Essays in macroeconomics and finance: Essay~I. Money demand, seigniorage and the welfare cost of inflation: Evidence from an intertemporal model of money and consumption for the United States economy. Essay~II. Implementation of the Heath-Jarrow-Morton an

Essay I. The first essay emphasizes that it is crucial to identify the proper specification of money demand as well as the appropriate definition of monetary aggregate and scale variable to find the exact welfare cost of inflation. The econometric test results obtained from the nonlinear form of money demand with Box-Cox restriction indicate that not the semi-logarithmic form but the double-log form with constant elasticity of less than one is a more accurate characterization of the actual data. Furthermore, the empirical results suggest that consumption spending produces more stable measures of monetary velocity and outperforms GDP in estimated money demand equations for the United States. This paper also shows the estimated welfare cost of inflation is proportional to the money stock and since M1 is about three times the monetary base in the United States, identifying M1 without modeling the distinctive roles of currency and deposits as the relevant definition of money overestimates the true welfare cost of inflation. I estimate the welfare cost of inflation for the U.S. economy using Bailey's (1956) consumer's surplus and Lucas's (1993) compensating variation approaches. The welfare cost estimates imply that for each monetary model (currency-deposit, single-asset) and each scale variable (income, consumption) the double-log function, compared to the constant semi-elasticity Cagan-type demand for money, yields substantial welfare gains in moving from zero inflation to the Friedman optimal deflation rate needed to bring nominal interest rates to zero. Essay II. The second essay explains arbitrage-free term structure models used for pricing options on Eurodollar Futures with particular emphasis on the Black-Derman-Toy (BDT) and the Heath-Jarrow-Morton (HJM) interest rate models and their applications. In this essay, I concentrate on valuing options on Eurodollar futures using the BDT and the HJM models with different volatility structures. I compare the estimated option prices of Eurodollar futures with the actual values to determine which of these two models (specified with different dynamics of interest rate volatility: historical volatility, exponentially smoothed volatility, implied volatility, GARCH, GARCH-X) perform better in pricing interest rate sensitive derivative securities.