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Lecture 7 Stephen G Hall IDENTIFICATION

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Lecture 7 Stephen G Hall IDENTIFICATION

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    1. Lecture 7 Stephen G Hall IDENTIFICATION

    27. But we need to identify the target relationships from the space spanned by these cointegrating vectors. We now illustrate this process

    34. Irreducibility As an underlying concept for identification

    35. Irreducible cointegrating vectors Davidson proposed the notion of irreducibility as a way of detecting and identifying structural relations. An irreducible vector is one where you can not remove any variables without loosing cointegration

    43. Conclusion If we want to understand structure identification is crucial We now have the technology to identify both the long and the short run structure of a model

    44. An Example Bargaining models and identifying the wage equation. G Chamberlin, S G Hall, and S G B Henry.

    45. Introduction Standard models of wage determination have followed the bargaining framework for many years Manning 1993 argued that the wage equation was not identified in this model A major problem not resolved

    46. Introduction this paper uses modern cointegration identification theory to argue that this view is wrong It Outlines identification Outlines wage theory Show how this identifies the wage equation Apply these ides to the UK

    47. The Manning problem Suppose the demand for employment is Ed=f(x) And supply is Es=g(z) Then a bargain over wages will result such that, the real wage w will be W=h(x,z)

    48. But problem The wage equation now contains all the variables in the system nothing is excluded Hence it can not be identified by the standard order condition

    49. The paper then outlines identification theory as earlier in this lecture

    50. The key thing is that these restrictions are on the cointegrating vectors. Not on the equations. Nothing needs to be excluded from any equations to identify the long run

    51. Bargaining theory Does the theory identify the long run relationships? go back to the key paper in this area McDonald Solow(1981) outline various cases

    52. Case 1 Firm; Maximise Profits R (L)-wL Union Maximise Utility L(U(w) - Un ) Which implies R(L)-w=0 (U(w)-Un )/wU(w)+LR(L)/R(L)=0 2 cointegrating vectors

    53. Case 2 This is a true bargaining model. A contract curve is derived (U(w)-U(wr))/U(w) = w- R (L) Which may imply (U(w)-U(wr))/U(w) = B w- R (L) = B 2 cointegrating relationships

    54. The message The more structure or theory we can bring to bare on a problem the more likely we are to be able to properly identify the system we are interested in.

    55. estimation We now estimate a model of the wage bargaining process in the UK. We assume cobb-douglas technology and estimate both the production function, the marginal revenue condition and the labour supply condition

    56. The core model

    57. Stationarity tests

    58. Weak exogeneity

    59. Testing r

    60. Model structure This gives us a 6-equation system to estimate with 3 long run relationships, which we hope to identify as the production function and the marginal product condition.

    61. The estimated long run structure

    62. The wage equation

    63. Some tests of restrictions

    64. conclusion The bargaining wage equation may be identified We have outlined the theory of identification and bargaining We have applied this with success to UK data.

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