showing all folders accessible by Matlab. Choose Add Folder to specify the desired folder and then press Save to save this setting for future sessions. The Matlab toolboxes have been changed since McCallum wrote the above-mentioned software package. The problems that may arise due to these changes, can be dealt with as follows: Start the m-…le editor to edit the …le 3 dimpulse.m and for the …rst line of the code, after the comments, write nargin = 6;. Save the dimpulse.m …le. Then you should be able to run the technologyshock.m …le. One way to do this is to type technologyshock in the Command Window and then press enter. The …le automatically generates Figure 1.
The …le that solves the model is divided into two separate parts. The …le is simple to apply to, e.g., an analysis of the sensitivity of the results to changes in key parameter values. Suppose, for example, that one would like to study how the results change, if a technology shock is transitory and the persistence of a technology shock is 0.8. This can be projected as follows. Replace ark = 1.0; with ark = 0.8; (in rows 55 and 464), then save the …le and run it again.

Equations
Equilibrium of the log-linear version of the LCP model can be described by the following equationŝ 3 Choose File and Open from the menu bar. 4 Note that if = 0:75 the economies do not reach the new steady state after ten periods.  (A28) is uncovered interest parity. 28 variables remain to be determinedĈ;Ĉ ;P ;P ;^ ;^ ;^;^ ;ŵ;ŵ ;D;x (z) ; v (x) ;x (z ) ;v (x ) ;ŷ;ŷ ;p (z) ;q (x) ;p (z ) ;q (x ) ;b (z) ;b (z) ;b (z ) ;b (x ) ; E;â andâ . The 28 equations that jointly determine them are (A1)-(A28). Note that the foreign consolidated budget constraint is left out because one equation is redundant by Walras' law. In the Matlab …le that solves the model, a number of other variables require specifying (e.g. predetermined variables and exchange rate expectations). As a result the …le contains 38 variables that are determined by 38 equations.
To simplify the …le that solves the model, de…ne t =P t +Ĉ t . Then equations (A1) can be written aŝ Using this equation and the de…nition of , the money demand function (A5) can be written as Equilibrium of the log-linear version of the PCP model can be described by the following equationŝ The PCP version of the model contains 20 unknown variables (Ĉ;Ĉ ;P ;P ; ;^ ;^;^ ;ŵ;ŵ ;D;ŷ;ŷ ;p (z) ;q (x ) ;b (z) ;b (z ) ;Ê;â andâ ) that are determined by 20 equations (A31)-(A50). As above, the foreign consolidated budget constraint is left out (Walras'law). In the Matlab …le a number of other variables have to be speci…ed. Thus, the part of the …le that solves the model in the case of PCP contains 28 variables that are determined by 28 equations.