Essays on public spending: a computational approach

September, 2009


Supervisors:

Diego Martinez (U. Pablo de Olavide)

Javier J. Pérez (Bank of Spain)


Ph.D. dissertation structure

  1. Contents, Introduction and Acknowledgements ()

Part I The role of public wages in an economy

  1. Is there a signalling role for public wages? Evidence for the euro area based on macro data

Part II The optimal provision of public inputs in a second-best scenario

  1. A diagrammatic approach to the optimal level of public inputs

  2. Returns to scale and the optimal level of productivity-enhancing public expenditures: a
    numerical approach

  3. Optimization in non-standard problems. An application to the provision of public inputs

Part III Revisiting the Parameterized expectations algorithm: Drawbacks and solutions

  1. Alternatives to initialise the Parameterized Expectations Algorithm

  2. Selection criteria among solutions of the Parameterized Expectations Algorithm

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Is there a signalling role for public wages? Evidence for the euro area based on macro data

We test if public sector wages exert pressures on private sector wages, or rather if the private sector is the wage leader. To do so we try to isolate the pure signalling effect that one sector might exert on the other by controlling for other determinants of wages (prices, productivity, institutions) for the main euro area economies (Germany, France, Italy and Spain) and the periods 1980-2007 and 1991-2007. We exploit available quarterly information not yet used in the literature, and combine different data sources in the framework of mixed-frequencies time series models. The quarterly frequency of our data allows us to check the existence of purely intra-annual links between public and private sector wages (signalling effect). Our results show strong evidence of public wages’ leadership, either in conjunction with bi-directional links from the private sector (Germany and Spain) or pure public wage leadership (France in the sample 1991-2007, Italy for within-the-year linkages). Our empirical approach allows us to also unveil a complex and rich structure of indirect links of wages with other variables (prices, productivity and institutional factors).

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Appendix 1.A: GDP deflator results
Appendix 1.C: Complementary results

A diagrammatic approach to the optimal level of public inputs

This chapter analyses whether the first-best level of public inputs exceeds that of the second-best case. On the basis of a simple model, we argue that the level of productivity-enhancing public expenditures is always higher than the level of public inputs provided with distortionary taxation.

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Returns to scale and the optimal level of productivity-enhancing public expenditures: a numerical approach

This chapter studies the optimal level of public inputs under two different tax settings. With this aim, we adapt the approach by Gronberg and Liu (2001) to the case of productivity-enhancing public spending. For this context, we find that it is not analytically clear whether the first-best level of public spending will always be greater than the second-best one. After taking account the type of public input (firm or factor-augmenting), a wide numerical simulation has been carried out. We obtain that the second-best llevel will always below the first-best level, but that some of the criteria set forth by Gronberg and Liu must be qualified.

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Optimization in non-standard problems. An application to the provision of public inputs

This chapter describes a new method for solving non-standard constrained optimization problems for which standard methodologies do not work properly. Our method (the Rational Iterative Multisection -RIM- algorithm) consists of different stages that can be interpreted as different precision requirements by obtaining the optimal solution. We have performed an application of RIM method to the case of public inputs provision. We prove that the RIM approach and comparable standard methodologies achieve the same results with regular optimization problems while the RIM algorithm takes advantage over others when facing non-standard optimization problems.

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Appendix 4.B: The RIM-toolbox, a Matlab problem-independent implementation

Alternatives to initialise the Parameterized Expectations Algorithm

This chapter analyses the convergence properties of some standard approaches to initialise the Parameterized Expectations Algorithm. We carry out a Monte Carlo experiment to compare their performance in computational terms. We do so within the framework of the
standard neoclassical growth model and of the monetary model of Cooley and Hansen (1989).

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Selection criteria among solutions of the Parameterized Expectations Algorithm

The solution of Parameterized Expectations Algorithm is well defined on the basis of asymptotic properties. In practice, it depends on the replication of exogenous shock(s) used during the resolution process. Typically, this problem is reduced when a sufficiently long replication is considered. In this chapter, we propose an alternative approach which consists of using several but shorter replications. Then, we propose some criteria which enable us to select among the different PEA solutions previously obtained. On the basis of a detailed Monte Carlo experiment, we discuss what criterion is more suitable to be followed. We do so within the framework of the standard neoclassical-growth model and of the Cooley and Hansen monetary model (1989).

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