# Interest Rate Pass Through Test In The Uk Finance Essay

Monetary policy is a very important instrument for government managing the economy. Compared with the other major macro-control instrument, fiscal policy, monetary policy could not make a difference at once but has much more powerful profound influences to real economic activities. That is because the monetary transmission mechanism could magnify and spread the effects through financial market (注释，货币非中性). To achieve different results, there are many kinds of monetary policy tools. They are interest rate, monetary base, reserve requirements, discount window lending, currency board and unconventional monetary policy at the zero bound.

Interest rate is significant to the whole economy through the transmission mechanism of monetary policy. According to economics situation, central bank would raise or reduce its official rate. For example if the economy is in a downturn trend, central bank may reduce the official rate to stimulate economy. The process is that the lower central rate would steer the money market rate going down, which is the main part of retail banks’ marginal pricing costs. Then the deposit and loan rates of the retail banks would fall considering the lower cost and the competition in the bank market. Hence with lower interest rate, investment and consumption would be enlarged by the holders and borrowers of the deposits. The transmission could be quick and powerful, or slow and ineffective dependent on the economy’s characteristics.

Normally there is a common view that a fast and complete interest rates band means a high efficient monetary transmission, thus the monetary policy is effective and could affect price stability. Furthermore, prices set by banks influence their margins and therefore bank profitability and consequently the soundness of the banking system and thus financial stability. (Gabe J. de Bondt, 2005).

We could let the interest-rate pass-through be a sign of the monetary policy efficiency and financial stability. In particular, it is crucial to assess the speed and degree of the pass through from official and money market rate to the retail bank rates. Normally, a high level interest-rate pass-through in short term is a good characteristic, which means the government’s monetary policy could be transferred into the market effectively and quickly without too much cost.

UK case

United Kingdom is a high developed and industrialized country, thus to maintain a stable financial and economy environment, its effectiveness of monetary policy should be under an intensive attention. Presumably the interest-rate pass-through of United Kingdom should be fast and complete since the banking system and financial market have been fully developed. In other words, once the official rate changes, the retail bank rates would have a corresponding movement in short term, and fully in long term. But actually the retail bank rates depend on a lot of factors, not just the money market rate. Hence we need to assess the interest-rate pass-through and analyze how much it reflects the effectiveness of the monetary policy.

前人成绩

Since the interest-rate pass-through is a very important topic in the policy investigation, there have been many studies on it. Recent years, cross-country comparison is a hot topic especially in the euro area due to the euro introduction.

Christoffer kok Sørensen and Thomas Werner(2006）investigated the cross-country pass-through comparison by a new panel-econometric methods to test for the heterogeneity in the process. What’s more, they matched the maturities of the bank and money market rates in their paper and found a high degree of heterogeneity of the pass through in euro area, which means there may be some fragmentation or lack of integration in retail bank market.

Apart from cross-country research, studies after 1995 found that the pass through is low after 3 months from official and/or money market rates to the short-term bank lending rates to enterprises, but higher in long term(BIS, 1994; Cottarelli and Kourelis, 1994; Borio and Fritz, 1995). Similar results were found by Gabe De Bondt (2002) that the highest pass-through is around 50% in short term, but the long one is close to 100%. In the area of the affecting factors, Gabe de bondt, Benoît Mojon and Natacha Valla(2005) took a lot of efforts on the resource of the sluggishness of retail bank interest rates, and found out the short term market rates is the key factor. Leonardo Gambacorta (2005) focused on the cross-sectional differences model and provided the heterogeneity in the banking rates pass-through in micro level. Boris Hofmann and Paul Mizen (2001) found that the level of pass-through is affected by the ‘gap’ base and retail rates. The adjustment speed is quicker when the gap is widening and slower when it is narrowing. Stefanie Kleimeier and Harald Sander (2005) concluded that the pass-through is also related with the communication between the policy maker and the market players.

As we can see from the previous literatures, the investigations on interest-rate pass-through could provide loads of information about the proportion, determinants and effects to economy.

本文工作

In this paper, we are going to assess the household interest-rate pass-through in United Kingdom banking system. The pass-through is from the official rate/ money market rate to retail banks rates, deposit (lending) rates from (to) household. We could obtain much information about the effectiveness of the monetary policy through this investigation. There have been lots of papers on this issue separating the banking market into deposit market and lending market according to the goods kinds (deposits and lending). I would like to separate the banking market refer to the participants. In United Kingdom financial market, the participants (excl. central bank) are Public Sector, Central and Local Government, Public Corporations, Banks, Building Societies (加注释), Monetary financial Corporations, Other Financial Corporations, Private Non-Financial Corporations, Households and Non-Profit Institutions. Considering household is a basic department in macro economy, I am focusing on household in this paper.

Since in the retail banks level, there are many kinds of interest rates so that we cannot draw a conclusion just estimating one or two sets of data. We will test the pass-through by various rates to get a more credible result.

I am going to establish the dynamic function and long run relationship variable (error-correction model) between central bank rates and retail bank rates. We are going to assess the sample from 1995 January to 2008 June ruling out the huge structure break due to the financial crisis.

本文贡献

The present writing mainly dedicates to analyzing the pass through for different kinds of retail banks rates with different maturities. Further more, different to the previous works separate the retail rates into deposit and loan. I would like to category into household market rates and enterprise. That is because retail bank rates are formed by the market power, we had better analysis them in the same market segment.

The paper starts with a literature review in Section One and explanation of the model section Two. After an introduction of the econometric methodology in section Three, the data and empirical results are presented separately in section Four and Five. Section Six is conclusion.

## Literature review 2000~3000(about 3500)

The transmission of monetary policy has two stages which is the process of interest-rate pass-through as well. The first stage is in the money market that the changes of the central bank rate would be transmitted to the money market rates (both short- and long-). The second stage is in the banking system that as a part of bank’s funding cost, money market rates would spread the influence to retail bank rates (deposit and loan, short maturity and long).

Most literatures focused on the second stage, particularly in the view of retail banks’ costs. There are three main costs that marginal pricing cost, switching cost and asymmetric cost.

“Interest rate pass-through: empirical result for euro area” (Gabe J. de Bondt 2005) expressed the bank rates by the marginal pricing cost in a linear function model. The bank rate is the dependent variable and the market rate is the independent variable. The bank rate equals to the reflection to the market rate plus a mark-up, and the reflection is proportional to market rate.

Estimating switching costs: the case of banking (Moshe Kim, Doron Kliger, and Bent Vale, 2001)

Besides the literature on the theory development, there are a lot of works on econometrics development.

Bank interest-rate pass-though in the euro area a cross country comparison (Christoffer kok Sørensen and Thomas Werner, 2006)

Background of UK banking system 英格兰银行介绍 701√

Bank of England

The bank of England is the central bank of United Kingdom from 27 July 1694 when the bank began to be the government’s bank and debt-manager. Nowadays besides the roles in old time, the bank is also dedicated in promoting and maintaining monetary and financial stability. Same to other central banks in the world, it is at the centre of the financial system and deploys policies.

However the bank of England has its own distinguishing feature compared with other central banks. It does not have the monopoly as big as other banks. Although in 1997 the bank of England got the full operational responsibility for monetary policy, HM treasury (The UK’s economics & finance ministry) is taking the charge of debt management and the new Financial Service Authority(regulator of the financial services industry) is on the Bank’s regulatory functions.

Obviously, in 1997 the key evolution gave the Bank of England operational independence to make monetary policy. What’s more, it could specify a point inflation target. Despite somewhat controversial at the beginning, the independence of the Bank is now strongly and widely supported.

As the banks’ bank, central bank is responsible to forecast money flows fairly and accurately. Since there are huge amounts of money flows between Government and commercial banks, central bank plays a critical role as a bridge, transferring and smoothing the imbalances. For instance central bank may publish that banks’ holding liquid assets are run down if more money flows to the Government account.

As the final supplier of cash to the economy, central bank is up to setting interest rate. Because the interest rate takes the main account on funding cost, the level of interest rate heavily affects how fast and how much fund is passed throughout the financial system and the whole economy. Thus in a certain sense, setting interest rate is more important than the forecast job for central bank.

Monetary policy history [1]

In the last 50 years of 20th century, monetary policy in UK changed many times with the evolution of politics and economy. The monetary policy became more and more important, public and prominent. In 1950s and 60s, monetary policy was deployed in direct controls(注释，direct and indirect control). Banks and individuals had many limits. In the 1970s, the United Kingdom's economic profile was not quite good, volatile growth and cyclical high inflation. UK's monetary policy was gradually transited to a much more market-related method. In 1971, 'Competition and Credit Control', new framework, gave interest rate a bigger role and lifted the limits on lending. Two years later, 1973, 'Supplementary Special Deposit Scheme' re-introduced the limits, but it was abolished in 1980 eventually. In 1980s, the new Conservative government of Mrs. Thatcher set targets for the growth of the money supply (注释，出处Medium Term Financial Strategy). In the mid-1980s, monetary policy placed extra emphasis on informal exchange rate target, which was replaced by a formal one in the shape of ERM membership from 1990 to 1992. In 1990s, it was the first time adopted an explicit inflation target. In 1997, the new Chancellor, Gordon Brown, gave the Bank 'operational independence' to achieve the inflation target. In 2003, the target inflation rate was set at 2%.

SETTING INTEREST RATE

UK's monetary policy is executed for economy stability. Meeting the inflation target is a sign of stability since it is a compound issue whether the economy is stable or not. 2% is the current inflation target [2] . It should be noted that the target is symmetrical since the inflation below 2% is as bad as above. Theoretically, Bank Rate is increased to reduce inflation, and decreased to raise it. Interest rates are set by a special committee, the Bank’s Monetary Policy Committee (MPC), to meet the inflation target [3] . MPC's aim is to set interest rate bringing the inflation back to target within a proper time period avoiding economy instability. The MPC meets every month to set the interest rate through analysis and vote. Thus the interest rate could be adjusted in time if the economy changed a lot. Furthermore, the MPC is responsible to explain the interest rate decision publicly, which increases policy's transparency.

## Interest-rate pass-through model 1000 (about 5500) 1439√

(一)Theory( process; 2 stag; incomplete reasons) 905

INTEREST RATE PASS THROUGH

--http://www.bankofengland.co.uk/monetarypolicy/overview.htm#meetings

Monetary policy process 400√

Official interest rate is the most common instrument which could influence the overall expenditure. There will be an increasing inflation if the growth of money spent is higher than output produced growth. Hence the adjustment of official rate could affect the expenditure, the money spent, and then control the inflation. After the central bank sets an official interest rate, there will a series of process transferring the policy effects to the institutions and individuals in the economy, controlling the inflation rate eventually.

Official Rate

Market

Rates

Asset

Prices

Expectations/

Confidence

Next external

Demand

Domestic

Demand

Exchange

Rate

Total

Demand

Import

Prices

Domestic

Inflationary

Pressure

Inflation

The figure shows the monetary policy process in United Kingdom. Firstly, the changed official rate would affect the financial market first. Commercial banks, building societies and other institutions would adjust their interest rate facing the new official rate. Since the close relationship between interest rate and yield curve, the financial assets would be re-evaluated and re-priced such as bonds and shares. Secondly, as a funding cost and opportunity cost for saving, a lower interest rates could stimulate spending, in the other hand, reduce the income from savings and payments for loan interest. Rational borrowers would like to allocate more money in expenditure not lending. In this view, there will be magnificent influence to the whole economy. When interest rate goes up the opposite occurs. Thirdly, the spending willingness of Shareholders and property owners would be higher if the interest rate is lower. That is because the prices of assets lift when the interest rate reduce. What’s more Shareholders and property owners will extend their mortgages in order to increase consumption. Finally, as a member in the global open economy, lowering or raising interest rates will influence the exchange rate and then economy demand [4] . Unexpected interest rate increase would raise the sterling value. But appreciation will reduce the imports price and cut down the foreign demand for UK goods and services.

The four effects above would have influences to the external and internal demand in different ways. The aggregate influence would increase or decrease the total demand. Both of the new total demand and the influence from import price could change the output, income allocation, and eventually consumer prices. That is a general monetary policy process.

Usually the effect of monetary policy could be seen after a period of the policy published. The speed depends on many factor, for example whether the policy is credible. In general the healthy economy system could have a fast and complete effect.

Two Stags 212

This writing is studying a part of the process just mentioned, from the official rate to the market rates. The interest-rate pass-through is a description to the speed and completeness of this part. There are two stages composing the interest-rate pass-through. The first stage assesses the transmission from official bank rate to short- and long-term market rates. The second stage measures the changes of retail banks rates which are affected by the market rate.

Theoretically, the first stage pass-through has a link with the yield curve. Since the official rate could change the yield cure, the twist in the yield curve would adjust the size of pass-through [5] . The second stage is typically analyzed based on the funding cost theory. There are many factors ensure the market rates’ effects are transmitted onto the retail banks rates. For lending rate, the relationship between the market rates and retail rates is established by the fact that retail banks fund (short-term) lending from the money market. That is the direct funding cost, at the same time, there are many costs in the second stage. Yields from the government securities can be viewed as opportunity costs for banks. What’s more, banks also could pool fund from deposits and other financial products in the retail banking market.

INCOMPLETE REASONS 282

Theoretically, we could not find out a complete interest-rate pas-through in short run. In economics view, the elasticity of demand for deposits and for loans to the deposit and the lending rate, respectively, should be smaller than one in short-term [6] . Thus the pass-through could not be proportionate.

There are many factors leading to a inelasticity demand such as (1) imperfect substitution between bank lending and other kinds of external finance ( stock or bond markets), (2) imperfect substitution between bank deposits and other money market products (e.g. Treasure bills and money market funds). Since the bank and non-bank market are not perfect competitive, the sensitivity of the interest rate is reduced [7] . Furthermore, the inevitable switching costs could lower down the demand elasticity as well.

Besides the economics reasons, there are many factors affecting the pass-through in real world. Firstly, the most common one should be the economy size. In normal situation, big economy size means the country has an advanced banking system where the high pass-through could be found out. Similarly the size of the pass-through can be affected by the macroeconomic conditions. Generally under the rapid economics growth time, the pass-through is relatively high. That is because in good time there are abundant funds and resources in the market which is close to a perfect competition market. Thus the sensitivity of the interest rate should be high. Secondly, inflation rates play a big role in the pass-through as well. Higher inflation rates favour more rapid and complete pass-through. Thirdly, interest rate volatility will weaken the pass-through. The public would suspect the credibility of the monetary policy, so that, there would a resistance to retail rate following the policy rate.

(二)Assumption

For simplicity, we are going to set some assumptions which are reasonable for UK’s banking system and helpful to our assessment.

First, we use some main kinds of deposit and lending rates to represent the retail banks rates. That is because the deposits and lending of household and enterprise take a big account in banking business. What’s more, the rates are influenced a lot by market, the demand and supply. Hence they could provide much more general explanation to the market.

Second, we use the same retail bank rate among different banks, for example, the personal deposit rate is same in every bank. The perfect information theory and the high banking development could support this assumption. Nobody wants to deposit at a lower rate and lend at a higher one if all the banks are around where he/she lives.

Third, the marginal pricing cost decides the retail bank interest rates. Here the marginal pricing cost is the money market rate which is obvious in short term, overnight for example. Theoretically there are a lot of factors: marginal cost, (expected) bank exposure to interest rate risk, credit and other risk-premia, competition and regulation in different segments of the deposit and credit market, bank-customer relations, the administrative cost of effectively changing interest rates, the degree of passive behaviour on the part of deposit holders and borrowers, etc (Gabe J. de Bondt, 2005).

(三)Model 模型 400

Under the assumptions mentioned earlier, we set the model same to the one in the paper of Gabe J. de Bondt(2005)

(1)

Where αis a mark up, is the retail bank rates, is the official rate, and stands for the reflection rate of bank rates with respect to official rate. There are many intuitions on the coefficient.

Obviously, the interest rate realistically cannot be zero, and there would be a constant in the equation, despite that there was a about ten-year zero interest rate history in Japan ( 注释). In United Kingdom, all interest rates have never been zero even now the official rate is 0.5% in a special financial crisis period. Academically, the markup theory supports the αa lot, especially for the loan interest rate.

In the view of elasticity, it should be less than one if the demand (supply) for deposits (loans) is not perfectly elasticity. Thus the bank rates would not move along with the money market rate in the same pace. At the same time in the view of market competition, is also supported to be less than one since the banks have some degree of market power. Therefore the theoretical pass-though is less than one.

Since the retail banks rates cannot react to the official rate instantly, we need to add some lag terms and difference to explain the time effect. After that, equation (1) will be changed into a dynamic function with short term influence and long term adjustment.

Theoretically the dynamic function could explain the change of the retail banks rates. The short term effects are from its previous change and official rate’s change in last and this period. The long term adjustment restricts the value of dependent variable not fluctuating too much.

## Research methodology 1000 (about 6500) 1147√

Unit root

In time series analysis, unit root test is the first and crucial test because data always can not satisfy the basic econometrics assumptions(具体 注释). Interest rates are always volatile especially in the retail bank market. There are many kinds of factors could affect the rates up and down. Even though, to keep the stability of monetary policy, the official bank rate is not as volatile as retail rates, it is potentially non-stationary. Hence we need to test whether the data are stationary or not through unit root test. Without this test most statistics results would lose credibility.

There are many tests available such as the Dickey-Fuller (DF) Test, Augmented Dickey-Fuller (ADF) Test, Philips-Perron (PP) Test, Dickey-Fuller Generalised Least Squares (DF-GLS), Ng and Perron (NP) and KPSS or Kwiatkowski, Phillips, Schmidt, Shin (KPSS, 1992) among others. In this paper, we are going to give every variable an ADF Test. Actually the DF Test’s results have been included in the statistics results of ADF Test.

The general idea of ADF Test is to examine the relationships between the differentiated variable (dependent) and the lag variable (independent) given a number of lagged differentiated variables as independent variables. If the coefficient of lagged variable is significant to be zero, this variable is stationary (注释, longest lag also need to be significant). According to the specific data, we could add constant, trend or seasonal variable in the test. Hence the ADF Test idea could be showed by equation (1) and (2).

Without Constant and Trend; (1)

With Constant; (2)

The original hypothesis is β=0, in other words, x has a unit root, non-stationary. Thus the alternative hypothesis is β≠0, x is stationary. When the term is removed, the test is Dickey-Fuller Test (DF Test). Compared with DF Test, ADF Test has a higher accuracy when the data is autocorrelation.

Cointegration test

Usually there are three ways for testing cointegration relationships, the Engle-Granger two-step method, Johansen Procedure and Phillips-Ouliaris Cointegration Test. The first two are quite popular in many papers. In the present writing, we will use both of them to have a double check for ensuring our results.

2-step

The Engle-Granger two-step method is strictly based on cointegration's basic idea. According to the economics theory, we would select dependent variable, , and independent variable, . To satisfy the necessary cointegrated condition, variables should be tested the integration order first using DF or ADF test. Variables with same integration order will be estimated by original least square regression. There should be no lag and differentiated term in the equation since it should be stationary in long run without dynamic effect. After regression, we need to test the integration order of the residuals using unit root test. If the residuals are stationary, I (0), it means this group of variables could drift together though they may trend up or down over down in a non-stationary fashion. That is the first step in the two-step procedure. The second step is to estimate a dynamic relationship of the variables with the long-run relationship (actually the residuals). The two-step could be manifested by equation (3) and (4). Equation 4 satisfies the basic econometrics assumptions, thus we could use the estimated coefficients explain some economy implication. Actually the εis an error correction mechanism term adjusting the dynamic function, which will be mentioned more later.

First step (3)

Second step (4)

Where,

Johansen Procedure

Johansen procedure is applied in more papers than The Engle-Granger two-step method because the former one has many advantages than latter. First, two-step method is invalid if the group of variables have more than one cointegration relationships, while the Johansen test is good at assessing the number of relationships and what their equations are. Second, Johansen procedure could make an indirect test to weak exogeneity (加注释) increasing more credibility to the estimation, in the other hand, two-step method just select independent variables based on economy theory.

Johansen test analyzes the cointegration relationships in a vector-autoregressive (VAR) model. Before ascertain the exogeneity, we establish a group of equations. Every variable would have its own autoregressive equation with other variables. We could express the multiple equations in vector form, and after transformation there would be a matrix equation whose left hand side is the economy variables and right hand side is their lag vector and coefficients matrix, like equation (5). After transformation we could obtain equation (6).

where = (5)

(6)

is an n-element vector containing all the variables, dependent and independent. is an n×n matrix of constants. is normalised distribution, implying that there is no linear combination of the elements of which is identically zero. If the has one or less unit root, the left hand side of the equation (6) should be stationary. Since the is stationary obviously, should be stationary to guarantee the station of right hand side.

The eigenvalues of the matrix could assess whether is stationary or not. The necessary and sufficient condition for stability is that all eigenvalues lie within the unit circle. The Johansen technique tests the number of Eigenvalues which are insignificantly different from one can be undertaken with the following two test statistics. The trace statistic tests the null hypothesis that the number of distinct cointegration vector is less than or equal to r against a general alternative. The further the estimated eigenvalues are from zero, the larger the trace statistic. The maximum eigenvalue test the null hypothesis of r cointegrating vectors against the alternative of r+1 cointegrating vectors. Thus the Johansen approach estimates long-run between non-stationary variables using a maximum likelihood procedure which tests for the number of cointegrating relationships and estimates the parameters of the cointegrating relationships.

Error correcting mechanism

Error correcting mechanism is a useful tool in the time series analysis. It could provide the long run adjustment to the short run volatility. In this writing the significance of the error correcting mechanism (ECM) is the direct explanation to the pass-through. If the ECM is significant, the monetary policy transmission is working, in the other hand, it is invalid. The value of the ECM’s coefficient could show whether the pass-through is complete or incomplete. Thus the ECM could be the core of this assessment.

The ε in the two-step test is a kind of ECM because it is the residual obtained from a long run equation (without any difference term). Hence the coefficient of γ in equation (4) could explain the long run adjustment to the dynamics relationship.

(4)

Where,

where = (5)

The in equation (5) is the ECM, and the α and βare both (p×r)matrices [8] . βare the parameters in the cointegrating relationship, andαmeasures the strength of the cointegrating vectors in the ECMs. The coefficients in theαvector correspond to the importance of the cointegrating vector in each equation in the VAR.

## Data 934√

Central bank rate

The official bank rate is the central bank rate in the present writing since the bank of England is the central bank of United Kingdom. It is the source of the monetary policy, and provides an initial and direct influence to the money market.

As the last resort lender, the bank of England could directly steer money market rate through changing its official bank rate. Although the official bank rate doesn’t change frequently for the economy’s stability, the bank of England would consider whether change the rate or not every month according to the current economy situation. Thus the official bank rate would have some fluctuations as well as other kinds of bank rates.

Considering the purpose of this paper is to assess the interest-rate pass-through not analyze UK’s economy in different time, we would like to choose a relative stable and modern sample, monthly data from January 1995 to June 2008. During this period, the monetary policy is quite stable under the rule of target inflation rate. Despite the rate of target inflation was set at 2% after 2003 lower than the previous 2.5%, there was no jump down or up of the official bank rate in short time. What’s more, the official bank rate started to sharply slip down from second half 2008 due to the global financial crisis, probably causing a structure break in this test.

Furthermore, to reduce the volatility of the data, we would like to use the monthly average of official bank rate instead of the end month official bank rate. That is just a statistics method without much influence to the result. Actually in most time, these two are equal to each other if the official bank rate does not change in couple months.

Money market rates

There are many kinds of money market rates, such as average of UK banks’ base rates [9] , sterling interbank lending rate [10] , Glit repo (general collateral) rates [11] , sterling certificate of deposit rates [12] , treasury bills [13] (3 months) and so on, short term and long term. The typical assess is firstly measure the pass-through from the official bank rate to every money market rate, and then test the pass-through from every money market rate to every retail banks rates. But the statistics results of many previous literatures are not good. There is a potential reason that it is difficult to find out the correct channel linking the specific money market rate to a specific retail bank rate. For example, some money market rate just could affect the deposit rate not the loan rate, thus there should be a higher level pass-though on deposit rate, lower on loan rate.

Fortunately, we could just assess the pass-through from the official bank rate to the retail banks rates, giving a general explanation to the theory and avoiding some errors. Thus in this writing, we don't use the money market rates. When we could make sure the correct interest rate transfer channel, it is very interesting to assess the pass-through from a specific money market rate to a retail bank rate.

Retail bank rates

Just like what we have mentioned previously, in this paper, we would focus on the pass-through of the interest rate related to the household, deposit rate from household and the loan rate to household. To increase the accuracy of the result, we will use many kinds of deposit rates and loan rates to assess, avoiding some coincident consequences.

Deposit rate from household

The quoted deposit rates continually published by the bank of England are the instant access, time, fixed rate bonds and cash individual savings accounts (ISA) deposit rates, while current accounts, internet deposit accounts and postal/telephone deposit accounts are discontinued, the instant access deposits is restricted withdrawal. To guarantee the credibility, we are going to use the continually published rates in this writing. All of the rates are the monthly interest rate of UK monetary financial institutions (excl. Central bank) not seasonally adjusted.

(1)The instant access deposit rate is the rate of sterling instant access deposits from households. The instant access accounts branch-based. Rates are selected for £1,000 balances. Obviously instant access deposit rate is a short term rate in household sector. (2)The sterling time deposit rates from households are selected for £10,000 balances in accounts requiring between 30 and 90 days’ notice to withdraw without penalty. Thus the term of time deposit rate is a little bit longer than the instant access rate. (3)The sterling fixed bonds rates from households have fixed initial maturity between 1 and 2 years, and are selected for £5,000 balances. Hence it is a long term deposit rate. The data is available from January 1996 to June 2008. (4) The sterling cash individual saving account (ISA) deposits rates are selected fro £3,000 balances. The data is available from April 1999 to June 2008.

Loan rates to households sector

There are two kinds of loan rates to households sector, secured loan (mortgage) rates and unsecured. The mortgage rates are available on the loans in the range of £25,000 to £500,000, and available to most borrowers. We are going to select the sterling standard variable rate mortgage to households and sterling (75% LTV [14] ) fixed rate mortgage to households in term of 2 years, 3 years, 5 and 10 years. Thus we could find out some time effects to the pass-through.

There are three kinds of unsecured loan rates, sterling credit card lending to households, sterling personal loan (10K) and sterling overdraft households. The sterling personal loan (5K) to households is just from 2005. Thus we would not use it this time.

## Research result 3000 (about 10000)

Unit root results—official rate, deposit and loan rates & first difference+ residuals

The unit root test is a necessary process of the time series analysis, thus we need to test the unit root for every variable. Since the bank interest rates don't have stationary trend, we will probably get no stationary results. In that situation, we would test the unit root of the difference until we get the stationary results and find out the integration order of the variable.

Official rate

official rate

Model

lag

t-adf

sigma

t-prob

AIC

level

constant

0

-1.101

0.02572

-7.308

2

-1.871

0.02092

0.0073

-7.708

4

-1.866

0.02066

0.1457

-7.719

6

-2.262

0.02036

0.0149

-7.736

constant & trend

0

-0.7078

0.02579

-7.295

2

-2.103

0.02092

0.0052

-7.701

4

-2.152

0.02065

0.2169

-7.717

6

-2.866

0.02022

0.0064

-7.704

first difference

constant

0

-6.513**

0.02155

-7.661

1

-4.683**

0.02117

0.0128

-7.69

5

-3.080*

0.02073

0.0346

-7.707

6

-3.763**

0.02025

0.0064

-7.746

constant & trend

0

-6.503**

0.02162

-7.649

1

-4.667**

0.02124

0.0138

-7.677

5

-3.038

0.0208

0.0359

-7.693

6

-3.744*

0.02032

0.0063

-7.733

Deposit rates from household

Unit root test summary without trend

lag

t-adf

sigma

t-prob

AIC

level

Instant access rate

1

-1.435

0.05885

0.0000

-5.646

2

-1.797

0.05691

0.0011

-5.706

Time deposit rate

1

-1.334

0.03730

0.0000

-6.558

2

-1.662

0.03595

0.0007

-6.625

Sterling fixed rate bond deposit

1

-1.563

0.03412

0.0000

-6.734

7

-1.731

0.03246

0.5384

-6.792

Cash ISA

0

-2.293

0.02509

-7.350

1

-2.140

0.02408

0.0031

-7.422

first difference

Instant access rate

1

-5.539**

0.05748

0.0018

-5.692

2

-4.275**

0.05685

0.0412

-5.708

Time deposit rate

1

1

-5.069**

0.03629

0.0011

2

2

-3.982**

0.03599

0.0663

Sterling fixed rate bond deposit

1

-4.403**

0.03277

0.0002

-6.815

7

-3.166*

0.03255

0.0941

-6.786

Cash ISA

0

0

-7.100**

0.02466

1

1

-4.075**

0.02355

0.020

Loan rates to household

Secured loan rate unit root summary

lag

t-adf

sigma

t-prob

AIC

level

Sterling standard variable rate

1

-1.550

0.01814

0.0000

-7.999

2

-2.036

0.01731

0.0001

-8.086

Sterling 2 year fixed mortgage

0

-1.173

0.03141

-6.908

3

-1.581

0.02921

0.2214

-7.033

Sterling 3 year fixed mortgage

0

-1.386

0.03090

-6.940

2

-1.808

0.02936

0.7277

-7.030

Sterling 5 year fixed mortgage

0

-1.497

0.02564

-7.314

Sterling 10 year fixed mortgage

0

-1.892

0.02722

--7.194

3

-1.987

0.02601

0.7301

-7.265

First difference

Sterling standard variable rate

1

-4.777**

0.01750

0.0004

-8.071

2

-3.723**

0.01728

0.0330

-8.089

Sterling 2 year fixed mortgage

0

-8.124**

0.02939

-7.041

3

-6.844**

0.02897

0.0270

-7.050

Sterling 3 year fixed mortgage

0

-8.614**

0.02949

-7.034

2

-6.892**

0.02935

0.0681

-7.031

Sterling 5 year fixed mortgage

0

-7.720**

0.02359

-7.481

Sterling 10 year fixed mortgage

0

-8.628**

0.02617

-7.273

3

-6.314**

0.02603

0.0536

-7.264

Unsecured loan rate unit root summary

lag

t-adf

sigma

t-prob

AIC

level

sterling credit card lending

0

-1.306

0.01269

-8.721

5

-1.293

0.01281

0.9056

-8.669

sterling personal loan

0

-1.600

0.02874

-7.086

sterling overdraft households

0

-1.114

0.01141

-8.933

8

-1.385

0.01161

0.9200

-8.846

First difference

sterling credit card lending

0

-10.95**

0.01270

-8.718

5

-3.580**

0.01275

0.0857

-8.678

sterling personal loan

0

-11.32**

0.02893

-7.073

sterling overdraft households

0

-11.51**

0.01146

-8.978

8

-3.57*

0.01157

0.0823

-8.854

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