Lecture Notes in Empirical Macroeconomics

Lecture Notes in Empirical Macroeconomics
(MiQEF, MSc course at UNISG)
Paul S¨oderlind
January 2005 (with some corrections done later)

Contents

1 Instrumental Variable Method 3
1.1 Consistency of Least Squares or Not? . . . . . . . . . . . . . . . . . 3
1.2 Reason 1 for IV: Measurement Errors . . . . . . . . . . . . . . . . . 3
1.3 Reason 2 for IV: Lagged Dependent Variable + Autocorrelated Shocks 5
1.4 Reason 3 for IV: Simultaneous Equations Bias (and Inconsistency) . . 5
1.5 Definition of the IV Estimator—Consistency of IV . . . . . . . . . . 9
1.6 Hausman’s Specification Test . . . . . . . . . . . . . . . . . . . . . . 15
1.7 Tests of Overidentifying Restrictions in 2SLS . . . . . . . . . . . . 16
2 Non-Spherical Errors 18
2.1 Summary of Least Squares . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Heteroskedasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Autocorrelation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Variance of a Sample Average (more details) . . . . . . . . . . . . . . 22
2.5 The Newey-West Estimator . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Vector Autoregression (VAR) 29
3.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Canonical Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Moving Average Form and Stability . . . . . . . . . . . . . . . . . . 30
3.4 Granger Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5 Forecasts Forecast Error Variance . . . . . . . . . . . . . . . . . . . 34
3.6 Forecast Error Variance Decompositions . . . . . . . . . . . . . . . 35
3.7 Structural VARs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.8 Cointegration, Common Trends, and Identification via Long-Run Restrictions 46
4 Monetary Policy in VAR Systems 53
4.1 VAR System, Structural Form, and Impulse Response Function . . . . 53
4.2 Fully Recursive Structural Form . . . . . . . . . . . . . . . . . . . . 54
4.3 Some Controversies . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Summary of Some Important Results from VAR Studies of Monetary
Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Microfoundations of Monetary Policy Models 78
5.1 Dynamic Models of Sticky Prices . . . . . . . . . . . . . . . . . . . 78
5.2 Aggregate Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.3 Recent Models for Studying Monetary Policy . . . . . . . . . . . . . 84
A Summary of Solution Methods for Linear RE Models 91
7 Solving Linear Expectational Difference Equations 93
7.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.2 Matrix Decompositions . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.3 Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.4 Time Series Representation . . . . . . . . . . . . . . . . . . . . . . 102
8 A Menu of Different Policy Rules 103
8.1 A “Simple” Policy Rule . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.2 Optimal Policy under Commitment . . . . . . . . . . . . . . . . . . . 104
8.3 Discretionary Solution . . . . . . . . . . . . . . . . . . . . . . . . . 106
9 Estimation of New Keynesian Models 109
9.1 “New Keynesian Economics and the Phillips Curve” by Roberts . . . 109
9.2 “Solution and Estimation of RE Macromodels with Optimal Monetary
Policy” by S¨oderlind . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.3 “Estimating The Euler Equation for Output” by Fuhrer and Rudebusch 112
9.4 “New-Keynesian Models and Monetary Policy: A Reexamination of
the Stylized Facts” by S¨oderstr¨om et al . . . . . . . . . . . . . . . . . 113