VARVAR

Małgorzata BednarekMałgorzata Bednarek

Maria DerezińskaMaria Derezińska

Magdalena SadowskaMagdalena Sadowska

TheoryTheory

About VARAbout VAR

Sims critiqueSims critique

Validity of interrelated analytical exercises Validity of interrelated analytical exercises (common in reality where everything depends on (common in reality where everything depends on everything) implicit incorrect analysis of applications if everything) implicit incorrect analysis of applications if econometric inquiry is dependent on prior theoretical econometric inquiry is dependent on prior theoretical restrictionsrestrictions

Vector autoregression (VAR model) is possible to Vector autoregression (VAR model) is possible to deal with dynamic relationships between macroeconomic deal with dynamic relationships between macroeconomic variables, where causality may be mutual variables, where causality may be mutual

Vector autoregressionVector autoregression

xxt t ==ΠΠ11xxt -1t -1+...++...+ΠΠkkxxt -kt -k++ΦΦDDt t ++εεt t

εεt t ~NID(0, ~NID(0, ΩΩ))

ApplicationsApplications of vector autoregressions of vector autoregressions

ForecastingForecastingVAR models allow complete flexibility in specifying VAR models allow complete flexibility in specifying the correlation between future, present and pastthe correlation between future, present and past

Causality testsCausality tests Granger testsGranger tests Sims testsSims tests

Both tests are implications of the same null Both tests are implications of the same null hypothesis. In the model joint significance of all lags hypothesis. In the model joint significance of all lags except the lags of variable supposed to be a cause is except the lags of variable supposed to be a cause is testedtested

Hypothesis-seekingHypothesis-seeking Data characterizationData characterization Impulse response analysisImpulse response analysis Monetary and fiscal policy analysis Monetary and fiscal policy analysis

VAR diagnosisVAR diagnosis

• Testing for number of lagsTesting for number of lags

• Testing for VAR stabilityTesting for VAR stability

• Testing for Granger causalityTesting for Granger causality

• Testing for autocorrelationTesting for autocorrelation

Empirical resultsEmpirical results

ModelModel

In our model we analyIn our model we analyzze the potential for lending and e the potential for lending and consumption booms in Hungary consumption booms in Hungary

DATA SOURCES: DATA SOURCES: OECD Maxdata database, OECD Maxdata database, extension of papers:extension of papers: Brzoza-Brzezina (2004) Brzoza-Brzezina (2004) and and Susan Susan

Schadler, Zuzana Murgasova, Rachel van ElkanSchadler, Zuzana Murgasova, Rachel van Elkan ( (20042004 ) )

DATA: DATA: quarterly dataset for Hungary for period 1996-quarterly dataset for Hungary for period 1996-20042004

1. lloan - logarithm of total nominal loans to the private sector1. lloan - logarithm of total nominal loans to the private sector 2. lrate - logarithm of Nominal interest rate 2. lrate - logarithm of Nominal interest rate 3. lgdp - logarithm of GDP at constant prices 3. lgdp - logarithm of GDP at constant prices 4. lcon - logarithm of Private Consumption, Volume4. lcon - logarithm of Private Consumption, Volume

Vector AutoregressionVector Autoregression for Hungary with for Hungary with consumption (quarterly dataset October 1995 - May consumption (quarterly dataset October 1995 - May

2004)2004)var lloan lrate lgdp lcon, exog(_q*)

Parameters of VAR model in standard form have no structural interpretations !!

Sample: 1996q2 2004q2

--------------------------------------------------------------------------Equation Obs Parms RMSE R-sq chi2 P--------------------------------------------------------------------------lloan 23 12 .001624 0.9960 5721.318 0.0000lrate 23 12 .742514 0.4584 19.46434 0.0533lgdp 23 12 .000417 0.9980 11602.81 0.0000lcon 23 12 .004917 0.9998 96633.75 0.0000--------------------------------------------------------------------------

Model lag order selection statistics------------------------------------ FPE AIC HQIC SBIC LL Det(Sigma_ml) 1.362e-17 -27.9393 -27.34332 -25.569572 369.30194 1.329e-19

------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------------lloan |lloan | L1 | .6797655 .1784921 3.81 0.000 .3299274 1.029604 L2 | .1464823 .2067421 0.71 0.479 -.2587247 .5516893lrate | L1 | -.0000959 .0007495 -0.13 0.898 -.001565 .0013732 L2 | -.0012674 .0007255 -1.75 0.081 -.0026895 .0001546lgdp | L1 | -.1985731 .7957318 -0.25 0.803 -1.758179 1.361033 L2 | .2478325 .688455 0.36 0.719 -1.101514 1.597179lcon | L1 | .0266011 .0772088 0.34 0.730 -.1247254 .1779276 L2 | -.0134382 .0670136 -0.20 0.841 -.1447824 .117906_q_2 | -.0015721 .001348 -1.17 0.243 -.0042141 .0010698_q_3 | -.0016634 .00163 -1.02 0.307 -.0048582 .0015313_q_4 | -.001651 .0007053 -2.34 0.019 -.0030334 -.0002686_cons | .269556 1.732104 0.16 0.876 -3.125306 3.664418-------------+----------------------------------------------------------------lrate |lloan | L1 | -6.605417 81.60332 -0.08 0.935 -166.545 153.3342 L2 | 115.7716 94.51868 1.22 0.221 -69.48158 301.0249lrate | L1 | .3951908 .3426723 1.15 0.249 -.2764345 1.066816 L2 | -.1638084 .3317012 -0.49 0.621 -.8139309 .486314lgdp | L1 | -145.4654 363.794 -0.40 0.689 -858.4885 567.5577 L2 | -455.4286 314.749 -1.45 0.148 -1072.325 161.4681lcon | L1 | -28.46556 35.29845 -0.81 0.420 -97.64925 40.71812 L2 | 36.38052 30.63737 1.19 0.235 -23.66762 96.42867_q_2 | .503419 .6162614 0.82 0.414 -.7044312 1.711269_q_3 | .5327072 .7452087 0.71 0.475 -.927875 1.993289_q_4 | -.472785 .3224592 -1.47 0.143 -1.104793 .1592233_cons | 1293.563 791.8863 1.63 0.102 -258.5061 2845.631

lgdp |lloan | L1 | .076064 .0458807 1.66 0.097 -.0138604 .1659885 L2 | -.0677189 .0531422 -1.27 0.203 -.1718757 .0364379lrate | L1 | .0000754 .0001927 0.39 0.696 -.0003022 .000453 L2 | -.0001645 .0001865 -0.88 0.378 -.00053 .0002011lgdp | L1 | .9302852 .2045396 4.55 0.000 .529395 1.331175 L2 | -.160274 .1769645 -0.91 0.365 -.5071181 .1865701lcon | L1 | .0047614 .0198462 0.24 0.810 -.0341365 .0436592 L2 | .000569 .0172256 0.03 0.974 -.0331925 .0343305_q_2 | .0001349 .0003465 0.39 0.697 -.0005442 .000814_q_3 | .0000478 .000419 0.11 0.909 -.0007734 .000869_q_4 | .0000322 .0001813 0.18 0.859 -.0003231 .0003876_cons | .5750082 .4452303 1.29 0.197 -.297627 1.447643-------------+----------------------------------------------------------------lcon |lloan | L1 | -1.00662 .5403622 -1.86 0.062 -2.065711 .0524706 L2 | 1.114147 .6258854 1.78 0.075 -.1125662 2.34086lrate | L1 | -.0035271 .0022691 -1.55 0.120 -.0079745 .0009203 L2 | -.0021112 .0021965 -0.96 0.336 -.0064162 .0021938lgdp | L1 | 2.890635 2.408977 1.20 0.230 -1.830874 7.612143 L2 | -4.470218 2.08421 -2.14 0.032 -8.555195 -.3852413lcon | L1 | 1.085324 .2337399 4.64 0.000 .6272024 1.543446 L2 | -.0913518 .2028751 -0.45 0.653 -.4889797 .306276_q_2 | .0017963 .0040808 0.44 0.660 -.0062019 .0097944_q_3 | -.0179587 .0049346 -3.64 0.000 -.0276304 -.008287_q_4 | -.0144019 .0021353 -6.74 0.000 -.0185869 -.0102169_cons | 4.021655 5.243726 0.77 0.443 -6.255859 14.29917

Table 1: Testing for number of lags Table 1: Testing for number of lags varsoc lloan lrate lgdp lcon, maxlag(3)varsoc lloan lrate lgdp lcon, maxlag(3)

Selection order criteria

endogenous variables: lloan lrate lgdp lcon

constant included in models

Sample: 1996q3 2004q2, with gapsObs = 20

-------------------------------------------------------------------------------lag LL LR df p FPE AIC HQIC SBIC------------------------------------------------------------------------------- 0 182.019 . . . 2.18e-13 -17.8019 -17.763 -17.6028 1 287.577 211.116 16 0.000 2.94e-17 -26.7577 -26.5633 -25.762 2 303.730 32.305 16 0.009 3.66e-17 -26.773 -26.4231 -24.9806 3 362.188 116.917* 16 0.000 1.08e-18* -31.0188* -30.5134* -28.4299*

Source: OECD maxdata 2004

Table 2: Testing for VAR stability Table 2: Testing for VAR stability varstablevarstable

All the eigenvalues lie inside the unit circle, which All the eigenvalues lie inside the unit circle, which means that VAR satisfies stability condition.means that VAR satisfies stability condition.

Eigenvalue stability condition---------------------------------------------- Eigenvalue Modulus---------------------------------------------- -.3669971 + .44064736 | .57346052 -.3669971 - .44064736 | .57346052 .3679289 + .43235172 | .56771447 .3679289 - .43235172 | .56771447 .8478558 + .14019235 | .85936801 .8478558 - .14019235 | .85936801 .9212941 | .92129405 .4716963 | .47169626

Source: OECD maxdata 2004

Table 3: Testing for autocorrelation Table 3: Testing for autocorrelation vargrangervargranger

H0: no autocorrelation at lag order j------------------------------------- j chi2 df p------------------------------------- 1 26.0522 16 0.05330 2 9.4846 16 0.03212

Source: OECD maxdata 2004

In this test a 0 hypothesis tells that there is no In this test a 0 hypothesis tells that there is no autocorrelation at lag of order j. autocorrelation at lag of order j.

We test it at the 5% level so the p-values bigger than We test it at the 5% level so the p-values bigger than 0,05 means that 0,05 means that there is no autocorrelation in the there is no autocorrelation in the modelmodel..

Table 4: Testing for Granger causality Table 4: Testing for Granger causality varlmarvarlmar

Granger causality Wald tests----------------------------------------------------------------------------Equation Excluded chi2 df Prob > chi2----------------------------------------------------------------------------lloan lrate 7.1690 2 0.0278lloan lgdp 0.1414 2 0.9318lloan lcon 0.8457 2 0.6552lloan ALL 19.0689 6 0.0040----------------------------------------------------------------------------lrate lloan 2.7777 2 0.2494lrate lgdp 3.3249 2 0.1897lrate lcon 6.3980 2 0.0408lrate ALL 6.8007 6 0.3397----------------------------------------------------------------------------lgdp lloan 2.7658 2 0.2509lgdp lrate 0.9085 2 0.6349lgdp lcon 2.7804 2 0.2490lgdp ALL 24.7132 6 0.0004----------------------------------------------------------------------------lcon lloan 3.8855 2 0.1433lcon lrate 11.6411 2 0.0030lcon lgdp 4.7092 2 0.0949lcon ALL 14.4984 6 0.0245

Source: OECD maxdata 2004

Graph 1: The temporal change of consumption in Graph 1: The temporal change of consumption in Hungary (impulse- lcon, response- lloan) Hungary (impulse- lcon, response- lloan)

varirf graph irf, i(lloan) r(lcon)varirf graph irf, i(lloan) r(lcon)

-.2

0

.2

.4

0 2 4 6 8

irf, lcon, lloan

95% CI irf

step

Graphs by irfname, impulse variable, and responsevariable

Source: OECD maxdata 2004

Graph 2: The permanent change of consumption in Graph 2: The permanent change of consumption in Hungary (impulse- lcon, response- lloan) Hungary (impulse- lcon, response- lloan)

varirf graph oirf, i(lloan) r(lcon)varirf graph oirf, i(lloan) r(lcon)

Source: OECD maxdata 2004

-.0005

0

.0005

.001

0 2 4 6 8

irf, lcon, lloan

95% CI orthogonalized irf

step

Graphs by irfname, impulse variable, and response variable

Graph Graph 44: Trend line of : Trend line of interest rateinterest rate since since 1995q4 and prediction for period (2004q1 1995q4 and prediction for period (2004q1

till 2008q2)till 2008q2)

-8

-7

-6

-5

-4

-3

-2

-1

0

lrate

Source: OECD maxdata 2004

Graph Graph 55: Trend line of: Trend line of a number of loans a number of loans since 1995q4 and prediction for period since 1995q4 and prediction for period

(2004q1 till 2008q2)(2004q1 till 2008q2)

2,632,642,652,662,672,682,692,7

2,712,722,73

1995

q4

1997

q1

1998

q2

1999

q3

2000

q4

2002

q1

2003

q2

2004

q3

2005

q4

2007

q1

2008

q2

lloan

Source: OECD maxdata 2004

Graph Graph 66: Trend line of : Trend line of GDPGDP since 1995q4 and since 1995q4 and prediction for period (2004q1 till 2008q2prediction for period (2004q1 till 2008q2))

2,68

2,685

2,69

2,695

2,7

2,705

2,71

2,715

2,7219

95q4

1997

q1

1998

q2

1999

q3

2000

q4

2002

q1

2003

q2

2004

q3

2005

q4

2007

q1

2008

q2

lgdp

Source: OECD maxdata 2004

Graph Graph 77: Trend line of : Trend line of consumptionconsumption since since 1995q4 and prediction for period (2004q1 1995q4 and prediction for period (2004q1

till 2008q2)till 2008q2)

0

1

2

3

4

5

6

lcon

Source: OECD maxdata 2004

GGraph raph 88: : Predicted trend lines for consumption and Predicted trend lines for consumption and loans for period 2004q1 till 2008q2loans for period 2004q1 till 2008q2

Source: OECD maxdata 2004

Both trend lines seem to be very stable. While consumption is slightly increasing the predicted amount of loans stays fairly constant and with hardly noticeable the tendency to decrease.

0

1

2

3

4

5

6

2004

q1

2004

q3

2005

q1

2005

q3

2006

q1

2006

q3

2007

q1

2007

q3

2008

q1

LOANS

CONS

Table Table 55: Comparison between data on : Comparison between data on consumption and prediction (quarterly consumption and prediction (quarterly dataset January 2004 - October 2004)dataset January 2004 - October 2004)

  JanuarJanuary y

0404 April 04April 04 JulyJuly 0404 October 04October 04

OECD dataOECD data 5,007395,00739 5,018375,01837 5,028865,02886 5,039245,03924

PredictionPrediction 5,007395,00739 5,017845,01784 5,010585,01058 5,002675,00267

StandardStandardErrorError 00 0,0001060,000106 0,0036350,003635 0,0072570,007257

Source: OECD maxdata 2004

Arguments for no Arguments for no lending boomlending boom

There isThere is no empirical evidence for the near future no empirical evidence for the near future threat threat accordingaccording a a possible lending boom in Hungary. possible lending boom in Hungary.

UUndoubtedlyndoubtedly , after the EURO adoption, , after the EURO adoption, the interest the interest rate will have to accommodate to the one in EMU but rate will have to accommodate to the one in EMU but some adjustments have already been accomplished. some adjustments have already been accomplished.

There is There is smaller deviation from the interest rate of smaller deviation from the interest rate of EMUEMU

Hungary still have less developed financial market Hungary still have less developed financial market than the old member statethan the old member state

Forecast is based on the internal outcome of the past Forecast is based on the internal outcome of the past events in Hungary. Awareness of an external shock or events in Hungary. Awareness of an external shock or unexpected twist in domestic economy is the key issueunexpected twist in domestic economy is the key issue for ruling elitesfor ruling elites. .

The endThe end

Now is time for Now is time for applause! applause!