Addressing International Empirical Puzzles: the Liquidity of Bonds

Abstract

Models that assume bonds denominated in different currencies are perfect substitutes can not explain certain empirical puzzles: the exchange rate volatility puzzle is that these models can not explain the observed volatility in real and nominal exchange rates; the Backus-Smith puzzle is that these models can not explain the observed low correlation between real exchange rates and the ratio of home to foreign consumption; the Backus-Kehoe-Kydland puzzle is that these models can not explain the observed low correlation between home and foreign consumption; and finally, the uncovered interest parity puzzle is that these models can not explain the observed deviations from that parity. These long standing puzzles make the models harder to defend. In this paper, we present a symmetric two country portfolio balance model in which home and foreign bonds are imperfect substitutes for money in each country’s transactions technology; this of course makes home and foreign bonds imperfect substitutes for each other. Our calibrated model is capable of addressing the Backus-Smith puzzle and the Backus-Kehoe-Kydland puzzle. It does not fully resolve the exchange rate volatility puzzle, but it makes some headway. And finally it generates deviations from uncovered interest parity, though by some estimates these deviations are not large enough to be consistent with the data.

Appendix: Estimated Model Parameters

• 1. Fiscal Variables

  • a. Government purchases

    • Regress: log(g_t) on a time trend and save residuals as detrended series ldt(g_t)

    • $$ \mathrm{ldt}\left( {{{\mathrm{g}}_{\mathrm{t}}}} \right)=\gamma +{\rho_{\mathrm{g}}}\,\mathrm{ldt}\left( {{{\mathrm{g}}_{{\mathrm{t}-1}}}} \right)+{\varepsilon_{\mathrm{g}\text{,}\mathrm{t}}} $$

    • Data: log(g_t) = log of real government consumption and investment, NIPA Table 1.1.5, deflated to real terms using the price index for GDP

    • Sample: 1974:1–2007:4

    • $$ \begin{array}{*{20}c} {\mathrm{Estimates}:} \hfill & {{\rho_{\mathrm{g}}}=0.98} \hfill \\ {} \hfill & {\sigma \left( {{\varepsilon_{\mathrm{g}}}} \right)=0.0086} \hfill \\ \end{array} $$

  • b. Taxes

    • Regress: log(x_t) on a time trend and save residuals as detrended series ldt(x_t)

    • $$ \mathrm{ldt}\left( {{{\mathrm{x}}_{\mathrm{t}}}} \right)=\gamma +{\rho_{\tau }}\,\mathrm{ldt}\left( {{{\mathrm{x}}_{{\mathrm{t}-1}}}} \right)+{\varepsilon_{\mathrm{x}\text{,}\mathrm{t}}} $$

    • Data: log(x_t) = log of real current government receipts, NIPA Table 3.1, line 1, deflated by price index for GDP

    • Sample: 1974:1–2007:4

    • $$ \begin{array}{*{20}c} {\mathrm{Estimates}:} \hfill & {{\rho_{\mathrm{x}}}=0.90} \hfill \\ {} \hfill & {\sigma \left( {{\varepsilon_{\mathrm{x}}}} \right)=0.02} \hfill \\ \end{array} $$

• 2. Foreign Official Demand for U.S. Treasury Securities

  • Regress: log(bGH_,t*) on a time trend and save residuals as detrended series, ldt(bGH_,t*)

  • $$ \mathrm{ldt}\left( {\mathrm{bG}{{\mathrm{H}}_{{,\mathrm{t}*}}}} \right)=\gamma +{\rho_{\mathrm{B}}}\,\mathrm{ldt}\left( {\mathrm{bG}{{\mathrm{H}}_{{,\mathrm{t}*-1}}}} \right)+{\varepsilon_{\mathrm{B}\text{,}\mathrm{t}}} $$

  • Data: bGH_,t* = foreign official holdings U.S. Treasury Securities, Flow of Funds, Table L.107, line 9 converted into real terms by dividing by the price index for personal consumption expenditures.

  • Sample period: 1974:1–2007:4

  • $$ \begin{array}{*{20}c} {\mathrm{Estimates}:} \hfill & {{\rho_{\mathrm{B}}}=0.964} \hfill \\ {} \hfill & {\sigma \left( {{\varepsilon_{\mathrm{B}}}} \right)=0.0434} \hfill \\ \end{array} $$

• 3. Elasticity of substitution in home consumption: Taken from Heathcote and Perri (2002).

  • The elasticity can also be estimated from the regression:

    $$ \log \left( {{{\mathrm{c}}_{\mathrm{F}\text{,}\mathrm{t}}}} \right)={\alpha_0}+{\alpha_1}\log \left( {{{\mathrm{c}}_{\mathrm{t}}}} \right)+{\alpha_2}\log \left( {{{\mathrm{p}}_{\mathrm{F}\text{,}\mathrm{t}}}} \right)+{\varepsilon_{\mathrm{u}}} $$

  • Data: We use two series for c_F,t, real imports of consumer goods and services. Both are taken from NIPA table 4.2.5. One is the sum of lines 26, 35, 36, 42, 43 converted into real terms by deflating by price index for non-oil imports. The other is line 38, imports of nondurable consumer goods, deflated by the corresponding price index.

    log(c_t) = log of real personal consumption of non-durables and services expenditures

    p_F,t = price index for non-oil imports/price index for PCE or the price index for imports of nondurable consumer goods/price index for PCE.

  • Sample period: 1974:1–2007:4

  • $$ \begin{array}{*{20}c} {\mathrm{Estimates}:} \hfill & {{\alpha_1}:\mathrm{The}\;\mathrm{two}\;\mathrm{estimates}\;\mathrm{are}\;0.97\;\mathrm{an}\mathrm{d}\;1.30\;\mathrm{an}\mathrm{d}\;\mathrm{neither}\;\mathrm{differs}\;\mathrm{significantly}\;\mathrm{from}\;1.0,\;\mathrm{the}\;\mathrm{value}\;\mathrm{implied}\;\mathrm{by}\;\mathrm{equation}\;25.} \hfill \\ {} \hfill & {{\alpha_2}:\mathrm{The}\;\mathrm{two}\;\mathrm{estimates}\;\mathrm{are} - 1.03\;\mathrm{an}\mathrm{d} - 0.83,\;\mathrm{which}\;\mathrm{bracket}\;\mathrm{the}\;\mathrm{Heathcoate}-\mathrm{Perri}\;\mathrm{value}, - 0.9.} \hfill \\ {} \hfill & {{\rho_{\mathrm{u}}}:\mathrm{Both}\;\mathrm{estimates}\;\mathrm{are}\;0.89.} \hfill \\ {} \hfill & {\sigma \left( {{\varepsilon_{\mathrm{u}}}} \right)=0.033\;\mathrm{at}\;\mathrm{an}\;\mathrm{an}\mathrm{nual}\;\mathrm{rate}\;\mathrm{or}\;0.00825\;\mathrm{per}\;\mathrm{quarter}} \hfill \\ \end{array} $$

• 4. Interest Rate Rule

  $$ \log \left( {{{\mathrm{R}}_{\mathrm{t}}}/\mathrm{R}} \right)={\rho_{\mathrm{R}}}\log \left( {{{\mathrm{R}}_{{\mathrm{t}-1}}}/\mathrm{R}} \right)+\left( {1-{\rho_{\mathrm{R}}}} \right){\varphi_{\pi }}\log \left( {{\prod_{\mathrm{t}}}/} \right)+{\varepsilon_{\mathrm{R}\text{,}\mathrm{t}}}. $$

  • Parameter values (ρ_R = 0.8, φ_π = 2.0, and σ(ε_R) = 0.0024).

  • Here, we just take values that are typical in the literature; the value of σ(ε_R) comes from Canzoneri et al. (2011). We have not included an income term because it would have made inflation too volatile to fit the data.

• 5. Interest Rate Differentials and Effective Exchange Rates

  • a. Effective Exchange Rates

    • Data: Nominal and real effective exchange rates from IFS (ULC definition because of length of sample for real effective exchange rate exceeds that based on CPIs).

    • Use first difference of logs

    • Sample: 1974:1–2007:4

    • $$ \begin{array}{*{20}c} {\mathrm{Estimates}:} \hfill & {\sigma \left( {\varDelta \log \mathrm{e}} \right)=0.028} \hfill \\ {} \hfill & {\sigma \left( {\varDelta \log \mathrm{q}} \right)=0.029} \hfill \\ {} \hfill & {\mathrm{corr}\left( {\varDelta \log \mathrm{e},\varDelta \log \mathrm{q}} \right)=0.943} \hfill \\ \end{array} $$

  • b. Interest rate differentials

    • Data: Money market interest rates for United States, United Kingdom, Canada, Germany, and Japan (IFS).

    • Sample: 1974:1–2007:4

    • $$ \begin{array}{*{20}c} {\mathrm{Estimates}:} \hfill & {\sigma \left( \mathrm{R} \right)=0.004} \hfill \\ {} \hfill & {\sigma \left( {\mathrm{R}-\mathrm{R}^*} \right)=.004\left( {\mathrm{average}\;\mathrm{of}\;\mathrm{the}\;\mathrm{four}} \right)} \hfill \\ \end{array} $$

  • c. CCAPM rate and Spread

    The CCAPM rate (equivalently, β) is, of course, unobservable. In Canzoneri et al. (2007) we compute CCAPM rates for several specifications of preferences. We set our real CCAPM rate to 1.0 % per quarter (β = 1/1.01) and our spread at 0.4 % per quarter.

    • Data: Three-month constant maturity Treasury bill rate from 1982 on. Prior to 1983, the secondary market rate on three-month bill, converted from a discount basis to an investment basis. Inflation data are computed as quarterly percent changes in the CPI-U.

• 6. Asset ratios

  • a. Treasury Securities

    • Data: B_H = Private US holdings of Treasury Securities = Total outstanding less sum of central bank holdings, ROW holdings, and Government holdings.

      Source: Flow of Funds, Table L.209.

      BGH_,t* = Official ROW holdings of Treasury Securities.

      Source Flow of Funds, Table L.107.

      B*F_,t = Private ROW holdings of Treasury Securities.

      Source Flow of Funds, Table L.107.

      M_t = Currency held outside of banks.

      Source Flow of Funds, Table L.108

      C = Personal Consumption Expenditures. Source NIPA Table 1.1.5.

    • Sample: 1974:1–2007:4

      B_H/C = b_H/c = 0.8

      M/C = m/c = 0.28 (We round to 0.3)

      BGH_,*/C = 0.63 (2007:4) (We round to 0.6)

      B*F_,t/C = 0.30 (2007:4)

    • We use a different sample for these two ratios to take into account the recent buildup in dollar balances both by foreign central banks and by the foreign private sector.