What Calls to ARMs? International Evidence on Interest Rates and the Choice of Adjustable-Rate Mortgages. Online Appendix

Transcription

1 What Calls to ARMs? International Evidence on Interest Rates and the Choice of Adjustable-Rate Mortgages Online Appendix Cristian Badarinza, John Y. Campbell, and Tarun Ramadorai This appendix contains five parts: A. Data sources B. Back-casting and imputation algorithm C. Description of the bootstrap procedure D. Additional figures and tables E. Cross-sectional analysis Badarinza: Department of Real Estate, Institute of Real Estate Studies, Architecture Drive, Singapore 7566, National University of Singapore, and CEPR. Campbell: Department of Economics, Littauer Center, Harvard University, Cambridge MA 28, USA, and NBER. john Ramadorai: Imperial College London, Tanaka Building, South Kensington Campus, London, UK, and CEPR.

2 Appendix A: Data Sources Belgium: National Bank of Belgium MIR Survey on interest rates applied to customers. Volumes: Part II. Amounts of loans in EUR to households - New Business. Loans for house purchases. Interest rates: Part I. Interest rates on loans in EUR to households - New Business. Loans for house purchases. Denmark: Danmarks Nationalbank, Table DNRNM Volumes and interest rates: MFI sector s interest rates on new lending by data type, item, fixed-interest period, currency and sector. Options: Business volume and effective interest rate Housing purposes excluding overdraft facilities Sector: Households (5) Ireland: Central Bank of Ireland, Retail Interest Rates, Table B.2. Volumes and interest rates: Loans to households for house purchases. Italy: Bank of Italy, Supplements to the Statistical Bulletin; Money and Banking Volumes: Table VTI2, euro-denominated loans to households: new business. Interest rates: Table TTI2, bank interest rates on euro loans to households: new business. Greece: Bank of Greece, Bank deposit and loan interest rates Volumes: Table a, Volume of new bank euro-denominated deposits and loans visa-vis euro area residents, Housing loans to households. Interest rates: Table, Bank interest rates on new euro-denominated deposits and loans vis-a-vis euro area residents, Housing loans to households. Germany: Deutsche Bundesbank, Housing loans to households Volumes: BBK.SUD26 to BBK.SUD29, New business (volumes) of German banks, Housing loans to households with an initial rate fixation. Spain: Banco de Espana 2

3 Volumes: DN CTI2TIE to DN CTI2TIE6, New business. Credit entities, except official credit. Housing loans. Initial interest rate fixation periods. Portugal: Banco de Portugal, OMFIs interest rates and profitability Volumes: New loans to MU households, housing Netherlands: De Nederlandsche Bank, Interest rates Volumes and interest rates: Table 5.2.7, Interest rates of MFIs on deposits and loans from households, Loans for house purchase. New business. Finland: Bank of Finland MFI balance sheet (loans and deposits) and interest rates Volumes and interest rates: Finnish MFI s new business on housing loans by reference rate Sweden: Statistics Sweden, Financial Market Statistics. Volumes:.26., Housing credit institutions volumes of lending, new loans each month Interest rates: Table (cont.), Housing credit institutions lending rates on new agreements each month. For the period until September 25, interest rate data is converted from quarterly to monthly frequency through linear interpolation. Australia: Australian Bureau of Statistics, Time Series Workbook, Housing Finance Volumes: TABLE 9a. Housing Finance Commitments, by type of buyer and loan Reserve Bank of Australia, Statistical Tables Interest rates: TABLE F5. Indicator lending rates, Housing loans by banks. Standard variable rate and -year fixed rate. United States: Federal Housing Finance Agency, Monthly Interest Rate Survey Loan-level data. Survey waves: 992 to 2. United Kingdom: Bank of England CFQBVA to CFQBVF, Quarterly percentage of UK resident monetary financial institutions - loans secured on dwellings, new advances on floating rate to households.

4 Appendix B: Back-casting and imputation We describe the procedure by which imputed values are obtained for ARM i,t K,t in the cases K = 2 and K = years and for ARM US,t during the months in which the US MIRS survey data is not reliable. Assume generically the following model for Y t as a function of X t : Y t = α + βx t + ε t. Let t = T be the first observation for which we have data on Y t, with the data on X t going back to t =. The idea is to use fitted values Ŷt wherever Y t is not available. If the regression is estimated in levels, however, there would be a discontinuity at t = T because we suddenly change from the fitted values to the actual ones. Therefore, we estimate the model in first-differences: Y t = α + β X t + ν t. and obtain an implied fitted time series for Y t. We then have: Ŷ T = Y T Y T Ŷ T 2 = ŶT Y T etc. Applied to our case, the variables are: Y t = ARM i,t K,t X t = R f i,t K,t for back-casting past ARM rates when K = 2 and K = years, and: Y t = ARM i,t X t = R f i,t for generating imputed values of ARM rates in the US during the periods November 28 to March 29, August 2 to November 2 and October 22 to April 2.

5 Appendix C: Bootstrap procedure Standard errors for all estimated coefficients are computed by using a non-parametric bootstrap procedure. The need to correct standard errors in this way arises because of the imputation and extrapolation carried out to correct for implausible observations towards the end of the sample in the US, as well as for the cases where K = 2 and K = years. In addition, this provides a robust way to account for the two-stage instrumental-variables estimation. The context in which we implement the bootstrap consists of an unbalanced panel of monthly observations which are serially and cross-sectionally correlated. We use a circular block bootstrap of random block length, along the lines of Politis and Romano (99) and Ramadorai (22). Consistency in terms of cross-sectional dependence is insured by having a unique re-sampling draw across countries and by re-ordering the time series such that the draw is consistent with the different sample coverages in each country. The algorithm starts by setting the value for a constant q and drawing a random number t =,..., T, where T is the length of the full sample. For the re-sampled observation corresponding to the next period, a random variable ξ is drawn from a uniform distribution defined on (,). If ξ is smaller than q, the consecutive observation to the first bootstrap draw is also included (i.e., if t = was first drawn, t = 5 is appended to it). When reaching the end of the sample, the procedure starts from the beginning with t =. If ξ is greater than or equal to q, a new observation t =,..., T is drawn with replacement. At each step, only countries for which observation t is available are included in the sample. This procedure insures that the time series pattern is preserved through the choice of q, while the cross-sectional dependence is built into the simultaneous random draws. We report the results for q =., with 5, draws used to compute the final standard errors. 5

6 Appendix D: Figures and tables Figure A. - Mortgage market structure and average fixation periods The figure illustrates the time series dynamics of the share of ARMs for the set of countries which we do not include in our panel analysis. Figure A.2 - Imputation of the ARM rate for the United States The figure shows the different paths for the ARM rate implied by the imputation procedure. Figure A. - Back-casting of average ARM rates The figure shows the different paths for the backward-looking average ARM rate implied by the back-casting procedure. Figure A. - The relationship between ARM rates and nominal short rates The figure shows moving averages of the two variables at a backward-looking horizon of years. Figure A.5 - Realizations and forecasts of short-term interest rates The figure plots the time series of -month nominal interest rates and survey-based forecasts for a horizon of one year. Figure A.6 - Fixation periods of new mortgage loans The figure shows the time series path of new mortgage loans to households, by interest rate fixation category. Figure A.7 - Time series of average fixation periods and FRM-ARM spreads at the country level The figure plots the time series of average fixation periods. Table A. - Determinants of the ARM share: rational forecasting The table reports results from pooled panel IV estimation, for the cases T =, 2, years. Table A.2 - Determinants of the ARM share: unit-root first-stage specification The table reports results from pooled panel IV estimation, when assuming a common unit root for interest rates. Table A. - Determinants of the ARM share: country-by-country results The table reports detailed country-by-country estimates, distinguishing between first- and second-stage results. Table A. - Average fixation period: IV approach The table reports panel estimation results when considering the average fixation period as dependent variable. 6

7 Table A.5 - Specifications with time fixed effects The table reports panel estimation results when including time fixed effects in our benchmark specification. Table A.6 - Determinants of the ARM share: interest rate forecasts The table reports the results for the cases K = 2 and K = years, when using consensus forecasts as additional instruments and explanatory variables. Table A.7 - Rationality of one-year ahead interest rate forecasts The table reports panel regressions of survey forecasts and actual realizations of interest rates, controlling for the complete set of instrumental variables. Table A.8 - Determinants of the ARM share in the US: Expectations of future rates based on Michigan survey data The table reports results from an instrumental-variables regression for the US, where we use one-year ahead interest rate forecasts from the Michigan survey of US consumers. Table A.9 - Robustness checks: Macroeconomic variables and Consensus expectations The table reports estimated coefficients from a regression specification which includes macroeconomic variables and survey expectations. Table A. - Relationship between the mortgage spread and the slope of the yield curve The table reports univariate correlation coefficients between the FRM-ARM spread and the 5-year slope of the yield curve. 7

8 Figure A. Mortgage market structure and average fixation periods The figure illustrates the time series dynamics of the share of ARMs for the set of countries which we do not include in our panel analysis. The series for the UK is only available at quarterly frequency Share of ARMs Average interest rate fixation period Germany Spain Finland Portugal UK 8

9 Figure A.2 Imputation of the ARM rate for the United States The figure shows the different paths for the ARM rate implied by the imputation procedure, by using either the short rate or the FRM rate as reference variables. As mentioned above, we use the short rate as a reference in all estimated model specifications. 7 Imputing ARM rates around October 28, September 2 and December Percent Actual FRM 2 Fitted ARM based on FRM Fitted ARM based on short rate Actual ARM

10 Figure A. Back-casting of average ARM rates The figure shows the different paths for the backward-looking average ARM rate implied by the backcasting procedure, for three cases: first, when the relationship between the ARM rate and the nominal short rate is estimated separately for each country; second, when this relationship is constrained to be the same for the whole panel and third, for the case of a simple rule that the change in the ARM rate is equal to the change in the nominal short rate. In all our estimated model specifications we use the second variant, i.e. common coefficients across the panel. Percent Australia Belgium Denmark Greece Ireland Italy Percent Percent Netherlands Sweden USA Country level Panel Simple rule Realized ARM rate: year moving average

11 Figure A. The relationship between ARM rates and nominal short rates The figure shows moving averages of the two variables at a backward-looking horizon of years. It corroborates the proposed preferred imputation method illustrated in Figure A., by showing that a moving average of the short rate, appropriately adjusted, is a good approximation for the moving average of the ARM rate. Australia Greece Netherlands Belgium Ireland Sweden Denmark Italy USA Realized short rate: year moving average Realized ARM rate: year moving average

12 Figure A.5 Realizations and forecasts of short-term interest rates The figure plots the time series of -month nominal interest rates (continuous line) and survey-based forecasts for a horizon of one year (dotted line). The timing of the plot is such that realizations and forecasts are depicted contemporaneously, i.e. they are plotted for the month during which the survey was conducted. Australia 6 Eurozone Percent Percent Italy Netherlands Percent Sweden USA month nominal interest rate Consensus one year ahead forecast of month nominal interest rate 2

13 Figure A.6 Fixation periods of new mortgage loans The figure shows the time series path of new mortgage loans to households, by interest rate fixation category. The volumes in each category are normalized by dividing through the size of total new mortgage lending. Belgium Denmark Greece Italy Netherlands USA ARM FRM: above year and up to 5 years FRM: above 5 years and up to years FRM: above years

14 Figure A.7 Time series of average fixation periods and FRM-ARM spreads at the country level The figure illustrates the dynamics of the average fixation period (in years, on the left axis) and the contemporaneous spread between the FRM rate for fixation periods above years and ARM rates (in percent, on the right axis). For the US, imputed values are used for the ARM rate during the periods November 28 to March 29, August 2 to November 2 and October 22 to April 2. Belgium Denmark Greece Years Percent Italy Netherlands USA Years Percent Average fixation period (left axis) FRM above years ARM spread (right axis)

15 Table A. Determinants of the ARM share in a cross-country panel: Current mortgage rates vs. rational expectations of future rates In Panel A, we report estimation results from pooled panel regressions of the form: ARMSHARE i,t = µ i +ρarmshare i,t +β C (F RM i,t ARM i,t )+β L (F RM i,t ARM i,t,t+t )+ν i,t, where µ i are country-specific fixed effects. ARM i,t, F RM i,t and ARM i,t K,t are used as instruments for ARM i,t,t+t, with T and K varying as indicated (in years). The first-stage model specification is given by: ARM i,t,t+t = α i + γ ARM i,t + γ 2 F RM i,t + γ ARM i,t K,t + γ B 5 i,t + γ 5 R f i,t + ε i,t. All estimations cover the same sample as the one with T = years. When K = 2 or K = years, extrapolated values are calculated for the part of the sample where ARM i,t K,t is missing. In Panel B, we report estimation results from pooled panel regressions of the form: ARMSHARE i,t = µ i + ρarmshare i,t + β C (F RM i,t ARM i,t ) + β L (F RM i,t ARM i,t,t+t ) + β S (R f i,t Rf,CF i,t,t+2 ) + ν i,t, where µ i are country-specific fixed effects and R f,cf i,t,t+2 is the consensus forecast of the one-year ahead nominal interest rate. The first-stage model specification is given by: ARM i,t,t+t = α i + γ ARM i,t + γ 2 F RM i,t + γ ARM i,t K,t + γ B 5 i,t + γ 5 R f i,t + γ 6R f,cf i,t,t+2 + ε i,t. We report the case K =. Statistical significance is indicated through at most three stars, referring to confidence levels of %, 5% and % respectively. Panel A Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = K = β C *.7*** -..65**.87*** β L.2***.55**..5***.76**.6* K = 2 β C.2.66**.77***.22.7**.89*** β L.78*.5.2.2*.52*.2 K = β C.5.72**.79***.8.8**.9*** β L Post-2 K = β C -.7.5*.8*** **.5*** β L.7***.9***.7***.85***.***.7** K = 2 β C -..58*.8*** -..77**.*** β L.2**.8***.65**.52***.86**.68** K = β C.2.65**.8***.26.8**.*** β L.5*.6*.5*.*

16 Table A. Determinants of the ARM share in a cross-country panel: Current mortgage rates vs. rational expectations of future rates (continued) Panel B Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = β C **.92***.66.***.59*** β L.26***.5*.8.7***.6*.22 β S..28.8*.86**.***.2*** Post-2 β C **.2.85*** 2.*** β L.5***.79** β S **.76*** 6

17 Table A.2 Determinants of the ARM share in a cross-country panel: Unit-root first-stage specification The table presents results from the panel instrumental-variables context, when accounting for possible non-stationarity in interest rates and an associated unique cointegration relationship. In Panel A, the estimation consists in running pooled panel regressions of the form: ARMSHARE i,t = µ i +ρarmshare i,t +β C (F RM i,t ARM i,t )+β L (F RM i,t ARM i,t,t+t )+ν i,t, where F RM i,t ARM i,t, ARM i,t K,t ARM i,t and the 5-year bond yield spread Bi,t 5 Rf i,t are used as instruments for ARM i,t,t+t ARM i,t. In this case, the first-stage specification is given by: ARM i,t,t+t ARM i,t = ϕ i + φ (F RM i,t ARM i,t ) + φ 2 (ARM i,t K,t ARM i,t ) + φ (B 5 i,t R f i,t ) + ξ i,t. In Panel B, the estimation consists in running pooled panel regressions of the form: ARMSHARE i,t = µ i + ρarmshare i,t + β C (F RM i,t ARM i,t ) + β L (F RM i,t ARM i,t,t+t ) + β S (R f i,t Rf,CF i,t,t+2 ) + ν i,t, where the first-stage model is given by: ARM i,t,t+t ARM i,t = ϕ i + φ (F RM i,t ARM i,t ) + φ 2 (ARM i,t K,t ARM i,t )+ φ (B 5 i,t R f i,t ) + φ (R f i,t Rf,CF i,t,t+2 ) + ξ i,t. We report the case K = year. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively, based on bootstrap standard errors. Panel A Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = K = β C β L.9***.*.8 2.2*** 2.7***.98 K = 2 β C * β L K = β C ** *** β L Post-2 K = β C *** *** β L 2.***.5** *** 2.*** 2.9* K = 2 β C *** *** β L **.87**.76 K = β C *** *** β L

18 Table A.2 Determinants of the ARM share: unit-root first-stage specification (continued) Panel B Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = β C -.95* *** β L 2.*** 2.2* *. -.2 β S * Post-2 β C *** β L 2.** β S *** 8

19 Table A. Determinants of the ARM share: country-by-country results for the unit-root first-stage specification The table presents results from the panel instrumental-variables context, when accounting for possible non-stationarity in interest rates and an associated unique cointegration relationship. The estimation consists in running both country-by-country and pooled panel regressions of the form: ARMSHAREi,t = µi + ρarmsharei,t + βc(f RMi,t ARMi,t) + βl(f RMi,t ARM i,t,t+t ) + νi,t, where F RMi,t ARMi,t, ARM i,t K,t ARMi,t and the 5-year bond yield spread B i,t 5 R f i,t are used as instruments for ARM i,t,t+t ARMi,t, with T = years and K = year. The first-stage specification is given by: ARM i,t,t+t ARMi,t = ϕi + φ(f RMi,t ARMi,t) + φ2(arm i,t K,t ARMi,t) + φ(b 5 i,t R f i,t ) + ξ i,t. Correlation coefficients among regressors are reported under the heading Γ. ϕ F E and µ F E capture estimated country-specific fixed effects in the pooled panel setup. ARM i,t K,t is extrapolated as mentioned above. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively, based on bootstrap standard errors. ϕ F E φ φ2 φ Γφ,φ2 Γφ,φ F E R2 obs. R2 µ F E ρ βc βl Γ β, βd Australia -.**.95***.** ***.9*** Belgium -.**.89*** -.7*** ***.9.2*** Denmark -.5**.8*** -.56***.8*** *.77*** Greece -.*** -..5*** *** Ireland -.52** ** ***.89*** Italy -.9*** ***.7*** ***.52* Netherlands -.**.*** -.*** ***.5** Sweden -.9***.2*** -.8.8** *** USA -.99***.2*..29* *** Panel -.9*** -.99***.56*** *** Panel (excl. USA) -.56*** -.***.8*** ***.98* Post-2 Australia **.89*** ***.98*** -.8.*** Sweden -.2***.67*** -.25* *** USA -.*** -..5.* **.9*** Panel -.2*** -.***.59*** ***.92*** Panel (excl. USA) -.59*** -.9***.67*** ***.*** 2.9*

20 Table A. Average fixation period: IV approach The estimation consists in running pooled panel regressions of the form: AV GF IX i,t = µ i + ρav GF IX i,t β C (F RM η i,t ARM i,t) β L (F RM η i,t ARM i,t,t+t ) + ν i,t, with country-specific fixed effects. AV GF IX i,t is the average fixation period and F RM η i,t is the rate on mortgage loans corresponding to a fixation period η. For all countries, we choose η = above years. ARM i,t, F RM η i,t and ARM i,t K,t are used as instruments for ARM i,t,t+t, with T and K varying as indicated (in years). The first-stage model specification is given by: ARM i,t,t+t = α i + γ ARM i,t + γ 2 F RM η i,t + γ ARM i,t K,t + γ B 5 t + γ 5 R f t + ε i,t. Alternatively, when accounting for possible non-stationarity in interest rates and an associated unique cointegration relationship, the first-stage model is: ARM i,t,t+t ARM i,t = ϕ i + φ (F RM η i,t ARM i,t) + φ 2 (ARM i,t K,t ARM i,t ) + φ (B 5 i,t R f i,t ) + ξ i,t. All estimations cover the same sample as the one with T = years. Except in the case K = year, extrapolated values are calculated for the part of the sample where ARM i,t K,t is missing. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively, based on bootstrap standard errors. Benchmark specification Unit root specification T = T = 2 T = T = T = 2 T = K = β C -..2*.8***.5.2***.27*** β L.8***.2***.6*** K = 2 β C -.8.2*.8***.2*.5***.2*** β L.5***.9***.5*** ** K = β C -.2.**.9***.***.52***.5*** excl. US β L.29***.5***.*** -.89*** -.*** -.28*** K = β C *** -.28*.9.2*** β L.5***.27***.2***.6***.***.*** K = 2 β C *** *** β L.5***.26***.2***.8***.28***.28*** K = β C -..*.22*** -.6.8*.26*** Post-2 β L.***.2***.2***.**.2**.2** K = β C -.2**..** -.25*.5.** β L.6***.25***.22***.7***.2**.6** K = 2 β C -.9**.5.** *** β L.2***.2***.2***.26*..8 K = β C -..7.**.*.29***.2*** β L.6***.2***.7***

21 Table A.5 Specifications with time fixed effects The table reports estimation results from panel regressions of the form: ARMSHARE i,t = µ i + δ t + ρarmshare i,t + β C (F RM i,t ARM i,t ) + β L (F RM i,t ARM i,t,t+t ) + ν i,t, where δ t are time fixed effects and µ i are country-specific fixed effects. ARM i,t, F RM i,t and ARM i,t K,t are used as instruments for ARM i,t,t+t, with T and K varying as indicated (in years). The first-stage model specification is given by. ARM i,t,t+t = α i + γ ARM i,t + γ 2 F RM i,t + γ ARM i,t K,t + γ B 5 i,t + γ 5 R f i,t + ε i,t. All estimations cover the same sample as the one with T = years. Except in the case K = year, extrapolated values are calculated for the part of the sample where ARM i,t K,t is missing. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively, based on bootstrap standard errors. Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = K = β C.8.7*.8**.9.**.** β L K = 2 β C.7.8*.85**..9**.8** β L K = β C.6.7*.8*.7.26**.29** β L.5.9.5* Post-2 K = β C **.2** β L K = 2 β C.89.96*.99*.55**.52***.5** β L K = β C..2*.*.6*.57**.5*** β L

22 Table A.6 Determinants of the ARM share: interest rate forecasts The table reports estimation results from panel regressions of the form: ARMSHARE i,t = µ i + ρarmshare i,t + β C (F RM i,t ARM i,t ) + β L (F RM i,t ARM i,t,t+t ) + β S (R f i,t Rf,CF i,t,t+2 ) + ν i,t, where µ i are country-specific fixed effects and R f,cf i,t,t+2 is the consensus forecast of the one-year ahead nominal interest rate. The first-stage model specification is given by (A): ARM i,t,t+t = α i + γ ARM i,t + γ 2 F RM i,t + γ ARM i,t K,t + γ B 5 i,t + γ 5 R f i,t + γ 6R f,cf i,t,t+2 + ε i,t. Alternatively, when accounting for possible non-stationarity in interest rates and an associated unique cointegration relationship, the first-stage model is (B): ARM i,t,t+t ARM i,t = ϕ i + φ (F RM i,t ARM i,t ) + φ 2 (ARM i,t K,t ARM i,t )+ φ (B 5 i,t R f i,t ) + φ (R f i,t Rf,CF i,t,t+2 ) + ξ i,t. We report the cases K = 2 year and K = years. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively, based on bootstrap standard errors. Panel A Benchmark specification (K = 2 years) Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = β C..72**.92***.99**.***.6*** β L.***.2.8.7*..2 β S.22..8*.5***.2***.*** Post-2 β C..69.6**..9*** 2.*** β L.***.75*.5* β S *.57**.76*** Panel B Unit-root specification (K = 2 years) Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = β C ***.***.28***.72*** β L.7*** 2.2***...6** -. β S ***.5*.2***.96***.7*** Post-2 β C -..95*.65***.65.99*** 2.5*** β L.6*** *** -.6 β S.8.5.8***.5*.25*** 2.52*** 22

23 Table A.6 Determinants of the ARM share: interest rate forecasts (continued) Panel C Benchmark specification (K = years) Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = β C..67**.87***.2*.2***.57*** β L.5**.9* β S.2.28.*.7***.7***.28*** Post-2 β C **.79* 2.9*** 2.7*** β L.9*.66* β S **.78**.85*** Panel D Unit-root specification (K = years) Panel Panel (excl. USA) T = T = 2 T = T = T = 2 T = β C **.99***.95***.8*** β L.69***.7***.65*** ***.59*** β S **.5.62***.58.5** Post-2 β C **.6***.9*.9*** β L.**.2***.6* β S ***.86.** 2

24 Table A.7 Rationality of one-year ahead interest rate forecasts The table reports estimation results from regressions of the form: R f i,t+2 Rf i,t = α i + βi(r f,s i,t,t+2 Rf i,t ) + τi,armi,t + τi,2f RMi,t + τi,b 5 i,t + τi,r f i,t + τ i,5arm i,t K,t + εi,t+2. In this specification, R f i,t is the -month interest rate in country i in period t and Rf,S i,t,t+2 is the one-year ahead average consensus forecast in country i in period t. Disaggregated forecast data are not available for Denmark, Belgium, Greece and Ireland. In our panel estimation, we use forecasts at the level of the Eurozone for the latter three of these countries. In Panel A, we estimate the coefficients unrestricted country-by-country. In Panel B, we consider the Eurozone to be a single unit and restrict the slope coefficients β to be identical across i. Standard errors are reported in parentheses below the coefficients. Statistical significance is indicated through at most three stars, referring to confidence levels of %, 5% and % respectively. Panel A Country-by-country estimation Intercept Slope Instruments αi βi τi, τi,2 τi, τi, τi,5 Australia.8*** -.77**.6*** -.***.59*** -.89*** -.52*** (.78) (.) (.) (.7) (.2) (.) (.2) Eurozone 7.85*** 2.*** -.*** -.9*** -.**.6***.6*** (.) (.5) (.) (.9) (.) (.2) (.8) Italy ***.6*** -.5*** -.** -.28* -.2 (.86) (.2) (.2) (.) (.7) (.6) (.26) Netherlands.7*** 2.*** **.2.8. (.72) (.9) (.) (.7) (.9) (.) (.28) Sweden -..8*** -.96**.85*** (.7) (.29) (.) (.29) (.2) (.5) (.5) USA 7.7*** *** * (.5) (.2) (.65) (.72) (.56) (.9) (.6) 2

25 Table A.7 Rationality of one-year ahead interest rate forecasts (continued) Panel B Panel estimation with fixed effects Slope Instruments p-value β τ τ2 τ τ τ5 {τj = }j=,...,5 Panel.29*** -.5* (.5) (.29) (.25) (.) (.8) (.7) 25

26 Table A.8 Determinants of the ARM share in the US: Expectations of future rates based on Michigan survey data In Panel A, we report the correlation coefficient between M t,t+2 and R f t+2 Rf t. Here, M t,t+2 captures one-year ahead interest rate forecasts from the Michigan survey. M t,t+2 is calculated as a balance statistic of categorical answers. It ranges between - (i.e. the entire population expects an interest rate decrease) and (i.e. the entire population expects an interest rate increase). Higher values of M t,t+2 correspond to higher interest rate forecasts. In Panel B, we report estimation results from instrumental-variables regressions for the US, where ARM t, F RM t and ARM t K,t are used as instruments for ARM t,t+t, with T = years and K = year: ARM t,t+t = α + γ ARM t + γ 2 F RM t + γ ARM t K,t + γ B 5 t + γ 5 R f t + γ 6 M t,t+2 + ε t. The second-stage model specification is given by: ARMSHARE t = µ + ρarmshare t + β C (F RM t ARM t ) + β L (F RM t ARM t,t+t ) β M M t,t+2 + ν t. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively. Panel A Correlation between Michigan survey forecasts and one-year ahead realized future changes in interest rates:.7 Panel B First-stage estimation Second-stage estimation γ γ 2 γ γ γ 5 γ 6 β C β L β M.26*** -.26**.***.6*** -.2***.65***.** * 26

27 Table A.9 Robustness checks: Macroeconomic variables and Consensus expectations The table reports the estimated coefficients β C and β D from panel regressions of the form: ARMSHARE i,t = µ i + ρarmshare i,t + β C (F RM i,t ARM i,t ) + β D Θ i,t + ν i,t. Here, Θ i,t stands for each of the variables below: a) rate of consumer price inflation, b) volatility of consumer price inflation, c) nominal interest rate volatility, d) FRM rate volatility, e) real house price growth rate, f) ARM rate, g) expected growth rate of GDP, h) expected growth rate of wages. i) expected rate of inflation. Panel A β C β D (a) (b) (c) (d) (e) Panel.88***.69***.67***.7***.76*** Panel (excl. USA).2***.8***.82***.92***.95*** Post-2 Panel.***.78***.77***.86***.89*** Panel (excl. USA).***.9***.9***.5***.*** Panel.9.2***.58***.5 -. Panel (excl. USA)..5***.66***.2 -. Post-2 Panel Panel (excl. USA) Panel B β C β D (f) (g) (h) (i) Panel.8***.68***.8***.7*** Panel (excl. USA).***.8***.***.9*** Post-2 Panel.2***.77***.***.99*** Panel (excl. USA).7***.9***.6***.2*** Panel.8 -.*** Panel (excl. USA).2 -.8***.*** -. Post-2 Panel.*** Panel (excl. USA).5***

28 Table A. Relationship between the mortgage spread and the slope of the yield curve The table reports univariate correlation coefficients between the mortgage spread (F RM i,t ARM i,t ) and the slope of the yield curve (B 5 i,t Rf i,t ). Australia.7 Belgium.62 Denmark.57 Greece.5 Ireland.8 Italy.5 Netherlands.88 Sweden.89 USA.29 Panel.7 28

29 Table A. Robustness check: Sample of countries with prepayment penalties The table reports estimation results from panel instrumental-variables regressions of the form: ARMSHARE i,t = µ i +ρarmshare i,t +β C (F RM i,t ARM i,t )+β L (F RM i,t ARM i,t,t+t )+ν i,t, where µ i are country-specific fixed effects. ARM i,t, F RM i,t and ARM i,t K,t are used as instruments for ARM i,t,t+t. In our benchmark case, T = years.the first-stage model specification is given by: ARM i,t,t+t = α i + γ ARM i,t + γ 2 F RM i,t + γ ARM i,t K,t + γ B 5 i,t + γ 5 R f i,t + ε i,t. We show the results for K = year. All estimations cover the same sample as the one with T = years. The estimation is carried out in the sample of countries where mortgage prepayment is subject to a penalty: Australia, Belgium, Greece, Ireland, Italy, Netherlands and Sweden. We report bootstrap standard errors in parentheses. Statistical significance is indicated through at most three stars, referring to confidence levels of %, 5% and % respectively. Benchmark T = β C.92*** -.7 (.) (.) β L.*.55*** (.2) (.) Post-2 β C.5*** -.2 (.5) (.8) β L.7***.89*** (.25) (.) 29

30 Table A.2 Robustness check: Non-linearity of mortgage interest rate effects The table reports the estimated coefficients β C and β D from panel regressions of the form: ARMSHARE i,t = µ i +ρarmshare i,t +β C (F RM i,t ARM i,t )+β D I(F RM i,t ARM i,t > d)+ν i,t, where we set d =.5%. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively, based on robust bootstrap standard errors. β C β D Panel.*** -. Panel (excl. USA).7*** -.2 Post-2 Panel.7*** -. Panel (excl. USA).*** -.7

31 Table A. Determinants of the ARM share at the country level: Current mortgage rates vs. rational expectations of future rates The table reports estimation results from country-by-country and panel instrumental-variables regressions where ARM i,t, F RM i,t and ARM i,t K,t are used as instruments for ARM i,t,t+t, with T = years and K = year: ARM i,t,t+t = α i + γ i, ARM i,t + γ i,2 F RM i,t + γ i, ARM i,t K,t + γ i, B 5 i,t + γ i,5 R f i,t + ε i,t. The second-stage model specification is given by: ARMSHARE i,t = µ i + ρ i ARMSHARE i,t + β i,c (F RM i,t ARM i,t ) +β i,l (F RM i,t ARM i,t,t+t ) + ν i,t. Correlation coefficients among regressors are reported under the column heading Γ. Statistical significance is reported through at most three stars, referring to confidence levels of %, 5% and % respectively, based on bootstrap standard errors. First-stage estimation γ γ 2 γ Γ γ,γ2 Γ γ,γ R2 obs. Australia.89***.2 -.9** Belgium -.77*** Denmark *** Greece *** Ireland ** -.2*** Italy.6 -.*** -.56** Netherlands.8*** -.57*** Sweden -..28*** -.*** USA.** -.7* Panel.***.25*** -.28*** Panel (excl. USA).62***.9** -.*** Post-2 Australia * Sweden.75*.7 -.6*** USA.6** Panel.* *** Panel (excl. USA).** ***

32 Table A. Determinants of the ARM share at the country level: Current mortgage rates vs. rational expectations of future rates (continued) Second-stage estimation ρ β C β L Γ βc, β L R2 obs. Australia.9*** Belgium.8***.7*** 2.*** Denmark.8*** Greece.97*** Ireland.88*** Italy.96*** 2.2* Netherlands.92***.2** Sweden.96*** USA.92***.2** -.** Panel.95***.7*** Panel (excl. USA).95***.87***.6* Post-2 Australia.99*** Sweden.95*** USA.95*** Panel.95***.8***.7*** Panel (excl. USA).95***.5***.7**

33 Appendix E: Cross-sectional analysis Our panel analysis is focused on uncovering the determinants of relatively short-term variation in the ARM share. Of course, there are likely broader macroeconomic determinants of preferred mortgage form across countries, which help to determine the country-average ARM share. One potentially important determinant is inflation volatility. If a fixed-rate mortgage cannot be prepaid without penalties, as in Germany or in the US in an environment of falling house prices, then a FRM is risky to the extent that inflation is volatile and persistent. If it can be prepaid without penalties, as in the US in an environment of rising house prices, then inflation volatility increases the FRM rate that banks will want to charge. While inflation volatility also makes an ARM risky for a borrowing-constrained household, because it makes the timing of required payments more volatile in real terms, it is likely that the net effect is to shift demand away from FRMs and toward ARMs (Campbell and Cocco 2, Campbell 2). While this is not our primary focus, we do find suggestive evidence for the role of historical country-specific inflation volatility in explaining the country-average ARM share using countries including the nine countries in our panel analysis. In the top two panels of Figure A.8, we plot the country-level average ARM shares and interest rate fixation periods against the average FRM-ARM rate spread over the sample. The very strong relationship between interest rate spreads and ARM shares which we documented in the time series dimension seems not to hold when we analyze the cross section of countries. If anything, higher spreads tend to be weakly associated with a lower share of ARMs. We do not find this surprising, though, given that the institutional structures of the different international mortgage markets are likely to be affected by numerous legal and regulatory factors, foreclosure and bankruptcy rules, different prepayment penalty regimes, as well as supply-side constraints related to the cost structure of banks. We review these factors in detail in the institutional appendix, Badarinza et al. (26), and highlight the challenges involved in generating comparable mortgage market statistics across countries. Following Campbell (2), the bottom part of Figure A.8 plots the average ARM share and average interest rate fixation period versus the historical level of inflation volatility in each country. The figure shows that there is a strong positive cross-sectional relationship between the average ARM share and the historical level of inflation volatility, and a negative relationship between the average fixation period and historical inflation volatility. This suggests that there is a significant role for household perceptions of inflation risk in determining household mortgage choice in the long run, consistent with the findings of Malmendier and Nagel (26). Viewed through this lens, the striking cross-country differences in the structure of mortgage markets seem plausible: in most of Northern and Western Europe and the US, inflation has been contained over the last few decades, and fixed-rate mortgages are more prevalent. In contrast, in Southern Europe and Australia inflation has been more volatile, and higher ARM shares and lower fixation periods are more prevalent.

34 Figure A.8 Cross-country patterns in mortgage market structure and historical inflation volatility Inflation volatility is measured as the realized standard deviation of the monthly year-on-year inflation rate during the entire available sample period. For Australia, Belgium, Germany, Spain and the US, the series starts in 956, Italy in 958, Greece in 96, Finland, the Netherlands, Portugal and Sweden in 96, Ireland in 97, Denmark in 98 and the UK in 989. Average fixation periods are derived based on the market share of mortgages falling within different fixation period categories. The green dots are distinguishing countries which are not included in the panel analysis. The FRM-ARM spread refers to the difference between the volume-weighted averages of interest rates on fixed-rate (FRM) versus adjustable-rate (ARM) mortgage loans advanced during the respective month. ARM share (percent) Australia Ireland Italy Greece Sweden Denmark BelgiumNetherlands United States Average fixation period (years) United States Belgium Denmark Netherlands Italy Greece ARM share (percent) FRM ARM spread (percent) Finland Spain Portugal Ireland Italy Greece Sweden UKDenmark Netherlands Belgium United States Germany Australia 5 5 Inflation volatility (percent) Average fixation period (years) FRM ARM spread (percent) Belgium Germany Denmark Netherlands UK United States Italy Spain Greece Inflation volatility (percent)

35 Additional references Campbell, J.Y., 2, Mortgage market design, Review of Finance 7,. Malmendier, U. and S. Nagel, 26, Learning from inflation experiences, The Quarterly Journal of Economics,, pp