RDP 2007-10: Trade Costs and Some Puzzles in International Macroeconomics 3. Main Results

Luke Willard

October 2007

Table 1 indicates that trade costs have tended to decline over time and there is substantial variation in trade costs across countries. The level and trends in average trade costs are broadly consistent with other studies, which also imply that trade costs have declined at least since the 1980s (see, for example, Hummels 1999).

Table 1: Summary Statistics
1974–1981 1982–1991 1992–2001
Trade costs (CIF compared to FAS) (per cent)      
Average 7 6 4
Standard deviation 3 2 2
Maximum 16 13 10
Minimum 2 1 0
Trade costs (also including duties) (per cent)      
Average 12 9 6
Standard deviation 5 3 3
Maximum 57 16 14
Minimum 4 2 1
Other variables      
Investment (per cent of GDP) average 26 23 21
Standard deviation 4 4 3
Saving (per cent of GDP) average 24 23 23
Standard deviation 5 4 5
Ln(output/output world) average 1.3 1.4 1.4
Standard deviation 0.4 0.4 0.4
Ln(cons/cons world) average 1.3 1.4 1.4
Standard deviation 0.3 0.4 0.3
Ln(GDP(PWT)) average 9.6 9.8 10.0
Standard deviation 0.2 0.2 0.2
Ln(consumption(PWT)*100) average 13.7 13.8 14.0
Standard deviation 0.2 0.2 0.2
Capital controls average 0.8 0.6 0.1
Investment and saving correlation 0.58 0.63 0.30
Real exchange rate and one year lag correlation 0.85 0.94 0.80
Consumption and output regression coefficient 0.84 0.79 0.64
Notes: These are summary statistics where each observation is country-year. There are 168 observations on trade costs for 1974–1981, 210 for 1982–1991 and 210 for 1992–2001. The number of observations used for calculating the investment and real exchange rate correlations are: 168 and 116, respectively, for 1974–1981; 210 for 1982–1991; and 210 for 1992–2001. Note that as the subsequent regression analysis includes a constant, using Ln(Consumption(PWT)*100) will be equivalent to using Ln(Consumption(PWT)). PWT indicates the Penn World Table per capita PPP data. The last row reports results controlling for country fixed effects.

Also there is some evidence that the investment-saving correlation and the strength of the consumption-output correlation have both decreased over time, consistent with trade costs falling.

3.1 Feldstein-Horioka Puzzle

Table 2 reports the estimates for the investment equation. Each row reports the coefficients from a single regression; results for a wide variety of specifications and samples are reported, providing evidence of the robustness of the results.

Table 2: Investment – Equation (1)
Model with country fixed effects
Trade-cost measure Specification
 		 Saving
 		 Interaction term Trade cost
1 With duties
 		 Baseline specification
 		 0.19*
(0.09)		 0.04*
(0.01)		 −0.40*
(0.18)
2 Without trade costs Baseline specification
 		 0.44*
(0.07)		 na na
3 With duties
 		 With country-decade fixed effects
 		 0.35*
(0.08)		 0.035*
(0.008)		 −0.69*
(0.16)
4 Without trade costs With country-decade fixed effects
 		 0.61*
(0.06)		 na na
5 No duties
 		 Baseline specification
 		 0.15
(0.08)		 0.07*
(0.01)		 −0.73*
(0.24)
6 With duties Weighted by population 0.56 0.006 0.22
7 With duties Weighted by GDP 0.63 −0.002 0.42
8 With duties
 		 With additional
control(a)		 1.88
(1.20)		 0.04*
(0.01)		 −0.45*
(0.19)
9 With duties
 		 Robust
regression(b)		 0.49*
(0.05)		 0.02*
(0.005)		 −0.10
(0.11)
10 No duties
 		 Trade cost average of whole sample −0.12
(0.10)		 0.14*
(0.02)		 na
11 With duties
 		 Trade cost average of whole sample −0.18
(0.11)		 0.10*
(0.01)		 na
12 With duties
 		 IV (lagged costs as
instruments)(c)		 0.58
(0.38)		 −0.007
(0.04)		 0.95
(1.25)
13 With duties
 		 Alternative investment measure
 		 0.17*
(0.09)		 0.02*
(0.01)		 −0.10
(0.23)
14 With duties
 		 With productivity and demographic controls 0.18*
(0.09)		 0.02*
(0.01)		 −0.25
(0.15)
Notes: Robust standard errors are reported in parentheses. There are 588 observations used to estimate the results in the first row. * indicates significance at the 5 per cent level. ‘na’ signifies no available estimate either because the terms are not included in the regression or because the variable is co-linear with the fixed effects.
(a) Additional control is log distance interacted with the main independent variable (here, saving).
(b) Calculated using Stata's rreg command.
(c) According to Stock-Yogo critical values, the instruments are not weak.

Proceeding from the top of Table 2, I first report the two regressions that are the focus of my analysis. The first regression estimates Equation (1) with trade-cost terms (including duties), while the second regression excludes trade costs. With trade costs, the interaction term is positive and statistically significant though the saving coefficient is not zero, suggesting that trade costs are only a partial explanation of the puzzle. The extent to which trade costs can account for the puzzle is indicated by the lower coefficient on saving in the model with trade costs compared to the coefficient without (0.19 versus 0.44). Though it is of less interest, the coefficient on trade costs is negative and significant.[17]

Results for a variety of reasonable alternative specifications are as follows. The third and fourth regressions include country-decade fixed effects (which can lead to better estimates if it is believed that the relationship between investment and saving may vary within the same country over time, say, because of productivity shocks). As the theory only describes trade costs in a simple way, it is reassuring that the results estimated using this regression are similar to those in the first two rows. The fifth row reports the results where the trade-cost measure does not include duties. The results are similar to the first row.

The sixth and seventh regressions estimate Equation (1), but weighted by population and GDP (which could reduce measurement error problems and may be more appropriate if one is more interested in the result among larger, more populated economies).[18] These results provide weaker evidence that trade costs play a role in the puzzle.

The eighth regression is estimated with log distance (from the US) interacted with saving (the main independent variable) included in the regression, as well as the standard monetary measure of trade costs. This is designed to examine whether the results are sensitive to the inclusion of other variables that may measure trade costs (at least with the largest economy in the world). One motivation for including this variable is to examine whether the main trade-cost variable may be picking up the effects of trade costs specific to the US. It is notable that the monetary trade cost-saving interaction term remains positive and significant (suggesting monetary trade costs play a role). However, the coefficient on saving becomes larger (though it is statistically indistinguishable from zero). This regression suggests that once a rich enough set of trade-cost measures are included, the positive correlation between saving and investment disappears.

The ninth regression reports the results using a robust regression procedure which seeks to downplay the role of potential outliers. This regression has similar results to the baseline specification, though the coefficient on saving is larger. Rows 10 and 11 report the results of using average trade costs over the sample as the measure of trade costs. This could help eliminate measurement error and so may yield better estimates. Consistent with this, the estimate on the interaction term is larger in this specification, at least compared to the baseline specification.

The twelfth row reports the results using instrumental variables (IV), where the lagged trade costs are used as an instrument. IV estimation is motivated by the trade-cost measure providing a noisy measure of the actual trade cost. Using an instrument (that is, lagged trade costs) can potentially resolve this problem by essentially providing a better measure of trade costs (see Hayashi 2000, ch 3).[19] However, the standard errors are large (as is common with IV estimation), suggesting that this method does not provide very informative results. The thirteenth row reports results using an alternative measure of investment (using gross fixed capital formation instead of gross capital formation). The fourteenth row reports results with demographic and productivity controls (proxied by GDP growth).[20] The latter is motivated by Taylor (1994), who finds evidence that demographic and productivity changes account for some of the puzzle, consistent with demographic and productivity changes affecting both investment and saving.

In summary, the regression results in Table 2 generally suggest that there is evidence that increased trade costs are associated with a larger correlation between investment and saving (as indicated by the tendency for the coefficient on the interaction term to be positive and significant). Even so, trade costs can explain some, but not all, of the Feldstein-Horioka puzzle, since the coefficient on saving tends to be typically lower in the model with transaction costs than the one without, though it remains positive and significant.

3.2 PPP Puzzle

Tables 3 and 4 present estimates from a similar set of regressions with the real exchange rate as the dependent variable and the lagged exchange rate as the main independent variable. They show that the coefficient for the trade-cost interaction term is of the correct sign (positive), though it is typically insignificant. The negative coefficient on the trade-cost term suggests that countries with higher trade costs have lower real exchange rates (perhaps consistent with a need to have a more competitive exchange rate to compensate for higher trade costs). It is noticeable that the lagged real exchange rate coefficient is somewhat smaller compared to models without trade costs.[21]

Table 3: Real Exchange Rate – Levels Equation (3)
Model with no fixed effects
Trade-cost measure Specification Lagged real exchange rate Interaction term Trade cost
1 With duties
 		 Baseline specification
 		 0.81*
(0.08)		 0.005
(0.009)		 −0.56
(0.92)
2 Without trade costs Baseline specification
 		 0.86*
(0.03)		 na na
3 With duties
 		 Decade fixed effects
 		 0.80*
(0.08)		 0.01
(0.01)		 −0.7
(0.9)
4 Without trade costs Decade fixed effects
 		 0.86*
(0.03)		 na na
5 No duties
 		 Baseline specification
 		 0.80*
(0.06)		 0.01
(0.01)		 −1.18 (1.01)
6 With duties Weighted by population 0.73 0.02 −1.93
7 With duties Weighted by GDP 0.68 0.03 −2.58
8 With duties
 		 With additional control(a)
 		 −0.25
(0.99)		 0.003
(0.02)		 −0.24 (1.47)
9 With duties
 		 Robust regression(b)
 		 0.81*
(0.04)		 0.01*
(0.005)		 −1.07*
(0.47)
10 No duties
 		 Trade cost average of whole sample 0.83*
(0.09)		 0.007
(0.016)		 −0.67 (1.64)
11 With duties
 		 Trade cost average of whole sample 0.80*
(0.10)		 0.009
(0.012)		 −0.98 (1.24)
12 With duties
 		 With four lags of first difference of lagged RER 0.82*
(0.06)		 0.007
(0.006)		 −0.73
(0.65)
Notes: Robust standard errors are reported in parentheses. There are 536 observations used to estimate the results in the first row. * indicates significance at the 5 per cent level. ‘na’ signifies no available estimate either because the terms are not included in the regression or because the variable is co-linear with the fixed effects.
(a) Additional control is log distance interacted with the main independent variable.
(b) Calculated using Stata's rreg command.
Table 4: Real Exchange Rate – Logs Equation (2)
Model with no fixed effects
Trade-cost measure Specification Lagged RER Interaction term Trade cost
1 With duties
 		 Baseline specification
 		 0.80*
(0.07)		 0.008
(0.008)		 −0.04
(0.04)
2 Without trade costs Baseline specification
 		 0.88*
(0.03)		 na na
3 With duties
 		 Decade fixed effects
 		 0.79*
(0.07)		 0.01
(0.01)		 −0.04
(0.04)
4 Without trade costs Decade fixed effects
 		 0.88*
(0.03)		 na na
5 No duties
 		 Baseline specification
 		 0.80*
(0.06)		 0.01
(0.01)		 −0.07
(0.04)
6 With duties Weighted by population 0.69 0.02 −0.11
7 With duties Weighted by GDP 0.62 0.03 −0.14
8 With duties
 		 With additional control(a)
 		 −0.03
(0.96)		 0.008
(0.012)		 −0.04
(0.06)
9 With duties
 		 Robust regression(b)
 		 0.84*
(0.04)		 0.007
(0.004)		 −0.03
(0.02)
10 No duties
 		 Trade cost average of whole sample
 		 0.87*
(0.07)		 0.001
(0.013)		 −0.004
(0.06)
11 With duties
 		 Trade cost average of whole sample
 		 0.85*
(0.09)		 0.004
(0.010)		 −0.02
(0.05)
12 With duties
 		 IV (lagged costs as
instruments)(c)		 1.20*
(0.13)		 −0.03*
(0.01)		 0.16*
(0.06)
13 With duties
 		 With four lags of first difference of lagged RER 0.80*
(0.06)		 0.011
(0.007)		 −0.05
(0.03)
14 With duties
 		 Estimated in first differences using IV (country fixed effects)(c) 1.09*
(0.20)		 −0.0001
(0.0003)		 0.001
(0.001)
15 With duties
 		 Using Imbs et al monthly data 0.96 −0.001 0.0009
16 With duties
 		 Using quarterly bilateral data and country fixed effects 0.96*
(0.02)		 0.0007
(0.002)		 −0.002
(0.008)
Notes: Robust standard errors are reported in parentheses. There are 536 observations used to estimate the results in the first row. * indicates significance at the 5 per cent level. ‘na’ signifies no available estimate either because the terms are not included in the regression or because the variable is co-linear with the fixed effects.
(a) Additional control is log distance interacted with the main independent variable.
(b) Calculated using Stata's rreg command.
(c) Based on Stock-Yogo critical values, the instruments are not weak.

The last three rows of Table 4 present results that use some alternative estimation methods and/or data that have been used in the existing literature. Specifically, row 14 reports results controlling for country fixed effects. Row 15 uses bilateral monthly real exchange rate data between the US and some European countries where prices are particular sub-components of the CPI index. This is designed to address the concern that the PPP puzzle is an artefact of using aggregated prices (see Imbs et al 2005).[22] The data for this come from Imbs' website. The last row uses monthly bilateral real exchange rates with the US. These last three rows suggest that the exchange rate is highly persistent and do not suggest a role for trade costs to explain the puzzle.

3.3 International Consumption Correlation Puzzle

Tables 5, 6 and 7 provide evidence about whether trade costs play a role in the international consumption correlation puzzle. The first two tables use data calculated using exchange rate measures (with consumption including government spending). Table 5 uses only country fixed effects (that is, it estimates Equation (4), the preferred specification), while Table 6 includes decade-country interactions. Both Tables 5 and 6 report a set of results based on consumption including the statistical discrepancy in case some hard-to-estimate components of consumption are in the discrepancy. Also, in rows 14 and 15 of Table 5, results are reported using consumption (excluding government spending) and including demographic controls. The last regression is similar to Townsend (1994), which includes demographic controls. The results from these regressions can be viewed as further robustness checks.

Table 5: Consumption – Equation (4)
Exchange rate measure (including government spending) – country fixed effects
Trade-cost measure Specification Output Interaction term Trade cost
1 With duties
 		 Baseline specification
 		 0.70*
(0.04)		 0.0001
(0.0002)		 −0.000
(0.003)
2 Without trade costs Baseline specification
 		 0.70*
(0.03)		 na na
3 No duties
 		 Baseline specification
 		 0.65*
(0.04)		 0.005
(0.003)		 −0.010*
(0.004)
4 With duties
 		 Consumption including statistical discrepancy 0.43*
(0.04)		 0.012*
(0.002)		 −0.006
(0.003)
5 With duties; Weighted by population 0.86 −0.0005 −0.0025
6 With duties Weighted by GDP 0.83 −0.0029 0.0000
7 With duties
 		 With additional control(a)
 		 0.70*
(0.03)		 0.0018
(0.0013)		 0.11*
(0.02)
8 With duties
 		 Robust regression(b)
 		 0.79*
(0.02)		 0.0082*
(0.001)		 −0.013*
(0.001)
9 No duties
 		 Trade cost average of whole sample 0.46*
(0.04)		 0.066*
(0.009)		 na
10 With duties
 		 Trade cost average of whole sample 0.36*
(0.04)		 0.057*
(0.006)		 na
11 With duties
 		 IV (lagged costs as
instrument)(c)		 0.70*
(0.11)		 0.001
(0.005)		 −0.0008
(0.01)
12 With duties
 		 Estimated in first differences
 		 0.64*
(0.04)		 −0.0002
(0.001)		 0.0003
(0.001)
13 With duties
 		 Year dummies and regression of log(C) on log(Y) 0.63*
(0.04)		 0.005*
(0.002)		 −0.044*
(0.014)
14 With duties
 		 Consumption (excluding government spending) 0.67*
(0.03)		 0.0002
(0.0002)		 0.001
(0.002)
15 With duties
 		 Including demographic controls
 		 0.61*
(0.03)		 0.0024*
(0.0012)		 −0.0001
(0.001)
Notes: Robust standard errors are reported in parentheses. There are 588 observations used to estimate the results in the first row. * indicates significance at the 5 per cent level. ‘na’ signifies no available estimate either because the terms are not included in the regression or because the variable is co-linear with the fixed effects.
(a) Additional control is log distance interacted with the main independent variable.
(b) Calculated using Stata's rreg command.
(c) Based on Stock-Yogo critical values, the instruments are not weak.
Table 6: Consumption – Equation (4)
Exchange rate measure (including government spending) – decade-country fixed effects
Trade-cost measure Specification Output Interaction term Trade cost
1 With duties
 		 Baseline specification
 		 0.72*
(0.03)		 −0.001
(0.001)		 0.001
(0.001)
2 Without trade costs Baseline specification
 		 0.72*
(0.03)		 na
 		 na
 
3 No duties
 		 Baseline specification
 		 0.67*
(0.03)		 0.005
(0.003)		 −0.010
(0.004)
4 With duties
 		 Consumption including statistical discrepancy 0.47*
(0.03)		 0.009
(0.002)		 −0.008*
(0.002)
Notes: Robust standard errors are reported in parentheses. * indicates significance at the 5 per cent level. ‘na’ signifies no available estimate either because the terms are not included in the regression or because the variable is co-linear with the fixed effects. There are 588 observations used to estimate the results in the first row.
Table 7: Consumption Smoothing – Equation (4)
PPP measure (excluding government spending) – country and year fixed effects
Trade-cost measure Specification Output Interaction term Trade cost
1 With duties
 		 Baseline specification
 		 0.70*
(0.04)		 0.005
(0.003)		 −0.05
(0.03)
2 Without trade costs Baseline specification
 		 0.74*
(0.04)		 na
 		 na
 
3 No duties
 		 Baseline specification
 		 0.72*
(0.04)		 0.004
(0.006)		 −0.04
(0.05)
4 With duties Weighted by population 0.88 0.0005 −0.006
5 With duties Weighted by GDP 0.88 0.0042 −0.042
6 With duties
 		 With additional control(a)
 		 −0.25
(0.20)		 0.005
(0.003)		 −0.05
(0.03)
7 With duties
 		 Robust regression(b)
 		 0.66*
(0.02)		 0.015*
(0.002)		 −0.15*
(0.01)
8 No duties
 		 Trade cost average of whole sample 0.70*
(0.03)		 0.014*
(0.005)		 na
 
9 With duties
 		 Trade cost average of whole sample 0.65*
(0.03)		 0.018*
(0.004)		 na
 
10 With duties
 		 IV (lagged costs as
instrument)(c)		 0.68*
(0.06)		 0.009*
(0.004)		 −0.08*
(0.04)
11 With duties
 		 Consumption (including government spending) 0.53*
(0.03)		 0.002
(0.02)		 −0.14*
(0.02)
12 With duties
 		 Including demographic controls
 		 0.65*
(0.04)		 0.003
(0.003)		 −0.029
(0.029)
Notes: Robust standard errors are reported in parentheses. There are 588 observations used to estimate the results in the first row. * indicates significance at the 5 per cent level. PPP regressions include year fixed effects which effectively controls for the level of ‘world’ output despite a world output measure being unavailable. ‘na’ signifies no available estimate either because the terms are not included in the regression or because the variable is co-linear with the fixed effects.
(a) Additional control is log distance interacted with the main independent variable.
(b) Calculated using Stata's rreg command.
(c) Based on Stock-Yogo critical values, the instruments are not weak.

Table 7 is based on PPP data (with consumption excluding government spending). Rather than using measures of world output and consumption (which are included in Equation (4)), it includes year fixed effects to capture these omitted variables. In some sense this specification could be viewed as allowing for a weaker form of global risk sharing. For example, it may be that there is perfect risk sharing among OECD countries (rather than the world as a whole), in which case these regressions should find an interaction term that is equal to zero. Rows 11 and 12 include results with consumption including government spending and demographic controls respectively.[23]

Tables 5–7 generally report an interaction coefficient which is positive, though often insignificant. In general, the introduction of trade-cost terms do not substantially change the size of the coefficient on the output term, suggesting that trade costs do not play a big part in the consumption correlation puzzle. This might be because non-tradables lead to a correlation between domestic consumption and output. The estimates for the interactive coefficient using trade costs averaged over the whole sample (which may eliminate measurement error) tend to be positive, significant and are often larger than the estimates obtained using other regressions.

Also, it can be seen from the results reported in Tables 5 and 7 that the results are generally not sensitive to whether consumption includes government spending or not. This suggests that government spending does not play a major role in reducing the consumption correlation puzzle in either high- or low- trade-cost countries.

In Tables 2–7, it is noticeable that when an additional control is included (that is, the inclusion of an interaction term between the main independent variable and log distance from the US), the main independent variable often becomes insignificant and/or negative. As log distance is a measure of trade costs, this could be viewed as suggesting that with a richer or more complete set of measures of trade costs, the apparent puzzles can be explained.

One potential concern with the above results is that the interaction term may just be capturing a trend decline in the puzzle over time (as trade costs have tended to decline over time). The inclusion of an additional interaction term between a time trend and the main independent variable provides mixed evidence on this (results not shown). The interaction term between trade costs and the main independent variable remains positive for the investment and log real exchange rate equation, while it becomes negative for some specifications of the consumption equation.[24]

Footnotes

For a number of the regressions estimated in this paper, I allowed for serial correlation of the errors by estimating Newey-West standard errors. However, they led to similar results and so are not reported. [17]

For all regression results using weighting, I have used Stata's pweight option. This reweights assuming that the weight is the inverse of the probability that the observation is included due to sampling design. For the point estimates, the results seem robust to the reweighting method used. I have not reported standard errors as the results are sensitive to the weighting method used and the most appropriate method is debatable. [18]

Using IV assumes that noise in the instrument, lagged trade cost, is uncorrelated with the noise in the regressor, current trade costs, which seems plausible. [19]

Unlike Taylor (1994), relative prices are not included as controls as they may be related to the relative prices faced by locals and foreigners. [20]

There is mixed evidence on time-series properties of the main economic series, but there are some theoretical reasons for thinking they may be stationary and hence the regression results being informative. In the context of Tables 3 and 4, a potential concern is that the real exchange rate may have a unit root. The existing literature suggests that it is difficult to distinguish between a unit root and a persistent stationary process and that, using very long runs of data, there is evidence that real exchange rates are stationary (see discussion in Schnatz 2006). Also, if the real exchange rate does have a unit root, then it suggests that it is not mean-reverting, which seems at odds with the characterisation of the puzzle – that the exchange rate just takes longer than expected but does revert to the mean. Potentially, some of the investment and consumption regressions I conduct could be viewed as robustness checks in case my baseline regressions are misleading due to the time series being non-stationary. [21]

The results are estimated using the mean group estimator used by Imbs et al (2005) and discussed in Pesaran and Smith (1995), which allows for country fixed effects. The use of country fixed effects is likely to be less problematic for rows 15 and 16 as they use monthly and quarterly data, which are more frequent. [22]

Row 13 of Table 5 reports the results of running a regression similar to those reported in Table 7 (that is, a regression of log consumption per capita on log output per capita with year and country fixed effects). [23]

Some analysis I conducted including developing countries provides less evidence that trade costs play a role in the puzzles, though there was some evidence for the investment equation. This may be because, for these countries, my proxy for trade costs less accurately reflects true trade costs. [24]