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A Philosophical Analysis of Causality in Econometrics A Philosophical Analysis of Causality in Econometrics Damien James Fennell London School of Economics and Political Science Thesis submitted to the University of London for the completion of the degree of a Doctor of Philosophy August 2005 1 UMI Number: U209675 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI U209675 Published by ProQuest LLC 2014. Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 Abstract This thesis makes explicit, develops and critically discusses a concept of causality that is assumed in structural models in econometrics. The thesis begins with a development of Herbert Simon’s (1953) treatment of causal order for linear deterministic, simultaneous systems of equations to provide a fully explicit mechanistic interpretation for these systems. Doing this allows important properties of the assumed causal reading to be discussed including: the invariance of mechanisms to intervention and the role of independence in interventions. This work is then extended to basic structural models actually used in econometrics, linear models with errors-in-the-equations. This part of the thesis provides a discussion of how error terms are to be interpreted and sets out a way to introduce probabilistic concepts into the mechanistic interpretation set out earlier. The resulting analysis is then critically compared with similar work by economists, Stephen LeRoy (1995) and Kevin Hoover (2001a) who both develop Simon’s work on causal order in different ways. In the latter part of the thesis, the mechanistic interpretation set out at the beginning is used to interpret identification conditions. Typically, these are presented in econometrics as mathematical conditions for determining whether unknown parameters in equations can be measured from observation. In the thesis it is shown that the identification conditions imposed on sets of equations when interpreted mechanistically require a sparseness of causal structure that ensures that experiments are hypothetically possible of the causal structure. It also analyses the role of identifiability conditions in causal inference. The final part of the thesis shows that the mechanistic interpretation developed in the thesis succeeds, unlike Simon’s own methods for analysing spurious correlation, in avoiding important criticisms by Nancy Cartwright (1989) whose own approach to inferring causal structure from observations is also critically analysed. 2 Contents Chapter 1 - Introduction.................................................................................................9 1. Causality in Philosophy and Economics ....................................................................9 2. Overview of Thesis .....................................................................................................13 Chapter 2 - Mathematical Equations and their Causal Interpretations: The Strong Reading of Herbert Simon’s Concept of Causal Order..............................16 1. Introduction ..................................................................................................................16 2. A Challenge to Representing Causal Relations with Mathematical Equations. 17 3. Simon’s Formal Ordering Method ........................................................................... 21 3.1. The Formal ‘Causal’ Order for Sets of Equations ...................................... 21 3.2. An Alternative formalism: Simon’s Logic of the Causal Order ............... 24 3.3. Does Simon’s Formal Order Help Solve the Conceptual Equivalence Problem ?............................................................................................................ 27 4. The Model Reading of the Equations ....................................................................... 28 4.1. Simon’s Empiricism ........................................................................................ 29 4.2. Interpreting Equations Causally ....................................................................31 4.3. The Model Interpretation of the Earlier Example ........................................37 5. Important Properties of Causal Order in the Model ............................................... 39 5.1. Aside: Some Supplementary Causal Relations ............................................40 5.2. Properties of the Causal Relations in the Model ..........................................43 5.2.1. Clarifying Mechanisms ...................................................................43 5.2.2. Change and Causal Order ............................................................... 44 5.2.3. Invariance of Mechanisms to Change ...........................................47 5.2.4. Independence of Directly Controllable Factors .......................... 49 5.2.5. Simon’s ‘In general’ Caveat: The Possibility of Cancelling Out......................................................................................................51 6. Conceptual Equivalence Revisited and The Strong Reading ................................52 6.1. Solving the Conceptual Equivalence Problem in the Earlier Example.... 53 6.2. The Importance of Stipulating the Coefficients and the Form of the Equations............................................................................................................ 55 6.3. Making the Strong Reading Explicit in Sets of Equations ......................... 58 3 7. Conclusion ..................................................................................................................61 Appendix 2.1. Beginnings of a Formalisation of Mechanisms and Causal Order. 63 Chapter 3 - Causally Interpreting Simple Models Used In Econometrics and Exploring Intervention..................................................................................................76 1. Introduction ..................................................................................................................76 2. Introducing External and Internal Variables: Complete vs. Incomplete Sets .... 78 2.1. Incomplete Sets of Equations and their Causal Interpretation ...................79 2.2. Constructing Incomplete Sets from Complete Sets .................................... 81 2.3. Causal Consistency of Incomplete and Complete Sets of Equations 83 2.4. Why some Indirectly Controllable Factors can be Treated as Directly Controllable ........................................................................................................85 3. Using Incomplete Sets to Explore Intervention .....................................................90 3.1. Different Ways to Vary Just One External Factor ...................................... 92 4. Introducing Error Terms ........................................................................................... 101 5. Constant Coefficients and Adding Stochasticity ...................................................106 5.1. Constant Coefficients .....................................................................................107 5.2. Introducing Stochasticity ..............................................................................107 5.3. Aside: The Extended Model Reading, Weak and Super Exogeneity 110 6. Conclusion ..................................................................................................................112 Appendix 3.1. A Necessary Condition for An Incomplete Set to be Causally Consistent with a Complete Set ..............................................................114 Chapter 4 - Alternative Views on Causality based on Simon: Stephen LeRoy and Kevin Hoover .........................................................................................................116 1. Introduction ................................................................................................................116 2. Stephen LeRoy’s Treatment of Causal O rder ....................................................... 117 2.1. LeRoy Causality - Simple and Conditional Causes ................................. 117 2.2. The Farmer Example and the Restrictiveness of the Sufficiency Condition .......................................................................................................... 122 2.3. Summary ......................................................................................................... 124 3. LeRoy’s Characterisation of Simon ....................................................................... 125 3.1. How Simon solves the Conceptual Equivalence Problem according to LeRoy ................................................................................................................126 4 3.2. A Counterexample to LeRoy’s Exclusion Condition ................................ 128 3.3. Relating LeRoy’s Causality and Simon’s Formal Order ..........................131 3.3.1. Aside: Proof for LeRoy’s Equivalence claim ............................131 3.3.2. Characterising Simon’s Causal Relation Using the Subset Condition ..........................................................................................132 4. Kevin Hoover
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