rats案例 In this project you will extend your understanding of empirical estimates of the Phillips

EC471/571 Monetary Theory Fall 2019

Applied Project #2 Objectives

In this project you will extend your understanding of empirical estimates of the Phillips
You will learn how to implement an econometric technique known as rolling orwindow
regressions to look for structural breaks in macroeconomic data.

You will learn how to create an interaction
You will learn three new techniques in RATS, running loops with the DO command, saving variables defined by regressions with a SET instruction, and making charts with the GRAPH instruction.


Introduction



Earlier in the class we read Janet Yellen’s speech Inflation Dynamics and Monetary Policy. In the speech, Yellen provides a model of core inflation based on the Phillips Curve. Recall that Yellen provided this inflation forecasting equation:

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In this project, we are going to use a simplified version in our econometric analysis:

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Recall the version of the Phillips curve we are using in class:

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To translate the classroom version of the Phillips curve to the econometric version, note that the

coefficient �. then becomes our estimate of inflation expectations (�)) and �   is our estimate of �. The

variable �����“ is the output gap (�“ − �∗) measured as the log difference (*100) between output (FRED code GDPC1) and potential output (FRED code GDPPOT). Inflation �“ is the year-over-year percentage change of core PCE prices (FRED code JCXFE).



In this project, we will study how the coefficients in our estimated Phillips curve evolve over time and whether or not we can stabilize the estimates using an interaction term that magnifies the relationship between inflation and the output gap.



Part 1: Reading



Read the following article:



Lansing, Kevin J. Improving the Phillips Curve with an Interaction Variable, FRBSF Economic Letter, May 6, 2019.



https://www.frbsf.org/economic-research/files/el2019-13.pdf



Answer the following questions:



Describe the regression the author implemented to derive Figure 1. What conclusions does the author derive from figure1?


How does the author explain the conclusions he derives from figure1?
To generate the results of figure 2, the author creates an “inflation-output gap” interaction variable. What is this variable and what is the economic intuition behind thisvariable?
What does the author conclude about the forecasting abilities of his differentmodels?


Part 1: Application



We are going to begin with a modification of the Lansing model. Instead of using the change in the headline inflation rate, we will follow Yellen and focus on the core inflation rate (what is the difference between headline and core inflation?).

Begin with data entry and transformation into the correct variables: CALENDAR(Q) 1900:1

ALLOCATE 2019:4

DATA(FORMAT=FRED) * * GDPPOT GDPC1 JCXFE PCEPI

***SET OUTPUT GAP AS LOG DIFFERENCE *** LOG GDPPOT

LOG GDPC1

SET YSLACK = (GDPC1 – GDPPOT)*100

***SET CORE INFLATION AS LOG DIFFERENCE ANNUALIZED OF PRICE*** LOG JCXFE

SET INF = (JCXFE-JCXFE{4})*100



Much of that code should look familiar. You need to set the interaction term described above: SET INTERACT =

Don’t panic, you have all of the variables!



Now, comes a rolling or window regression. The idea is to regress our model over 20 year time spans to see how the coefficients evolve over time. That means the first regression is over the sample 1960:1 to 1980:1, the next is 1960:2 to 1980:2, and so on, until the last end date is reached, in this case 2019:2.



This is easier to accomplish than it sounds. All we need is the end date from the first regression, 1980:1, and the end date of the sample, 2019:2. Then we use the DO instruction to create a loop over those dates.



DO JJ = 1980:1, 2019:2

LINREG(NOPRINT) INF JJ-80 JJ #CONSTANT YSLACK{4}

SET COEFB1 JJ JJ = %BETA(1) SET COEFB2 JJ JJ = %BETA(2)

END DO JJ



The variable JJ is just a counter. The first time you run the loop, it is equal to 1980:1. When the program reaches the END DO instruction, it goes back to the beginning of the block and resets JJ to equal 1980:2. The process continues until JJ reaches 2019:2 and then stops.



Now, look at the LINREG code:



LINREG(NOPRINT) INF JJ-80 JJ #CONSTANT YSLACK{4}



Specifically, look at the start and end dates. The start date is JJ-80. The first value of JJ is 1980:1, so the start date of the first regression is 1980:1 – 80 quarters which is 1960:1. The end date is JJ or 1980:1. So, in effect, RATS is running the regression:



LINREG(NOPRINT) INF 1960:1 1980:1 #CONSTANT YSLACK{4}

Then the next time RATS moves through the loop it runs the regression LINREG(NOPRINT) INF 1960:2 1980:2

#CONSTANT YSLACK{4}



Until the last regression:



LINREG(NOPRINT) INF 1999:4 2019:4 #CONSTANT YSLACK{4}



The lines:



SET COEFB1 JJ JJ = %BETA(1) SET COEFB2 JJ JJ = %BETA(2)



collect the coefficients �. and �0 at each step and put them in the series COEFB1 and COEFB2. The first entry in the series is 1980:1 (JJ in the first run) and the last entry is 2019:4.



Now we repeat the process but replace the output gap as the dependent variable with the interaction term:



DO JJ = 1980:4, 2019:1

LINREG(NOPRINT) INF JJ-80 JJ #CONSTANT INTERACT{4}

SET COEFB1A JJ JJ = %BETA(1) SET COEFB2A JJ JJ = %BETA(2)

END DO JJ



Now we need to chart the results:



GRAPH(HEADER=”Coefficients on Beta 1, modified Lansing model”, $ SUBHEADER=”Core inflation is dependent variable”, $ KEY=BELOW, KLABELS=||”Slack Model”|”Interaction Model”||) 2

#COEFB1 1980:1 2019:2

#COEFB1A 1980:1 2019:2



Notice the $ at the end of the first two lines of code. The $ is needed to break up long lines of code onto separate lines. Review carefully the GRAPH instruction:



(https://estima.com/ratshelp/index.html?graphinstruction.html)



to understand how RATS produces charts. Now for the project:

Replicate the Lansing paper using core inflation as the dependent variable. You can usethe LansingStudent.rpf file; all you need to add is the interaction term and the chart to view the coefficients on the output gap and the interaction
Replicate the Lansing paper using the change in headline inflation as the dependent variable. To do this, you use the program above but you need to create a new dependent variable. You need a new inflation rate using headline PCE price index (code PCEPI) and then another variable (the dependent variable) that is the change in the inflation rate over four


You will turn in the 4 charts created by this project. Questions:

Lansingdoes not report the coefficients on �., which we can interpret as inflation expectations. For Part A, compare the estimates of inflation expectations from the two models. Are the same? Different?
Using core inflation as the dependent variable, do you reach the same conclusions as Lansing regarding the stability of the Phillips curve? Is the slack version stable or unstable over time? What about the interaction version?
In part B, did you replicate the charts produced byLansing?