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An empty promise: average cost savings and scale economies among Canadian and American manufacturers, 1910-1988.

I. Introduction

On January 1, 1989, a bilateral trade agreement between Canada and the United States came into effect. This free-trade agreement (FTA) called for the reduction and eventual removal of Canadian and American tariff barriers on a wide range of goods traded between the two countries. In Canada, at least, there was considerable debate surrounding the negotiation and implementation of this pact. Economists' claims that there would be significant welfare improvements accruing to both Canada and the United States as a result of the exploitation of scale economies, triggered by the removal of tariff protection, played an important role throughout the course of this debate.

Recently, a large and growing body of literature focusing on the effects of bilateral tariff reductions has developed. This work adopts an ex post perspective in an effort to determine what effect trade liberalization has had on economic variables, such as productivity (Harrison 1994; Tybout and Westbrook 1995; Bernard and Jensen 1999), wages and employment (Gaston and Trefler 1997; Beaulieu 2000), plant production levels (Head and Ries 1999), and the trade-off between short-run adjustment costs and long-run efficiency gains (Trefler 2001). In general, these studies have found that the costs and benefits associated with trade liberalization are both difficult to isolate and unlikely to be substantial. This generalization holds with particular strength among wealthy, industrialized nations, such as Canada and the United States.

In light of the optimistic expectations regarding welfare improvements that were articulated prior to the introduction of the Canada-U.S. FTA, it is surprising that the ex post empirical evidence has been so muted. In this article, I argue that the ex ante expectations were overly optimistic. This revisionist exercise is relevant far beyond a specifically Canadian or historical context. Any assessment of the efficacy of trade liberalization between Canada and the United States will be dependent on the anticipated costs and benefits; a successful trade pact is one that exceeds expectations; an unsuccessful trade pact is one that falls short of expectations. Therefore, it is important to determine the extent to which our ex ante expectations were reasonable. More generally, the revisionist exercise undertaken in this article can help to determine the conditions under which we can safely anticipate welfare improvements stemming from the exploitation of scale economies induced through the liberalization of international trade.

In the sections that follow, I investigate the extent to which average cost savings were available through the exploitation of scale economies (1) among a sample of 44 Canadian and American manufacturing firms, representing four industries in each nation, covering the years 1910-1988. The results indicate that ex ante optimism regarding the potential for average cost convergence that was founded on data exclusively from the 1972-1988 period and that relied on the estimation of local scale elasticities alone would not have been unreasonable. However, a consideration of the global curvature properties of Canadian and American producers' long-run average cost functions and the employment of data from a much longer time series could have substantially undermined this ex ante optimism. I conclude, therefore, that the formation of reasonable expectations requires an investigation of global as well as local scale effects and the employment of data that spans macroeconomic cycles.

Section 2 provides a brief review of some of the quantitative literature that contributed to the formation of optimistic expectations concerning the economic effects of trade liberalization between Canada and the United States. In this section, I also illustrate that reliance on data from 1972-1988 and the estimation of local scale economies lead us to a fairly sanguine conclusion regarding the potential for average cost savings as a result of output adjustment following the implementation of the FTA. In section 3, two caveats are introduced; I report on the implications stemming from a consideration of global curvature properties, and I discuss the impact of employing a longer time series. The final section summarizes the conclusions.

2. The Formation of Optimistic Expectations

A Review of the Literature

Average costs, [C.sub.t]/[Q.sub.t] = f([A.sub.t], [Q.sub.t], [W.sub.xt]), are a product of technology, f(***), productivity, [A.sub.t], the scale of production, [Q.sub.t], and input prices, [W.sub.xt]. Optimistic expectations regarding welfare gains stemming from trade liberalization are based, at least in part, on the belief that average costs will decline as output adjusts in response to increased competition in the domestic market and increased access to foreign markets.

There has been considerable empirical study of the relationship between trade liberalization and the scale of production. Tariff protection, in conjunction with transport costs, differentiated products, and regional tax and industrial policies may allow firms to price their output over marginal cost. One of the implications of this "tariff-limit pricing behavior," in which firms set prices at the international market price plus the domestic tariff regardless of their marginal costs, is that, in equilibrium, it may be optimal for firms to produce to the left of their point of minimum efficient scale (MES). (2) A bilateral reduction of trade barriers and the accompanying increase in competition may, therefore, encourage firms to increase output, resulting in lower average costs as firms move toward their point of minimum efficient scale. This view has been consistently articulated by those who have studied the relationship between Canadian tariffs, market structure, and manufacturers' performance. (3)

In particular, Wonnacott and Wonnacott (1967, p. 5) claimed that, "... (tariff) protection results in higher Canadian prices and costs because of three organizational factors: the size of the firm; the level of managerial efficiency necessary to survive; and oligopolistic opportunities offered by the protected market." They predicted that trade liberalization

would result in lower Canadian average costs and prices, increased exports and nominal wages, and an increase in Canadian GNP of approximately 10.5%. (4) More recently, Harris (1984) and Cox and Harris (1985, 1986) provided impetus to the formation of optimistic expectations at a key juncture in the debate surrounding the negotiation of the FTA. Cox and Harris argued that, "... freer trade, by subjecting domestic industry to increased foreign competition and allowing access to the larger world market, results in lower price-cost margins and in firms' achieving ... lower costs of production." (1985, p. 116). They predicted that Canadian GNP could increase by 8-12% (5) after the complete removal of tariff barriers between Canada and the United States, 2-5% (6) if Canada unilaterally removed tariff barriers, and they claimed that there could be as much as a 37% (7) increase in the value added generated in individual sectors subject to bilateral-sectoral tariff reductions.

The optimistic predictions made by Wonnacott and Wonnacott, and Cox and Harris relied on two key assumptions. First, they assumed that firms practiced tariff-limit pricing. Second, they argued that firms' average costs were sensitive to output adjustment. The tariff-limit pricing assumption implies that the scale of production among Canadian and American producers could potentially expand dramatically in response to the bilateral removal of trade barriers. In this article, I accept the tariff-limit pricing assumption because it implies an expansion of output levels following trade liberalization that biases my results in favor of average cost savings. This allows me to focus all of my attention on a critical assessment of the second central assumption underlying the formation of ex ante optimism regarding the implementation of the Canada-U.S. bilateral trade agreement; that there were considerable scale economies available for exploitation.

Average Cost Performance

To begin my investigation of the strength of the empirical foundations underlying the ex ante optimism surrounding the FTA, it is necessary to establish the pattern and extent of average cost differentials between Canadian and American producers. Annual average cost figures specific to each of the 21 Canadian and 23 U.S. firms included in my sample have been calculated by adding firm-specific labor, capital, and intermediate input costs (8) to derive total cost, then dividing this figure by firm-specific output. (9) Because I am interested in the connection between output and average costs at the industry and sectoral levels, the experiences of individual firms are not discussed in this article. In an effort to reflect average cost performance at the industry level, I have used three different aggregation schemes to derive nation-specific average cost series for oil refineries, paper mills, steel mills, and textile mills (10): an unweighted geometric mean across all firms in each industry and nation, an industry- and nation-specific mean weighted by each firm's share of the domestic industry's capital stock, and the median firm's average costs. In Table 1, the ratio of Canadian relative to American industry average costs are reported for all three aggregation schemes averaged over four time periods: all available years, the years prior to 1946, the years between 1946 and 1971, and the years between 1972 and 1988. (11)

Among all four industries studied in this article, the firm-level average cost distributions overlapped. This implies that the lowest average cost producer among the firms in the high-cost nation had lower average costs than the highest average cost producer among the firms in the low-cost nation. Despite the overlapping distributions, when aggregated across firms within each nation over the entire 1910-1988 period, there have been some substantial industry-level average cost differences. Canadian textile mills had dramatically higher average costs, at the mean of the data, relative to their American counterparts, while Canadian paper mills had dramatically lower average costs. Canadian steel mills had slightly higher average costs, relative to their American counterparts, while Canadian oil refineries had slightly lower average costs. One point that deserves emphasis is that, contrary to the impression one receives from most of the Canadian literature on scale and productivity performance, Table 1 reveals that not all of the Canadian industries were relatively high-cost producers. Over the entire 1910-1988 period and in each of the three subperiods, there was at least one U.S. industry that produced subject to average costs that exceeded the matched Canadian industry's average costs. This is of interest because it suggests that potential average cost convergence stemming from liberalized trade between Canada and the United States was not a "one way street." Among the four industries, I have examples of Canadian and American industries for which, ex ante, I could have expected welfare improvements through trade-induced average cost convergence.

If I consider the subperiods identified in Table 1, I find average cost divergence over the 20th century among Canadian and American oil refineries and textile mills, with the Canadian producers in both industries losing their average cost advantage during the post-1946 period. I observe average cost convergence only among the steel mills in the sample. There is no obvious trend in relative average costs among the paper mills.

To place these average cost ratios in the appropriate comparative context, we must focus our attention exclusively on the post-1972 era. During this period of macroeconomic volatility, I find that Canadian oil refineries and textile mills suffered from considerably higher average costs relative to their U.S. counterparts. Even among the paper mills and steel mills, average costs differed by between 10% and 20%, depending on aggregation scheme. The point I wish to make here is that qualitative conclusions with respect to relative average cost performance may be persistent across subperiods, but quantitative conclusions are not. The average cost differential during the 1972-1988 period was larger than the average cost differential during the entire 1910-1988 period for three of the four industries in the sample: oil refineries, steel mills, and textile mills. From Table 1, I conclude that, particularly if I consider only the post-1972 era, there was room for considerable average cost convergence among the industries represented in the sample and the benefits of any trade-induced average cost convergence would not have been monopolized by Canadian producers.

Output Levels

Implicit in much of the early literature promoting the bilateral liberalization of trade between Canada and the United States was the notion that relatively low output levels produced by Canadian producers could be indicative of an inability, or unwillingness, to exploit all available scale economies, lower average costs, and hence, lower output prices. (12) Relatively low output levels, therefore, were offered as empirical evidence indicating increasing returns to scale, high average costs, and an inability to compete against U.S. producers. Annual output figures for each of the Canadian and American firms in the sample have been derived by deflating annual firm-specific total revenue by an industry-specific index of output prices. (13) As with the average cost ratios, I have used three aggregation schemes to derive nation- and industry-specific output series: an unweighted geometric mean across all firms in each industry and nation, an industry- and nation-specific mean weighted by each firm's share of the domestic industry's capital stock, and the median firm's output level. In Table 1, the ratio of Canadian relative to American industry output levels are reported for all three aggregation schemes averaged over four time periods; all available years, the years prior to 1946, the years between 1946 and 1971, and the years between 1972 and 1988.

Similar to the average cost results, in all four industries, the firm-specific output distributions overlapped. This implies that the producer with the highest output levels among the firms in the low-output nation had higher output figures than the producer with the lowest output levels among the firms in the high-output nation. Despite the overlapping output distributions, for the 1910-1988 period as a whole and in each subperiod, the Canadian firms in my sample did produce less output than their U.S. counterparts. Across the three subperiods, I observe output divergence among the paper mills and textile mills, convergence among the steel mills, and no trend among the oil refineries. During the 1972-1988 period, the largest output differentials existed among the papers mills and textile mills, and all four Canadian industries produced less than 50% of their U.S. counterparts' mean output levels.

I do not wish to suggest that the output ratios reported in Table 1 are indicative of the presence of unexploited scale economies among the Canadian firms. Relatively low output levels would necessarily be consistent with increasing returns to scale if and only if the Canadian producers had relatively high average costs, Canadian and American producers shared common long-run average cost functions, and the American firms were producing output levels equal to or less than their minimum efficient scale. As the average cost ratios reported in Table 1 and the local scale elasticity estimates reported in the subsection below illustrate, none of these conditions hold among the sample of firms in any of the time periods considered.

Local Returns to Scale

In addition to average cost and output performance, local scale elasticities have also been offered as empirical evidence in support of the view that output adjustment, induced by trade liberalization, could result in substantial average cost convergence between Canadian and American manufacturers. I have used firm-level cost data and industry-level price data (14) to estimate industry- and nation-specific translog cost functions, with fixed effect controls for cross-panel heteroskedasticity. (15) The resultant cost function parameter estimates facilitate the derivation of jointly determined local returns to scale for each of the four Canadian and four American industries represented in the sample, at the mean of the data over the entire 1910-1988 period and in three subperiods: 1910-1945, 1946-1971, and 1972-1988. (16)

Joint [bar]RTS = d[[bar]lnQ]/d[[bar]lnC] = [([[beta].sub.q] + [[beta].sub.qq][[bar]lnQ] + [[beta].sub.qL][[bar]ln[W.sub.L]] + [[beta].sub.qK][[bar]ln[W.sub.K]] + [[beta].sub.qM][[bar]ln[W.sub.M]] + [[beta].sub.qa][bar]t).sup.-1]

The Joint [bar]RTS estimates are elasticities that identify scale economies and indicate how sensitive output was to small changes in input levels. More specifically, the figures reported in Table 2 reveal what the percentage change in output would have been in response to a 1% increase in the employment of all three inputs, evaluated at the mean of the data. If output increased by greater than 1%, then there were local economies of scale available for exploitation. If output increased by less than 1%, then we have evidence that there were local diseconomies of scale present. If the change in output was not statistically significantly different from 1%, then constant returns to scale applied.

From Table 2, we can see that, over the entire 1910-1988 period, all four of the Canadian industries were producing subject to locally increasing returns to scale, with very dramatic scale economies present among the textile mills. Among the U.S. producers, two industries, paper mills and textile mills, had Joint [bar]RTS estimates greater than one and two industries, oil refineries and steel mills, had Joint [bar]RTS estimates less than one, although only the paper mills' and steel mills' returns to scale estimates were statistically significant. (17)

There is some variation in the local scale estimates across the three subperiods. Because I wish to place my estimates in the appropriate comparative context, I must focus my attention on the results from the 1972-1988 subperiod. All four of the Canadian Joint [bar]RTS estimates from the 1972-1988 period were greater than one and statistically significant with at least 95% confidence, and they were all more elastic than the estimates from the full 1910-1988 period. I can also see that, during the 1972-1988 period, all four of the U.S. Joint [bar]RTS estimates were less than one and statistically significant with at least 95% confidence. Like the Canadian estimates, the U.S. scale elasticities from the late period were larger (in absolute value) than the estimates from the entire 1910-1988 period. These results imply that the Canadian industries had fairly substantial local scale economies available for exploitation during the period just prior to the implementation of the FTA, and therefore, based on this evidence, it would not have been unreasonable to expect that these industries could have lowered their long-run average costs through output expansion. The U.S. industries, on the other hand, were producing subject to locally decreasing returns to scale just prior to the implementation of the FTA. These industries, therefore, could have lowered their long-run average costs through output contraction. (18)

The local scale estimates reported in Table 2, particularly those from the post-1972 period, are broadly consistent with other empirical estimates found in the literature. For example, Trefler (2001, section 10.2) argues that four-digit Canadian manufacturing industries had Joint [bar]RTS slightly less than 1.10 during the decade prior to the implementation of the FFA; Cox and Harris (1986, table 1) provide local scale estimates for a sample of Canadian manufacturing industries that range from 1.103 to 1.277; Morrison (1993, table 2) reports cost elasticities for U.S. manufacturing industries between 0.667 and 0.860, estimated over the period 1953-1986; and the estimates of Diewert and Wales (1987, table 6) of Joint [bar]RTS for the American manufacturing sector range from 0.61 in 1971 to 0.94 in 1947. (19)

If I based my expectations on the average cost, output, and local returns to scale results from the 1972-1988 period, then the evidence presented here is consistent with the ex ante formulation of optimistic expectations regarding changes in long-run average costs in response to output adjustment induced by the FTA's bilateral tariff reductions. Particularly among the Canadian producers, for whom output expansion could have been advantageous, optimism was reasonable. Virtually all of the pre-FTA empirical work on scale and performance stops at the identification of high-cost and low-output industries and the estimation of local increasing returns to scale. However, the identification of local scale economies tells me little about the sensitivity of average costs to larger changes in output levels. If an industry has been producing on a flat portion of its long-run average cost function, it may have statistically significant returns to scale but only minor cost savings associated with output adjustment. To quantify the responsiveness of Canadian and American oil refineries', paper mills', steel mills', and textile mills' average costs with respect to output adjustment, we must focus on global-scale effects rather than simply the statistical significance of the local scale elasticities reported in Table 2.

3. Two Caveats

Caveat 1: Global Curvature Properties

In general, movements along a long-run average cost curve in response to changing output levels are coincident with changing local scale elasticities. Therefore, the results reported in Table 2 identify potential average cost savings in response to only small, or local, changes in output levels. To determine the extent to which it was reasonable to anticipate average cost reductions in response to more substantive changes in Canadian and American manufacturers' output levels, we must study the global curvature properties implied by the cost function estimates. In particular, I can ask: Was it reasonable to expect that Canadian and American manufacturers would produce output levels equal to their minimum efficient scale? And was it reasonable to expect that output adjustment alone could eliminate the differences between the Canadian and American average costs? If it was not reasonable to expect that minimum efficient scale could be attained, then not all scale economies were available for exploitation. Even if minimum efficient scale could have been reached, this does not necessarily mean that we should have anticipated complete average cost convergence among the Canadian and American industries.

Minimum Efficient Scale

I can determine the output level at which Canadian and American oil refineries', paper mills', steel mills', and textile mills' long-run average costs would have been minimized using the estimated parameters from their translog cost functions and the independent variables evaluated at their period-specific means. Setting the derivative of the translog average cost function, with respect to output, equal to zero and solving for output reveals the point of minimum efficient scale (20)

ln[Q.sup.mes] = -(([[beta].sub.q] - 1) + [[beta].sub.qL][[bar]ln[W.sub.L]] + [[beta].sub.qK][[bar]ln[W.sub.K]] + [[beta].sub.qM][[bar]ln[W.sub.M]] + [[beta].sub.qa]t) / [[beta].sub.qq].

Table 3 reports the industry output level, using an unweighted geometric average across firms to generate the industry series, relative to the output level at which long-run average costs would have been minimized, by industry, nation, and time period. The point of minimum efficient scale has been calculated at the mean of the period-specific data. The qualitative conclusions drawn from the evidence presented in this section are not dependent on the aggregation scheme used to generate the industry-level output series. The ratios reported in Table 3 reflect the output adjustment required for the exploitation of all available scale economies (or diseconomies) by the Canadian and American industries. (21)

Over the 1910-1988 period, with the possible exception of the Canadian and American oil refineries, all of the industries considered in this study would have required very dramatic changes in their output levels to reach minimum efficient scale. For some of the industries (Canadian steel mills and textile mills), even a doubling of average output levels would not have brought them close to the low point on their long-run average cost functions. For U.S. steel mills, an average output reduction of over 42% would have been required to exploit all available output-induced average cost savings, while U.S. paper mills would have required an increase in average output levels of almost 44% to exploit all of their available scale economies. Only Canadian steel mills and oil refineries could have achieved minimum efficient scale by matching the greater output levels produced by their U.S. counterparts.

For all eight of the industries represented in the sample, the change in average output levels required to reach minimum efficient scale would have been larger during the 1972-1988 period than during the entire 1910-1988 period. Between 1972 and 1988, the Canadian paper mills, steel mills, and textile mills would have had to more than double their output levels to minimize long-run average costs. For the U.S. oil refineries, steel mills, and textile mills, the required contraction in output levels during the 1972-1988 period was greater than 50%. The contrast between the required output adjustment during the 1910-1988 period and the later 1972-1988 period again illustrates that, during periods of macroeconomic fluctuation, measured scale effects may be exaggerated due to cyclical output fluctuations.

The output ratios reported in Table 3 reflect the shape of the industries' long-run average cost functions. The cost functions employed by all four industries in both nations were very flat over most of the 20th century. This conclusion is consistent with cost function and scale estimates reported by economic historians for earlier stages in U.S. industrial development. (22) The Canadian industries tended to have cost curves characterized by very long, slightly downward sloping portions, while the U.S. industries tended to have cost curves characterized by very long, slightly upward sloping portions. With such flat long-run average cost curves, the penalty, in terms of forgone average cost savings, associated with production to the left, or fight, of minimum efficient scale was small.

Potential Average Cost Savings

Having illustrated that dramatic output adjustment would have been required for the industries studied in this article to achieve minimum efficient scale, I now assume that this output adjustment was feasible and move to an investigation of the extent to which long-run average costs could have been reduced through this hypothetical output adjustment. More specifically, in an effort to bias my results toward the achievement of average cost convergence, I assume that inputs could be supplied perfectly elastically to the Canadian and American producers, and I consider both output expansion and contraction. The first assumption implies that output adjustment would not be accompanied by changing input prices. The second assumption implies that the increased continental market size and competitive pressures associated with trade liberalization could have encouraged output expansion among the Canadian industries and output expansion or contraction among the U.S. industries, depending on the adjustment that entailed a reduction in long-run average costs.

Table 4 reports the industry average costs, using an unweighted geometric average across firms to generate the industry series, relative to average cost at minimum efficient scale, by industry, nation, and time period. The average cost at minimum efficient scale has been calculated at the mean of the period-specific data. The qualitative conclusions drawn from the evidence presented in this section are not dependent on the aggregation scheme used to generate the industry-level average cost series. The ratios reported in Table 4 reflect the long-run average cost savings available through the exploitation of all available scale economies (and diseconomies) by each Canadian and American industry.

The figures in Table 4 reveal that, over the 1910-1988 period, with the possible exception of Canadian steel mills and Canadian textile mills, there were only small average cost savings available through output adjustment. Complete exploitation of all scale economies (and diseconomies for U.S. oil refineries and steel mills) would have resulted in less than a 10% reduction in long-run average costs for six of the eight industries considered here. For the Canadian steel mills and textile mills, the two industries that were farthest from their points of minimum efficient scale, long-run average costs could have been reduced by 35.2% and 21.4%, respectively.

To provide some context for the figures in Table 4, I can return to the Canadian relative to American average cost ratios reported in Table 1. Over the 1910-1988 period, Canadian oil refineries had average costs that were 4.3% lower than their U.S. counterparts (using an unweighted geometric mean across firms to aggregate up to the industry level). If oil refineries in both nations had adjusted their output levels to minimize their long-run average costs, then this average cost differential would have increased by 1.2%. If only the high-cost American producers adjusted their output levels, the average cost differential would have been reduced by only 2.6%. For the paper mills in the sample, the Canadian firms had average costs that were 18% lower than the American paper mills. Again, output adjustment by producers in both nations would have increased this differential by 2.5%. If only the high-cost American producers adjusted their output levels, the average cost differential would have been reduced by only 1%. Canadian textile mills could have enjoyed fairly substantive average cost reductions if they had expanded output levels following the implementation of the FTA. Unfortunately, the 12.4% reduction in the Canada-U.S. average cost differential following the exploitation of all scale economies by textile mills on both sides of the border would have reduced the observed average cost differential by just over one third. Even if only the Canadian firms adjusted their output levels, the observed 35.4% average cost differential would have been reduced by only 21.4%. Steel mills are the only industry considered in this study for which output adjustment could have resulted in complete average cost convergence. If both Canadian and American steel mills had minimized long-run average costs through output adjustment, then the 4.1% average cost differential in favor of the U.S. firms would have become a 30% differential in favor of the Canadian firms. The Canadian steel mills would have had to increase output levels by only 13.1%, or one fifth of the output adjustment required to reach minimum efficient scale, to match U.S. average cost performance during the 1910-1988 period.

Similar to the subperiod results reported in Table 3, among six of the eight industries, the available average cost savings through output adjustment were largest during the 17 years just prior to the implementation of the FTA. Only Canadian oil refineries and U.S. steel mills could have had lower anticipated average cost savings if I relied on data from the post-1972 period, relative to the average cost results derived with the use of data from the longer time series.

Despite quantitatively larger average cost reductions available to the producers in both nations during the 1970s and early 1980s, we still should not have expected average cost convergence through changes in output levels. What we should have predicted, after consideration of the global curvature properties of the industries' long-run average cost functions during the 1972-1988 period, was average cost divergence through output adjustment among the oil refineries, paper mills, and steel mills. Even for textile mills, during the post-1972 period, the average cost differential would have fallen by just slightly over half if all scale economies (and diseconomies) had been exploited.

Caveat 2: A Longer Time Series

Throughout the preceding sections of this article, I have repeatedly noted the quantitative differences and qualitative similarities between the results derived using data from the 1910-1988 period relative to the 1972-1988 subperiod. The observed average cost and output differentials between the Canadian and American producers tended to be larger during the late subperiod, the local scale elasticity estimates tended to be larger during the late subperiod, the distance to the point of minimum efficient scale tended to be larger during the late subperiod, and the potential average cost savings available through output adjustment tended to be larger during the late subperiod. I conclude from these results that reliance on data from the post-1972 period of macroeconomic instability may have led to an "exaggeration" of the potential average cost savings and hence an exaggeration of potential welfare gains, following trade liberalization between Canada and the United States. I refer to the more dramatic results derived from the post-1972 subperiod as an exaggeration for two reasons.

First, it is possible that the measurement of scale effects based on output figures collected during a period of cyclical contraction in the macroeconomy may imply potential average cost savings that were temporary and could not be realized through output adjustment associated with trade liberalization, but only through output adjustment associated with recovery in the macroeconomy. If this output measurement issue was serious, then not all of the scale economies that were identified using post-1972 data could be realized through trade-induced output expansion or contraction, and the accurate formation of ex ante expectations with respect to trade-induced output adjustment would require a longer time series over which no single macroeconomic environment was dominant.

Second, it is also possible that, during periods of macroeconomic instability, firms may alter input utilization rates in a manner that is not measured in firm-level data sources (to say nothing of aggregate data sources). If input measurement problems were a serious issue, then scale estimates may be systematically biased and dependent on the cyclical behavior of the macroeconomy. This implies that the use of a longer time series over which no single macroeconomic environment was dominant could avoid this bias and provide for the more accurate formation of ex ante expectations.

This discussion implies that there is good reason to prefer local and global scale results based on a longer time series that spans several iterations of the macroeconomic cycle, in addition to the advantageous features of longer time series that are not specific to scale estimation; an increase in statistical power due to the employment of more observations per industry, and the emphasis on a more permanent, long-run view that focuses on underlying trends and historical context.

4. Conclusions

On January 1, 1989, Canada and the United States implemented a bilateral trade agreement that called for the reduction and eventual elimination of tariff barriers on most traded goods. During the debate preceding the implementation of the FTA, those who predicted substantial welfare improvements attracted considerable attention. Their optimistic predictions were based primarily on the notion that trade liberalization would lead to output expansion, which would lead to the exploitation of scale economies, average cost convergence between Canada and the United States, and increasing exports and income. The evidence presented in this article uses data drawn from a sample of 44 manufacturing firms, representing four industries, covering the years 1910-1988. I find that, prior to 1989, there were persistent, and in some cases substantial, average cost and output differences among Canadian and American producers. It is also apparent that many Canadian and American manufacturers were producing subject to locally increasing returns to scale. This empirical evidence is even stronger if one considers only the 17 years immediately preceding the implementation of the FTA. However, a consideration of the global curvature properties of the industries' long-run average cost functions indicates that the manufacturers were producing on flat portions of these curves. Calculation of the potential average cost savings available for exploitation through output adjustment reinforces this conclusion and indicates that substantive average cost convergence was unlikely. Therefore, although there were some average cost reductions to be achieved through output adjustment, a consideration of the global curvature properties of the cost functions employed by Canadian and American producers during the 1910-1988 period could have undermined any claims that there might be economically substantive average cost convergence following the implementation of the FTA. Although the measured scale effects were larger during the late, post-1972 subperiod, the qualitative conclusion that average cost convergence was an unreasonable expectation continues to hold, even based on evidence from this era of macroeconomic volatility.

Based on these results, I offer two conclusions. First, the ex ante expectations with respect to potential average cost savings stemming from trade liberalization between Canada and the United States under the FTA were overly optimistic. Second, the formation of more reasonable expectations requires a consideration of global scale effects and a reliance on data drawn from a period that spans macroeconomic cycles. The first conclusion is relevant for any assessment of the efficacy of the FTA. The second conclusion is more general, in that it implies conditions under which we should anticipate substantive average cost savings as a result of trade-induced output adjustment.
Table 1. Canadian:American Average Cost and Output Ratios (By
Aggregation Scheme)

 Average Cost Ratios

 All Years Early Mid Late
Oil
 Unweighted 0.957 0.769 0.899 1.179
 K weights 0.946 0.758 0.874 1.189
 Median 0.933 0.771 0.856 1.167
Paper
 Unweighted 0.820 0.808 0.790 0.876
 K weights 0.812 0.810 0.740 0.924
 Median 0.827 0.801 0.808 0.882
Steel
 Unweighted 1.041 1.312 0.800 0.851
 K weights 0.997 1.258 0.714 0.893
 Median 1.056 1.322 0.807 0.887
Textiles
 Unweighted 1.354 0.551 1.358 1.965
 K weights 1.159 0.812 1.041 1.541
 Median 1.489 0.802 1.496 2.008

 Output Ratios

 All Years Early Mid Late
Oil
 Unweighted 0.413 0.195 0.492 0.445
 K weights 0.338 0.135 0.410 0.370
 Median 0.464 0.253 0.584 0.429
Paper
 Unweighted 0.812 0.339 1.508 0.221
 K weights 1.071 0.311 2.159 0.169
 Median 0.653 0.385 1.073 0.277
Steel
 Unweighted 0.128 0.057 0.158 0.230
 K weights 0.053 0.020 0.058 0.111
 Median 0.205 0.126 0.237 0.319
Textiles
 Unweighted 0.602 1.248 0.487 0.224
 K weights 0.652 1.023 0.562 0.458
 Median 0.742 1.873 0.536 0.084

Early = 1910-1945, Mid = 1946-1971, Late = 1972-1988.

Table 2. Local Scale Elasticities

 Joint [bar]RTS

 All Years Early Mid Late
Oil
 Canada 1.027 * 1.721 * 0.761 * 1.049 *
 US 0.933 1.267 * 0.721 * 0.553 *
Paper
 Canada 1.136 * 1.451 * 1.105 * 1.351 *
 US 1.007 * 1.013 * 1.010 * 0.992 *
Steel
 Canada 1.117 * 1.136 * 1.100 * 1.125 *
 US 0.970 * 1.017 * 0.930 * 0.920 *
Textiles
 Canada 1.704 * 1.488 * 1.389 * 1.835 *
 US 1.399 1.917 * 0.785 0.556 *

Early = 1910-1945, Mid = 1946-1971. Late = 1972-1988.

* Statistical significance at 95%.

** Statistical significance at 90%.

Table 3. Output at Minimum Efficient Scale

 [bar]Q/[Q.sub.Mes]

 All Years Early Mid Late
Oil
 Canada 0.965 0.560 1.545 0.929
 US 1.140 0.683 2.017 4.304
Paper
 Canada 0.564 0.227 0.637 0.289
 US 0.662 0.431 0.515 1.647
Steel
 Canada 0.293 0.244 0.343 0.271
 US 1.428 0.824 2.375 2.727
Textiles
 Canada 0.391 0.474 0.530 0.250
 US 0.800 0.697 1.239 2.573

Ealy = 1910-1945, Mid = 1946-1971, Late = 1972-1988.

Table 4. Average Cost at Minimum Efficient Scale

 [bar]AC/[C.sub.MES]

 All Years Early Mid Late
Oil
 Canada 1.038 1.581 1.430 1.009
 US 1.026 1.136 1.014 1.594
Paper
 Canada 1.035 1.260 1.022 1.175
 US 1.010 1.007 1.017 1.020
Steel
 Canada 1.352 1.425 1.293 1.390
 US 1.011 1.011 1.008 1.004
Textiles
 Canada 1.214 1.130 1.093 1.528
 US 1.090 1.315 1.030 1.035

Note: Early = 1910-1945, Mid = 1946-1971, Late = 1972-1988.


I would like to thank seminar participants at the Canadian Economics Association meetings in Vancouver, British Columbia, June 2000, and the Canadian Conference on the Use of Quantitative Methods in Economic History in Stratford, Ontario, October 2000. Herbert Emery, Byron Lew, Frank Lewis, Cherie Metcalf, Chris Minns, Angela Redish, Sean Rogers, Ronald Shearer, two anonymous referees, and the editor of this journal have read earlier drafts and offered comments and suggestions. Their contributions are gratefully acknowledged. All remaining errors and omissions are my own. Funding provided by the McGill Institute for the Study of Canada has been appreciated.

(1) Throughout this article, the term "economies of scale" refers to internal economies only. Issues associated with external economies, economies of scope, and rationalization through entry and exit are potentially substantive determinants of trade-induced average cost convergence. However, these issues have largely been ignored in the FTA literature, particularly the empirical literature, and the ex ante, firm-based approach adopted in this article constrains our ability to do more than acknowledge their importance and suggest the need for further research.

(2) Minimum efficient scale is the level of output that can be produced at the lowest possible long-run average cost, given technology, productivity, and input prices. See Varian (1992, p. 68). Muller and Rawana (1990) illustrate that tariff-limit pricing and production to the left of MES may be observed in the absence of collusion among firms.

(3) In addition to the work referred to in this section, see Eastman and Stykolt (1967), Daly, Keys, and Spence (1968), and Baldwin and Gorecki (1986).

(4) Wonnacott and Wonnacott (1967. p. 335).

(5) Harris (1984, p. 1017).

(6) Cox and Harris (1985, p. 140).

(7) Cox and Harris (1986, p. 392).

(8) Intermediate input costs include the cost of raw materials, fuel, and services.

(9) All of the price and cost series used in this article have been converted into Canadian dollars using the official annual average exchange rate. A complete data appendix is available from the author or can be found in Keay (1999, section 2.3 and appendix 2.A). The firm-specific data have been drawn from income accounts and balance sheets included in corporate annual reports and annual industrial manuals published by The Financial Post, Moody's, and Standard and Poor's, The firms in the sample produced between 25% and 80% of the value added generated by the industries they represent, depending on industry, nation, and time period.

(10) These industries have been selected for inclusion in this study because they are economically important due to their size and the fact that they produce intermediate inputs employed by a wide range of manufacturing industries. Because these industries employed production processes that am continuous, horizontally integrated, and vertically integrated, they include, according to Chandler (1977) and Lamoreaux (1986), exactly the type of producers for whom internal returns to scale should be important. All of the industries in our study enjoyed some tariff protection over the period of study, with Canadian textile mills enjoying the highest rotes of protection (as high as 48.1%) and Canadian oil refineries enjoying the lowest rates of protection (as low as 0% by the very end of the period). For more information on tariff rates see Trade of Canada, U.S. Statistical Abstracts.

(11) Each of the subperiods considered in this article roughly coincide with a macroeconomic policy and performance regime in both Canada and the United States. Other break points have been used without substantively altering the qualitative or quantitative results. Hughes (1990, pp. 560-3) argues that U.S. steel mills underwent extensive restructuring during the 1960s and early 1970s, This implies that, for U.S. steel mills, at least, my subperiods may also coincide with a technological discontinuity.

(12) See Eastman and Stykolt (1967), Daly, Keys, and Spence (1968), or Wonnacott and Wonnacott (1967).

(13) I do not have firm-specific price information. Therefore, price figures have been compiled from national statistical agency sources in Canada and the United States. The concurrent use of industry-specific price data and firm-specific cost data requires that the firms in the sample faced the industry average prices reported by national statistical agencies. Where available, physical output proxies have been compared with the deflated revenue figures. The qualitative conclusions that follow are robust to the choice of output measure.

(14) I assume that none of the individual firms in my sample were large enough to control domestic input prices. This assumption allows me to treat input prices as exogenous in my econometric estimation.

(15) A complete econometric appendix is available from the author. I employ translog cost functions because they are flexible and yield local scale elasticities that are output dependent, which in turn allow me to study the global curvature properties of the industries' cost functions. I have followed Fuss (1977, p. 99) in my use of fixed effects heteroskedasticity controls, Berndt (1991, pp. 477-8) in my method of controlling for autocorrelation, Judge et al. (1985, chapter 13), in my use of iterative seemingly unrelated regression techniques to estimate industry- and nation-specific systems of equations with unbalanced panel data, and Diewert and Wales (1987, table 1) and Cain and Paterson (1981, appendix) in my imposition of concavity on the cost function estimates.

(16) In this article, the term "jointly determined returns to scale" is used to distinguish the estimated returns to scale for the entire production process from input-specific returns to scale estimates. Paul-Morrison and Siegel (1999) illustrate that any bias in the estimation of internal returns to scale due to the use of disaggregate data will be inconsequential.

(17) I can reject the hypotheses that the Canadian and American industries were employing common translog cost functions or that they were producing subject to common returns to scale for all four industries with at least 95% confidence.

(18) Because I am using a long time series of firm-specific rather than plant-specific data to estimate industry cost functions, there may be bias introduced as a result of firm entry and exit (the survivor problem) and changes in the quality of inputs employed and outputs produced. See Olley and Pakes (1996). These biases will tend to exaggerate any scale effects I estimate. Because I seek to put the scale effects in the most favorable light possible, the presence of any bias of this type strengthens the conclusions presented in the final section of this article.

(19) Additional input-specific scale estimates for the early years of the 20th century can be found in Cain and Paterson (1986. table 4).

(20) The second-order condition for the determination of the point of minimum efficient scale requires that the average cost functions are convex in output. This condition has been imposed in the estimation of the translog cost functions for all industries in this study.

(21) I can reject the hypothesis that the Canadian and American producers had common Qmes for all four industries with at least 95% confidence.

(22) For examples, see Atack (1977), James (1983), Sokoloff (1984), and Cain and Paterson (1981, 1986).

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Ian Keay, Queen's University, Department of Economics, Kingston, Ontario K7L 3N6, Canada.

Received December 2001; accepted November 2002.
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