Trade Balances in an Integrated World

The representative consumer in each province maximizes the expected value of an identical time-separable utility function with a constant subjective rate of discount equal to ρ,³

where E is the expectations operator, C is consumption, t and j refer to time periods, and the superscript i refers to the province. The consumption decision is subject to the budget constraint that the discounted value of consumption equals wealth, defined as the discounted value of future net income available for consumption plus the value of initial assets,⁴

where Y-I-G represents provincially produced income available for consumption, r is the real interest rate. Aⁱ is net asset holdings for the province, and Qⁱ is the net present value of future consumption or, equivalently, the wealth of the province. Net assets can be of any type (conventional debt, equity) so long as certainty equivalence holds, that is, the value of the asset is equal to the discounted value of expected future net income. The lack of a provincial superscript on the interest rate reflects the assumption that national asset markets are integrated and hence that consumers in provinces face a common (and possibly time-varying) real interest rate.

Provincially produced net income available for consumption (hereafter simply net income) is equal to gross provincial product (the provincial analogue to GDP) less investment less provincial government consumption.⁵ It refers to the level of consumption that could be achieved under autarky. Asset markets allow individuals to increase their welfare by reallocating this net income over time. We do not model the behavior of investment or government consumption explicitly since results from this analysis follow regardless of the behavior of investment and government consumption as long as all sectors in the economy face the same real interest rate.⁶ The function derived here is thus relatively general.

The first-order condition for this problem is the familiar

In the commonly studied case where there is a constant coefficient of relative risk aversion equal to θ, the utility function takes die form $U\left(C_t^i\right)={\left(C_t^i\right)}^{1-\theta }/\left(1-\theta \right)$ and equation 3 takes the form

The first-order condition (4) and the budget constraint (2) imply that consumption in any period t is a fraction of total wealth,

For any two provinces i and.j with a common discount factor and facing the same expected path of interest rates due to integrated capital markets we have

Extending equation (6) across all provinces implies that the ratio of world consumption to world wealth equals the ratio of consumption to wealth in any province. As world consumption equals world income available for consumption, this implies that

where the superscript W refers to the world.

An equation for the trade balance of province i, $T{B}_t^i$ can be derived by noting that the trade balance equals the difference between provincial net income and provincial consumption,

Equation (8) demonstrates the extent to which the trade balance can be used to smooth provincial consumption over time. Differences between provincial net income and world net income will be manifested in the trade balance but aggregate changes in net income will be met by concomitant movements in provincial consumption.

We derive from equation (8) an estimating equation in first differences that includes expectational error terms. As shown in the Appendix, the change in the trade balance is

where the error, ∈_t is a linear combination of the “news” obtained between times t - 1 and t about current wealth of the province at time t, ${ϵ}_t^i$, and the current wealth of the world at time t,${ϵ}_t^W$⁷

Equation (9) is the basic building block of our study. It states that, in a fully integrated world, the per capita trade balance for any province i should vary with expected changes in per capita net provincial income relative to that of the rest of the world. A striking feature of equation (9) is its simplicity and ease of estimation.⁸

Heterogeneous Levels of Economic Integration

Equation (9) holds across any area with fully integrated goods and asset markets. We now extend the analysis to consider situations in which access to such markets is more limited. Ideally, one would develop a fully optimizing model involving fundamentals such as costs of transactions to look at this question. We adopt a somewhat simpler approach based on the type of model developed by Campbell and Mankiw (among others) to look at the dependence of consumption upon income.⁹

Assume that there are two types of consumers: those who are fully integrated with world markets and those who are limited to markets within the country. If consumers with access to foreign resources represent a constant share λ of consumption while the consumers with restricted options represent the remaining (1 - λ) share of consumption, the expected change in the overall trade balance for province i is a weighted average of the behavior when international access is perfect—equation (9)—and the behavior of consumers with access only to Canadian markets (which is described by a version of equation (9) in which national variables replace world ones). This implies that

The term representing the change in world net income reflects the impact of the aggregate world resource constraint on behavior even in a fully integrated world. The term representing national net income captures the effect of limited international integration on the consumption of a proportion of consumers.

Empirical Specification

Equation (10) suggests specifications for estimating the determinants of the provincial trade balance. In the case of full financial integration of the province with the rest of the world, that is, when λ = 1, the trade balance equation can be estimated by

where

and αi and βi are estimated coefficients and ${ϵ}_t^i$ is an error that is uncorrelated with information known at t - 1. The βi coefficients indicate the proportion of consumption that is integrated with the behavior in the rest of the OECD (which proxies for the “world” in our empirical analysis) and is not directly linked to current income.

This empirical specification assumes that consumers who have access to borrowing do not have differential access to national as compared to international financial markets. An alternative specification, which nests equation (11), is

where

The coefficient βⁱ represents the estimate of the proportion of consumption in province i that is not directly linked to current income. We call this the proportion of “smoothed consumption.” Thus the specification (12) allows for the possibility that some consumers lack access even to national Canadian markets. These consumers would behave in a completely autarkic manner. For example, if βⁱ = 0.8, then 20 percent of consumption in province i is estimated to be linked to current income and not smoothed with respect to national or world income. The coefficient on the second variable in (12), λⁱ, represents the proportion of total consumption that is smoothed only through access to the national capital markets. The difference between the first and second coefficients, βⁱ - λⁱ, indicates the proportion of consumption that is smoothed through access to the national capital market but not the world capital market. For example, if βⁱ = 0.8 and λⁱ = 0.3, then the estimate is that 80 percent of consumption is smoothed but of this value only 50 percent uses access to the world capital market. The other 30 percent is smoothed only within Canada.

These trade balance equations are run for each province as well as for Canada as a whole. The implied equation for the Canadian trade balance from equation (12) is

If coefficients are equal across provinces, this implies the coefficient restriction βⁱ = β^CAN. This cross-equation restriction between the regressions for each province and that for Canada as a whole can be used as a further test of the validity of the model.

Lagged instrumental variables are used in the estimation because the error term includes revisions in expectations between time t - 1 and time t. We use past changes in income and the trade balance as our instruments. Past changes in income should be useful in helping to predict current changes in income. Since consumption is smoothed over time, it follows that the past changes in the trade balance will also include information about changes in income. Accordingly, in addition to constant terms, the first and second tags of the change in provincial income relative to the rest of the OECD, the change in provincial income relative to Canada, and the provincial and national trade balances were used as instruments.

Data Sources and Statistics

The source of provincial Canadian data is the annual Provincial National Accounts published by Statistics Canada. This publication provides real and nominal expenditures and nominal income (as well as population) for the ten provinces and two territories of Canada.¹⁰ Provincial expenditures are subdivided into domestic categories such as public and private consumption and investment but do not include spending on exports and imports.¹¹ The income accounts divide nominal gross provincial product (the provincial equivalent of gross national product) into categories such as wages and profits as well as nominal net exports of goods and services. Net exports are calculated indirectly as the difference between total provincial expenditures (calculated from the expenditure data) and gross provincial product (the provincial equivalent of GDP, calculated from the income data). Hence any statistical discrepancies are included in net exports. The nominal data start in 1961, while the real data start in 1971. Both end in 1992.

These accounts provide all the data needed to estimate the model. Per capita real domestic net income available for consumption was calculated as nominal gross provincial product minus government consumption and total investment, deflated by population and the implicit consumption deflator. Per capita real trade balances were calculated as nominal net exports, again deflated by population and the consumption deflator.¹²

There are two issues associated with the data that deserve further discussion. One is the inclusion of a statistical discrepancy in the data for net exports. According to the national accounts identity, net exports should equal the difference between total expenditure and income. However, in most national accounts net exports are derived from direct estimates of exports and imports. The difference between the direct estimate and that implied by the national accounts identity is then labeled a statistical discrepancy. The provincial accounts do not contain a direct measure of net exports, however, and by assuming that the national accounts identity holds, net exports are derived as a residual. This could potentially affect our regression results since there would be a correlation between changes in net income and the trade balance due to errors in the measurement of provincial expenditures and product. As mentioned above, we estimate equations using instrumental variables and therefore the errors present in the measurement of provincial expenditures and product only affect estimates of net exports to the extent that they are predictable. We consider it unlikely that the predictable errors in provincial estimates of product and expenditure are large enough to bias the coefficient estimates significantly.

Another issue concerns the Canadian federal government. While the federal government has a budget constraint with respect to the whole of Canada, it does not have one with respect to individual provinces. Different provinces may either receive or contribute net resources to the federal government, and such flows are used to equalize incomes across provinces. Both net income and the trade balance should be adjusted for these flows since they are, in effect, unrequited transfers and hence income for the province. Fortunately, the data include information on federal deficits by province. We measured these resource transfers by the deviation between per capita net lending by the federal government to a specific province, which does not have to satisfy a budget constraint, and per capita net lending by the federal government at the national level, which does.¹³ This difference was added to the provincial series on per capita net income available for consumption and the per capita trade balance.¹⁴

Some time-series plots and summary statistics provide a first look at our data set. Figure 1 shows the evolution of the first difference of per capita values of real income available for consumption, the trade balance, and the real gross provincial product for Canada as a whole and for each province separately, while Figure 2 illustrates levels of the same series.¹⁵ The striking feature of the figures is the close relationship between provincial net income and the provincial trade balance.¹⁶ This relationship holds more closely for smaller provinces (and territories), such as Prince Edward Island or the Yukon and the Northwest Territories, and less closely for the larger provinces, such as Ontario, and for Canada as a whole.

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Canada: Change in GDP, Income, and Trade Balance

(In thousand of 1986 dollars per capita)

Citation: IMF Staff Papers 1997, 004; 10.5089/9781451930962.024.A006

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Canada: GDP, Income, and Trade Balance

(In thousand of 1986 dollars per capita)

Citation: IMF Staff Papers 1997, 004; 10.5089/9781451930962.024.A006

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^{Table 1.}

Provincial Income and Correlations Between Changes In Per Capita Income and Changes in the Trade Balance

Note: All series are measured in 1986 Canadian dollars and are adjusted for differences in federal net lending.

^{Table 1.}

Provincial Income and Correlations Between Changes In Per Capita Income and Changes in the Trade Balance

	1992 GDP (billions of C$s)	Change in real GDP	Change in income available for consumption
Alberta	72.9	0.52	0.96
British Columbia	86.7	0.05	0.81
Manitoba	24.0	0.22	0.92
New Brunswick	13.9	11.48	0.97
Newfoundland	9.2	0.29	0.93
Nova Scotia	18.0	0.26	0.82
Ontario	277.5	0.19	0.75
Prince Edward Island	2.2	0.37	0.91
Quebec	157.1	0.10	0.73
Saskatchewan	20.2	0.10	0.98
Yukon & Northwest	3.1	0.32	1.00
Territories
Canada	684.7	0.15	0.64

Note: All series are measured in 1986 Canadian dollars and are adjusted for differences in federal net lending.

View Table

^{Table 1.}

Provincial Income and Correlations Between Changes In Per Capita Income and Changes in the Trade Balance

	1992 GDP (billions of C$s)	Change in real GDP	Change in income available for consumption
Alberta	72.9	0.52	0.96
British Columbia	86.7	0.05	0.81
Manitoba	24.0	0.22	0.92
New Brunswick	13.9	11.48	0.97
Newfoundland	9.2	0.29	0.93
Nova Scotia	18.0	0.26	0.82
Ontario	277.5	0.19	0.75
Prince Edward Island	2.2	0.37	0.91
Quebec	157.1	0.10	0.73
Saskatchewan	20.2	0.10	0.98
Yukon & Northwest	3.1	0.32	1.00
Territories
Canada	684.7	0.15	0.64

Note: All series are measured in 1986 Canadian dollars and are adjusted for differences in federal net lending.

These visual impressions can be supplemented by some simple statistics. Tables 1 and 2 show correlations and standard deviations of the change in real provincial product, net income, and the trade balance for each province and for Canada as a whole. In addition, to give a sense of relative size of the provinces, Table 1 also reports GDP in 1992 for each province. The correlation between net income and the trade balance is generally higher for the smaller provinces than for the larger ones, while the lowest correlation of all is for the whole of Canada.¹⁷ There is also a close connection between the variability of the trade balance and the variability of net income.

The finding that there is a closer connection between net income and the trade balance for small provinces than for large provinces or for Canada as a whole is consistent with the view that integration is higher within Canada than between Canada and the rest of the world. Small provinces, which are economically less self-sufficient and whose economic relations are largely within Canada, are able to use Canadian markets to smooth consumption. For Canada as a whole, however, it is integration with the rest of the world that matters, so any lack of integration will limit the ability of some of the larger provinces to use the capital markets to smooth consumption.¹⁸ A formal test of this hypothesis is investigated in the next subsection.

^{Table 2.}

Standard Deviation of Per Capita Variables

(Thousands of 1986 Canadian dollars)

Note: All series are adjusted for differences in federal net lending.

^{Table 2.}

Standard Deviation of Per Capita Variables

(Thousands of 1986 Canadian dollars)

	Changes in real GDP	Changes in income available for consumption	Changes in trade balance
Alberta	1.12	0.91	0.90
British Columbia	0.65	0.43	0.40
Manitoba	0.55	0.46	0.46
New Brunswick	0.51	0.58	0.55
Newfoundland	0.36	0.48	0.43
Nova Scotia	0.41	0.34	0.33
Ontario	0.61	0.33	0.25
Prince Edward Island	0.60	0.48	0.49
Quebec	0.47	0.30	0.29
Saskatchewan	0.87	0.90	0.92
Yukon & Northwest Territories	2.72	3.37	3.43
Canada	0.53	0.26	0.19

Note: All series are adjusted for differences in federal net lending.

View Table

^{Table 2.}

Standard Deviation of Per Capita Variables

(Thousands of 1986 Canadian dollars)

	Changes in real GDP	Changes in income available for consumption	Changes in trade balance
Alberta	1.12	0.91	0.90
British Columbia	0.65	0.43	0.40
Manitoba	0.55	0.46	0.46
New Brunswick	0.51	0.58	0.55
Newfoundland	0.36	0.48	0.43
Nova Scotia	0.41	0.34	0.33
Ontario	0.61	0.33	0.25
Prince Edward Island	0.60	0.48	0.49
Quebec	0.47	0.30	0.29
Saskatchewan	0.87	0.90	0.92
Yukon & Northwest Territories	2.72	3.37	3.43
Canada	0.53	0.26	0.19

Note: All series are adjusted for differences in federal net lending.

Regression Results

Table 3 shows the results from estimating equation (11), which assumes that Canadian provinces are equally integrated with all parts of the world, using a panel that includes data on each province and aggregate data for Canada as a whole. The first column, which shows the estimated constant terms for each equation, indicates that all of the estimated constant terms are small and insignificantly different from zero. As shown in the lower part of the tables, a Wald test of their joint significance also indicates that they are insignificantly different from zero, a result that holds for all other estimates in this paper.

^{Table 3.}

Basic Model

Notes: All standard errors are adjusted for heteroscedascity. The instruments for the provincial regressions were to first and second lags of the change in provincial income relative to adjusted OECD income, the change in the provincial trade balance, the adjusted change in Canadian income relative to adjusted OECD income, and the Canadian trade balance. For the Canadian regression, Canadian values were used in place of provincial ones, and OECD values in place of Canadian ones. One asterisk indicates that the coefficient is significant at the 5 percent confidence level; two asterisks indicate significance al the 1 percent level.

^aΔ(y-i-g)^i,OECD=Δ(y-I-G)ⁱ-(Cⁱ/C^OECD)Δ(Y-I-G)^OECD

^{Table 3.}

Basic Model

ΔTBi = αi + βiΔ(y - i - g)i,OECDa
		Net income coefficient	Durbin - Watson
	Constant (αi)	(βi)	statistic	R2
Alberta	0.00 (.05)	1.05 (0.08)**	1.37	0.97
British Columbia	-0.01 (.04)	0.61 (0.18)**	1.92	0.61
Manitoba	0.03 (.03)	0.93 (0.09)**	1.70	0.83
New Brunswick	-0.03 (.03)	1.00(0.07)**	1.63	0.94
Newfoundland	-0.02 (.02)	0.90(0.14)**	1.31	0.86
Nova Scotia	0.00 (.03)	0.75(0.10)**	1.80	0.69
Ontario	0.02 (.03)	0.59(0.17)**	1.98	0.56
Prince Edward Island	-0.01 (.03)	0.88 (0.09)**	1.55	0.87
Quebec	-0.02 (.04)	0.79(0.18)**	1.35	0.61
Saskatchewan	0.01 (.05)	1.12(0.07)**	1.64	0.92
Yukon & Northwest	0.02 (.06)	0.99 (0.06)**	1.87	0.99
Territories
Canada	0.01 (.03)	0.52(0.18)**	2.07	0.46
Wald tests (on provincial equations only):
Constant terms are equal to 0 χ2(12)	3.7
Income coefficients are equal to 1 χ2(12)		24 2**
Income coefficients arc equal to χ2 (11)		21.7**

Notes: All standard errors are adjusted for heteroscedascity. The instruments for the provincial regressions were to first and second lags of the change in provincial income relative to adjusted OECD income, the change in the provincial trade balance, the adjusted change in Canadian income relative to adjusted OECD income, and the Canadian trade balance. For the Canadian regression, Canadian values were used in place of provincial ones, and OECD values in place of Canadian ones. One asterisk indicates that the coefficient is significant at the 5 percent confidence level; two asterisks indicate significance al the 1 percent level.

^aΔ(y-i-g)^i,OECD=Δ(y-I-G)ⁱ-(Cⁱ/C^OECD)Δ(Y-I-G)^OECD

View Table

^{Table 3.}

Basic Model

ΔTBi = αi + βiΔ(y - i - g)i,OECDa
		Net income coefficient	Durbin - Watson
	Constant (αi)	(βi)	statistic	R2
Alberta	0.00 (.05)	1.05 (0.08)**	1.37	0.97
British Columbia	-0.01 (.04)	0.61 (0.18)**	1.92	0.61
Manitoba	0.03 (.03)	0.93 (0.09)**	1.70	0.83
New Brunswick	-0.03 (.03)	1.00(0.07)**	1.63	0.94
Newfoundland	-0.02 (.02)	0.90(0.14)**	1.31	0.86
Nova Scotia	0.00 (.03)	0.75(0.10)**	1.80	0.69
Ontario	0.02 (.03)	0.59(0.17)**	1.98	0.56
Prince Edward Island	-0.01 (.03)	0.88 (0.09)**	1.55	0.87
Quebec	-0.02 (.04)	0.79(0.18)**	1.35	0.61
Saskatchewan	0.01 (.05)	1.12(0.07)**	1.64	0.92
Yukon & Northwest	0.02 (.06)	0.99 (0.06)**	1.87	0.99
Territories
Canada	0.01 (.03)	0.52(0.18)**	2.07	0.46
Wald tests (on provincial equations only):
Constant terms are equal to 0 χ2(12)	3.7
Income coefficients are equal to 1 χ2(12)		24 2**
Income coefficients arc equal to χ2 (11)		21.7**

Notes: All standard errors are adjusted for heteroscedascity. The instruments for the provincial regressions were to first and second lags of the change in provincial income relative to adjusted OECD income, the change in the provincial trade balance, the adjusted change in Canadian income relative to adjusted OECD income, and the Canadian trade balance. For the Canadian regression, Canadian values were used in place of provincial ones, and OECD values in place of Canadian ones. One asterisk indicates that the coefficient is significant at the 5 percent confidence level; two asterisks indicate significance al the 1 percent level.

^aΔ(y-i-g)^i,OECD=Δ(y-I-G)ⁱ-(Cⁱ/C^OECD)Δ(Y-I-G)^OECD

By contrast, the estimated coefficients on net income per capita relative to the OECD are all highly significant, and many of these coefficients are close to the value of unity that would occur if all consumers had full access to world markets. Paradoxically, however, among the three provinces that fail this test are two of the largest and most important: Ontario, which makes up some 40 percent of the Canadian economy, and British Columbia, the largest western province in economic terms. The aggregate Canadian equation also rejects the restriction that the coefficient is unity. Indeed, at 0.52, the estimated coefficient on the change in relative net income in the Canadian regression is lower than that estimated for any of the provinces individually.

A Wald test that all of the coefficients on relative income are jointly equal to unity, and hence that all consumers have full access to world markets, is rejected whether or not the aggregate Canadian data are included. The weaker restriction that coefficients are equal across provinces is also rejected by the data. The results appear to indicate that integration is lower in many of the larger (and relatively rich) provinces than in smaller ones. In addition, results from aggregate Canadian data show lower international integration than do the results from individual provinces.

The results from the extended model, which allows for differential access to national and international resources, are reported in Table 4.¹⁹ As in Table 3, the coefficients on the change in provincial net income relative to the rest of the OECD (that is, the βⁱs) are large and generally significant. Unlike the simpler specification, however, the coefficients are jointly insignificantly different from unity, which implies that Canadian consumers have access to at least the national capital market.

The coefficients on the change in net income in Canada relative to the OECD generally have the expected negative sign. The joint hypothesis that all of the coefficients are zero, and hence that there is no difference in integration between national and international markets, is easily rejected. The subsidiary hypothesis that all of the coefficients are equal is accepted, as is the cross-equation restriction between the individual provincial regressions and the regression for Canada as a whole discussed earlier (not reported).²⁰ Hence, the results indicate high integration within Canada, but more limited integration between Canada and the rest of the OECD. The Durbin-Watson statistics in Table 4 indicate no problems with autocorrelation, while the level of fit is similar to that found in Table 3.

The coefficient restrictions discussed above point to a highly simplified version of equations (12) and (12′) in which the constant terms are eliminated, the coefficients on the change in provincial net income relative to OECD (β_i) are constrained to be unity, the coefficients on changes in Canadian income relative to the OECD (λ_i) are constrained to be equal across provinces, and the implied cross-equation restriction is imposed on the regression for the aggregate Canadian data. The results from estimating the following system,

^{Table 4.}

Extended Model

Notes: See Table 3.

^a$\Delta {\left(y-i-g\right)}^{i,OECD}=\Delta {\left(Y-I-G\right)}^i-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}.$

^b$\Delta {\left(y-i-g\right)}^{CA.OECD}=\Delta \left(C^{CA}/C^{OECD}\right)-{\left(Y-I-G\right)}^{CA}-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}.$

^{Table 4.}

Extended Model

ΔTBi =αi +βiΔ(y-i-g)i,OECD-λiΔ(y-i-g)CA,OECDa
ΔTBCA =βCAΔ(y-i-g)CA,ECDb
		Coefficient on provincial	Coefficient on Canadian	Durbin - Watson
		income (βi)	income (λi)	statistic	R2
Alberta		1.07 (.06)**	-0.57 (.35)	1.87	0.94
British Columbia		0.46 (.40)	0.36 (.58)	2.01	0.46
Manitoba		1.22 (.12)**	-1.24 (.40)**	2.32	0.88
New Brunswick		1.00 (.07)**	-0.04 (.18)	1.64	0.94
Newfoundland		0.90 (.11)**	-0.53 (.26)*	1.75	0.92
Nova Scotia		1.13 (.21)**	-0.92 (.49)	2.31	0.69
Ontario		0.95 (.29)**	-0.61 (.40)	2.42	0.53
Prince Edward Island		0.94 (.14)**	-0.30 (.55)	1.74	0.89
Quebec		l.08(.24)**	-0.44 (.28)	1.74	0.72
Saskatchewan		1.16 (.07)**	-0.61 (.31)	1.48	0.95
Yukon & Northwest
Territories		1.02 (.06)**	-1.50(1.47)	2.48	0.99
Canada		0.52(.18)**		2.07	0,46
Wald tests (on provincial equations only):
	Income coefficients are equal to 1 χ2(11)	12.9
	Income coefficients are equal to 0 χ2(11)		31.2**
	Income coefficients are equal χ2(10)		13.3
	Income coefficients are equal plus restriction on Canadian equation χ2(11)		13.3

Notes: See Table 3.

^a$\Delta {\left(y-i-g\right)}^{i,OECD}=\Delta {\left(Y-I-G\right)}^i-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}.$

^b$\Delta {\left(y-i-g\right)}^{CA.OECD}=\Delta \left(C^{CA}/C^{OECD}\right)-{\left(Y-I-G\right)}^{CA}-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}.$

View Table

^{Table 4.}

Extended Model

ΔTBi =αi +βiΔ(y-i-g)i,OECD-λiΔ(y-i-g)CA,OECDa
ΔTBCA =βCAΔ(y-i-g)CA,ECDb
		Coefficient on provincial	Coefficient on Canadian	Durbin - Watson
		income (βi)	income (λi)	statistic	R2
Alberta		1.07 (.06)**	-0.57 (.35)	1.87	0.94
British Columbia		0.46 (.40)	0.36 (.58)	2.01	0.46
Manitoba		1.22 (.12)**	-1.24 (.40)**	2.32	0.88
New Brunswick		1.00 (.07)**	-0.04 (.18)	1.64	0.94
Newfoundland		0.90 (.11)**	-0.53 (.26)*	1.75	0.92
Nova Scotia		1.13 (.21)**	-0.92 (.49)	2.31	0.69
Ontario		0.95 (.29)**	-0.61 (.40)	2.42	0.53
Prince Edward Island		0.94 (.14)**	-0.30 (.55)	1.74	0.89
Quebec		l.08(.24)**	-0.44 (.28)	1.74	0.72
Saskatchewan		1.16 (.07)**	-0.61 (.31)	1.48	0.95
Yukon & Northwest
Territories		1.02 (.06)**	-1.50(1.47)	2.48	0.99
Canada		0.52(.18)**		2.07	0,46
Wald tests (on provincial equations only):
	Income coefficients are equal to 1 χ2(11)	12.9
	Income coefficients are equal to 0 χ2(11)		31.2**
	Income coefficients are equal χ2(10)		13.3
	Income coefficients are equal plus restriction on Canadian equation χ2(11)		13.3

Notes: See Table 3.

^a$\Delta {\left(y-i-g\right)}^{i,OECD}=\Delta {\left(Y-I-G\right)}^i-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}.$

^b$\Delta {\left(y-i-g\right)}^{CA.OECD}=\Delta \left(C^{CA}/C^{OECD}\right)-{\left(Y-I-G\right)}^{CA}-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}.$

are presented in Table 5. The estimate of λ is 0.45 and, with a standard error of 0.07, it is highly significant. This estimate implies that 55 percent of the consumption smoothed through access to the Canadian but not the greater OECD markets.²¹ Durbin-Watson and adjusted R² statistics for each provincial equation are reported in Table 5. in spite of the simplicity of the specification—the behavior of the trade balances of the 11 provinces and territories we use, as well as Canada as a whole, is explained using only one estimated coefficient, λ—the Durbin-Watson statistics indicate that autocorrelation is not a problem in the equations. The adjusted R² statistics indicate no noticeable deterioration in the fit of the data compared to the earlier specifications. Indeed, in many cases the statistics rise, reflecting the greater parsimony of the specification.

^{Table 5.}

Constrained Model Results

Notes: See Table 3.

^aΔ(y-i-g)^i,OECD = Δ(Y_I_G)^{i _}(Cⁱ/C^OECD)Δ(Y-I-G)^0ECD.

^bΔ(y-i-g)^CA,OECD = (C^CA/C^OECD)Δ(Y- I- G)^CA-(Cⁱ/C^OECD)Δ(Y-I-G)^OECD.

^{Table 5.}

Constrained Model Results

ΔTBi = Δ(y-i-g)i,ECD-λ Δ(y-i-g)CA,OECDa
ΔTBCA = (1 - λ) Δ(y - i - g)CA, OECDb
Proportion of consumption constrained outside Canada (λ) = 0,45 (.07)**
Regional results	Durbin - Watson statistic	R2
Alberta	1.57	0.95
British Columbia	2.05	0.72
Manitoba	1.88	0.92
New Brunswick	1.87	0.94
Newfoundland	1.35	0.91
Nova Scotia	2.04	0.79
Ontario	1.82	0.59
Prince Edward Island	1.87	0.89
Quebec	1.87	0.74
Saskatchewan	1.54	0.96
Yukon & Northwest Territories	2.13	0.99
Canada	2.00	0.48

Notes: See Table 3.

^aΔ(y-i-g)^i,OECD = Δ(Y_I_G)^{i _}(Cⁱ/C^OECD)Δ(Y-I-G)^0ECD.

^bΔ(y-i-g)^CA,OECD = (C^CA/C^OECD)Δ(Y- I- G)^CA-(Cⁱ/C^OECD)Δ(Y-I-G)^OECD.

View Table

^{Table 5.}

Constrained Model Results

ΔTBi = Δ(y-i-g)i,ECD-λ Δ(y-i-g)CA,OECDa
ΔTBCA = (1 - λ) Δ(y - i - g)CA, OECDb
Proportion of consumption constrained outside Canada (λ) = 0,45 (.07)**
Regional results	Durbin - Watson statistic	R2
Alberta	1.57	0.95
British Columbia	2.05	0.72
Manitoba	1.88	0.92
New Brunswick	1.87	0.94
Newfoundland	1.35	0.91
Nova Scotia	2.04	0.79
Ontario	1.82	0.59
Prince Edward Island	1.87	0.89
Quebec	1.87	0.74
Saskatchewan	1.54	0.96
Yukon & Northwest Territories	2.13	0.99
Canada	2.00	0.48

Notes: See Table 3.

^aΔ(y-i-g)^i,OECD = Δ(Y_I_G)^{i _}(Cⁱ/C^OECD)Δ(Y-I-G)^0ECD.

^bΔ(y-i-g)^CA,OECD = (C^CA/C^OECD)Δ(Y- I- G)^CA-(Cⁱ/C^OECD)Δ(Y-I-G)^OECD.

We carried out a number of checks of the robustness of our results to alternative hypotheses. One of the assumptions in the theoretical model is that the path of the trade balance only depends upon the path of net income, defined as output less investment and government consumption. It is possible, however, that these three components have differing effects on the trade balance.²² To investigate this, we reestimated the constrained model presented in equation (13) allowing the coefficient that measures the level of integration between Canada and the rest of the world to vary between net income, investment, and government consumption. Specifically, we estimated the regression

where

In this case the coefficient on net income for Canada as a whole, λ, provides a general estimate of the luck of integration between Canada and the rest of the OECD while the coefficients on Canadian investment and on Canadian government consumption measure the deviations from this underlying value for these components of spending.²³ The equation is parameterized so that a positive coefficient on investment or government consumption represents higher levels of integration. Hence, for example, the implicit coefficient on Canadian investment, which measures the lack of integration of investment between Canada and the rest of the OECD, is λ + λ_t.

The results from this specification are reported in Table 6. The coefficient on provincial net income is very close to unity, indicating that markets are fully integrated within Canada. The coefficient on Canadian net income is -0.45, very similar to that found in the earlier estimation, again implying that integration with the rest of the world, measured in terms of the response of the trade balance to disturbances in net income, is about half of that found within Canada. The coefficient on the change in Canadian investment, however, is significantly positive, indicating that investment spending is more integrated with the rest of the OECD than is the bulk of net income. Indeed, the implied coefficient on the change in Canadian investment is insignificantly different from zero, indicating that investment spending may be completely integrated with the rest of the OECD. The results for government consumption also show some offset, but it is not statistically significant, indicating that the trade balance may respond to this component in a similar manner to the rest of net income.

^{Table 6.}

Results with Separate Coefficients on Investment and Government Saving

Notes: See Table 3.

^aThe equation for Canada as a whole is ΔTB = (β - λ)Δ(y-i-g)^CA,OECD+λ_IΔi^CA,OECD+ λ_GΔ_g^CA,OECD.

The variables are $\begin{array}{c}\Delta {\left(y-i-g\right)}^{i,OECD}=\Delta {\left(Y-I-G\right)}^i-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}\\ \Delta {\left(y-i-g\right)}^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{CA}-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}\\ \Delta i^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta G^{CA}-\left(C^i/C^{OECD}\right)\Delta I^{OECD}\\ \Delta g^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta G^{CA}-\left(C^i/C^{OECD}\right)\Delta G^{OECD.}\end{array}$

^{Table 6.}

Results with Separate Coefficients on Investment and Government Saving

ΔTBi = β Δ(y - i - g)i,OECD - λ Δ(y - i - g)CA,OECD - λt ΔiCA,OECD - λG ΔgCA,OEDa
Provincial net income (β)	1.02 (.03)**
Canadian net income (λ)	-0.45 (.07)**
Canadian investment (λt)	0.39 (.07)**
Canadian government consumption (λG)	0.39 (.26)
Regional results	Durbin-Watson statistic	R2
Alberta	1.55	0.98
British Columbia	1.70	0.81
Manitoba	2.16	0.93
New Brunswick	1.88	0.95
Newfoundland	1.90	0.93
Nova Scotia	2.06	0.86
Ontario	1.35	0.84
Prince Edward Island	2.00	0.88
Quebec	1.95	0.85
Saskatchewan	1.72	0.97
Yukon & Northwest Territories	2.37	0.99
Canada	1.89	0.82

Notes: See Table 3.

^aThe equation for Canada as a whole is ΔTB = (β - λ)Δ(y-i-g)^CA,OECD+λ_IΔi^CA,OECD+ λ_GΔ_g^CA,OECD.

The variables are $\begin{array}{c}\Delta {\left(y-i-g\right)}^{i,OECD}=\Delta {\left(Y-I-G\right)}^i-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}\\ \Delta {\left(y-i-g\right)}^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{CA}-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}\\ \Delta i^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta G^{CA}-\left(C^i/C^{OECD}\right)\Delta I^{OECD}\\ \Delta g^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta G^{CA}-\left(C^i/C^{OECD}\right)\Delta G^{OECD.}\end{array}$

View Table

^{Table 6.}

Results with Separate Coefficients on Investment and Government Saving

ΔTBi = β Δ(y - i - g)i,OECD - λ Δ(y - i - g)CA,OECD - λt ΔiCA,OECD - λG ΔgCA,OEDa
Provincial net income (β)	1.02 (.03)**
Canadian net income (λ)	-0.45 (.07)**
Canadian investment (λt)	0.39 (.07)**
Canadian government consumption (λG)	0.39 (.26)
Regional results	Durbin-Watson statistic	R2
Alberta	1.55	0.98
British Columbia	1.70	0.81
Manitoba	2.16	0.93
New Brunswick	1.88	0.95
Newfoundland	1.90	0.93
Nova Scotia	2.06	0.86
Ontario	1.35	0.84
Prince Edward Island	2.00	0.88
Quebec	1.95	0.85
Saskatchewan	1.72	0.97
Yukon & Northwest Territories	2.37	0.99
Canada	1.89	0.82

Notes: See Table 3.

^aThe equation for Canada as a whole is ΔTB = (β - λ)Δ(y-i-g)^CA,OECD+λ_IΔi^CA,OECD+ λ_GΔ_g^CA,OECD.

The variables are $\begin{array}{c}\Delta {\left(y-i-g\right)}^{i,OECD}=\Delta {\left(Y-I-G\right)}^i-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}\\ \Delta {\left(y-i-g\right)}^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{CA}-\left(C^i/C^{OECD}\right)\Delta {\left(Y-I-G\right)}^{OECD}\\ \Delta i^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta G^{CA}-\left(C^i/C^{OECD}\right)\Delta I^{OECD}\\ \Delta g^{CA,OECD}=\left(C^{CA}/C^{OECD}\right)\Delta G^{CA}-\left(C^i/C^{OECD}\right)\Delta G^{OECD.}\end{array}$