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Latent Heterogeneity in the Marginal Propensity to Consume. (2019). Melcangi, Davide ; Lewis, Daniel ; Pilossoph, Laura.
In: Staff Reports.
RePEc:fip:fednsr:902.

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  1. Age, wealth, and the MPC in Europe: A supervised machine learning approach. (2023). Radermacher, Jan W ; Dutt, Satyajit.
    In: SAFE Working Paper Series.
    RePEc:zbw:safewp:383.

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  2. A Fair Days Pay for a Fair Days Work: Optimal Tax Design as Redistributional Arbitrage. (2022). Werquin, Nicolas ; Hellwig, Christian.
    In: TSE Working Papers.
    RePEc:tse:wpaper:126368.

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  3. A Fair Days Pay for a Fair Days Work: Optimal Tax Design as Redistributional Arbitrage. (2022). Werquin, Nicolas ; Hellwig, Christian.
    In: Working Paper Series.
    RePEc:fip:fedhwp:93617.

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  4. Fiscal Policy in the Age of COVID: Does it ‘Get in all of the Cracks?’. (2021). Kalemli-Ozcan, Sebnem ; Gourinchas, Pierre-Olivier ; Sander, Nick ; Penciakova, Veronika.
    In: NBER Working Papers.
    RePEc:nbr:nberwo:29293.

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  5. A Model of Expenditure Shocks. (2020). Young, Eric ; Miranda-Pinto, Jorge ; Walsh, Kieran ; Murphy, Daniel ; Miranda-Pino, Jorge.
    In: Working Papers.
    RePEc:fip:fedcwq:87435.

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  1. A simple modification of Lemma 2 of Yang and Yu (1992) completes the proof: Lemma 2. (Yang and Yu (1992)) Let θ∗ be a minimizer of Lm (Π, θ) among all θ ∈ Θ. Then the pair (reg (θ∗) , θ∗) is a minimizer of J reg m (Π, , θ) among all θ and weights .
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  5. η (θ, yi, xi) η (θ, yi, xi)0 is assumed to be positive definite in Assumption 4.4. Combining these two results with the conditions of Assumption 4, the standard conditions for asymptotic normality of a GMM estimator are satisfied (e.g., Hayashi (2011) Proposition 7.10). Since the weighting matrix is the identity (the problem is just-identified), √ N θ̂ − θ∗ d → N 0, H−1 VH−1 . B Supplemental theoretical results In this section, we report extensions of our main theoretical results. First, we provide expressions for the Hessian to compute the asymptotic variance in the case of panel data. Second, we extend all regression results from the main text to a TSLS implementation.
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  35. Proof. The proof follows directly from that of Lemma 2 of Yang and Yu (1992).
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  36. Proof. The proof is identical to that of Lemma 1 of Yang and Yu (1992).
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  45. Z Z G ∑ g=1 y − θgx −2/(m−1) !1−m Πy|x (dy | x) Π (dx) , which is the formulation of L reg m (Π, θ). Parallel to the development of Yang and Yu (1992) for the cluster means case, we now show that minimization problem of J reg m is equivalent to that of L reg m , based on two lemmata from that paper.
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