Economtrics of Money and Finance Lecture one: Introduction · Some monetary and nancial time...

Economtrics of Money and FinanceLecture one: Introduction

Zongxin Qian

School of Finance, Renmin University of China

September 24, 2014

Table of Contents

Course outline

Review of basic econometrics

Introduction to Eviews

How to think about economic/financial questions in aneconometric way

Textbook

I Main textbook张成思，金融计量学–时间序列分析视角，人大出版社

I Other references(more advanced)General time series: Hamilton, Time Series Analysis,Princeton University Press.Multivariate time series: Lutkephol, New Introduction toMultiple Time Series Analysis, Springer.Cointegration: Juselius, The Cointegrated VAR model:Methodology and Applications, Oxford University Press.

I Some contents are not covered in the textbook. In that case,additional materials will be given.

Textbook

Objectives

I grasp basic tools to understand money, banking, and financialmarkets econometrically

I learn the difference between correlation and causality, andunderstand the importance of exogeneity and identification

I be able to read academic papers with modest technicalcontents

Objectives

Evaluation

I group assignment (20%)

I referee report (20%)

I final closed-book exam (60%)

Contents

I Basic tools for dynamic econometrical modeling

I Reduced-form time series models: ARIMA/VAR/CVAR andVECM

I Causality, identification and structural models

I Heteroscedasticity modeling

Softwares

I Relatively simple-to-use softwaresEviews/Microfit/RATS/Sata/jmultiThe last one is a free software

I More flexible but also more technical softwaresGauss/Matlab/OX/RAgain the last one is for free

I We shall learn how to apply the methods in the course withEviews. We may use other softwares occasionally.

I Caution: econometrics is not about clicking windows inEviews, copying and pasting result tables. Telling an economicstory with your results is far more important!!!

I Models, both theoretical and econometric ones, should onlybe tools to help you elaborate your idea to readers of yourpaper/report/book. It is the idea itself that is the mostimportant. Being able to build complicated models does notnecessarily mean that you are a good economist.

Softwares

Table of Contents

Course outline

Suppose our empirical model is Y = Xβ + u

e(β̂) = Y − X β̂The OLS estimator chooses a β̂ which minimizes S(β̂) = e(β̂)′e(β̂)Assumptions

I E (u|X ) = 0

I E (uu′) = σ2I

I X is of full collumn rank

Under those assumptions, the OLS estimator is the most efficient inthe class of linear unbiased estimator (the Gauss-Markov theorem)

Suppose our empirical model is Y = Xβ + ue(β̂) = Y − X β̂

The OLS estimator chooses a β̂ which minimizes S(β̂) = e(β̂)′e(β̂)Assumptions

I E (u|X ) = 0

I E (uu′) = σ2I

Suppose our empirical model is Y = Xβ + ue(β̂) = Y − X β̂The OLS estimator chooses a β̂ which minimizes S(β̂) = e(β̂)′e(β̂)

Assumptions

I E (u|X ) = 0

I E (uu′) = σ2I

Suppose our empirical model is Y = Xβ + ue(β̂) = Y − X β̂The OLS estimator chooses a β̂ which minimizes S(β̂) = e(β̂)′e(β̂)Assumptions

I E (u|X ) = 0

I E (uu′) = σ2I

Suppose our empirical model is Y = Xβ + ue(β̂) = Y − X β̂The OLS estimator chooses a β̂ which minimizes S(β̂) = e(β̂)′e(β̂)Assumptions

I E (u|X ) = 0

I E (uu′) = σ2I

Specialty of financial time series

I Financial econometrical models typically use time series dataand do not satisfy those assumptions.

I Financial time series are persistent and in many models, theconditional variance is not a constant.

I In those cases, most obviously, assumption 2 fails.

I Assumption 1 also fails if the dependent variable is a persistentfinancial time series. This is because even if ut is uncorrelatedto yt−1, ut−1 certainly is correlated to yt−1. In this case, theOLS estimator is biased but still consistent if some additionalassumptions holds (will discuss in coming lectures). In thiscase, you can still use OLS if your sample is large enough.

Some monetary and financial time series: CPI

Figure: China’s Quarterly CPI

1102001/01

2001/08

2002/03

2002/10

2003/05

2003/12

2004/07

2005/02

2005/09

2006/04

2006/11

2007/06

2008/01

2008/08

2009/03

2009/10

2010/05

2010/12

2011/07

2012/02

2012/09

2013/04

CPI CPI

Some monetary and financial time series: exchange rate

Figure: China’s real effective exchange rate

Source: CEIC

Figure: China’s 3m treasury bill rate

Source: CEIC

Figure: Shanghai Stock index A share

Source: CEIC

Model specifications and OLS

I Including redundant variables to the r.h.s. reduces estimationefficiency.

I Omitting important explanatory variables causes estimationbias.

I Adding restrictions to the model may improve estimationefficiency.

I But adding false restrictions to the model generatesestimation bias.

I Those results not only apply to OLS but also to many otherestimators. They are frequently encountered byeconometricians interested in many fields of economicsincluding financial economics.

Basic inference based on OLS estimation

I Simplest assumption on the error term u ∼ i .i .d .N(0, σ2I )

I Under this assumption β̂ ∼ N(β, σ2(X ′X )−1)

I t = β̂i−βiσ̂ξ

−1/2ii

, where ξii is the row i , column i element of the

matrix (X ′X )−1

β̂i−βiσξ

−1/2ii

∼ N(0, 1)

σ2 ∼ χ2(T − K )

β̂i−βiσξ

−1/2iiσ̂σ

∼ t(T − K )

−1/2ii

β̂i−βiσξ

−1/2ii

∼ N(0, 1)

σ2 ∼ χ2(T − K )

β̂i−βiσξ

−1/2iiσ̂σ

∼ t(T − K )

−1/2ii

β̂i−βiσξ

−1/2ii

∼ N(0, 1)

σ2 ∼ χ2(T − K )

β̂i−βiσξ

−1/2iiσ̂σ

∼ t(T − K )

−1/2ii

β̂i−βiσξ

−1/2ii

∼ N(0, 1)

σ2 ∼ χ2(T − K )

β̂i−βiσξ

−1/2iiσ̂σ

∼ t(T − K )

OLS: more complicated cases

Figure: OLS asymptotics in more general cases

Source: Hamilton(1994)

I L(Y |β) =∏T

t=1 L(Yt |β)L(Yt |β) is conditional probability/density of Yt given β

I The MLE choose parameters in β which maximize thelikelihood function.

I Typically, it is easier to work with the log likelihoodlogL(Y |β) = ΣT

t=1logL(Yt |β)

I L(Y |β) =∏T

t=1 L(Yt |β)L(Yt |β) is conditional probability/density of Yt given β

I The MLE choose parameters in β which maximize thelikelihood function.

I Typically, it is easier to work with the log likelihoodlogL(Y |β) = ΣT

t=1logL(Yt |β)

MLE under normality

I Yt = a + bXt + ut , u ∼ N(0, σ2)

I L(Yt |β) = (2πσ2)−1/2exp{−[Yt − (a + bXt)]2/2σ2}I logL(Y |β) = ΣT

t=1logL(Yt |β) =

−Tlog(2πσ2)2 − 1

2σ2 ΣTt=1[Yt − (a + bXt)]2

I The maximum obtains when ΣTt=1[Yt − (a + bXt)]2 is

minimized. MLE=OLS!

MLE under normality

I Yt = a + bXt + ut , u ∼ N(0, σ2)

I L(Yt |β) = (2πσ2)−1/2exp{−[Yt − (a + bXt)]2/2σ2}

I logL(Y |β) = ΣTt=1logL(Yt |β) =

−Tlog(2πσ2)2 − 1

2σ2 ΣTt=1[Yt − (a + bXt)]2

minimized. MLE=OLS!

MLE under normality

I Yt = a + bXt + ut , u ∼ N(0, σ2)

t=1logL(Yt |β) =

−Tlog(2πσ2)2 − 1

2σ2 ΣTt=1[Yt − (a + bXt)]2

minimized. MLE=OLS!

MLE under normality

I Yt = a + bXt + ut , u ∼ N(0, σ2)

t=1logL(Yt |β) =

−Tlog(2πσ2)2 − 1

2σ2 ΣTt=1[Yt − (a + bXt)]2

minimized. MLE=OLS!

Table of Contents

Course outline

Starting Eviews

Figure: Eviews interface

Create a new workfile

Figure: Create a new workfile

Create a new object

Figure: Create a new object

Estimate an equation

Figure: Estimate an equation

Postestimation

Figure: postestimation

Dependent Variable: INF_COREMethod: Least SquaresDate: 09/10/13 Time: 19:35Sample (adjusted): 1978 2007Included observations: 30 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

INF_CORE(-1) 0.640693 0.082579 7.758561 0.0000INF_CORE(-1)*DV -0.568887 0.157075 -3.621752 0.0013

OKY_OECD(-1) -5.368782 3.429265 -1.565578 0.1300YGAP_OECD(-1) 2.123996 0.941751 2.255369 0.0331

C 2.615833 0.618778 4.227419 0.0003

R-squared 0.828510 Mean dependent var 4.889859Adjusted R-squared 0.801071 S.D. dependent var 3.362778S.E. of regression 1.499847 Akaike info criterion 3.799614Sum squared resid 56.23849 Schwarz criterion 4.033147Log likelihood -51.99422 Hannan-Quinn criter. 3.874324F-statistic 30.19523 Durbin-Watson stat 1.370900Prob(F-statistic) 0.000000

Importing data

file: open: foreign data as workfileor there is a software called stattransfer which can flexibly transferdata formats. But you have to pay for it yourself since our schooldoes not buy license for it.

Table of Contents

Course outline

Instability

Figure: US Phillips curve slope over time

197510

1974 19798

19711972

1976197719786

19671968

196919734

19611962

196519662

1960 1963

00 1 2 3 4 5 6 7 8 9 10

Unemployment rate (%)

Figure: Source: Gorton(2011)

Omitted variable and media claims

I Many media articles use some informal form of OLS forargumentation

I Look at this one: China’s financial development is lower thanthe USA, but its growth rate is higher, so finance is notrelevant for real development.

I But is this example representative?

I Can’t the difference in growth caused by other factors?

I USA is a more development economy which is normally slowerin growth since it is already close to the steady state butChina is in transition

I China has a higher population density which can create alarger market which provides more space for divisions of laborand specialization

Reverse causality

I You find financial stock returns negatively correlated with gov.bond spreads

I Can you jump to conclude that worse financial sectorincreases the probability of gov. default?

I Not sure, ’cause there is possibility that the reality is the otherway around.

I The gov. default risk is too high and the financial sector holdstoo high a share of gov. bonds, so its performance isnegatively affected.

Reverse causality

Summary

I You have to think right before you can model right.

Roadmap for an empirical study typically looks like this:

I You first think about the causality chains, then write down amodel.

I Second, you derive testable hypothesis from the model andput it to data.

I If the hypothesis is accepted, then maybe your model is good.Otherwise, you may have to think again and rework on yourmodel.

I Notice that, models are only abstraction of the real world.Very often, there are omitted factors in the model. In manycases, you have to test your model in a much richer contextand require statistical identification of the model.

Summary

I You have to think right before you can model right.Roadmap for an empirical study typically looks like this:

Summary

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