Quantile regression methods for recursive structural equation models

Ma, Lingjie; Koenker, Roger

doi:10.1016/j.jeconom.2005.07.003

Cited by 146 publications

(38 citation statements)

References 32 publications

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“…However, their estimator is hard to implement for computational reasons, since we have a model with four endogenous variables. We therefore choose the estimator proposed by Ma and Koenker () that relies on a recursive structural model . We therefore need to impose a more restrictive structure on the errors in Equations (3 and 5) and consider the wage earnings equation in terms of a linear location‐scale model (Koenker, , p. 17; Ma & Koenker, ).…”

Section: Empirical Modelsmentioning

confidence: 99%

“…To obtain instrumental variables estimates of the functions for the conditional quantiles we reformulate Equations (3 and 5) as

{\ln w}_{italicit} = α_{0 t} + \sum_{p = 1}^{4} α_{p} {\ln E}_{pit} + \sum_{k = 1}^{K} γ_{k} X_{kit} + \sum_{r = 2}^{R} ρ_{r} D_{italicrit} + ε_{4 it} \sum_{p = 1}^{4} {normalln E}_{italicpit} + \sum_{p = 1}^{4} {\ln E}_{pit} ω_{p} ε_{5 italicpit}

and

{italicln E}_{italicpit} = θ_{p 0 t} + \sum_{p = 1}^{4} true[θ_{p 1} normalln true({nonsteep area}_{pit} true) + θ_{p 2} true({water}_{pit} true) true] + \sum_{k = 1}^{K} μ_{pk} X_{kit} + \sum_{r = 2}^{R} δ_{r} D_{italicrit} + + ε_{5 pit},

respectively. Ma and Koenker (, p. 4) suggest that we should think of this estimation framework in terms of a thought experiment where we do not manipulate the value of the treatment (in our case the economic mass in each distance band) but instead the entire distribution of the treatment variable. Thus, when assessing the effect on the distribution of the outcome (in our case wage earnings) we isolate the effect at various percentiles of the treatment distribution.…”

Section: Empirical Modelsmentioning

confidence: 99%

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The spatial extent of agglomeration economies across the wage earnings distribution

Håkansson

Isacsson

2018

Journal of Regional Science

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We investigate the spatial extent of agglomeration economies across the wage earnings distribution using economic mass (total employment) in four distance bands around each individual’s establishment in a quantile regression framework. We control for observable and unobservable individual and establishment characteristics. Remaining endogeneity in the model is assessed with a set of instrumental variables. Results indicate a positive effect of economic mass on wage earnings up to 25 km away from the establishment. The spatial extent of agglomeration economies is similar across the wage earnings distribution. However, increases in economic mass shift the wage earnings distribution in a nonsymmetric way.

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Section: Empirical Modelsmentioning

confidence: 99%

“…To obtain instrumental variables estimates of the functions for the conditional quantiles we reformulate Equations (3 and 5) as

{\ln w}_{italicit} = α_{0 t} + \sum_{p = 1}^{4} α_{p} {\ln E}_{pit} + \sum_{k = 1}^{K} γ_{k} X_{kit} + \sum_{r = 2}^{R} ρ_{r} D_{italicrit} + ε_{4 it} \sum_{p = 1}^{4} {normalln E}_{italicpit} + \sum_{p = 1}^{4} {\ln E}_{pit} ω_{p} ε_{5 italicpit}

and

{italicln E}_{italicpit} = θ_{p 0 t} + \sum_{p = 1}^{4} true[θ_{p 1} normalln true({nonsteep area}_{pit} true) + θ_{p 2} true({water}_{pit} true) true] + \sum_{k = 1}^{K} μ_{pk} X_{kit} + \sum_{r = 2}^{R} δ_{r} D_{italicrit} + + ε_{5 pit},

Section: Empirical Modelsmentioning

confidence: 99%

The spatial extent of agglomeration economies across the wage earnings distribution

Håkansson

Isacsson

2018

Journal of Regional Science

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“…12 For the case in which Y 1 is continuous, see Koenker and Bassett (1978), Koenker and d'Orey (1987), and Ma and Koenker (2004) for parametric estimation; see Chaudhuri, Doksum, and Samarov (1997), Kahn (2001), and Lee (2003Lee ( , 2004 for semiparametric estimation; and see Chaudhuri (1991) for nonparametric estimation. Machado and Santos Silva (2005) propose a procedure for the parametric case when Y 1 is discrete.…”

Section: Estimationmentioning

confidence: 99%

Nonparametric Identification under Discrete Variation

2005

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This paper provides weak conditions under which there is nonparametric interval identification of local features of a structural function that depends on a discrete endogenous variable and is nonseparable in latent variates. The function delivers values of a discrete or continuous outcome and instruments may be discrete valued. Application of the analog principle leads to quantile regression based interval estimators of values and partial differences of structural functions. The results are used to investigate the nonparametric identifying power of the quarter‐of‐birth instruments used in Angrist and Krueger's 1991 study of the returns to schooling.

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“…Chesher (2002) considered identification under index restrictions with multiple disturbances. Ma and Koenker (2006) considered identification and estimation of parametric nonseparable quantile effects using a parametric, quantile based control variable. Our triangular model results require that the endogenous variable be continuously distributed.…”

Section: Introductionmentioning

confidence: 99%

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

2009

Econometrica

341

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This paper uses control variables to identify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance. Here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable. Also, for any control variable, identification results are given for quantile, average, and policy effects. Bounds are given when a common support assumption is not satisfied. Estimators of identified objects and bounds are provided, and a demand analysis empirical example is given. Copyright 2009 The Econometric Society.

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Quantile regression methods for recursive structural equation models

Cited by 146 publications

References 32 publications

The spatial extent of agglomeration economies across the wage earnings distribution

The spatial extent of agglomeration economies across the wage earnings distribution

Nonparametric Identification under Discrete Variation

Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

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