Table 1 Properties of exchange rates and consumer price indices

Country Relative to U.S.  Europe

Relative

Statistic  Austria Denmark Finland France Germany Italy Netherlands Norway Spain Switzerland UK  to U.S.

Standard Deviations

Price ratio 1.59 1.23 1.80 1.17 1.42 1.67 1.62 1.80 2.29 1.49 1.74 1.18

Exchange rate

Nominal  8.19  8.08  8.28  8.52  8.37  8.51  8.30  6.23  8.88  9.08  8.20  7.95
Real  7.93  8.00  7.71  7.95  8.06  7.80  7.99  6.08  8.42  8.83  7.89  7.52

Autocorrelations

Price ratio 0.89 0.74 0.92 0.92 0.90 0.87 0.93 0.90 0.90 0.90 0.79 0.90

Exchange rate

Nominal  0.83  0.84  0.85  0.86  0.83  0.85  0.84  0.78  0.87  0.82  0.84  0.85
Real  0.82  0.83  0.83  0.84  0.82  0.83  0.82  0.77  0.86  0.82  0.81  0.83

Cross-Correlations

Real and nominal exchange rates  0.98  0.99  0.98  0.99  0.99  0.98  0.98  0.96  0.97  0.99  0.98  0.99

Table 2 Properties of exchange rates and disaggregated consumer price indices

Country Relative to U.S.  Europe

Relative

Statistic  France  Italy  Netherlands  Norway  to U.S.

Standard Deviations Price ratio

All goods  1.01  1.57  1.44  1.82  1.24
Traded goods  1.42  2.00  1.97  2.13  1.65

Exchange rate

Nominal  8.72  8.68  8.50  6.39  8.25
All goods real  8.25  8.10  8.24  6.14  7.78
Traded goods real  8.05  8.12  8.05  6.34  7.76

Autocorrelations Price ratio

All goods  0.90  0.83  0.88  0.91  0.91
Traded goods  0.90  0.85  0.84  0.90  0.89

Exchange rate

Nominal  0.86  0.86  0.84  0.79  0.85
All goods real  0.84  0.83  0.83  0.76  0.83
Traded goods real  0.84  0.83  0.82  0.79  0.83

Cross-Correlations of Exchange Rates Real and nominal

All goods  0.99  0.98  0.99  0.96  0.99
Traded goods  0.99  0.97  0.97  0.94  0.94
All and traded goods real  1.00  0.99  0.99  0.99  1.00

See notes at the end of the Tables.

Table 3 Properties of exchange rates and wholesale price indices

Country Relative to U.S.  Europe

Relative

Statistics  Austria Denmark Finland Germany Italy Netherlands Spain Switzerland UK  to U.S.

Standard Deviations

Price ratio 2.19 2.25 1.92 2.04 2.86 2.59 2.85 1.99 2.52 2.08

Exchange rate

Nominal  8.19  8.08  8.28  8.37  8.51  8.30  8.88  9.08  8.20  7.98
Real  7.45  6.52  7.29  7.74  7.35  7.59  7.79  8.71  7.25  7.30

Autocorrelations

Price ratio 0.76 0.86 0.83 0.88 0.83 0.90 0.87 0.85 0.85 0.87

Exchange rate

Nominal  0.83  0.84  0.85  0.83  0.85  0.84  0.87  0.82  0.84  0.85
Real  0.79  0.80  0.82  0.81  0.82  0.82  0.84  0.80  0.79  0.82

Cross-Correlations

Real and nominal exchange rates  0.97  0.97  0.98  0.97  0.95  0.95  0.95  0.98  0.95  0.97

Table 4 Parameter values

Benchmark Model

Preferences  β = .99, ψ = 10, γ = 5, σ = 5, η = .39, ω = .94
Final good technology  ρ = 1/3, a_{1} = .9397, a_{2} = .0603
Intermediate good technology  α = 1/3, δ = .021, θ = .9, N = 4
Money growth process  ρ_{μ} = .683, corr(ε_{μ}, ε_{μ}^{∗}) = .5

Variations^{a}

High exports  a_{1} = .7607, a_{2} = .2393

Real shocks

Technology  ρ_{A} = .95, var(ε_{A}) = var(ε_{A}^{∗}) = (.007)^{2}, corr(ε_{A}, ε_{A}^{∗}) = .25
Government consumption  μ_{g} = .13, ρ_{g} = .97, var(ε_{g}) = var(ε_{g}^{∗}) = (.01)^{2}
Taylor rule  ρ_{r} = .79, α_{π} = 2.15, α_{y} = .93/4, corr(ε_{r}, ε_{r}^{∗}) = .5
Incomplete markets  No changes
Sticky wages  ϑ = .87, M = 4
Nonseparable preferences  ξ = 2.25

Table 5 Exchange rates and prices for the models

Variations on the Benchmark Economy^{a}

Benchmark High Nonseparable Real  Taylor  Sticky Incomplete
Statistic  Data^{b}  Economy Exports Preferences Shocks  Rule  Wages  Markets

Standard Deviations Relative to GDP^{c}

Price ratio  .71  3.00  3.26  .02  2.98  1.35  2.11  2.98
(.75)  (.77)  (.00)  (.74)  (.33)  (.59)  (.75)

Exchange rate

Nominal  4.67  4.32  4.27  .07  4.27  4.66  4.14  4.22
(.80)  (.79)  (.01)  (.80)  (.66)  (.80)  (.78)
Real  4.36  4.27  4.09  .05  4.26  4.98  4.35  4.19
(.72)  (.67)  (.01)  (.71)  (.72)  (.83)  (.71)

Autocorrelations

Price ratio  .87  .93  .92  .81  .93  .92  .95  .93
(.02)  (.02)  (.06)  (.02)  (.02)  (.02)  (.02)

Exchange rate

Nominal  .86  .69  .69  .83  .69  .46  .69  .69
(.08)  (.08)  (.05)  (.08)  (.10)  (.08)  (.08)
Real  .83  .62  .58  .77  .62  .48  .69  .62
(.08)  (.08)  (.06)  (.08)  (.09)  (.08)  (.08)

Cross-Correlations

Real and nominal exchange rates  .99  .76  .70  .98  .76  .96  .88  .75
(.06)  (.07)  (.00)  (.06)  (.01)  (.04)  (.06)

Table 6 Business cycle statistics for the models

Variations on the Benchmark Economy

Benchmark High Nonseparable Real  Taylor  Sticky Incomplete
Statistics  Data^{a}  Economy Exports Preferences Shocks  Rule  Wages  Markets

Standard Deviations Relative to GDP

Consumption  .83  .83  .83  .92  .83  .83  .83  .83
(.01)  (.04)  (.00)  (.02)  (.01)  (.02)  (.01)
Investment  2.78  1.59  1.70  1.32  2.34  1.62  1.49  1.59
(.01)  (.08)  (.01)  (.05)  (.01)  (.03)  (.01)
Employment  .67  1.51  1.49  1.51  1.56  1.51  1.50  1.50
(.01)  (.03)  (.00)  (.09)  (.00)  (.01)  (.01)
Net exports  .11  .09  .69  .04  .11  .09  .19  .09
(.01)  (.08)  (.00)  (.02)  (.01)  (.03)  (.01)

Autocorrelations

GDP  .88  .62  .65  .03  .61  .49  .70  .62
(.08)  (.07)  (.10)  (.08)  (.09)  (.07)  (.08)
Consumption  .89  .61  .60  .03  .61  .48  .67  .61
(.08)  (.08)  (.10)  (.08)  (.09)  (.07)  (.08)
Investment  .91  .60  .59  .03  .60  .47  .68  .60
(.08)  (.08)  (.10)  (.08)  (.09)  (.07)  (.08)
Employment  .90  .61  .63  .03  .61  .48  .69  .61
(.08)  (.07)  (.10)  (.08)  (.09)  (.07)  (.08)
Net exports  .82  .72  .53  .12  .77  .68  .84  .71
(.05)  (.07)  (.11)  (.05)  (.06)  (.04)  (.05)

Cross-Correlations

Between foreign and domestic

GDP  .60  .49  .58  .50  .47  .51  .43  .49
(.14)  (.14)  (.09)  (.14)  (.12)  (.18)  (.14)
Consumption  .38  .49  .52  .50  .48  .50  .49  .49
(.14)  (.13)  (.09)  (.14)  (.12)  (.16)  (.14)
Investment  .33  .49  .52  .41  .48  .50  .48  .49
(.14)  (.13)  (.10)  (.14)  (.12)  (.16)  (.14)
Employment  .39  .49  .60  .50  .48  .51  .44  .49
(.14)  (.13)  (.09)  (.14)  (.12)  (.18)  (.14)
Between net exports and GDP  −.41  .04  .11  −.50  .05  −.04  .26  .04
(.16)  (.15)  (.09)  (.17)  (.15)  (.18)  (.16)

Between real exchange rates and

GDP  .08  .51  .34  .17  .51  .49  .52  .51
(.13)  (.15)  (.09)  (.13)  (.11)  (.15)  (.13)
Net exports  .14  −.04  −.47  −.26  .03  −.20  .30  −.04
(.13)  (.09)  (.06)  (.16)  (.13)  (.13)  (.13)
Relative consumptions  −.35  1.00  1.00  .32  1.00  1.00  1.00  1.00
(.00)  (.00)  (.04)  (.00)  (.00)  (.00)  (.00)

Table 7

The Correlation Between the Real Exchange Rate and Relative Consumptions

France  Germany  Italy  U.K.
U.S.  −.06  −.15  −.35  −.48
France  .24  −.17  .05
Germany  −.08  .17
Italy  .14

Footnotes to the Tables

Table 1. The statistics are based on logged and H-P-filtered quarterly data for the period 1973:1–2000:1. The statistics for Europe are trade-weighted aggregates of countries in the table. (See the text for details on construction of the data for Europe.)

Table 2. The statistics are based on logged and H-P-filtered quarterly data for the period 1973:1–1998:4. The statistics for Europe are trade-weighted aggregates of countries in the table. (See the text for details.)

Table 3. The statistics are based on logged and H-P-filtered quarterly data for the period 1973:1–2000:1. The statistics for Europe are trade-weighted aggregates of countries in the table. (See the text for details.)

Table 4. a Other parameters in the variations are the same as in the benchmark model, except for two parameters. The adjustment cost parameter is chosen to keep the relative volatility of consumption and output the same as in the data. The innovations to the monetary policy are chosen to keep the volatility of output the same as in the data.

Table 5. The statistics are based on logged and H-P filtered data. For each economy the standard deviation of monetary shocks are chosen so that the standard deviation of GDP is the same as it is in the data from 1973:1-1994:4, namely, 1.82 percent. Numbers in parentheses are standard deviations of the statistic across 100 simulations. a See Table 4 for specifications of the variations of the benchmark economy. b The statistics are based on a European aggregate with France, Italy, the U.K., and West Germany over the sample period 1973:1-1994:4. c The standard deviations of the variables are divided by the standard deviation of GDP.

Table 6. Notes a and c of Table 5 also apply here. With the exception of net exports, the standard deviation of each variable is divided by the standard deviation of output. Throughout the table we measure net exports as the H-P-filtered ratio of real net exports to real gross domestic product. Thus, the standard deviation of net exports is simply the standard deviation of this ratio. a With the exception of net exports, the standard deviations and autocorrelations in the data column are based on logged and H-P-filtered U.S. quarterly data for the period 1973:1–1994:4. The cross-correlations between domestic and foreign variables are based on the U.S. and a European aggregate of France, Italy, the U.K., and West Germany.

Table 7. The table reports the correlation between bilateral real exchange rates, q̂_{t}, and relative consumptions, ĉ_{t} − ĉ_{t}^{∗}.