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InformationChoiceinMacroeconomicsandFinancebyLauraVeldkampIntroductionThebookillustrateshowinformationchoiceisusedtoanswerquestionsinmonetaryeconomics,portfoliochoicetheory,businesscycletheory,interna ...

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Information Choice in Macroeconomics and Finance
by Laura Veldkamp
Introduction
The book illustrates how information choice is used to answer questions in monetary economics, portfolio choice theory, business cycle theory, international finance, asset pricing, and other areas. It shows how to build and test applied theory models with information frictions. And it covers recent work on topics such as rational inattention, information markets, and strategic games with heterogeneous information.
Contents
I Preliminaries 9
1 Why Study Information Choice? 11
1.1 Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 Bayesian Updating 21
2.1 Normal Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Uniform Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 The Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Bayesian Updating in Continuous Time . . . . . . . . . . . . . . . . . . . . . 26
2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3 Measuring Information Flows 29
3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Entropy and Rational Inattention . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Additive Cost in Signal Precision . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Diminishing Returns to Learning and Unlearnable Risk . . . . . . . . . . . . 34
3.5 Inattentiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.6 Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.7 Information Processing Frictions . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.8 Learning When Outcomes Are Correlated . . . . . . . . . . . . . . . . . . . . 37
3.9 Open Question: What is the Right Learning Technology? . . . . . . . . . . . 40
3.10 Appendix: Matrix Algebra and Eigen-decompositions . . . . . . . . . . . . . 41
3.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Games with Heterogeneous Information 45
4.1 Preliminary Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Heterogeneous Information Eliminates Multiple Equilibria . . . . . . . . . . . 47
4.3 Information and Covariance: A Beauty Contest Model . . . . . . . . . . . . . 51
4.4 Strategic Motives in Information Acquisition . . . . . . . . . . . . . . . . . . 54
4.5 Example: Information Choice and Real Investment . . . . . . . . . . . . . . . 59
4.6 Public Information Acquisition and Multiple Equilibria . . . . . . . . . . . . 62
4.7 Broader Themes and Related Literature . . . . . . . . . . . . . . . . . . . . . 65
4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
II Information Choice with Complementarity in Actions 69
5 Disclosing Public Information 71
5.1 Payo® Externalities and the Social Value of Information . . . . . . . . . . . . 72
5.1.1 Coordination and Overreaction to Public Information . . . . . . . . . 72
5.1.2 Morris and Shin's Social Cost of Public Information . . . . . . . . . . 72
5.1.3 Can Private Information Also Be Socially Costly? . . . . . . . . . . . 74
5.1.4 A More General Approach . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.5 The Central Bank Transparency Debate . . . . . . . . . . . . . . . . . 76
5.2 Public Information Crowds Out Private Information . . . . . . . . . . . . . . 76
5.2.1 Amador and Weill (2007) . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.2 Complementary Public and Private Information . . . . . . . . . . . . 79
5.3 More Information Increases Price Volatility . . . . . . . . . . . . . . . . . . . 82
5.4 Public Information Makes Money Neutral . . . . . . . . . . . . . . . . . . . . 83
5.5 Broader Themes and Paths for Future Research . . . . . . . . . . . . . . . . . 84
5.5.1 Speculative Currency Attacks . . . . . . . . . . . . . . . . . . . . . . . 84
5.5.2 A Coordination-Based Theory of Leadership . . . . . . . . . . . . . . 85
5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6 Informational Inertia and Price-Setting 89
6.1 Lucas-Phelps Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2 A Recipe for Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.3 Inattentiveness in Price-Setting . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.4 Rational Inattention Models of Price-Setting . . . . . . . . . . . . . . . . . . 101
6.5 Are Prices State-Dependent or Time-Dependent? . . . . . . . . . . . . . . . . 105
6.6 Broader Themes and Paths for Future Research . . . . . . . . . . . . . . . . . 110
6.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
III Information Choice with Substitutability in Actions 115
7 Information Choice and Investment Choice 117
7.1 A One-Asset Model with Information Choice . . . . . . . . . . . . . . . . . . 118
7.2 Multiple Assets and Exogenous Information . . . . . . . . . . . . . . . . . . . 125
7.3 Multiple Assets with Information Choice . . . . . . . . . . . . . . . . . . . . . 128
7.3.1 Gains to Specialization . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.3.2 Identical Investors Hold Di®erent Portfolios . . . . . . . . . . . . . . . 131
7.4 Interpreting Information Constraints in Equilibrium . . . . . . . . . . . . . . 132
7.5 Broader Themes and Paths for Future Research . . . . . . . . . . . . . . . . . 134
7.6 Appendix: Computing Expected Utility . . . . . . . . . . . . . . . . . . . . . 138
7.7 Appendix: Correlated Assets . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
8 Returns to Scale in Information 145
8.1 Returns to Scale in Real Investment (One Asset) . . . . . . . . . . . . . . . . 146
8.2 Gains to Specialization (N assets) . . . . . . . . . . . . . . . . . . . . . . . . 149
8.2.1 Result: Optimal Portfolio Choice . . . . . . . . . . . . . . . . . . . . . 152
8.2.2 Result: Optimal Information Choice . . . . . . . . . . . . . . . . . . . 153
8.2.3 Indi®erence Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2.4 Preference for Early Resolution of Uncertainty . . . . . . . . . . . . . 156
8.3 Markets for Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.4 Broader Themes and Paths for Future Research . . . . . . . . . . . . . . . . . 161
8.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
9 Information as an Aggregate Shock 167
9.1 News About Future Productivity . . . . . . . . . . . . . . . . . . . . . . . . . 168
9.1.1 Model 1: Cross-Industry Complementarity . . . . . . . . . . . . . . . . 168
9.1.2 Model 2: Gradual Capital Adjustment . . . . . . . . . . . . . . . . . . 171
9.1.3 Matching Stock Market Fluctuations . . . . . . . . . . . . . . . . . . . 173
9.1.4 Empirical Evidence on News Shocks . . . . . . . . . . . . . . . . . . . 174
9.2 News about Current Productivity . . . . . . . . . . . . . . . . . . . . . . . . . 175
9.2.1 Model 3: Aggregate News Shocks . . . . . . . . . . . . . . . . . . . . . 175
9.2.2 Model 4: Confusing Private and Public News . . . . . . . . . . . . . . 179
9.3 Broader Themes and Paths for Future Research . . . . . . . . . . . . . . . . . 183
9.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
IV Measurement 187
10 Testing Information Theories 189
10.1 Measuring Flows of News . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
10.2 Forecast Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
10.3 Using Covariances to Infer Information Sets . . . . . . . . . . . . . . . . . . . 191
10.4 Realized Proˉts as Proxies for Information . . . . . . . . . . . . . . . . . . . . 193
10.5 Information Choice as a Substitute for Information Data . . . . . . . . . . . . 194
10.6 The Bid-Ask Spread and the Probability of Informed Trading . . . . . . . . . 196
11 Conclusions
（有些章节的顺序乱了，抱歉。）

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