New Lending Services Price Index

Methodology Summary Document

1. Context

Statistics Canada is in the process of developing a comprehensive suite of services producer price indexes. As part of this effort, the Finance, Insurance and Professional Services (FIPS) section is currently developing indexes for a variety of financial services, including banking, insurance, and securities brokerage and dealing.  More indexes will be developed as current projects move into production and priorities are identified.

In an effort to explore alternative administrative data sources, FIPS has obtained and analyzed data from the Bank of Canada’s A4 New Lending Report. The analysis has shown that it is possible to create a high quality New Lending Services Price Index (NLSPI) using this data.

2. Data

The data for the New Lending Services Price Index was obtained from the Bank of Canada’s Report on New Lending as well as from the Canadian System of Macroeconomic Accounts’ Gross Domestic Product by Income and Expenditure Accounts, and Financial Market Statistics used in the preparation of the Bank of Canada Review.

The Report on New Lending is collected monthly by the Bank of Canada through a survey of all Canadian chartered banks. Each bank is required to provide data on interest rates^Note1 and funds advanced for 10 lending products by 6 interest rate term maturities as well as for the aggregate of all products and all maturities (See Appendix A). In order to calculate prices for each lending product, a reference rate (See Section 5.3) was deducted from each product`s lending rate (by bank and maturity).

The reference rate was derived from data on Financial Market Statistics used in the preparation of the Bank of Canada Review and available on CANSIM. Certain market instruments were chosen and their yields were aggregated in order to produce the reference rate.

Since the value of money is eroded over time, a deflation factor is applied to the spread. The deflation factor is derived using the implicit price index for Final Domestic Expenditure from the Canadian System of Macroeconomic Accounts’ Gross Domestic Product by Income and Expenditure Accounts.

The data set is of a high quality and it presents significant detail in terms of maturity which allows for the construction of a mixed reference rate.

Furthermore, it imposes no further burden on respondents since they are already filling out this survey for the Bank of Canada.

3. Coverage

The NLSPI collects data on newly issued loans. Therefore, it is narrower in scope than a full Banking Services Price Index (BSPI) which includes all loans and deposits as well as explicit fees.

4. Usefulness

The primary purpose of the NLSPI is to provide supplemental information to help inform the deflation of output for the National Accounts. The industry in question is Canadian System of Macroeconomic Accounts (CSMA) industry BS5221A0 Banking and Other Depository Credit Intermediation. This corresponds to North American Industry Classification System (NAICS) industry 52211, Banking and industry 52219, Other Depository Credit Intermediation.  The NLSPI covers a portion of the output contained in MPS52X002 Residential mortgage services indirectly measured (FISIM) and MPS52X003 Other loan services indirectly measured (FISIM). Those commodities cover the output generated by all of the loans contained on the banks’ balance sheets while the NLSPI covers the output of only those loans issued in the reference period.  In terms of having a smaller coverage than the product heading, the NLSPI could be considered to meet the requirements of a B-method price. ^Note2

In terms of calculating a fuller BSPI, the NLSPI could serve as a component of a comprehensive index that would measure prices for all bank output including outstanding loans, deposits, and explicit fees.  Since the NLSPI measures the flow of lending at a detailed level of maturity, over time this data could be used to estimate weights for loan maturities when constructing a broader BSPI.

5. Methodology

5.1. New Lending Prices

The primary activity of a bank is to transform the deposits of savers into loans for borrowers. This is called depository credit intermediation. There are a variety of functions associated with this activity such as cheque clearing, debit card services, and credit analysis. For many of these services, banks charge explicit fees such as ATM fees and wire transfer fees. Banks also earn significant income indirectly by collecting more in interest on loans then they pay on deposits. This spread between interest income and interest expense is called Financial Intermediation Services Indirectly Measured (FISIM). The NLSPI seeks to measure changes over time in the portion of this spread associated with newly issued loans.

5.2. User-Cost of Money

Prices in banking are measured using the User-Cost of Money approach. The user-cost approach defines the price of a loan as the difference between the effective rate^Note3 on that loan and some reference rate plus explicit fees per dollar of loan.

p_lj = (r_lj - r_j) + s_lj

where p_lj is price for each bank l’s product, j; r_lj is the interest rate for each bank l’s product, j; r_j represents the reference rate, and s_lj represent the explicit fees.

For the purposes of the NLSPI, explicit fees are not included and we are left with simple loan margins.

p_lj= (r_lj - r_j)

Since the value of money is eroded over time, a deflation factor is applied to the spread.

This gives:

p_lj = (r_lj - r_j) * d

All variables in this equation are described above, and d is the estimated monthly value rate of the implicit price index for Final Domestic Expenditure. For a more detailed explanation of deflation see Appendix B.

5.3. Reference Rate

The reference rate that we have been discussing is defined as the theoretical opportunity cost of money. There exists no consensus, either in the literature or international practice, as to the choice of reference rate. While we have experimented with several individual reference rates as well as with a multiple reference rate approach that matches reference rates to maturities, we have opted to use a single, mixed maturity reference rate.  This method is based on the Report of the Intersecretariat Working Group on National Accounts (ISWGNA) Task Force on FISIM and the method has been reviewed by Statistics Canada’s Price Measurement Advisory Committee.

The mixed rate is constructed by taking the yields of a variety of market instruments each of which matches one of the loan maturities (See Appendix C). The yields are aggregated using the trailing 12 month funds advanced of the matching maturities as quantity weights.^Note4

This brings the price calculation to:

p_lj = (r_lj - r) * d

where p_lj, r_lj and d remain as described above, and where r represents the mixed reference rate.

5.4. Aggregation

The NLSPI is currently produced using a commodity-based aggregation which allows for the production of a variety of sub-indexes. Although it might be possible to provide series at a more detailed level to the CSMA, we are not currently planning to publish sub-indexes.

In order to weigh the prices from the microdata level, we use derived revenues as weights. Revenues are derived by multiplying the derived prices by the funds advanced for each product at each maturity for each bank.

Appendix A
A1 Products

Section I – Interest rates – Percentages

• To individuals:
  • Personal loan plans
  • Personal lines of credit, secured
  • Personal lines of credit, unsecured
  • Other personal
  • Residential mortgages, insured
  • Residential mortgages, uninsured
• Total personal loans and mortgages
• To the business sector
  • Loans to regulated non-bank financial institutions
  • Lease receivables
  • Loans to individuals and others for business purposes
  • Non-residential mortgages
• Total selected business loans

Section II – Funds advanced – Thousands of dollars

• To individuals:
  • Personal loan plans
  • Personal lines of credit, secured
  • Personal lines of credit, unsecured
  • Other personal
  • Residential mortgages, insured
  • Residential mortgages, uninsured
• Total personal loans and mortgages
• To the business sector
  • Loans to regulated non-bank financial institutions
  • Lease receivables
  • Loans to individuals and others for business purposes
  • Non-residential mortgages
• Total selected business loans

A2 Maturities

All
Variable rate
Fixed rate <1 year
Fixed rate 1 to <3 years
Fixed rate 3 to <5 years
Fixed rate 5 to <7 years
Fixed rate 7 years and over

Appendix B
Deflation

The APR that is reported on the A4 is the interest rate banks quote to their clients. It is equal to the effective rate if and only if there is a single interest payment made annually without compounding. The user-cost approach requires the use of effective interest rates but since those are not available in the A4, we are using the APR as a proxy. In that case, it’s important to keep in mind that the APR is a function of interest income and funds advanced:

APR = (Interest Income / Funds Advanced)

The same is also true of the assets that make up the reference rates:

Yield = (Interest income / Funds advanced)

As discussed in Section 5.2, the funds advanced must be discounted to account for the decline in the purchasing power of money over time on a cumulative basis.

For the purposes of the NLSPI, we have chosen the monthly estimated^Note5 level of the implicit price index for Final Domestic Expenditure as the deflator. We then apply this value to the spread^Note6 to obtain the final price for month t:

P_t = (APR_t – r_t) * d_t

d_t = d_t-1* h_t

where d_t = 1 in the first month. In subsequent months, d_t-1 represents the previous month’s deflator, and h_t is the monthly growth rate of GDI calculated as the cubic root of the quarterly growth rate.

Appendix C
Reference rate for the NLSPI

Mixed Reference Rate

The reference rate for the NLSPI is a weighted average of the yields to maturity for the market instruments listed below. The weight of each instrument is the 12-month trailing funds advanced for the corresponding term maturity. The data is obtained from CANSIM Table 176-0043.

This table displays the results of reference rate for the nlspi. The information is grouped by maturity (appearing as row headers), market rate and cansim vector (appearing as column headers).

Maturity	Market Rate	CANSIM Vector
Variable Rate	Overnight Rate	V122514
Fixed Rate <1 year	6 month Treasury Bill	V122532
Fixed Rate 1 to <3 years	1-3 year Government Bonds	V122558
Fixed Rate 3 to <5 years	3-5 year Government Bonds	V122485
Fixed Rate 5 to <7 years	5-10 year Government Bonds	V122486
Fixed Rate 7 years and over	5-10 year Government Bonds	V122486

Notes:

1. The interest rates that are provided are in the form of Annual Percentage Rates (APRs) which is the same as the effective rate only if the loan is held for exactly one year with a single interest payment without default.
2. See Handbook on Price and Volume Measures in National Accounts, p. 30, 31.
3. Interest Income divided by Balance of Outstanding Loans.
4. Note that for reference year 2011; the reference rate is weighted using the fixed value of 2011 funds advanced.
5. Since this implicit price index is only available quarterly, we take the third root of the quarterly growth rate and then multiply it by the previous month’s deflator to arrive at a cumulative monthly deflator.
6. Deflating the funds advanced is equivalent to multiplying the spread by the monthly deflator.