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Title
Abstract
Introduction
Baseline Results
Conclusion
References
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Economics
Econometrics

Estimation of Threshold Distributions for Market Participation

Profile image of Patrick MussoPatrick Musso

2020, Sciences Po publications

Abstract

We develop a new method to estimate the parameters of threshold distributions for market participation based upon an agent-specific attribute and its decision outcome. This method requires few behavioral assumptions, is not data demanding, and can adapt to various parametric distributions. Monte Carlo simulations show that the algorithm successfully recovers three different parametric distributions and is resilient to assumption violations. An application to export decisions by French firms shows that threshold distributions are generally right-skewed. We then reveal the asymmetric effects of past policies over different quantiles of the threshold distributions.

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References (38)

  1. Ackerberg, D. A., K. Caves, and G. Frazer (2015). Identification properties of recent production function estimators. Econometrica 83(6), 2411-2451.
  2. Alogoskoufis, G. and A. Manning (1991). Tests of alternative wage employment bargaining models with an appli- cation to the UK aggregate labour market. European Economic Review 35(1), 23 -37.
  3. Atkinson, A. B. and J. E. Stiglitz (1969). A new view of technological change. The Economic Journal 79(315), 573-578.
  4. Bernard, A. B. and J. B. Jensen (2004). Why some firms export. The Review of Economics and Statistics 86(2), 561-569.
  5. Boulhol, H. (2009, April). The convergence of price-cost margins. Open Economies Review 19(2), 221-240.
  6. Brown, S. and K. Taylor (2013). Reservation wages, expected wages and unemployment. Economics Letters 119(3), 276 -279.
  7. Caves, D. W., L. R. Christensen, and W. E. Diewert (1982). Multilateral comparisons of output, input, and produc- tivity using superlative index numbers. Economic Journal 92(365), 73-86.
  8. Cogan, J. F. (1981). Fixed costs and labor supply. Econometrica 49(4), 945-963.
  9. Cohen, W. M. and D. A. Levinthal (1989). Innovation and learning: The two faces of r&d. The Economic Jour- nal 99(397), 569-596.
  10. Das, S., M. J. Roberts, and J. R. Tybout (2007). Market entry costs, producer heterogeneity, and export dynamics. Econometrica 75(3), 837-873.
  11. De Loecker, J. and P. Goldberg (2014). Firm performance in a global market. Annual Review of Economics 6, 201-227.
  12. DellaVigna, S., A. Lindner, B. Reizer, and J. F. Schmieder (2017, 05). Reference-Dependent Job Search: Evidence from Hungary*. The Quarterly Journal of Economics 132(4), 1969-2018.
  13. Dixit, A. (1989). Entry and exit decisions under uncertainty. Journal of Political Economy 97(3), 620-638.
  14. Eaton, J., S. Kortum, and F. Kramarz (2011, September). An anatomy of international trade: Evidence from french firms. Econometrica 79, 1453-1498.
  15. Fan, Y. and M. Xiao (2015). Competition and subsidies in the deregulated us local telephone industry. The RAND Journal of Economics 46(4), 751-776.
  16. Good, D. H., M. I. Nadiri, and R. Sickles (1997). Handbook of applied econometrics: Microeconometrics. Chapter Index Number and Factor Demand Approaches to the Estimation of Productivity. Blackwell, Oxford.
  17. Hall, R. E. (1988). The relation between price and marginal cost in u.s. industry. Journal of Political Economy 96(5), 921-947.
  18. Hopenhayn, H. (1992). Entry, exit, and firm dynamics in long run equilibrium. Econometrica 60(5), 1127-1150.
  19. Impullitti, G., A. A. Irarrazabal, and L. D. Opromolla (2013). A theory of entry into and exit from export markets. Journal of International Economics 90(1), 75 -90.
  20. Jiménez, G., V. Salas, and J. Saurina (2006). Determinants of collateral. Journal of Financial Economics 81(2), 255 -281.
  21. Jovanovic, B. (1982). Selection and the evolution of industry. Econometrica 50(3), 649-670.
  22. Kau, P. and L. Hill (1972). A threshold model of purchasing decisions. Journal of Marketing Research 9(3), 264-270.
  23. Khorunzhina, N. (2013). Structural estimation of stock market participation costs. Journal of Economic Dynamics and Control 37(12), 2928 -2942.
  24. Lyons, B. (1980). A new measure of minimum efficient plant size in uk manufacturing industry. Economica 47(185), 19-34.
  25. Mayer, T., M. J. Melitz, and G. I. P. Ottaviano (2014, February). Market size, competition, and the product mix of exporters. American Economic Review 104(2), 495-536.
  26. McDonald, R. and D. Siegel (1986, 11). The Value of Waiting to Invest*. The Quarterly Journal of Economics 101(4), 707-727.
  27. Melitz, M. J. (2003, November). The impact of trade on intra-industry reallocations and aggregate industry produc- tivity. Econometrica 71, 1695-1725.
  28. Melitz, M. J. and G. I. P. Ottaviano (2008, 01). Market size, trade, and productivity. The Review of Economic Stud- ies 75(1), 295-316.
  29. Pissarides, C. A. (1974). Risk, job search, and income distribution. Journal of Political Economy 82(6), 1255-1267.
  30. Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57(2), 307-333.
  31. Wei, Z. and H. Timmermans (2008). Cut-off models for the 'go-home' decision of pedestrians in shopping streets. Environment and Planning B: Planning and Design 35(2), 248-260.
  32. Wooldridge, J. M. (2009). On estimating firm-level production functions using proxy variables to control for unob- servables. Economics Letters 104(3), 112-114.
  33. fix a set of probability density functions F = f1, f2, . . . , fK to be used for the generation of the true thresholds and as priors (i.e. F) for the estimation of the threshold distribution parameters;
  34. using the information available to the social researcher (i.e., θ and χ), estimate via maximum likeli- hood the parameters Ω that characterize all the threshold distributions priors F;
  35. Monte Carlo Settings -Testing Assumption A4 The Monte Carlo simulations are carried out as follows: 1. fix a sufficiently large number of agents N ;
  36. simulate the true threshold data C T from the known distribution f k ; • generate also the noisy threshold data C ε = C T + ε c ;
  37. let the agents compute their individual decision outcomes χ according to Equation 12;
  38. using the information available to the social researcher, estimate via maximum likelihood the param- eters Ω that characterize the threshold distribution f k ;

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