代写assignment|收入和利率在确定房价中的作用

代写assignment|收入和利率在确定房价中的作用
The Role of Income and Interest Rates In Determining House Prices

我提出的假设是，利率和家庭收入的变化，对英国房价产生不同的影响。在过去的20年里，我将分析数据，使我的研究更为最新。这将有助于证明我的假设在英国经济的相关性，由于经济衰退所带来的剧烈变化。我的目标是发现利率的变动与房屋的价格是一致的。这是说，如果有一个下降的抵押贷款利率，这将反过来导致住房价格的增加。这种存在的原因是，较低的利率将导致房屋需求增加，因为家庭更愿意自己的房子，总是减少住房供应。随着住房的供应超过需求，因此，不平衡；通过法律的需求和供应，这将导致在消耗存量住房价格的增长。我也的目标是将家庭收入水平，因为这有一个影响，对贷款的数额，可以从金融机构贷款。

The hypothesis I have put forward states that the changes in interest rates and household income, exert different impact on house prices in the United Kingdom. I will be analysing data over the past 20 years making my research more up to date. This will help prove the relevance of my hypothesis in the UK economy given the drastic changes brought about by the recession. I aim to find that movements in interest rates are in line with the price of houses. This is to say that if there is a decrease in the mortgage interest rate, this will in turn lead to an increase in the price of housing. The reason for this being that a lower interest rate will cause demand for houses to increase, as households are more willing to own houses, invariably reducing the supply of housing. With the demand of housing exceeding its supply, there is therefore disequilibrium; and by the laws of demand and supply this will result in an increase in the price of the depleting housing stock. I also aim to incorporate the household income levels as this has an influence, on the amount of loans that can be borrowed from financial institutions.

A theoretical model of house prices will be created and variables will be defined:
P-t is the actual house prices.
Bt is the amount of loan that can be borrowed.
St is the supply of housing stock in the UK.
Yt is the disposable income per UK household.
Rt is the mortgage interest rate.
τ is the duration of mortgage.
κ is the proportion of household income going on mortgage repayments.

One of the key variables involved is the actual house price data ranging from 1990 to 2009, which has been sourced from the Regulated Mortgage Survey (CML) and it is the mix-adjusted average of house prices. This is to say that different types of properties have taken into consideration while calculating the average and it simply isolates price changes during the year. I have chosen this as it is a more accurate measure because whilst the year-on-year change in the simple average house price can be used as a rough estimate of house price inflation, it is not ideal. This is because movements in the simple average house price can be affected by changes in the proportions of different property types being sold from one year to the next. Although inflation is not being looked at in detail, it is important that it is taken into consideration.

I sourced the quarterly supply of housing of data between 1990 and 2010 from Housing Statistics and it includes completed dwellings and those of which, construction work has been started on. I assume this would potentially give an insight as to future housing projections.

With regards to the disposable income per household variable, the data collected was sources from the Office of National Statistics (ONS). Although I will be focusing on real disposable income over from 1990-2010 it should be said, that over the past 40 years, UK households spending pattern has changed. Households are seen to spend less on goods in recent times (precisely 46 per cent in 2008 from the 66 per cent level in 1970) and considerably more, on services. This can be attributed to the decline and rise of manufacturing and service sectors respectively in the UK; an issue that should be addressed by the government to further promote economic growth. I will interpolate this data to arrive at a series for disposable income per UK household annually

In relation to mortgage interest rates, the vast majority of mortgage credit during my sample will be at variable rates i.e. rates that are fixed for a period less than one year and this account for a majority of the outstanding stock of mortgage debt and about the same amount of new lending over the past years. Hence the use a variable rather than a fixed mortgage rate in my study. The source of the data is provided by the Bank of England. I will be finding the correlation between the actual price level and the amount that can be borrowed based on the first equation. A high correlation between the series would therefore suggest a long term relationship between actual house prices and the price based on the average amount borrowed. I will also be performing cointegration tests based on Johansen's (1995) systematic approach to testing for cointegration between the actual price and the amount that can be borrowed. Based on my results from my cointegration test, I will proceed to estimate a long run relationship between the logs of the actual house prices and the amount that can be borrowed. I will be employing the dynamic ordinary least squares (DOLS) methodology of Stock and Watson (1993). The DOLS estimator falls under the single-equation Engle Granger (Engle and Granger, 1987) approach to cointegration while allowing for endogeneity (i.e. when correlation exists between a parameter or variable and an error term) is within the specified long run relationships.

Data relating to K which is the amount of household income that goes on mortgages, is provided by the Office for National Statistics and the Council of Mortgage Lenders. Figured show that as of July 2010, households spend 13.5 per cent of their income on mortgage repayment.

In this model, the demand side factors are being looked at in detail with respect to income and interest rates. I particularly argue that housing demand is primarily a function of the amount that potential home-owners, can borrow from financial institutions and is in turn, depends on the mortgage rate in that time period and also the current disposable income. This lead me to the term, annuity. This is a fraction of a households' current disposable income signified by κYt, that goes towards mortgage repayments and is treated by discounting, at the present mortgage interest rate such that it is equal to the mortgage term τ. This leads on to the derivation of the amount of financing that can be borrowed B-t

This equation, in reality simulates the idea that people seek to maximise the amount of leverage available to them. This equation is then going to be integrated within a more generalised model of the housing market as seen below.

From the model above, I have firstly defined Xt as the time-varying component of Bt as I have not taken into consideration, the proportion of household income that goes towards mortgage repayments. Secondly I have incorporated the time varying component (Xt) and proportion of household income going on mortgage repayments (κ) into an inverted demand function of:

Following basic economic theory I assume a downward sloping demand curve with the price elasticity of demand for housing indicated by the inverse of the parameter μ. Changes in income or interest rates are the demand shifting factors in this context. The housing supply variable S comes into this function through the own price elasticity thus resulting in negativity. 

Delta is the supply functions intercept which primarily causes shifts in the supply of housing stock. Which is determined by construction firms and government policies that affect them? It should be noted that supply is assumed to be inelastic in the short-run as there is a time interval in the provision of new-builds (S=S^-). Furthermore, house prices in the short-run depend on the amount of funding that can be borrowed by households in that time period.