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TÜRK HANEHALKI TASARRUF DAVRANIŞLARININ SENTETİK PANEL VERİ İLE TAHMİN EDİLMESİ

Yıl 2022, Cilt: 21 Sayı: 2, 645 - 674, 30.04.2022
https://doi.org/10.21547/jss.1004454

Öz

Bu çalışmada 2002-2013 dönemi TÜİK Hanehalkı Bütçe Araştırması (HBA) mikro verileri kullanılarak Türk hanehalkının tüketim ve tasarruf davranışı modeli analiz edilmiştir. Bu çalışmanın amacı Türk hanehalkının gelir dinamiğini, tüketim ve tasarruf davranışlarını anlamaya katkıda bulunmak ve Türkiye ekonomisinde Yaşam Döngüsü Hipotezi ve İhtiyati Tasarruf Hipotezi’nin geçerliliğini sınamaktır. Çalışmada ekonometrik yöntem olarak Deaton (1985) u takiben sentetik panel veri/kohort teknikleri kullanılmış ve ayrıca tüketim için iki aşamalı Sistem-GMM tekniği ile log doğrusallaştırılmış Euler denklemi tahmin edilmiştir. Elde edilen tüm ampirik bulgular tüketimin gelire aşırı duyarlı olduğunu gösterirken, bu durum Türkiye için Yaşam Döngüsü Hipotezi’nin geçerliliğine yönelik bir kanıt elde edilemediğini göstermektedir. Son olarak Türkiye için log doğrusallaştırılmış Euler denklemi ile İhtiyati Tasarruf Hipotezi’nin geçerliliği test edildiğinde, sonuçlar (gelecek dönem işgücü belirsizliği gibi) belirsizlik oluştuğunda hanehalkının yaşam boyu tüketimlerini sabit tutmak için cari tüketimlerini erteleyeceklerini ve tasarruf düzeylerini artırabileceklerini göstermektedir. Bu nedenle ampirik analiz sonuçları 2002- 2013 dönemi TÜİK HBA verileri dikkate alındığında Türkiye için İhtiyati Tasarruf Hipotezi’nin geçerliliğini destekler niteliktedir.

Kaynakça

  • Aktaş, A., Güner, D., Gürsel, S. ve Uysal, G. (2012). Structural determinants of household savings in Turkey: 2003-2008. Bahçeşehir University Center for Economic and Social Research BETAM Working Paper Series, 007, 1-51.
  • Arellano, M. (2003). Panel data econometrics. Oxford. University Press.(20.07.2017). https://books.google.com.tr/books?id=LoDnCwAAQBAJ&dq=Hsiao,+(2003),+Analysis+of+Panel+Data,+2nd+edition,+Cambridge+University+Press,+Ch.+6.2,+6.7+and+6.8&lr=&hl=tr&source=gbs_navlinks_s
  • Attanasio, O.P. (1993). A cohort analysis of saving behavior by U.S. households. NBER Working Papers, 4454, 1-31.
  • Attanasio, O.P. (1994). The intertemporal allocation of consumption: theory and evidence. NBER Working Papers, 4811, 1-34.
  • Attanasio, O.P., Banks,J., Meghir, C. ve Weber, G. (1995). Humps and bumps in lifetime consumption. NBER Working Papers, 5350, 1-25.
  • Attanasio, O.P. ve Browning, M. (1993). Consumption over the life cycle and over the business cycle. NBER Working Papers, 4453, 1-25.
  • Attanasio, O.P. ve Szekely, M. (1998). Household savings and income distribution in Mexico. Inter-American Development Bank Working Paper, 390, 1-55.
  • Attanasio, O.P. ve Szekely, M. (2000). Household saving in developing countries inequality, demographics and all that: How different are Latin America and South East Asia? Inter-American Development Bank Working Paper, 427, 1-61.
  • Attanasio, O.P. ve Weber, G. (1995). Is consumption growth consistent with intertemporal optimization? evidence from the consumer expenditure survey. Journal of Political Economy,103(6), 1121-1157. DOI: http://dx.doi.org/10.1086/601443
  • Attanasio, O.P. ve Weber, G. (2010). Consumption and saving: models of intertemporal allocation and their implications for public policy. Journal of Economic Literature, 48, 693–751. DOI: 10.1257/jel.48.3.693
  • Baltagi, B.H. (2008). Econometric analysis of panel data. John Wiley&Sons Ltd. United Kingdom. pp.147-179.
  • Banks, J., Blundell, R. ve Brugiavini, A. (2001). Risk pooling, precautionary saving and consumption growth. The Review of Economic Studies, 68(4), 757-779. DOI: https://doi.org/10.1111/1467-937X.00189
  • Bernheim, B.D., Skinner, J. ve Weinberg, S. (2001). What accounts for the variation in retirement wealth among U.S. households? The American Economic Review, 91(4), 832-857. DOI: 10.1257/aer.91.4.832
  • Beyaz Sipahi, B. (2021). Hanehalkı tasarruf oranının ekonomik ve demografik belirleyicileri: GMM yaklaşımı. Journal of Yasar University, 16(61), 248-263. DOI: https://doi.org/10.19168/jyasar.809671
  • Blundell, R., Browning, M. ve Meghir, C. (1994). Consumer demand and the life cycle allocation of household expenditure. Review of Economic Studies, 61(1), 57-80. DOI:10.2307/2297877
  • Bozkuş, S. ve Üçdoğruk, Ş. (2007). Hanehalkı tasarruf tercihleri: Türkiye örneği. 8. Ekonometri ve İstatistik Kongresi, 24-25 Mayıs, Malatya, Türkiye.
  • Browning, M., Deaton. A ve Irish, M. (1985). A profitable approach to labor supply and commodity demand over the life-cycle. Econometrica, 53(3), 503-544.
  • Browning, M. ve Lusardi, A. (1996). Household saving: micro theories and micro facts. Journal of Economic Literature,34(4), 1797-1855.
  • Browning, M. ve Ejrnaes, M. (2009). Consumption and children. The Review of Economics and Statistics, 91(1), 93-111. DOI: https://doi.org/10.1162/rest.91.1.93
  • Carroll, C.D. (1994). How does future income affect current consumption? The Quarterly Journal of Economics, 109(1), 111–147. DOI: https://doi.org/10.2307/2118430
  • Carroll, C.D. (1996). Buffer stock theory of saving and the Life Cycle/ Permanent Income Hypothesis. NBER Working Paper, 5788, 1-49.
  • Carroll, C. D. (2001). A theory of the consumption function, with and without liquidity constraints. The Journal of Economic Perspectives, 15(3), 23–45. DOI: 10.1257/jep.15.3.23
  • Carroll, C.D., Dynan, K.E. ve Krane, S.D. (2003). Unemployment risk and precautionary wealth: evidence from households balance sheets. The Review of Economics and Statistics, 85(3), 586-604.
  • Carroll, C.D., Hall, R.E. ve Zeldes, S.P. (1992). The buffer-stock theory of saving: some macroeconomic evidence. Brookings Papers on Economic Activity, 23(2), 61-156.
  • Carroll, C.D. ve Kimball, M.S. (1996). On the concavity of the consumption function. Econometrica, 64(4), 981-992.
  • Carroll, C.D ve Kimball, M.S. (2001). Liquidity constraints and precautionary saving. NBER Working Papers, 8496, 1-40.
  • Carroll, C.D. ve Samwick, A.A. (1997). The nature of precautionary wealth. Journal of Monetary Economics, 40(1), 41-71. DOI: https://doi.org/10.1016/S0304-3932(97)00036-6
  • Carroll, C.D. ve Summers, L.H. (1991). Consumption growth parallels income growth: some new evidence. B.D. Bernheim ve J. B Shoven. (Ed.). National Saving and Economic Performance. University of Chicago Press, pp. 305-348.
  • Ceritoğlu, E. (2009). The empirical importance of precautionary saving in Turkey. Ph.D. Thesis, University of Nottingham, England. pp.1-260.
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  • Kızılgöl, Ö.A. ve İpek, E. (2019). Türkiye’de hanehalkı tasarruf davranışının analizi. İzmir İktisat Dergisi, 34(3):331-344.
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TÜRK HANEHALKININ TASARRUF DAVRANIŞLARININ SENTETİK PANEL VERİ İLE TAHMİN EDİLMESİ

Yıl 2022, Cilt: 21 Sayı: 2, 645 - 674, 30.04.2022
https://doi.org/10.21547/jss.1004454

Öz

Bu çalışmada 2002-2013 dönemi TÜİK Hanehalkı Bütçe Araştırması (HBA) mikro verileri kullanılarak Türk hanehalkının tüketim ve tasarruf davranışı modeli analiz edilmiştir. Bu çalışmanın amacı Türk hanehalkının gelir dinamiğini, tüketim ve tasarruf davranışlarını anlamaya katkıda bulunmak ve Türkiye ekonomisinde Yaşam Döngüsü Hipotezi ve İhtiyati Tasarruf Hipotezi’nin geçerliliğini sınamaktır. Çalışmada ekonometrik yöntem olarak Deaton (1985) u takiben sentetik panel veri/kohort teknikleri kullanılmış ve ayrıca tüketim için iki aşamalı Sistem-GMM tekniği ile log doğrusallaştırılmış Euler denklemi tahmin edilmiştir. Elde edilen tüm ampirik bulgular tüketimin gelire aşırı duyarlı olduğunu gösterirken, bu durum Türkiye için Yaşam Döngüsü Hipotezi’nin geçerliliğine yönelik bir kanıt elde edilemediğini göstermektedir. Son olarak Türkiye için log doğrusallaştırılmış Euler denklemi ile İhtiyati Tasarruf Hipotezi’nin geçerliliği test edildiğinde, sonuçlar (gelecek dönem işgücü belirsizliği gibi) belirsizlik oluştuğunda hanehalkının yaşam boyu tüketimlerini sabit tutmak için cari tüketimlerini erteleyeceklerini ve tasarruf düzeylerini artırabileceklerini göstermektedir. Bu nedenle ampirik analiz sonuçları 2002- 2013 dönemi TÜİK HBA verileri dikkate alındığında Türkiye için İhtiyati Tasarruf Hipotezi’nin geçerliliğini destekler niteliktedir.

Kaynakça

  • Aktaş, A., Güner, D., Gürsel, S. ve Uysal, G. (2012). Structural determinants of household savings in Turkey: 2003-2008. Bahçeşehir University Center for Economic and Social Research BETAM Working Paper Series, 007, 1-51.
  • Arellano, M. (2003). Panel data econometrics. Oxford. University Press.(20.07.2017). https://books.google.com.tr/books?id=LoDnCwAAQBAJ&dq=Hsiao,+(2003),+Analysis+of+Panel+Data,+2nd+edition,+Cambridge+University+Press,+Ch.+6.2,+6.7+and+6.8&lr=&hl=tr&source=gbs_navlinks_s
  • Attanasio, O.P. (1993). A cohort analysis of saving behavior by U.S. households. NBER Working Papers, 4454, 1-31.
  • Attanasio, O.P. (1994). The intertemporal allocation of consumption: theory and evidence. NBER Working Papers, 4811, 1-34.
  • Attanasio, O.P., Banks,J., Meghir, C. ve Weber, G. (1995). Humps and bumps in lifetime consumption. NBER Working Papers, 5350, 1-25.
  • Attanasio, O.P. ve Browning, M. (1993). Consumption over the life cycle and over the business cycle. NBER Working Papers, 4453, 1-25.
  • Attanasio, O.P. ve Szekely, M. (1998). Household savings and income distribution in Mexico. Inter-American Development Bank Working Paper, 390, 1-55.
  • Attanasio, O.P. ve Szekely, M. (2000). Household saving in developing countries inequality, demographics and all that: How different are Latin America and South East Asia? Inter-American Development Bank Working Paper, 427, 1-61.
  • Attanasio, O.P. ve Weber, G. (1995). Is consumption growth consistent with intertemporal optimization? evidence from the consumer expenditure survey. Journal of Political Economy,103(6), 1121-1157. DOI: http://dx.doi.org/10.1086/601443
  • Attanasio, O.P. ve Weber, G. (2010). Consumption and saving: models of intertemporal allocation and their implications for public policy. Journal of Economic Literature, 48, 693–751. DOI: 10.1257/jel.48.3.693
  • Baltagi, B.H. (2008). Econometric analysis of panel data. John Wiley&Sons Ltd. United Kingdom. pp.147-179.
  • Banks, J., Blundell, R. ve Brugiavini, A. (2001). Risk pooling, precautionary saving and consumption growth. The Review of Economic Studies, 68(4), 757-779. DOI: https://doi.org/10.1111/1467-937X.00189
  • Bernheim, B.D., Skinner, J. ve Weinberg, S. (2001). What accounts for the variation in retirement wealth among U.S. households? The American Economic Review, 91(4), 832-857. DOI: 10.1257/aer.91.4.832
  • Beyaz Sipahi, B. (2021). Hanehalkı tasarruf oranının ekonomik ve demografik belirleyicileri: GMM yaklaşımı. Journal of Yasar University, 16(61), 248-263. DOI: https://doi.org/10.19168/jyasar.809671
  • Blundell, R., Browning, M. ve Meghir, C. (1994). Consumer demand and the life cycle allocation of household expenditure. Review of Economic Studies, 61(1), 57-80. DOI:10.2307/2297877
  • Bozkuş, S. ve Üçdoğruk, Ş. (2007). Hanehalkı tasarruf tercihleri: Türkiye örneği. 8. Ekonometri ve İstatistik Kongresi, 24-25 Mayıs, Malatya, Türkiye.
  • Browning, M., Deaton. A ve Irish, M. (1985). A profitable approach to labor supply and commodity demand over the life-cycle. Econometrica, 53(3), 503-544.
  • Browning, M. ve Lusardi, A. (1996). Household saving: micro theories and micro facts. Journal of Economic Literature,34(4), 1797-1855.
  • Browning, M. ve Ejrnaes, M. (2009). Consumption and children. The Review of Economics and Statistics, 91(1), 93-111. DOI: https://doi.org/10.1162/rest.91.1.93
  • Carroll, C.D. (1994). How does future income affect current consumption? The Quarterly Journal of Economics, 109(1), 111–147. DOI: https://doi.org/10.2307/2118430
  • Carroll, C.D. (1996). Buffer stock theory of saving and the Life Cycle/ Permanent Income Hypothesis. NBER Working Paper, 5788, 1-49.
  • Carroll, C. D. (2001). A theory of the consumption function, with and without liquidity constraints. The Journal of Economic Perspectives, 15(3), 23–45. DOI: 10.1257/jep.15.3.23
  • Carroll, C.D., Dynan, K.E. ve Krane, S.D. (2003). Unemployment risk and precautionary wealth: evidence from households balance sheets. The Review of Economics and Statistics, 85(3), 586-604.
  • Carroll, C.D., Hall, R.E. ve Zeldes, S.P. (1992). The buffer-stock theory of saving: some macroeconomic evidence. Brookings Papers on Economic Activity, 23(2), 61-156.
  • Carroll, C.D. ve Kimball, M.S. (1996). On the concavity of the consumption function. Econometrica, 64(4), 981-992.
  • Carroll, C.D ve Kimball, M.S. (2001). Liquidity constraints and precautionary saving. NBER Working Papers, 8496, 1-40.
  • Carroll, C.D. ve Samwick, A.A. (1997). The nature of precautionary wealth. Journal of Monetary Economics, 40(1), 41-71. DOI: https://doi.org/10.1016/S0304-3932(97)00036-6
  • Carroll, C.D. ve Summers, L.H. (1991). Consumption growth parallels income growth: some new evidence. B.D. Bernheim ve J. B Shoven. (Ed.). National Saving and Economic Performance. University of Chicago Press, pp. 305-348.
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  • Ceritoğlu, E. (2020). Do household consumption and saving preferences vary between birth-year cohorts in Turkey? Central Bank of the Republic of Turkey Working Paper, 20(15), 1-30.
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  • Cilasun, S.M. (2009). Income, consumption and saving behavior of Turkish households. Doktora Tezi, Orta Doğu Teknik Üniversitesi Sosyal Bilimler Enstitüsü, Ankara. ss.1-205.
  • Cilasun, S.M. ve Kırdar, M.G. (2009). Türkiye’de hanehalklarının gelir, tüketim ve tasarruf davranışlarının yatay kesitlerle bir analizi. İktisat İşletme ve Finans Dergisi, 24(280), 9-46. DOI: 10.3848/iif.2009.280.2791
  • Cilasun, S.M. ve Kırdar, M.G. (2012). Household structure, and household ıncome and its components over the life-cycle in Turkey. Turkish Economic Association Discussion Paper, 63, 1-35. DOI: http://hdl.handle.net/10419/81620
  • Çolak, Ö.F. ve Öztürkler, H. (2012). Tasarrufun belirleyicileri: küresel tasarruf eğiliminde değişim ve Türkiye’de hanehalkı tasarruf eğiliminin analizi. Bankacılar Dergisi, 82, 3-44.
  • Deaton, A. (1985). Panel data from time series of cross-sections. Journal of Econometrics, 30(1-2), 109-126. DOI: https://doi.org/10.1016/0304-4076(85)90134-4
  • Deaton, A. (1991). Saving and liquidity constraints. Econometrica, (59)5: 1221-1248. DOI: 10.3386/w3196
  • Deaton, A. (1992a). Understanding consumption. Clarendon, Oxford University Press, New York, first published. pp.1-214.
  • Deaton, A. (1992b). Saving and income smoothing in Cote d'lvoire. Journal of African Economies, 1(1), 24-26. DOI: https://doi.org/10.1093/oxfordjournals.jae.a036737
  • Deaton, A. (1997). The Analysis of household surveys, A microeconomic approach to development policy. The Johns Hopkins University Press. Baltimore and London, pp.1-474.
  • Deaton, A. ve Paxson, C. (1994a). Intertemporal Choice and Inequality. The Journal of Political Economy, 102(3), 437-467.
  • Deaton, A. ve Paxson, C. (1994b). Saving, growth, and aging in Taiwan. Studies in the Economics of Aging. Wise, D.A. (Ed.). University of Chicago Press, Chicago, pp. 331-362.
  • Deaton, A. ve Paxson, C. (2000a). Growth, demographic structure, and national saving in Taiwan. Population and Development Review, 26, 141-173.
  • Deaton, A. ve Paxson, C. (2000b). Growth and saving among individuals and households. The Review of Economics and Statistics, 82(2), 212-225.
  • Deaton, A. ve Paxson, C. (1998a). Aging and inequality in income and health. The American Economic Review, 88(2), 248-253.
  • Deaton, A. ve Paxson, C. (1998b). Health, income, and inequality over the life cycle. Frontiers in the Economics of Aging. Wise, D.A. (Ed.). University of Chicago Press, Chicago, pp. 431-462.
  • Deaton, A. ve Paxson, C. (1998c). Saving and growth: another look at the cohort evidence. Research Program in Development Studies Princeton University, 225, 1-32.
  • Dynan, K.E. (1993). How prudent are consumers? Journal of Political Economy, 101(6), 1104-1113. DOI: http://dx.doi.org/10.1086/261916
  • Flavin, M.A. (1981). The adjustment of consumption to changing expactations about future income. The Journal of Political Economy, 89(5), 974-1009. DOI: http://dx.doi.org/10.1086/261016
  • Friedman, M. (1957). A theory of the consumption function. Front Matter. Princeton University Press, New York, pp:1-240.
  • Gourinchas, P.O. ve Parker, J.A. .(1999). Consumption over the life cycle. NBER Working Paper Series, 7271, 1-47.
  • Güngör Parlakyiğit, M. (2020). Hanehalkı tasarruf eğiliminin belirleyicileri: Türkiye üzerine bir uygulama. Doktora Tezi, Gaziantep Üniversitesi Sosyal Bilimler Enstitüsü, Gaziantep, ss.1-236.
  • Hall, R.E. (1978). Stochastic implications of the life cycle-permanent income hypothesis: theory and evidence. Journal of Political Economy, 86(6), 971-987.
  • Hall, R.E. ve Mishkin, F.S. (1982). The sensitivity of consumption to transitory ıncome: estimates from panel data on households. Econometrica, 50(2), 461-481.
  • Hansen, L.P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029-1054.
  • Hsiao, C. (2003). Analysis of panel data. Cambridge University Press, New York, pp:283-585.
  • İpek, E. ve Sekmen, Ö. (2016). Household savings in Turkey: evidence from microdata. Balkan and Near Eastern Journal of Social Sciences, 02(04), 102-108.
  • Jappelli, T. (1999). The age-wealth profile and the life-cycle hypothesis: a cohort analysis with a time series of cross-sections of Italian households. Review of Income and Wealth, 45(1), 57–75. DOI: https://doi.org/10.1111/j.1475-4991.1999.tb00312.x
  • Jappelli, T. ve Modigliani, F. (1998). The age-saving profile and the life-cycle hypothesis. CSEF Working Paper, 9, 1-26.
  • Jappelli, T. ve Modigliani, F. (2005). The age-saving profile and the life-cycle hypothesis. The Collected Papers of Franco Modigliani Franco, F. (Ed.). Volume 6. Massachusetts Institute of Technology Press, Cambridge, pp.141-172.
  • Jappelli, T., Padula, M. ve Pistaferri, L. (2007). A direct test of the buffer-stock model of saving. CSEF Working Paper, 29, 1-35.
  • Jappelli, T. ve Pistaferri, L. (2000). The consumption response to income changes. CSEF Working Paper, 237:1-52.DOI:0.1146/annurev.economics.050708.142933
  • Jappelli, T., Pistaferri, L. ve Weber, G. (2006). Health care quality, economic ınequality, and precautionary saving. Health Economics, 16(4): 327–346. DOI:10.1002/hec.1172
  • Kızılgöl, Ö.A. ve İpek, E. (2019). Türkiye’de hanehalkı tasarruf davranışının analizi. İzmir İktisat Dergisi, 34(3):331-344.
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  • Öksüz Narinç, N. ve Küçükönder, H. (2020). Hanehalkı tasarruf tercihlerinin ardışık logit modelle belirlenmesi: Türkiye örneği, İşletme Araştırmaları Dergisi, 12(2):1554-1572. DOI: 10.20491/isarder.2020.929
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  • Rijckeghem C.V. ve Üçer M. (2009). The evolution and the determinants of the Turkish private saving rate: what lessons for policy? Koç Üniversitesi-TÜSİAD Economic Research Forum Çalışma Tebliği, 09(01), 1-94.
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  • Şengür, M. ve Taban, S. (2016a). Gelir dağılımı-tasarruf ilişkisi: Türkiye’de hanehalkı gelir türünün tasarruflar üzerindeki etkisi. Anadolu Üniversitesi Sosyal Bilimler Dergisi, 16(1), 49-72.
  • Şengür, M. ve Taban, S. (2016b). Türkiye’de hanehalkı tasarruflarının gelir dışındaki belirleyicileri. Optimum Ekonomi ve Yönetim Bilimleri Dergisi, 3(1), 29-53. DOI: https://doi.org/10.17541/oeybd.84848
  • TCMB Elektronik Veri Dağıtım Sistemi. (15.06.2017). http://evds.tcmb.gov.tr/
  • Türkiye İstatistik Kurumu, Hanehalkı Bütçe Anketi 2002-2013.
  • Yao, R., Wang, F., Weagley, R.O. ve Liao, L. (2011). household saving motives: comparing American and Chinese consumers. Family & Consumer Sciences Research Journal, 40(1), 28–44. DOI: https://doi.org/10.1111/j.1552-3934.2011.02086.x
  • Yılmazer, T. (2010). The profile and determinants of household savings. Report for the World Bank,1-53.
  • Yükseler, Z. ve Türkan, E. (2008). Türkiye’de hanehalkı: işgücü, gelir, harcama ve yoksulluk açısından analizi. TÜSİAD Economic Research, 03(455), 1-155.
  • Zeldes, S. P. (1989). Optimal consumption with stochastic income: deviations from certainty equivalence. The Quarterly Journal of Economics, 104(2), 275-298. DOI: https://doi.org/10.2307/2937848
Toplam 89 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Ekonomi
Bölüm İktisat
Yazarlar

Merve Güngör Parlakyiğit 0000-0002-6546-3415

Ömer Özçiçek 0000-0001-5617-2360

Yayımlanma Tarihi 30 Nisan 2022
Gönderilme Tarihi 7 Ekim 2021
Kabul Tarihi 8 Aralık 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 21 Sayı: 2

Kaynak Göster

APA Güngör Parlakyiğit, M., & Özçiçek, Ö. (2022). TÜRK HANEHALKI TASARRUF DAVRANIŞLARININ SENTETİK PANEL VERİ İLE TAHMİN EDİLMESİ. Gaziantep University Journal of Social Sciences, 21(2), 645-674. https://doi.org/10.21547/jss.1004454