Microsoft Word - Final Work 2010

8/9/2019 Microsoft Word - Final Work 2010

1/21

Our aim is to study the theory

data from the IMF analysing v

percentage annual growth of

study stationarized variables.

To do this analysis, we start b

and prices running the regressi

Prices t=beta1+ beta2 money t

Hence for each country we obt

Bolvia

reg prices money

Source | SS

-------------+-------------

Model | 134755251

Residual | 1257373.81

-------------+-------------

Total | 136012625

quantity of money in the long-run an

ariables like M3 and IPC consumer i

oney and prices. We decided to anal

studying the relation between annu

n:

ut

in the following results:

df MS Numbe

---------------- F( 1

1 134755251 Prob

52 24180.2656 R-squ

---------------- Adj R

53 2566275.94 Root

d for that we took the

dex and we took the

yse yearly variables to

al % change in money

r of obs = 54

, 52) = 5572.94

> F = 0.0000

ared = 0.9908

-squared = 0.9906

MSE = 155.5


2/21

------------------------------------------------------------------------------

prices | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

money | 1.656262 .0221864 74.65 0.000 1.611742 1.700783

_cons | -46.48212 21.57874 -2.15 0.036 -89.78302 -3.181215

Conclusions for this especific country:

The regressor money is statistically significant since we obtain a p-value of 0.000

99% of the variation of the inflation is explained linearly by the variable annual% change in

money.

19561957195819591960196119621963196419651966196719681969197019711972197319741975197619771978197919801981198219831984

1985

1986198719881989199019911992199319941995199619971998199920002001200220032004200520062007200820090

.2

.4

.6

.8

1

Leverage

0 .2 .4 .6 .8Normalized residual squared


3/21

Take the observation of year 1985, 1984

Reggressing model with dummys for Hyperinflationary period

(1984-1985)

To see whether there is a structural change in the model during the hyperinflationary times

I will introduce a Dummy in the model:

Dummy=1 if t=hyperinflationary times (Bolivia case(1984,1985) t=29, t=30)

Dummy=0 if not

Model with dummy

Pricest=beta1+ beta2*moneyt+ beta3*dummyt+ beta4 dummy*money+ ut

If Dummy=1

Model: prices t=(beta1+beta3)+ (beta2+beta4)money t + u t

If dummy=0

0

5000

10000

15000

0 2000 4000 6000 8000money

prices Fitted values


4/21

Model: prices t= beta1 + beta2 money t + ut

Under H0: Beta3=beta4=0 (there is no structural change in the model)

Codes in stata:

generate obs=_n

. gen dummy=0

. replace dummy=1 if obs==29

(1 real change made)



gen dmoney=money*dummy

reg prices money dummy dmoney

Source | SS df MS Number of obs = 54

-------------+------------------------------ F( 3, 50) =46859.71

Model | 135964266 3 45321422 Prob > F = 0.0000

Residual | 48358.6224 50 967.172447 R-squared = 0.9996

-------------+------------------------------ Adj R-squared = 0.9996

Total | 136012625 53 2566275.94 Root MSE = 31.099

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

money | .9679052 .0822909 11.76 0.000 .802619 1.133191

dummy | -1403.398 40.24342 -34.87 0.000 -1484.229 -1322.567

dmoney | .9152123 .0826704 11.07 0.000 .749164 1.081261

_cons | -6.038745 5.229494 -1.15 0.254 -16.54249 4.465003


5/21

By introducing the dummy variable we conclude that during hyperinflationary periods, a

unit change in annual % in money is reflected in a 1.99 percentual points in inflation,

reflecting that there is some exogenous shock, apart from changes in prices, that are

causing this change in the value of inflation. When the dummy takes the value zero

meaning that we are in non-hyperinflationary period, this relation is closer to one-to-one.

Notice R2 is almost 100% showing the introduction of the new variables increased the

explicative power of the model over inflation

Testing the structural change

The RSSE of the F-statistic corresponds to the SSE of the original model, since under H0

there is no structural change on the model (which corresponds to the original model)

The RSSE=1.257.373,81 and SSE=48.358,6224

Since F-value> Fcritic, we reject the null hypothesis and then we conclude with a level of

significance of 5% that there is a statistically significant structural change in the model

during the hyperinflationary period


6/21

Argentina

Model

Prices t=beta1+ beta2*Money t+ ut

reg prices money

Regression with 49 observations


-------------+------------------------------ F( 1, 47) = 755.31

Model | 13552690.4 1 13552690.4 Prob > F = 0.0000


-------------+------------------------------ Adj R-squared = 0.9402

Total | 14396024.5 48 299917.178 Root MSE = 133.95

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

money | 1.468127 .0534197 27.48 0.000 1.36066 1.575593

_cons | -37.97795 21.0049 -1.81 0.077 -80.23435 4.278448


7/21

------------------------------------------------------------------------------

Comments:

Relation of price and money=1.46

By P- value=0 we can see that we reject the null hypothesis (H0: beta2=0)

concluding with a level of significance of 5% that money is statistically

significant when explaining the evolution of prices

R2=0,94 = everything else constant, 94% of the variability of prices can be

explained by the aggregate variable M3.

Stata code for graphic:

summarize leverage

Variable | Obs Mean Std. Dev. Min Max

-------------+--------------------------------------------------------

leverage | 49 200.0563 531.364 -66.45961 3243.579

code: twoway( scatter prices money)(lfit prices money)

lvr2plot, mlabel(year)

0

100

0

2000

3000

0 500 1000 1500 2000 2500money



8/21

.

Reggressing model with dummys for Hyperinflationary period

(1989-1990)

To see whether there is a structural change in the model during the

hyperinflationary times I will introduce a Dummy in the model:

Dummy=1 if t=hyperinflationary times (Argentina case(1989,1990) t=29,

t=30)

Dummy=0 if not

Model with dummy


If Dummy=1


If dummy=0



1961196219631964196519661967196819691970197119721973197419751976197719781979198019811982 19831984

198519861987 1988

1989

1990

19911992199319941995199619971998199920002001200220032004200520062007200820090

.2

.4

.6

.8

Leverage

0 .2 .4 .6Normalized residual squared


9/21

Stata codes

. gen obs=_n

. gen dummy=0





. gen dmoney=money*dummy

. reg prices money dummy dmoney


-------------+------------------------------ F( 3, 45) = 2176.84

Model | 14297504.4 3 4765834.8 Prob > F = 0.0000


-------------+------------------------------ Adj R-squared = 0.9927

Total | 14396024.5 48 299917.178 Root MSE = 46.79

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

money | 1.045071 .0487685 21.43 0.000 .9468459 1.143295

dummy | 1582.43 102.8682 15.38 0.000 1375.243 1789.617

dmoney | -.3712628 .075946 -4.89 0.000 -.5242259 -.2182996

_cons | -8.715363 8.334931 -1.05 0.301 -25.50278 8.07205

------------------------------------------------------------------------------


unit change in annual % in money is reflected in a 0,6 percentual points in inflation,

reflecting that there is some exogenous shock apart from changes in prices which are

causing this change in the value of inflation. When the dummy takes the value zero, this

relation is closer to one-to-one (beta2=1,045)


10/21




The RSSE=843.334,13 and SSE=98.520,1186

Since F-value> Fcritic, we reject the null hypothesis and then we

conclude with a level of significance of 5% that there is a

statistically significant structural change in the model during the

hyperinflationary period


11/21

Nicaragua

Full regresin

Source | SS

-------------+-------------

Model | 162370961

Residual | 9313436.64

-------------+-------------

Total | 171684398

---------------------------

prices | Coef.

-------------+-------------

money | .8866074

_cons | 125.0878

df MS Numbe

---------------- F( 1

1 162370961 Prob

34 273924.607 R-squ

---------------- Adj R

35 4905268.51 Root

--------------------------------

Std. Err. t P>|t| [9

--------------------------------

.036416 24.35 0.000 .8

91.14757 1.37 0.179 -60

r of obs = 36

, 34) = 592.76

> F = 0.0000

ared = 0.9458

-squared = 0.9442

MSE = 523.38

------------------

5% Conf. Interval]

------------------

126011 .9606137

.14633 310.322


12/21

0

5000

100

00

0 5000 10000 15000money


197319741975197619771978197919801981198219831984198519861987

1988

1989

1990

1991199219931994199519961997199819992000200120022003200420052006200720080

.2

.4

.6

.8

Leverage

0 .2 .4 .6Normalized residual squared


13/21

Reggressing model with dummys for Hyperinflationary period (1988-

1991)

To see whether there is a structural change in the model during the hyperinflationary times I will introduce a

Dummy in the model:

Dummy=1 if t=hyperinflationary times (Nicaragua case(1988-1991) t=16-19)

Dummy=0 if not

Model with dummy


If Dummy=1


If dummy=0



By looking at the leverage graphic we can see the the influential observations are the ones for the years of

1988,1989,1990,1991 which are composed either by high leverage observations wither by outliers.

Stata codes

. gen obs=_n

. gen dummy=0




(1 real change made).







14/21



-------------+------------------------------ F( 3, 32) = 2429.82

Model | 170934013 3 56978004.5 Prob > F = 0.0000


-------------+------------------------------ Adj R-squared = 0.9952

Total | 171684398 35 4905268.51 Root MSE = 153.13

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

money | 1.860181 .2740634 6.79 0.000 1.301932 2.41843

dummy | 2575.911 135.2056 19.05 0.000 2300.506 2851.316

dmoney | -1.236711 .2746246 -4.50 0.000 -1.796103 -.6773195

_cons | -29.30189 30.83229 -0.95 0.349 -92.10521 33.50144


unit change in annual % in money is reflected in a 0,6 percentual points change in inflation,



relation is closer to one-to-one.




The RSSE=9.313.436,64 and SSE=750.384,37


15/21

Since F-value> Fcritic,

conclude with a level

statistically significan

hyperinflationary period

Israel

Model with all the 54 obser

Source | SS

-------------+-------------

Model | 217697.428

Residual | 39795.8832

we reject the null hypoth

of significance of 5% t

structural change in the

vations

df MS Numbe

---------------- F( 1

1 217697.428 Prob

52 765.305445 R-squ

sis and then we

hat there is a

model during the

r of obs = 54

, 52) = 284.46

> F = 0.0000

ared = 0.8454


16/21

-------------+------------------------------ Adj R-squared = 0.8425

Total | 257493.311 53 4858.36436 Root MSE = 27.664

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

money | .8276106 .0490701 16.87 0.000 .7291443 .926077

_cons | -3.095239 4.353302 -0.71 0.480 -11.83078 5.6403

------------------------------------------------------------------------------

0

100

200

300

400

0 100 200 300 400 500money



17/21


18/21

Stata codes

. gen obs=_n

. gen dummy=0




(1 real change made).




-------------+------------------------------ F( 3, 50) = 453.11

Model | 248358.083 3 82786.0276 Prob > F = 0.0000


-------------+------------------------------ Adj R-squared = 0.9624

Total | 257493.311 53 4858.36436 Root MSE = 13.517

------------------------------------------------------------------------------


-------------+----------------------------------------------------------------

money | .813224 .0481041 16.91 0.000 .716604 .909844

dummy | 275.4169 21.39669 12.87 0.000 232.4404 318.3934

dmoney | -.6105901 .0737808 -8.28 0.000 -.7587832 -.4623969

_cons | -4.980728 2.462908 -2.02 0.049 -9.927624 -.0338329

------------------------------------------------------------------------------


unit change in annual % in money is reflected in a 0,2 percentual points change in inflation,



19/21


relation is closer to one-to-one.




The RSSE=39.795,8832 and SSE= 9135.22809

Since F-value> Fcritic, we reject the null hypothesis and then we conclude with a level of

significance of 5% that there is a statistically significant structural change in the model

during the hyperinflationary period.

Pannel Analysis

In the last part of the problem set we want to see whether the four countries analysed

previously influence the overall relation between money and prices for the 18 countries.

To check this we will use a panel data which makes this analysis over countries and over

years.


20/21

For this purpose we need to construct a proper data with all the countries with the same

period where the variables were observed.

Then we will proceed to our econometric work:

We will estimate the following model:

Pricesit= beta1+ beta2*moneyit+ beya3*dummyit+ beta4dummoneyit+ uit

Where i represent the countries and t the time period

We construct our dummy by defining:

Dummyit=1 of country i was subject to hyperinflation

Dummyit=0 if country i was not subject to hyperinflation

Our null hypothesis will be that:

H0:beta3=beta4=0 (the hyperinflationary countries do not influence the relationship

between annual percentage change in money and prices over the 18 countries under

analysis)

Stata codes

Gen dummoney=money*dummy

xtreg prices money dummy dummoney, re i(code)

Random-effects GLS regression Number of obs = 486

Group variable (i): code Number of groups = 18

R-sq: within = 0.8836 Obs per group: min = 27

between = 0.9836 avg = 27.0

overall = 0.8928 max = 27

Random effects u_i ~ Gaussian Wald chi2(3) = 4016.05

corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------


21/21

prices | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

money | .7527448 .6407409 1.17 0.240 -.5030844 2.008574

dummy | 51.03512 32.60992 1.57 0.118 -12.87915 114.9494

dummoney | .2863953 .6409639 0.45 0.655 -.9698708 1.542661

_cons | -1.263624 17.59736 -0.07 0.943 -35.75381 33.22656

-------------+----------------------------------------------------------------

sigma_u | 0

sigma_e | 278.86117

rho | 0 (fraction of variance due to u_i)

Since beta2+beta4= 1.03 we can conclude that there is almost a perfect one-to-one relation

between Money and prices within these 4 countries.

By doing the wald test we obtain a Wald-value=4016.05 for which prob(Wald-value>wald

critic)=0.0000 and hence we conclude that there is a statistically significant change in the

model including hyperinflationary countries or not.

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Microsoft Word - Final Work 2010