Tariffs and growth: The dales hypothesis

EXPLORATIONS

IN ECONOMIC

HISTORY

25, 147-163 (1988)

Tariffs and Growth: The Dales Hypothesis* STEPHEN T. EASTON, Department

WILLIAM of Economics,

A. GIBSON, AND CLYDE G. REED Simon

Fraser

University

The impact of Canadian tariff policy on economic growth has been a source of conjecture among economic historians for decades. The dominant model of this interaction has been devised by John Dales (1966). Dales has argued that although the tariff reduced real per capita income in Canada, it stimulated extensive economic growth. This follows directly from three assertions: (1) The tariff caused the aggregate demand for labor in Canada to rise. (2) Per capita income was not an argument in the Canadian immigration function, and therefore, the tariff did not cause the supply of foreign labor (immigrants) to decrease. (3) Immigration was instead determined by the policies of Canadian immigration authorities who regulated the flow of immigrants in an effort to maintain a constant money wage level. This paper examines these assertions. We conclude that the effect of the tariff on aggregate labor demand depends upon untested assumptions about the nature of production technology, and that, on the basis of regression results, we fail to reject per capita income as a significant determinant of Canadian immigration. We find only limited statistical evidence to support the proposition that the Canadian authorities allocated immigration on the basis of a wage rule. Q 19% Academic

Press, Inc.

INTRODUCTION The historical impact of tariff policy on economic growth is a major issue in both economic history and current policy analysis. For Canada, the dominant model of this interaction has been that of John Dales (19&a).’ Prior to Dales, it was commonly held that the tariff, by increasing the aggregate demand for labor in the Canadian economy, promoted immigration, and thereby caused total output to expand.2 By making * We thank John Dales, Larry Neal, and two anonymous referees for their helpful comments on an earlier draft. Easton thanks the Social Science and Humanities Research Council for Sabbatical Leave Assistance. ’ See, for example, Powrie and Wilkinson (1974, p. 63) for an uncritical acceptance of Dales’ conclusions. For a textbook discussion of the Dales hypothesis see Pomfret (1981, pp. 83-84). ’ For a review of the earlier literature, see Dales (1964). 147 0014-4983BS $3.00 Copyright 0 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.

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Canada too large to be absorbed easily into the United States, the tariff served to preserve a political independence that might otherwise have been lost. Thus tariffs have been rationalized by Aitken (1959) and others as an instrument of “defensive expansionism.“3 Occasionally it was noted that the tariff had the additional effect of misallocating resources, and therefore lowering per capita income, but the implication that this would reduce the supply of labor via decreased net immigration was ignored. Dales recognized the theoretical problem4 and suggested a model of the Canadian labor market to solve it. The model contains three key assertions: (1) The tariff caused the aggregate demand for labor in Canada to rise. (2) Per capita income was not an argument in the Canadian immigration function, and therefore, the tariff did not cause the supply of foreign labor (immigrants) to decrease. (3) Immigration was instead determined by the policies of Canadian immigration authorities who regulated the flow of immigrants in an effort to maintain a constant money wage level. These assertions allow Dales to conclude that, although the tar8 reduced real per capita income in Canada, nevertheless it stimulated extensive economic growth. This paper begins an assessment of this view. In Part I, we elaborate the Dales model and derive a set of testable hypotheses from it. Part II develops an empirical test of the immigration function imbedded in the model that is consistent with Dales’ initial view of immigration policy. Part III extends the empirical analysis to deal with an additional specification of the immigration function that has been proposed by Dales in private communication to the authors. Part IV provides a summary and conclusions. I. THE DALES MODEL

In Dales’ model, there are three countries: Canada, the United States, and the Rest of the World. Immigration is unrestricted between Canada and the United States. Immigrants are not allowed into the United States in large numbers from the Rest of the World.’ Immigrants from the Rest of the World are allowed into Canada if the Canadian authorities recognize that an excess demand for labor exists at the existing money wage.6 Per 3 There are other arguments than that of national expansionism to explain the historical structure of Canadian tariffs. See, for example, Caves (1976), Helleiner (1977), or Pomfret (1981) for a summary of the debate which includes elements of both revenue and rent seeking as motivating the levels of tariff. 4 “How can a country attract immigration by cheapening the price of labor?” (Dales, 1966a, p. 3). ’ U.S. quota restrictions on immigration were in place by the mid 1920s. Dales argues that his model is applicable to Canada from this date through to the mid-1960s. His reasons for setting an end date are given in Dales (1966b, p. 174) and in footnote 3. 6 Note that there is no true supply schedule of labor facing Canada in this model, since the rate of immigration is determined by the authorities. The immigration rule, however,

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FIGURE 1

capita income in Canada and the United States is equal-or at least in equilibrium-so that no substantial net migration exists. Per capita income in both countries is above that in the Rest of the World. An initial equilibrium is depicted in Fig. 1 at point A, where the nominal wage is plotted on the vertical axis and the quantity of labor is on the horizontal axis. DD is the value of the marginal product of labor. Given a supply of labor S, the initial equilibrium will be a nominal wage of wO with LO units of labor employed. Now let Canada impose a tariff on manufactured goods. Dales assumes that this increases the aggregate demand for labor-a shift of the labor demand schedule from DD to D’D’. The initial effect is that the nominal wage rises to w,. The higher nominal wage encourages the immigration authorities to allow immigrants to enter Canada until the nominal wage returns to its original level w. at point C, where the labor force is now L1. Since money wages remain unchanged while the tariff has raised the price of “protected goods,” it follows that real wages must fall. It should be noted that this result is quite sensitive to Dales’ modeling of a small open economy. Alternative models yield sharply different conclusions about the way income will be redistributed because of the tariff. Chambers and Gordon (19663, for example, argue for a model that implies that the real wage will unambiguously rise as a function of an increase in the domestic price of manufactured goods, and that owners of land-specific to agricultural goods-will unambiguously lose.’ The standard Stolperimplies an equilibrium locus that is horizontal at the chosen money wage. In Dales’ words, “immigrants from [the rest of the World] are always available in unlimited quantrty: the amount of immigration therefore depends entirely on the operation of the immigration rule. In effect, we assume that the supply of labor available to [Canada] ,and [the United States] is infinitely elastic, for increases in supply at the going wage.” (Dales, 1966, p. 34). 7 See Easton and Reed (1980, 1983) for an elaboration of this point. See also Burges$ (1980).

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Samuelson result is that real wages will rise if manufacturing is labor intensive. Only in Dales’ model is the decline in real wages unambiguous. In addition, the tariff causes per capita income to decline. This occurs for two reasons. The first is that the tariff directly misallocates resources by driving a wedge between prices in Canada (a small country) and world prices. The second is that by promoting immigration, the tariff gives rise to diminishing returns as the additional labor is combined with fixed supplies of other factors of production. Dales further assumes that the lower per capita income in Canada will cause some of the pretariff labor force to emigrate to the United States. Thus, the total amount of immigration is greater than LI - LO. The model yields the very strong result that gross immigration will increase as a result of the tariff, that emigration will increase because of the tar@ and that net immigration will also increase. These conclusions hold even were we to relax the assumption that the immigration authorities wish to fix the money wage at its original level. Any attempt on the part of authorities to reduce the money wage below wl in Fig. I will result in the same qualitative conclusions. Dales’ model as outlined above appears reasonable as a matter of theory, but there are several links in the chain of logic that yield implications amenable to empirical investigation. First, did the tariff on manufactured goods lead to an increase in the aggregate demand for labor? Second, did the immigration authorities attempt to fix the nominal wage rate by regulating the flow of immigration? And, third, were immigration flows independent of the tariff’s implied effect on per capita income and real wages? In the remainder of this section we will derive the theoretical properties of Dales’ model that give rise to increased aggregate labor demand. In the next section we undertake an empirical examination of the other two questions. Tariff and Labor Demand Whether the tariff actually led to an increase in the aggregate demand for labor depends upon the details of the production process. Consider the simplest model that is capable of capturing the essentials of Dales’ view of the Canadian economy. This model includes an importable, x,, and an exportable, x2, both produced by a constant returns to scale production technology. The prices of labor, w, and capital, r, are exogenous, Wages are set (implicitly) by the immigration authorities, and the rental price of capital is set on the world capital market, Canada being a pricetaker in that market. The prices of the two goods @, and pJ are also determined exogenously since Canada is a “small country.” In order to close the model, specific factors, T, and T,, must be added in the production of importables and exportables respectively.’ All product and factor markets a Note that specialization.

we must

have

a different

specific

factor

in each

sector

to avoid

complete

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151

are assumed competitive. Equations (1) to (6) describe the static equilibrium.9 c L = aLlxl + aLzx2

61)

K = a&l

(2)

+ @K$tZ

TI

=

aTIXl

(3

Tz

=

aTZx2

(41

PI = aLlw + aKlr + aTIt

(3

P2 = aL2w + aK2r + aT2t2,

6)

where the au’s refer to unit input (i) - output 0’) coefficients. The tilde over K and L is to indicate that the supply of these factors is endogenous and their returns, w and r, are set exogenously. The specific factors are in inelastic supply and receive rents tl and t2. There is some ambiguity in writing aT] and aR, since each refers to a factor specific to industry one and two, respectively. Rather than add a correct but cumbersome subscript, aT,l, aTB, we simply note that the Ts are industry specific. The long-run demand for labor is given by Eq. (1). Proportionally differentiating Eq. (1) yields 2 = h&iL,

+ 2,) + XJJ(&* -I- a,)

(7)

where the “hat” is the proportional change operator, k = -.dx Since rjA x = ci, + 5, we can substitute Jjy and rewrite Eq. (1) as id = AL&& - LZT,+ ?,) + AL&,2 - &Z + ?2), (8) where h, is the proportion of the labor force engaged in producing xj. Since changes in the input-output coefficients are a function of changes in factor rewards it follows that

where Ei is the percentage change in a, when factor price k changes.” From homogeneity of factor demand, we know that q + Gj + Eg = 0, and we also know that “own” elasticities such as EFj, ~~j, and E$j are negative. 9 This set of equations represents our interpretation of what Dales has in mind. We must proceed in this way since Dales himself does not provide a formal specification of his model. ” A discussion of the properties of the B,‘s can be found in Ruffin and Jones (1977) or Jones and Easton (1983).

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We can substitute Eq. (9) into Eq. (8) to find the change in the demand for labor resulting from the imposition of a tariff. Recall that r+ = ? = 0 in the long run, and that for purposes of the experiment, the amount of the specific factors, Tj, are kept constant. Thus: e = ALI (EZ, - ET, + $) + XL2 (EFz2- E$ + &).

(10)

With the imposition of a tariff, b1 > 0, the domestic price of the importable rises, while the nominal prices of exportables remains unchanged. This implies that ;, = 0.” To determine whether there is an excess demand for labor, we need to sign t”, and (EF, - E&). Differentiating Eq. (5) yields

A 2,=$,

(11) Tl

where GTi is the distributive sha;e of the factor specific to industry one. Imposing the tariff implies that P, > 0 and therefore that i, > 0. Turning to (E:, - E&), we know from “own” substitution effects that E$ < 0. Thus the effect of the tariff on labor demand depends upon Efl’. If labor and the specific factor are substitutes, EC, > 0, an increase in the price of manufactured goods due to the imposition of the tariff, implies that the aggregate demand for labor increases. It is possible, however, that if the two factors are strongly complementary, labor demand will decrease as a result of the tariff. This theoretical ambiguity is reinforced if the model is made more “realistic” through the inclusion of nontraded goods and/or intermediate goods. Thus we conclude that some empirical estimation of the production process is necessary to generate Dales’ results even using the simplest model. Theory alone is insufficient. Although the above demonstration is lengthy, its value lies first in the explicit characterization of the underlying model, and second in the isolation of the crucial parameter to be estimated. It is worth observing that even recent evidence on manufacturing technology is at best ambiguous. Using a translog production function, Berndt and Christensen (1973) find that skilled labor is more complementary with capital than unskilled labor. Berndt and Wood (197.5) and Fuss (1977) find that energy is a substitute for all factors except capital with which it is complementary. Griffin and Gregory (1976) argue that in the long run there is substitutability among all inputs. Thus using recent data, which incidentally cover at least some of the period at issue, the exact structure of labor substitution remains an open issue.” ” Differentiating Eqs. (5) and (6) yields P, = 0,,ti + &,P + &,i,, p2 + && f 6,,; + t&i,, where $ is the distributive share of factor i in the unit cost of activity j. Since by assumption P2 = ti = P = 0, it follows that i, must also equal zero. ‘* Other recent evidence derived in the context of a two-factor, many-good model lends

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I.53

Our strategy in assessing Dales’ contribution in this first section has been to high&&t the limitations of the framework on the most rudimentary level. But now, to bias the case in favor of his interpretation, let us assume with Dales, and most economic historians, that the tariff did in fact increase the demand for labor. This leads to the second link in the chain of logic described above: Did the immigration authorities attempt to target the nominal wage by regulating the flow of immigration? II. TESTS OF DALES’ IMMIGRATION MODEL The Dales’ immigration model can be interpreted in several ways. In its simplest form, the model claims that during the second quarter of the 20th century the immigration authorities rationed immigration so as to maintain a constant money wage. This is clearly refuted by the facts. The trend in Canadian money wages is significantly positive over the period in question.13 A more flexible formulation of the immigration authorities’ reaction function asserts that immigration is rationed in response to a target money wage, with that target varying through time. A further refinement derives from Dales’ suggestion at one point that an alternative means to generate his conclusion (i.e., that the tariff resulted in declining per capita income and positive net immigration) is to assume that potential immigrants made their decision on the basis of job ,avaiIabi&ty rather than income.‘4 Note that this assumption and the target wage assumption for the immigration authority are complimentary. When the tariff increases aggregate demand for labor, it decreases unemployment and therefore motivates foreign labor to seek admission into Canada. At the same time the tariff’s effect of increasing wage levels causes the immigation authorities to let increasing numbers of immigrants into Canada. It is this expanded version of the Dales immigration model that we attempt to test in the remainder of this section, The’ immigration authority component of the model can be described as follows: I, = b() + b,(w, - wp) + u,,

w

where immigration at time t is a linear function of the deviation in the nominal wage, wI, from the immigration authority’s target wage, w$, and some support to Dales’ view. Boadway and Treddenick (1978) find that the tariff does tend to increase the wage in manufacturing. It must be stressed, however, that these data are for the year 1966 and are estimated using very strong assumptions about the substitution possibilities available in the economy since they use a modified Cobb-Douglas pro&t&m function. Fixed quantities of primary factors also make this model less appropriate for addressing the issues raised by Dales’ approach. I3 A regression of the nominal wage on time in the form w, = +q,e”’ yields a significant coefficient on a! = 2.1. I4 Dales (1966a, pp. 3-4).

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a random error, u,. The target wage, wT, is formed as WT = kw-1 + (1 - k)M$-,,

(13)

where the change in the target wage between periods (t - 1) and t is a linear function of the error in meeting the target in period (t - 1). The fraction of partial adjustment, k, is assumed to lie between zero and unity. A simple interpretation of Dales in which the immigration authority attempts to hold nominal wages constant corresponds to a special case of this formulation; i.e., where k = 0. Equations (12) and (13) can be combined to give I, = kb,, + b&v, - w,-J + (1 - k)I,-,

+ u, - (1 - k)u,-,.

(14)

Since there are well-known problems associated with estimating Eq. (14), as there is both a lagged dependent variable and a potentially complicated error structure, we chose instead to generate a series for w: and then to estimate Eq. (12) directly. For values of k between zero and unity, Eq. (13) can be repeatedly lagged and substituted into itself to yield an infinite series:i5 wf = kg (1 - k)‘w,+. i=o

(15)

In Eq. (15) the infinite series in (1 - k) falls rapidly toward zero. We approximated w: by letting i run for 10 periods using values of k in increments of tenths between k = 0 and k = 1. We then took each of the 11 series of wT and ran regression Eq. (12). We chose the regression with the highest R2 to indicate the appropriate value for k. The procedure is equivalent to a maximum likelihood approach.“j We are now in a position to test Dales’ hypothesis. The expanded version of his model combines the immigration authority component (i.e., our “best” estimate of Eq. (12)) with the Canadian unemployment rate. This results in Eq. (16) I* = bo + b*(w, - w:) + b2U&n + ut,

(16)

where Uc, is the rate of unemployment in Canada during year t representing Dales’ expanded job availability version of the model.17 ” For k = 0 or k = 1. Eq. (13) immediately yields an operational value of wT = WE, (= W*) and w? = w,- ,, respectively. ‘6 See Maddala (1977, pp. 141-148) for a discussion of estimation procedures applicable to lagged dependent variable equations. I7 It might be argued that there is a simultaneity problem in interpreting the results of regression Eq. (16) as wages are assumed to fall in response to immigration. So long as there is some observed discrepancy in the actual versus the target wage-so that it can be observed by the immigration authority as postulated by the Dales model-then any observed inflow of immigrants will be associated with this difference. To the extent that

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There are three tests that are appropriate. First, the impact of the wage target must be consistent with the hypothesis that the immigration authorities acted so as to allow increased immigration when the actual wage exceeded the target wage. That is, the coefficient on the deviation of the actual to target wage is positive: In Eqs. (12) and (16), b, is positive. Second, the regression (Eq. (16)) itself should explain a significant atiount of the immigration observed. That is, the regression should pass an F test at the usual significance level. Should the regression pass this test, then the third test is that no additional explanatory power should be obtained if we add other variables to the model. These other variables are ones that have been identified in the traditional immigration literature as “push” and “pull” factors and include domestic and foreign real wages and per capita incomes, and unemployment rates abroad.” If tbe addition of these other explanatory variables significantly improves the explanatory power of the regression equations, then we would also have to reject Dales’ immigration model as factors other than rationing and Canadian &employment would appear to have played a significant par~‘~ This constitutes evidence against Dales’ interpretation since he argues that there is a perfectly elastic supply of labor available (see footnote 6). Indeed, the addition of nonwage arguments, such as unemployment, in the immigration function diminishes the credibility of a perfectiy elastic supply of labor. But to allow full scope to Dales’ original contribution, we have included the unemployment term as a part of the specification of the Dales model. The addition of real wage and real income terms, however, is not admissible. Recall the original question: how can a tariff that lowers real per capita income and possibly real wages2’ induce immigration? This can only be assured if neither per capita. income nor real wages are quantitatively important arguments in the iinmigratitsn function. It: has been Dales’ explicit task to build an immigration function that depends on other arguments (i.e., rationing by the immigration authority and unem@loyment in Canada).” immigrants within the year depresses the wage toward the target wage, the coefficient on the wage difference will overestimate the immigration response biasing the case in favor of the Dales hypothesis. The wages used in the estimation are average wages for each year. ” See Green (1976) both as an example and for a summary of other immigration studies for Canada and Canada-like countries. I9 The statistic calculated is F(Q-K,N-Q) = [Rc - Rz,i/(l-R~),)[(N-Q)/(Q-~1, where Q is the number of regressors in the larger equation, K is the number of regressors in the smaller equation, and N is the number of observations. See Kamenta (1971, p. 371). *’ In his initial formualtion, Dales held nominal wages constant and therefore the tariff implied declining real wages. In the expanded version, nominal wages are allowed to increase with the tariff and therefore the effect on real wages is uncertain. ” Given the emphasis placed on the distinction between skilled and unskilled labor in the general immigration literature, an interesting extension of the Dales model would be

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The Evidence Our tests involve several “push and, pull” variables which exist conceptually for all countries. As a practical matter real wages, unemployment rates, and real income are available for the United Kingdom and in most cases are not available for other countries from which immigrants arrived. Thus we initially separated the immigration statistics into a series of immigration flows from the United Kingdom and a series for all other immigrants. This is also desirable because immigrants from the United Kingdom made up a large proportion of the total amount of immigration over the period. Immigration by those of UK ethnic origins comprised some 44% of the total in 1926, 44% in 1930, and 32% in 1955. For each immigration series, UK and non-UK, a simple regression, representing the Dales’ hypothesis was run with each of the 11 possible values of WT. The results of these regressions were used to select the value of w* which yielded the highest R*. These represent the strongest cases for the Dales hypothesis: the equations which maximize the explanatory power of the rationing rule. We then proceeded with our threepart test of the Dales hypothesis. In addition, we were able to gather sufficient data to carry out our tests on a specific non-UK region: Germany, Austria, and Luxembourg. For brevity, we shall refer to this region as Germany. ** Immigration

from the United Kingdom

The regression results for the United Kingdom are reported in Table 1. Our search for a “best” value of k failed to produce a single significant equation although the correct sign on the term (w - w*) was obtained. But in no case using any value of k between zero and unity and any corrective procedure on the residuals was a regression result produced which passed the F test at the 5% level of significance. A relative best occurred when k was set equal to 0.5 (R* = 0.05), but asking which is the best k is not really a meaningful question in this case. The regression which yields the highest R* presents the best case for the Dales hypothesis, but failure to produce a significant result is in itself a rejection of the wage rule portion of the hypothesis.23 Our next step was to see if the wage rule variable combined with the Canadian unemployment variable “explained” a significant portion of UK immigration. In fact it did (R* to run separate regressions for skilled and unskilled immigrants. Unfortunately this is not possible for the period under study. Data on the skill mix of immigrants is not available, nor are economy-wide wage, unemployment, and real income series by skill catagory. 22 Immigration by people from the “German” region represented 10.1% of total immigration in 1926, 12.9% in 1930, and 19.5% in 19.55. *3 One interpretation of this result is that immigrants of U.K. ethnic origins were free to immigrate to Canada as they wished. the Canadian authorities did not ration a large segment of total immigration, at least in the manner suggested by Dales.

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TABLE 1 Results of Regressions Involving UK Immigration: Dependent variable, Z, (immigration Constant w--w*”

1926-1939, 1951-1960

into Canada from the United Kingdom)

28,171 (3.69) 1,399 (1.72)

25,301 (1.72) 1,552 (1.11)

82,598 (7.00) -1244 (- 1.64) - 5,202 (-5.14)

81,280 (6.10) -1199 (-1.40) -5,106 (-4.48)

0.12 2.95 0.77 OLS

0.05 1.23 1.97 AR1 0.63

0.61 16.39 1.64 OLS

0.54 12.32 1.88 ARI 0.16

RYcm RYUK

RZ F L)W Method P

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THE DALES HYPOTHESIS

- 1897 (0.398) - 3998 f-2.02) -3,207 (- 0.90) 1,451 (0.35) 1,319 (1.43) - 2,356 (-0.87) 478 (1.95) - 271 ( - 0.90) 0.72 5.81 2.34 GLS

- 28,355 (-0.28) -5,108 (-2.77) -2,890 (-0.82) 1,898 (0.48) 1,714 (1.60) -3,873 (- 1.47) 611 62.653 - 337 (-1.13) 0.82 10.30 2.19 AR1 -0.31

Note. 24 observations 1926-1939, 1951-1960. W, wage rate; ARW, change in real wage rate; w*, target wage rate; RY, real per capita income; U, unemployment rate; ARI, GLS procedure for correction of first degree autocorrelation. ’ w* calculated with k = 0.5. Sources. Canadian data are from Urquhart and Buckely, (1965). U.K. unemployment and real income series are from Mitchell (1980). U.K. real wage series is from Feinstein (1972).

= 0.54). The F statistic measuring the increase in explanatory power is significant [F( 1, 22) = 23.41. When we added the other push-pull variables to this regression, however, a further significant improvement occurred. [R2 = 0.82, F(5, 17) = 5.31. Thus our overall finding is that the Dales immigration model must be rejected for the UK case. The addition of the variables real wages and real incomes means that the necessary condition linking the tariff to immigration is violated. If real wages and incomes have a significant effect upon immigration, as they do in the case of UK immigrants, then the higher tariff which is assumed to raise nominal wages, may lower real wages, and will lower real incomes. The aggregate effect of the tariff depends upon the importance of each in the immigration function. The unambiguous connection between the tariff and immigration suggested by Dales’ formulation does not’exist in this case. This is not to deny that there is merit in Dales’ argument that the immigration authorities affected the flow of immigration. It suggests only that such regulation must be balanced against competing forces The

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obvious virtue of Dales’ model is that if the wage target explains the bulk of the variation in immigration, then the effects of real income and wages can be ignored and the tariff must promote immigration-and growth at the extensive margin-even as real income declines. We expand on this point formally in the conclusion and in footnote 23. Non-U.K.

Immigration

For regressions involving aggregate non-UK immigration statistics, the best result, in terms of having the highest R2, was obtained with k = 0.3 and k = 0.9 using GLS to correct for first-order autocorrelation. The two produced almost identical statistics. The results obtained where k = 0.9 are listed in Table 2. The wage rule variable alone yielded an R2 of 0.43. When Canadian unemployment was added, the R2 rose to 0.69; a significant improvement [F(l, 22) = 18.451. The inclusion of additional variables was hindered by the fact that the “push” variables are not available for non-UK countries as a whole. However, it was still possible to add the “pull” variables to the basic equation in order to test for their significance. When Canadian real wages and real per capita income were added to the regression, its explanatory power remained the same (R* = 0.71). Thus we are unable to reject Dales’ model for aggregate non-UK immigration. TABLE Results of Regressions Involving Non-UK (immigration Constant w-ww*O

2 Immigration:

Dependent variable, Z, into Canada from non-UK

34,174 (4.17) 9,191 (6.12)

35,540 (1.86) 8,452 (4.06)

90,656 (7.14) 4,588 (3.29) - 5,529 (-4.98)

77,212 (4.43) 5,636 (3.08) - 4,268 (-2.79)

0.63 37.43 0.46 OLS

0.43 16.46 2.03 AR1 0.81

0.83 51.32 1.26 OLS

0.69 23.08 1.94 AR1 0.45

c?an L=Wch” RYca. R2 F DW Method P

Note. See Table 1. a w* calculated with k = 0.9. Sources. Canadian data are in Table 1

1926-1939; 1951-1960 sources) 63,266 (1.94) 2,964 (1.35) -5,149 (-4.19) 238 (-0.24) 70.7 (0.W 0.84 24.64 1.35 OLS

67,129

(1.60) 4,975 (2.01) (-- 4,271) ( -2.60) 171 (0.W (OT,‘,, 0.71 11.48 1.93 AR1 0.44

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German Zmmigration The German regression results are presented in Table 3. This is the only non-UK region for which we were able to gather data roughly comparable to those used in the U.K. regressions. The best k was found to be 0.4 when the wage rule variable was run by itself (R2 = 0.27). Using the expanded formulation of Dales’ model by adding Canadian unemployment improved the result significantly [R* = 0.54, F(1, 22) = 12.911. As in the case of UK immigration, however, the inclusion of real wage and per capita income data resulted in a further improvement in the R2 [R* = 0.94, F(15, 17) = 5.881. This militates against accepting Dales’ hypothesis for non-UK immigration. TABLE 3 Results of Regressions Involving German Immigration: (immigration Constant W-W”

Dependent variable, Z, into Canada from “German

6,429 (2.91) 1,138 (6.20)

5,667 (1.05) 1,080 (2.77)

18,483 (4.74) 674 (3.36) - 1,155 (-3.85)

15,809 (2.76) 720 (-2.31) -931 ( - 2.03)

(0.65) 38.4.5 0.59 OLS

(0.27) 7.76 1.84 AR1 0.76

(0.78) 35.39 0.99 OLS

(0.54) 11.62 1.83 AR1 0.55

UC,, u Cm ARWti. ARWoe, RYcan RYar R2 F DW

Method P

1926-1938; 1951-1960. region”) - 18,022 (- 1.37) -129 (-0.27) -89 (-0.16) - 158 (-0.45) 185 (0.81) 46 (0.44) 180 (2.77) - 17.44 ( - 2.69) 0.90 19.60 2.25 OLS

-21,261 (- 1.85) - 773 (-0.64) - 377 f-0.01) -206 (-0.64) 243 (l.nl) 99.9 (0.86) 197 (3.31) - 18.8 (-3.17) 0.94 3 1.22 2.20 ARI -0.26

Note. See Table 1. ” w* calculated with k = 0.4. Sources. Canadian data as in Table 1. German data are from Mitchell (1980). Using immigration, emigration, birth and death series, a net change in population series was calculated. This series was used to estimate population levels for those years for which figures were not given. The resulting annual series was checked for consistency with figures given in B. R. Mitchell’s Statistical Appendix in Cipolla (1976). Slight revision of the estimates was necessary. The resulting series was used in calculating the German real per capita income series.

160

EASTON,

GIBSON,

III. AN ALTERNATIVE

AND

REED

FORMULATION

In a less well-known paper Dales (1964) hints at an alternative specification of the Canadian immigration function. He has amplified his thoughts on this alternative in private correspondence. Central to his view is the notion that immigration into Canada depends on relative unemployment rates between Canada and the “Rest of the World,” while emigration is a function of relative Canadian and U.S. wages. His target wage for the Canadian immigration authorities becomes “the wage that would yield a constant Canadian/American wage ratio.” This view can be easily integrated into our regression equations. The immigration authority component of the immigration function now becomes Zt = A, + A,(W, - K) and x

where W, = W,,,/W,,; rearranging yields

+ u,

(12”)

= C, a constant. Substituting

for K and

Z, = A0 - A,(C) + A,(W,) + u,. Adding the unemployment specification zt

=

4)

+

&tWJ

variables +

(12”“)

Uc,,, and Uror+nt completes

B2(uCan3

+

&(~foreignt)

+

vt-

the W*)

We estimated Eq. (16*) for the two geographical areas for which we have sufficient data, the United Kingdom and Germany. The regression results are presented in Tables 4 and 5. Turning first to the UK results, we find that our alternative Dales formulation (i.e., Eq. (16*)) passes the F test and the inclusion of real wage and real income variables does not significantly improve the results. Thus Dales passes two of our tests. Unfortunately, he fails the third. The sign on his critical variable, the ratio of Canadian and US. nominal wages, is incorrect. The expected result was positive and significant. The actual result was negative and insignificant. In the case of German immigration, Dales fails all three tests. Equation (16”) does not pass the F test, the sign on the relative wage variable is incorrect, and the inclusion of real wage and real income data significantly improves R* (0.21 to 0.94). We conclude that this alternative formulation of the Dales immigration model must also be rejected. IV. CONCLUSION

In 1966 John Dales advanced a model of Canada’s tariff and growth experience. Although Dales’ interpretation of Canadian history has been widely accepted, little empirical evidence has been developed to test the

TARIFFS

AND GROWTH:

THE DALES HYPOTHESIS

TABLE 4 Results of Regressions Involving UK Immigration for Dales’ Alternative 1926-1939;

(immigration Constant

WC,/wus uCan uUK

- 66,233 ( - 0.69) -4,878 (-3.22)

1,099 (1.15)

1.113 E + 0.5 (1.08) -45,363 (-0.46) -4,974 (-3.09) 1,122 (1.07)

ARWcan ARWu,

-8496 (-0.04) - 1,546 (-0.01) -5,349 (- 1.39) 3,841 (0.83) 652 (0.65) -307

(-0.11)

RYUK RZ F DW

Method P

0.61 10.34

1.66 OLS

Speciticiation:

1951-1960

Dependent variable, Z, into Canada from the United Kingdom)

1.336 E + 0.5 (1.35)

161

0.54 7.9 2.85

AR1 0.145

198 (0.72) -73.4 (-0.21) 0.65 4.17 1.82 OLS

10907 (0.05) -1,448 (- 0.06) -5,020

(- 1.31) 3,329 (0.72) 701 (0.74) -318 (-0.11) I87 (0.68) -87.6 (-0.26) 0.61 3.62 1.89 ARI 0.078

Note. See Table 1. Wc,,,/Wus, Nominal wage rate in Canada relative to nominal wage rate in U.S. This relative wage was adjusted for changes in the Canada/U.S exchange rate. Sources. See Table 1. The U.S. wage series is from U.S. Bureau of the Census (1975).

underlying model. In essence Dales asserts a set of sufficient conditions that link the tariff with extensive economic growth. Our evidence casts significant doubt on the empirical existence of these conditions and thereby deprives Dales’ model of the theoretical mechanism by which the tariff can promote immigration. This is unfortunate since Dales’ model provided an unambiguous link between the tariff and the extensive margin of Canadian economic growth. The issue now hinges on the empirical estimation of the immigrationpromoting and immigration-discouraging effects of the tariff. To the extent that the tariff decreased unemployment and increased nominal and real wages, immigration into Canada was higher than it otherwise would have been. To the extent that the tariff decreased real wages and per capita income. immigration flows were reduced.24 The historical effect of the Canadian National Policy is indeterminate. Dales’ hypothesis linking the 24 In formal terms we can write the total change in immigration, I, with respect to a change in the tariff, T, as dl/dr = (az,/aw)dwJdT + (aZ/aU,,)dU,,,/dr + ~~ZlaR~~W~~~ f (aZ/aRY)dRY/d~, where RW and RY refer to the real wage and real income per capita

162

EASTON,

GIBSON,

AND REED

TABLE 5 Results of Regressions Involving German Immigration for Dales’ Alternative Specification: 1926-1939; 1951-1960 (immigration Constant

WC,./ w*, uOer

51,246 (0.88) -21,453 (-0.39) -1,811 (-2.61) 34.1 (0.08)

Dependent variable, Z, into Canada from the “German Region” 33,330 (0.75) - 10,261 (-0.25) - 1,176 (- 1.75) 85.2 (0.20)

ARWca. ARWoe, RYcm

RZ F DW Method P

0.66 12.46 0.74 OLS

0.22 1.73 2.20 AR1 0.7984

-57.517 (- 1.09) 36,890 (0.81) -583 (-0.84) 216 (0.43) 76.7 (0.32) 43.7 (0.43) 163.5 (4.57) - 14.6 (-2.62) 0.91 20.44 2.35 OLS

- 76,073 (- 1.43) 53,342 (1.16) -816 (- 1.20) 393 (0.81) 78.6 (0.28) 92.2 (0.81) 159.2 (5.02) - 13.6 (-2.69) 0.94 34.11 2.26 AR1 -0.2807

Note. See Tables 2 and 4.

tariff to the expansion of national income does not bear the weight of the evidence. There is no simple link that we can discern between the tariff and the expansion of national income through the mechanism of immigration. This negative conclusion regarding the tariff should not obscure the significance of Dales’ approach to immigration which specifically incorporates the behavior of the immigration authority. Although many studies are aware of quotas, and other barriers to entry facing immigrants, Dales’ observation of an elastic supply of immigrants places the behavior of the immigration authorities at center stage in the immigration process. in Canada, w refers to the money wage and U,, refers to the Canadian rate of unemployment. Dales asserts that aZ/aw > 0 > aZ/XJ,,, and all other partial derivations are zero. He also maintains that dw/dr > 0 > dU,,/dr, dRW/dr, dRY/dT. Thus dI/dr is unambiguously positive. To the contrary, our evidence suggests that both (aZ/aRW)dRW and (aZ/aRY)dRY are non-zero and contribute significantly to immigration into Canada. We have not yet seen an empirical measurement of the effect of the tariff on nominal wages, unemployment, real wages, and real income in Canada. Like Dales we tend to agree that a tariff reduces per capita income in a small country, but we have a very different view of the effect of the tariff on real wages (Easton and Reed, 1980; Easton, Reed, and Gibson, 1983).

TARIFFS

AND GROWTH:

THE DALES

HYPOTHESIS

163

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