Unobserved heterogeneity and dependence in aggregate panel models: methods and applications
- Autores: Lucciano Villacorta
- Directores de la Tesis: Stéphane Bonhomme (dir. tes.), Manuel Arellano (codir. tes.)
- Lectura: En la Universidad Internacional Menéndez Pelayo (UIMP) ( España ) en 2015
- Idioma: español
- Tribunal Calificador de la Tesis: Christian Hansen (presid.), Pedro Mira (secret.), Iván Fernández Val (voc.), Jesús Carro (voc.), Raül Santaeulàlia-Llopis (voc.)
- Materias:
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- Resumen
Panel Data models open several possibilities for estimation and inference of economic models that were unfeasible if we only rely on a simple-cross section or time-series database.
The great advantage of panel data models is that they allow to control for unobserved heterogeneity, providing identification of common parameters and average marginal effects, without the need of external instruments. They also enable us to uncover aspects of the distribution of the unobserved heterogeneity itself, which might be useful for calculating interesting economic objects. Moreover, panel data offer the possibility to deal with error dependence in a very flexible way by using cluster standard errors.
One particular field that might be benefited from all the recent advances in panel data is empirical macroeconomics. Nowadays, researchers have at their disposal several rich and harmonized databases of aggregate macroeconomic variables for a wide range of countries and sectors for many years. The availability of those databases allows researchers to look for new stylized facts, and to estimate and test more flexible models, enriching the analysis of fundamental questions in macroeconomics, specially the ones related to growth and productivity patterns around the world.
In this thesis I study different methodological frameworks for considering rich patterns of unobserved heterogeneity and error dependence in the estimation and inference of aggregate panel models. Chapter 1 and 3 of this thesis are devoted to the estimation of nonlinear aggregate Constant Elasticity of Substitution (CES, henceforth) production functions using non linear panel data techniques. Chapter 2, instead, is devoted to the study of different approaches to compute robust standard errors when there is spatial and time error dependence in the panel model.
The aggregate CES is a powerful tool to analyze broad patterns of economic changes across countries. In particular, its parameters -the elasticity of substitution between capital and labor and the capital- and labor- augmenting technologies- are crucial in explaining: (i) the decline in the labor share (Karabarbounis and Neiman, 2014; Piketty and Zucman, 2014) and (ii) development accounting (Caselli, 2005).
As opposed to previous studies, in chapter 1, I consider a CES production function model with country-specific elasticity of substitution. Additionally, the growth rates of the capital- and labor-augmenting technologies are allowed to vary over time and across countries while retaining some commonalities across the panel via underlying factors. Therefore, when we look at the world there is a joint distribution of elasticities and technologies.
I develop a flexible framework to estimate this joint distribution. In my model, all parameters are unit-specific. I obtain Bayesian fixed effects estimates of economically meaningful quantities, which can be regarded as characteristics of the joint distribution of my parameters.
To do so, I use posterior distributions that are computed using Markov Chain Monte Carlo. My framework helps shed light on questions related to the literature of the decline in the labor share and development accounting. I find evidence of heterogeneity in the elasticity of substitution across countries, with a mean of 0.90 and a standard deviation of 0.23.
I also find that the bias in the technical change is the dominant mechanism in explaining the evolution of the labor share for the majority of countries in the database. However, the increase in the capital-labor ratio is also an important mechanism for some countries. The results also show heterogeneity in the growth rates of the capital- and labor-augmenting technologies. I finally find a strong correlation between both technologies, the elasticity of substitution and the relative endowment of capital and labor.
In chapter 3 we also estimate aggregate CES functions for many countries as a part of a structural model for studying the relationship between changes in investment rates and structural transformation.1 The standard hump-shaped relationship between the size of the industrial sector and the level of development of countries has been a challenge for theories of structural transformation under balanced growth path. Using a standard multi-sector neo-classical growth model, we argue that this relationship can be explained 1Chapter 3 is joint work with Josep Pijoan-Mas and Manuel Garcia-Santana from CEMFI and Pompeu Fabra, respectively. Although this chapter has been a genuine joint effort from Josep, Manuel and myself , my main contributions lie in the parts related to estimation and computation of the structural model.
by countries in transition towards balanced growth paths with higher capital intensity. Our key mechanism is that the set of goods used for final consumption is different from the set of goods used to form physical capital. Hence, when the investment rate of the economy changes so does the relative demand of different goods. We exploit this insight to estimate the sectoral composition of an aggregate consumption good and an aggregate investment good as the investment rate of the economy changes over time. Using panel data from a large set of economies we show that the changes in investment demand are quantitatively important. First, for some selected episodes of economic development they account for a large part of the increase in the size of the industrial sector. For instance, for China (between 1952 and 2010), Costa Rica (1950 to 2006), India (1950 to 2010), South Korea (1960 to 1992), or Vietnam (1988 to 2008) the increase in the investment rate accounts for more than 10 percentage points increase in the relative size of the industrial sector. Second, the investment decline since the 70’s in some rich countries help explain the contraction of their manufacturing sectors. For instance, in Finland (between 1974 and 1995) or Japan (1970-2011) the investment rate accounts for a fall of the industrial sector of around 10 percentage points, while in France, Germany, Norway or Sweden it explains more than 5 percentage points. Third, when looking at the data for all countries together, we show that the evolution of the investment rate accounts for part of the hump in manufactures.
In chapter 2, I study different approaches to estimate standard errors in panel models that are robust to spatial and time error dependence when neither N nor T are very large.
The classical literature on panel data has allowed time series dependence but has generally assumed that the observations are cross-sectionally independent. However, spatial dependence is likely to be presented in aggregate panels, such as, state-year, country-year or industry-year panels, as these units are likely to be connected through neighboring effects, economic trade or linkage in productions. Although it is well understood that not taking into account the error dependence invalidates statistical inference, computing standard errors that are robust to both time and cross sectional dependence, is not common in applied econometrics. Chapter 2 begins by analyzing, analytically and numerically, the two-way cluster estimator (2WCCE, henceforth). The speed of convergence of the 2WCCE is min . More importantly, its variance is also affected by the two forms of dependence.
As a consequence, when N and T are not large enough, inference based on the SUMMARY xiii 2WCCE estimator may be misleading. Then, I propose a more parsimonious structure to estimate robust standard errors based on the spatial autoregressive model (SAR) . Also, I make a connection between the cluster estimator and the SAR. In a calibrated Monte Carlo exercise of state minimum wage, I show that using a parametric model or a naive i.i.d bootstrap yields substantially better results than using clustering when N and T are as small as 50 and 30. Finally, I study the implications of considering both types of dependence on a state-year panel data of wage inequality and minimum wage in the US. When both types of error dependence are considered, the marginal effect of the minimum wage over wage inequality is no longer significant.
