This paper uses the semi-structural Laubach and Williams model to estimate the time- varying natural rate of interest by Kalman filter and Maximum Likelihood method, applying it for the first time to Czech data. The results show a significant decrease of the natural interest rate during the past decade, which constitutes further evidence for the wide-spread notion that structural factors in many countries have shifted after the global financial crisis. The paper's contribution is mainly represented by preparing ground for further research. It concludes that the basic version of the Laubach and Williams model is not optimal for the Czech environment and suggests appropriate adjustments to it. It discusses and analyzes sources of potential problems with the estimation, notably the issues of singularity and model specification. Eventually the paper concludes that due to the low significance of results and the uncertainty of gains and losses related to a policy switch, the best reaction of the central bank would be to keep the current regime and inflation target. JEL Classification C32, E43, E52, O40 Keywords natural real interest rate, inflation target, inflation measurement, monetary policy, Kalman filter, trend growth Author's e-mail lucie.scheer@gmail.com Supervisor's e-mail tomas.holub@fsv.cuni.cz v

[pt] Eu desenvolvo um modelo de gerações sobrepostas com crescimento salarial ao longo do ciclo de vida (LCWP, por sua sigla em inglês), taxa de mortalidade dependente da idade, restrições de liquidez e rigidez nominal. O modelo é calibrado para capturar a transição demográfica dos EUA, estimativas de LCWP e outras características importantes da economia dos EUA durante o período 3;72-4239. O modelo é usado para examinar a relação entre dados demográficos e taxas de juros reais assim como os principais mecanismos de transmissão em jogo. Eu encontro que o rápido aumento da população em idade ativa entre 3;72 e 3;:2 contribuiu significativamente para o aumento das taxas de juros reais. A reversão desse processo, juntamente com o aumento da expectativa de vida, desencadeou um rápido declínio nas taxas de juros desde então. A heterogeneidade na propensão marginal a consumir entre os trabalhadores desempenha um papel importante na conexão desses movimentos de fertilidade e taxa de juros real. Num exercício adicional, devido à evidência de grandes erros de previsão da expectativa de vida, eu estendo o modelo com um processo de aprendizado sobre longevidade e encontro que ele pode aumentar significativamente a relevância de fatores demográficos na explicação dos movimentos reais das taxas de juros. Por fim, encontro que a falha dos bancos centrais em levar em conta a relação entre dados demográficos e taxas de juros pode gerar, devido a mudanças não monitoradas na taxa de juros natural, variações na taxa de inflação. / [en] I develop an overlapping generations model with life cycle wage profile (LCWP), age-dependent mortality rate, liquidity constraints, and nominal rigidities. The model is calibrated to capture US demographic transition, LCWP estimations, and other salient features of the US economy during 3;72-4239. The model is then used to examine the relationship between demographics and real interest rates and the main transmission mechanisms in play. I find that the rapid increase in the working age population from 3;72-3;:2s has significantly contributed to the rise of real interest rates. The reversion of this process together with the increase in life expectancy triggered a rapid decline in the interest rates ever since. The heterogeneity in the marginal propensity to consume among workers plays a major role in connecting these fertility and real interest rate movements. In an additional exercise, due to the evidence on large life expectancy forecast errors, I introduce a learning process about longevity and find that it can significantly a ugment t he r elevance o f d emographic f actors in explaining real interest rate movements. Finally, I find t hat t he central banks failure to recognize the relationship between demographics and interest rates can generate, due to unaccounted changes in the natural interest rate, inflation rate variations.

台灣幅員狹小，天然資源不足，唯有藉著大量出口才能換取外匯，情況使得台灣逐漸發展成一小型開放經濟。長久以來，美國一直是台灣最大的貿易夥伴，使得台灣產品對美輸出的多寡往往直接影響台灣總體經濟的表現。隨著政府外匯政策的逐漸自由化，匯率在總體經濟中所扮演的角色也越顯重要。近幾年來，台幣匯價在外匯市場上時有波動，不但影響政府政策的擬定、經貿活動的往來，外匯市場上的投炒作更造成熱錢的流動。是故，新台幣對美元匯率的決定及波動因素是值得我們深入探討的課題。基於此點，本文擬建立一個可供實証的小型開放經濟模型，試圖探討新台幣對美元匯率的決定因素。首先，參照Frankel(1979)所提出的實質利率差價模型(Real Interest Rate Differential Model)，作為實証研究的基礎。其次，利用Johansen(1988,1991)、Johansen & Juselius(1990)的共整合(cointegration)分析方法，以台灣地區1981年至1993年間的月資料，驗証縮減式的長期關係是否成立。最後，採用誤差修正模型(error correction model)，估計匯率的動態調整途徑，並對匯率變動率進行樣本後預測。 　　實証結果發現：(1)實質匯率差價模型所刻畫的匯率與其他經濟變數的長期關係在台灣是可以成立的；(2)傳統貨幣學派對兩國結構喜數相同的假設過於嚴苛，對於台灣及美國並不適用；(3)除了名目利率外，台灣及美國的貨幣供給、產出水準及通貨膨脹率具有一對一的關係；(4)以誤差修正模型預測台幣／美元匯率變動率，其效果優於隨機漫步模型。

The aim of this study was to highlight the final evaluation of the money invested in pension insurance due to the client's age and to develop model examples for various types of participants in pension plans. This aim of the study was achieved through the data collection, analysis, calculation and deduction of results.The performed analysis allowed to assess the profitability of pension. It enabled insight into the situation III. pillar pension system. It referred to the total amount saved after the end of the savings and to the number of percentage return the savings bring.It was concluded that pension schemes are only worth it for a short term. After some time, profitability is greatly reduced.

Submitted by Felipe Verceze Augusto (felipea60@gmail.com) on 2018-08-29T19:37:38Z No. of bitstreams: 1 dissertação felipeaustoversaomkmv5.docx: 408849 bytes, checksum: 14de694c8b7e6dbd8c416aa45fdad1db (MD5) / Approved for entry into archive by Joana Martorini (joana.martorini@fgv.br) on 2018-08-29T20:39:47Z (GMT) No. of bitstreams: 1 dissertação felipeaustoversaomkmv5.docx: 408849 bytes, checksum: 14de694c8b7e6dbd8c416aa45fdad1db (MD5) / Approved for entry into archive by Suzane Guimarães (suzane.guimaraes@fgv.br) on 2018-08-30T12:10:47Z (GMT) No. of bitstreams: 1 dissertação felipeaustoversaomkmv5.docx: 408849 bytes, checksum: 14de694c8b7e6dbd8c416aa45fdad1db (MD5) / Made available in DSpace on 2018-08-30T12:10:47Z (GMT). No. of bitstreams: 1 dissertação felipeaustoversaomkmv5.docx: 408849 bytes, checksum: 14de694c8b7e6dbd8c416aa45fdad1db (MD5) Previous issue date: 2018-08-02 / Este trabalho propõe estimar a taxa de juro real neutra para o mercado brasileiro, utilizando uma metodologia abordada por autores como Perreli e Roache (2014) e Goldfajn e Bicalho (2011). Utilizando variáveis estruturais, baseado em fundamentos econômicos e conjunturais, os autores buscam estimar a taxa neutra de juro separando-a de acordo com o período, isto é, em taxa de juro de longo prazo e curto prazo. Após a análise destes estudos, foram estimados modelos a partir da mesma metodologia,isto é, buscando estimar a taxa neutra de juro entre longo e curto prazo, no período de 2003 à 2017. A partir desses estudos analisados foi possível verificar o impacto das variáveis de forma mais didática. Para os resultados de longo prazo, variáveis como crédito e surpresa inflacionária mostraram uma grande siginificância, já para a estimação de curto prazo, foram as variáveis de crédito direcionado e confiança do consumidor que tiveram grande significância, como também veremos nesse trabalho. Como será utilizado uma amostra de 15 anos, é possível fazer essa análise para diversos governos e diferentes gestões do Banco Central brasileiro. Com a estimação feita neste estudo também poderá ser viável acompanhar a condução de política monetária do Banco Central e sua assertividade. / This paper proposes to estimate the real neutral interest rate for the Brazilian market and uses a methodology addressed by authors such as Perreli and Roache (2014) and Goldfajn and Bicalho (2011). Using structural variables, based on economic and conjunctural fundamentals, the authors seek to estimate the neutral interest rate by separating it according to the period, that is, in long-term and short-term interest rates. After analyzing these studies, models were estimated using the same methodology in the period from 2003 to 2017. The studies allowed us to analyze the impact of the variables in a more didactic way. For the long-term results, variables such as credit and inflationary surprise showed a great significance, for the short-term estimation, were the directed credit and consumer confidence variables that had great significance, as we will see in this work. With the estimation made in this work it is also possible to follow the conduct of monetary policy of the Central Bank and its assertiveness. As the work covers a sample of 15 years, we can make this analysis for several governments and different managements of the Brazilian Central Bank.

[pt] Eu desenvolvo um modelo de ciclo de vida para avaliar a importância relativa de vários determinantes de londo prazo da taxa de juros. O modelo é uma generalização de Gertler (1999), incluindo imperfeições no mercado de crédito e heterogeneidade entre trabalhadores para capturar totalmente os efeitos da transição demográfica. O modelo é calibrado para a economia brasileira, incluindo perfis para os gastos do governo, gastos com previdência, dívida pública, crescimento da produtividade e variáveis demográficas. O modelo explica 71 porcento da variação total na taxa de juros brasileira entre 2000 e 2019. Fatores demográficos, especialmente aumentos na expectativa de vida, são os principais determinantes da queda nas taxas de juros reais. Essas forças são parcialmente compensadas por aumentos na dívida pública e nos gastos com previdência. Além disso, o arcabouço sugere que as taxas de juros reais continuarão caindo nos próximos 20 anos, atingindo o patamar de 1.5 porcento a.a., apesar de aumentos razoáveis na dívida pública. No entanto, possíveis efeitos de prêmios de risco e juros globais nas taxas de juros domésticas não são incluídos na análise. / [en] I develop a life cycle model to evaluate the relative importance of several long-term drivers of real interest rates. The model is a generalization of Gertler (1999), including credit market imperfections and heterogeneity among workers to fully capture the effects of the demographic transition. I calibrate the model to the Brazilian economy, feeding it with profiles for government spending, public debt, productivity growth and demographic variables. The model explains 71 percent of the overall change in real interest rates in Brazil between 2000 and 2019. Demographic factors, especially increases in life expectancy, are the key drivers of the fall in real interest rates. These forces are partially compensated by increases in public debt and social security spending. Moreover, the framework suggests that real interest rates will keep falling over the next 20, reaching a level of 1.5 percent despite reasonable increases in government debt. However, possible effects of risk premia and global rates on domestic interest rates are absent from the analysis.