Endogeneity in Engel Curves and the Nonparametric Instrumental Variables Method

Öz

Instrumental variable methods are widely used in identifying models with endogeneity problems and obtaining consistent estimation results. Nonparametric approaches allow for flexible estimations without functional form constraints. In the literature, Engel curves represent a key application area where endogeneity is frequently observed, analysing the relationship between total expenditure and expenditure categories. This study aims to avoid biased and inconsistent estimates by accounting for the endogeneity of total expenditure in Engel curve estimation. To address this problem, we employ the nonparametric instrumental variable method, and the ill-posed problem is resolved using Landweber–Fridman regularization. In application, the head of household earnings is used as a valid instrument variable for the household’s total expenditure. Moreover we compare the performance of parametric and nonparametric methods in the presence of endogeneity. The analysis is based on the TÜİK 2022 Household Budget Statistics microdata, comprising 5300 observations of households with children and employed household heads aged 15-64 years. The results highlight the importance of appropriate model specification in Engel curve analysis. Moreover, the findings supported by wild bootstrap confidence intervals indicate that the nonparametric instrumental variables approach implemented with Landweber–Fridman regularization provides a flexible and empirically feasible alternative for estimating consumption relationships in the presence of endogeneity.

Anahtar Kelimeler

• Endogeneity
• Nonparametric Instrumental Variables Method
• Landweber-Fridman Regularization
• Engel Curve

Engel Eğrilerinde İçsellik ve Parametrik Olmayan Araç Değişken Yöntemi

Öz

İçsellik problemine sahip modellerin tanımlanmasında ve tutarlı tahmin sonuçlarının elde edilmesinde araç değişken yöntemleri yaygın olarak kullanılmaktadır. Parametrik olmayan yaklaşımlar, fonksiyonel form kısıtlaması olmadan esnek tahminler yapılmasına olanak sağlamaktadır. Literatürde içsellik sorununun sıkça karşılaşıldığı alanlarından biri Engel eğrileridir. Engel eğrilerinde, hanelerin toplam harcamaları ve dağılımları arasındaki ilişki incelenmektedir. Bu çalışmanın temel amacı, toplam harcamanın içsel değişken olması nedeniyle içsellik problemini göz ardı etmenin yol açabileceği sapmalı ve tutarsız tahminleri önlemektir. Bu sorunu ele almak için parametrik olmayan araç değişken yöntemi kullanılmış ve yöntemdeki ters tanımlama problemi Landweber-Fridman düzgünleştirme yöntemiyle çözülmüştür. Uygulamada, toplam harcama için araç değişken olarak hanehalkı reisinin geliri kullanılmıştır. Ayrıca, içsellik sorununa sahip parametrik ve parametrik olmayan yöntemlerin Engel eğrilerini tahmin etme başarısı karşılaştırılmış ve hangi yaklaşımın daha etkili sonuçlar verdiği analiz edilmiştir. Çalışmada TÜİK 2022 Hanehalkı Bütçe İstatistikleri mikro veri seti kullanılarak, 15-64 yaş aralığında çalışan hane reisi bilgilerini ve sadece çocuklu haneleri kapsayan 5300 gözlem için Engel eğrileri tahmin edilmiştir. Elde edilen sonuçlar, Engel eğrisi analizinde doğru model tanımlamasının önemini vurgulamaktadır. Aynı zamanda wild bootstrap güven aralıklarıyla desteklenen bulgular, Landweber-Fridman düzgünleştirmesiyle parametrik olmayan araç değişken yönteminin, içselliğin varlığında tüketim ilişkilerini tahmin etmek için esnek ve uygulanabilir bir alternatif sunduğunu göstermektedir.

Anahtar Kelimeler

• İçsellik
• Parametrik Olmayan Araç Değişken Yöntemi
• Landweber-Fridman Düzgünleştirmesi
• Engel Eğrisi

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