When it all began

The first empirical macroeconomic mode! was constructed by Tinbergen in 1936 jor the Netherlands economy. The paper discusses the intellectual and political context within which it emerged, its major characteristics, structural specification, dynamic properties and use jor policy analysis. It also re-estimates the model with current estimation techniques. It appears that given the short sample (11 years) simuJtaneous inconsistency does not make itselj felt. The model is a rather refined, dynamic, policy-oriented, empirical, macroeconomic model jor an open economy. Since the 193á model progress has no doubt been made; but less than might be thought. values. This suggests that the differcna is due to computational aspeas rather than to statistical properties. In conclusion we may say that our experiments do not indicate that least squares inconsistency has caused serious problems.

To assess the distance covered in a discipline it is natural to look back to its beginnings. In the case of empirical macroeconomic modelling the beginning is clear and unambiguous: the model built by Tinbergen in 1936 for the Dutch economy. It emerged almost out of nothing and began a tradition of macrceconometric modelling which has continued until today and generates a multitude o( modeis of an enormous variety of scope, purpose and complexity. It is our purpose to take a close look at this 193tí Tinbergen model. First, the political and intellectual contexts in which it developed are briefly sketched. Then the main characteristics of the model will be presented. Next, its structural equations are reviewed. It is of some interest to see how Tinbergen went about solving his 24~quation model in order to trace out seven alternative policy scenarios ( the topic of the fiRh section). We then turn to a description of the dynamic properties of the model. The model reveals these properties in its impact and interim multipliers, some of which are presented and discussed in the seventh section.
The seven alternative policy scenarios, together with their consequences, are taken up in the eighth section. The 1936 model was the first of its kind. In the concluding section its direct successor, the Tinbergen 1937 model and some other models that were built The authors are with the Catholic University of Leuven, CES, E. van Evenstraat 2B, 3000 Leuven, Belgium.
The authors wish to thank Profasor Jan Tinlxrgen for his rcmarks on an earlier draft of the paper. Dr Peter Solar's comments have also been very uxful. before World War II are reviewed. The concluding remarks are followed by two appendices dealing with estimation aspects.

The context
Tinbergen presented his model at the 1936 annual .,terting nf the Dutch Association for Economics and Statistics. Since t893 this association of professional economists had organized its annual meeting around a theme introduced by three or more speakers, usually from different backgrounds. The 193tí theme was the recovery of the domestic economy, with or without government action, and possibly even without an improvement in exports.
The theme implicitly referred to the deterioration in the Dutch economic situation since 1929. The Depression had initially been less severe than eg in the USA; but in contrast to countries like the UK and the USA there was still no sign o( recovery in the mid-1930s. By 1936 Dutch international trade, historically the major source of Holland's prosperity, had dwindled to one-third of its 1929 level. With a conviction more deeply rooted in ethics than in economic reasoning, the government stuck to the gold (exchange) standard to which the country, together with the UK, had returned in 1925. ít tried to cope with the overvaluation of the Dutch guilder by a politically painful downward adjustment of domestic prices, wages and costs.
Tinbergen approached the theme set by the Association board by considering several alternativc policy scenarios: P, a three-year investment programme; Q, the limitation of imports o( finished consumer goods; R, an increase in labour productivity combined 0264-9993~89~020203-17 503.00 Q 1989 Butterworth Bc Co ( Publishers) Ltd 203 When it all began: the I936 Tinbergen modef reuisited: G. Dhaene and A.P. Barten with price reduction and no increase in investment; R', a reduction in prices without changes in labour efficiency and without wage reductions; S, a nonrecurrent roduction in the wage rate; and T, a devaluation of the guilder, taking into account reprisals by foreign countries. To study the consequences of these policy alternatives he constructed a model, a system of 24 empirically verified equations, which was amply documented in hís memorandum for the meeting -see Tinbergen [11]. The idea of building a model and using it for policy analysis was without precedent. The Great Depression was the Great Boom for business cycle theory, but there was little in its mainstream that suggested anything like a model. In his review of business cycle analysis Haberler [4] briefly mentions ( as a kind of afterthought in a footnote at the end of Part I) the work of Frisch and Tinbergen as examples of the dynamic, mathematical approach that he considered virtually unfeasible.
Frisch and Tinbergen were the nucleus of a small group ( Kalecki was also a member) within the newly formed Econometric Society that applied the theory of difference and differential equations to the analysis of the phenomenon o( the business cycle. In his well known contribution to the Cassel Festschrifr Firsch [2] presented a'macrodynamic' system of equations able to generate cycles of realistic periodicity in response to non-periodic impulses. For the parameters of this system he used rough guesses, but he believed 'that it [would] be possible by appropriate statistical methods to obtain more exact information about them'. He thought, indeed, 'that the statistical determination oC such structural parameters [would] be one of the main objectives of the economic cycle analysis of the future'. In a 1935 Economerrica survey of recent quantitative business cycle theory Tinbergen went one step further. He presented a kind of cobweb model for national consumption which he fitted by a variant of least squares to quarterly data for FRGermany and the USA. This was the very first example of an empirically verified dynamic ( business cycle) model. It was not, however, a useful tool for policy analysis and can hardly count as a predecessor of the 1936 model. in another paper Tinbergen [10] presented a more refined model which was, however, not estimated. Its specification resembles that of the 1936 model, the main characteristics of which are discussed in the next sec[ion. The 1936 model consists of 24 equations. Compared to uveral current modelling projects it is small but rather sizable for a beginner. As Tinbergen [ 16] points out, its siu was minimal considering the desire to distinguish between two social groups (]abour and others), two kinds of goods (consumer and investment goods), two kinds of use for non-labour income (consumption and saving), two points in time at which to measure this income (moment of earning and that of actually receiving), two stages of processing goods (finished goods and raw materials) and two economies (The Netherlands and the rest of the world). Table I gives the variables of the model with their original symbols. Their description ref~ects the desired distinctions. The original memorandum supplied the observations for all variables for 1923-33. In some cases values are given for 1934 and 1935, while it was possible to reconstruct some values for 1921 and 1922 used in lags. The data came from various sources, mostly from the Central Bureau of Statistics of which Tinbergen was an employee at the time. He constructed several of the series himselL It is important to realiu when going over the table that the system of national accounts had not yet been established. We note the absence of government related variables like taxes or government expenditures. Note also the absence of investment, though'means of production' comes close to that concept. Monetary and financial variables, even the rate of interest, are also missing. The model is concerned with the real sector only.

Main characteristics of the 1936 Tinbergen model
The nominal values are expressed in units of 17.54 million guilders, which is 10"~0 of the average wage bill over the period 1923-33. All prices, except pw, have base 1923-33 -100. This means that all quantities have as unit the quantity whose average value for the 1923-33 period was 17.54 million guilders. Table I also indiqtes which variables are endogenous and which are exogenous. The trend, all import prices as well as the world price level, pw, are exogenous. Moreover the volume of world exports and income from investment abroad are exogenous. Otherwise said, the international environment is taken as given. Observe that exports, value, volume and price, are endogenous.
To the 24 remaining variables -the endogenous ones -correspond 24 structural equations, summariud in Table 2 the intention to construct a business cycle model. The long-run development was not specified and was simply represented as a trend. It was realized that estimating the trcnd ccefricients along with the other coefficients was equivalent to first detrending the series and then estimating the coefficients of these variables -see Frisch and Waugh [3]. A number of the coellicients of the structural equations were fixed a priori; the othets were estimated. Tinbergen [10] was aware of the fact that among the numerous multiple regression techniques available at the time none was adequate because they all basically assumed that only one o( the variables was random. As a way out he applied least squares with the ccefïicients divided by the (overall) correlation ccefficient. In the caso of bivariate regression this procedure removes the asymmetry between regressand and regressor. For multiple regression this is, of course, not the case. Since many of the equations display a good fit, this procedure does not lead to large diflerences from least squares. In Appendix 1 we report the re-estimation of the system by least squares. Standard errors, ccefficients of determination and Durbin-Watson statistics are also given there. One conclusion is that recalculation by and large confirms the Tinbergen results. The same appendix also presents the results of consistent, instrumental variables estimations. These are also rather similar to the values obtained by Tinbergen. Appendix 2 rcports on two morc formal tests of the seriousness of least squares inconsistency. Generally speaking, the test outcomes do not rcveal that this inconsistency is an important issue.  The model counts nine identities. Equations (5) and (20) are additive. Equations (7), (14). (19) and (21)-(24) are linearized multiplicative, linking the value, volume and price of the various concepts. The linearization is around the sample mean. The approximation errors are minor. The small number of additive, accounting identities is another symptom of the fact that the model predates the system of national accounts.

ECONOMIC MODELLING April I989 205
As far as the contemporaneous interdependence is concerned it appears that Equations (17)

Structural equations
In this section the various structural equations will be reviewed. They are taken up block by block. is an accounting identity. It expresses the idea that total consumer expenditure, U', is the sum of consumption outlays by workers, L, and those by otherincome earners, E'. However, this equation also reflects a behavioural assumption: that all labour income is spent on consumption. This assumption is not testable because E' has been calculated as U' -L.
The other behavioural assumptions about consumption concern the relation between consumption out of other income, E', and that income when paid out, E, and between E and other income as earned, Z. The first relation is expressed in Equation (l7) as Here a two-year moving average in consumption by

ECONOMIC MODELLING April 1989
When it alf began: thr I936 Tinbergen modef recisited: G. Dhaene and A.P. Bwten other-income earners is made dependent on other income earned the year before. The term in t reprcxnts a trend. Thc implied marginal propensity to consume is 13"~0. The equation was estimated ( l7a) as Er, f E' -0.26E -1.8t t intercept (or the period 1923-32 because of lack of a value for E' (or 1934. The Rj is 0.939. There is no autocornlation in thc residuals. The moving average on the lefthand side is slightly awkward becaux it causes currcnt consumption to depend negatively on pazt consumption. A marginal propensity to consume of 13 "~o seems to be on the low side, considering the fact that farmers and small businessmen arc among the other-income earners. It might reflect the possible undercstimation of consumption by this group resulting from the overestimation of consumption by workers, who were a priori attributed a marginal propensity to consume of unity. Moreover, the income concept used herc is that of income before taxes. Analogous to Equation ( 17) there is the savings equation (l8): where E" is savings out of other income. For estimation the time subscript was shifted; but given a 1934 value for E" the full sample period 1923-33 could be used. The R' is 0.862. The esiimetcd ccxfPicicni of E-, turned out to be 1.65 but this value was replaced by 1.74 to preserve thc identity E-E' f E".
The way in which other income paid out, E, depends on other income when earned, Z, is exprcsxd in Equation (16) by E-0.482 f 0.202 -, t 52.47 with R2 -0.991. Obviously, not all other income is being paid out. About 32"~o appears to be retained.
Combining Equations ( 16), (I7) and ( 20) we may conclude that other income, Z, affects consumption ezpenditure very marginally and with a considerable delay.
Using Equation ( 20) we can rewrite Equation (7), (Equation ( 7a)), with p being the cost of living. It appears from ( 7a) that ít is a linearization of a value-volume conversion. The structural volumeprice elasticity is -1 due to the absence of structural price efiects in the determination of U'. The cost of living is explained by Equation (2): with Rj -0.978. In this equation p;,, the price of imported finished consumer goods, reprexnts competition between locally produced and imported consumer goods. The xcond tet~rt is a cost term, with r~being the import prices of the raw materials going into the production of consumer goods, while I is the wage rate. The term with t represents productivity increase. Its coefficient is set a priori. The coefficient 2 of 1 reflects the assumption that wages constitute two-thirds of production costs. Finally, the term with u, total output, expresses the nature o( the cquation as a price xtting rulc (or the suppliers. Note that the variable in question is not u', consumption. In current parlance the presence of u in such a price equation would be justified as a tension effect. as the investment equation, ( 8). On the lefthand side is the sum of impor[ed means of production, r~, and domestically produced means o( production. The latter are assumed to requíre imported raw materials, y~, for about one-third of their value in the bax period. This explains the a priori fixed value of 3 for the coefficient of y~. Equation ( 8) follows a profit explanation of investment, which is a recurring feature in most later models for the Dutch economysec Barten [1]. The rate of interest was not able to add to the explanation. It had not varicd much over the sample period, while capital costs were a relatively unimportant part of total investment costs. According to Tinbergen [9], littk unambiguous empirical evidence was (ound in favour of the acceleration principle, which was popular with the business cycle analysts of the time. The ability to raix finance for new investments can be linked to the price of shares. Thex are suppoxd to reflect profits, Z. This then explains the prexnce of Z-, as an ezplanatory variable next to the usual explanation of investment by profit expectations as generated by actual profits. The strong positive trend captures gradual tcchnological and structural changes. The equation has a reasonable fit: R2 -0.887.

Investment
The price of ineans of production, q, is determined in Equation (3) as: Competition with ímported finished means of production is reprexnted by their price, q,,. Its etTect is much stronger than in the case of Equation (2), the

ECONOMIC MODELLING April 1989 207
When it alt began: the J936 7inbergen model revisited: G. Dhaene and A.P. Barten consumption price equation. This is natural. Moreover, imported finished means of production are on average a quarter of total investment, so for that reason their price, q~, has a place in Equation (3). The cost term is of about the same type and importance as in Equation ( 2), except that here s~, the price of imported raw materials for means of produciion, appears. An extra trend is added, which somewhat corrects for the effect of productivity increases in the costs term.
righthand side, will be taken up when reviewing the labour market. Here we will consider Equations (12) and (13). Equations (12) and (13) aim to explain the choice between home produced goods and imported goods as a function of their relative prioes. Domestic production requires the import o( raw materials and is considered to be proportional to that. In the case of choice betwcen domestically produced and imported consumer goods, the basic relation is then

Exports
In a model which is meant to study, inter alia, the effects of devaluation, the presence of an export equation depending on foreign and domestic prices is natural. This is the case for the equation for exports, uA, (Equation (6)): In this equation z represents the volume of world exports, to which the Dutch exports were largely parallel. These latter are positively influenced by world market prices, p,,, as seen in the second term and negatively by their own price, pA, as the third term shows. The elasticity of exports evaluated [or 1934 with respect to p" is 1.83, that with respect to pA is -0.96. The Rj of this relation is 0.976.
The price of exports, pA, is specified in Equation (4)  where the first term reflects competition and the second term costs, with r~being the price of imported materials (or consumer goods. A modern model builder would be worried by the lack of homogeneity of this equation. The R' is 0.991. Finally, the value-volume conversion equation, (9), completes the block of export equations.

Imports
Tinbergen distinguishes between imports of finished goods for consumption, u~, those for investment, v~, imports o( raw materials for the production of consumer goods, x~, and those (or the production of investment goods, y'A. Those four variables appear on the righthand side of Equations (8), (10), (12) and (t3). Equation (8) where q is the price of ineans of production and qt hat of imported raw materials for means of production. The sample means of y~and v~are equal: 13. Linearization of (C) around the sample means along the same lines as (B) leads to Tinbergen's Equation (13): where the coefficient of the time trend has been fixed a priori. The implied value of t:j, the substitution elasticity, is -6.tí. This is substantially more than that for consumer goods. This might reflect the fact that the degree of substitutability between domestic and imported means of production is larger than that for domestic and imported consumer goods. The R' of Equation (13)

Tota! output
There are two equations with u, the volume of total output, on the righthand side: Equations ( 5) and (11).
Equation (5) u-ua~-u'-2 where we have ori the left the ditTerence between total employment, a, and employment in the investment industries, b. So a -b is employment in the production of consumer goods, whether for local use or export.
Obviously, less labour is needed to further process imported finished consumer goods, u~, than for the transfot~rtation of imported raw materials for consumer goods, x~. In the latter case 0.98~0.20 -4.9 more units of labour per unit of imports are needed than for the former. This rate comes close to that implied by Equatíon ( 11) for total value-addcd, namely 4.7 -3.35~0.72. It is not quite clcar how Equation (9) was estimated. It seems that 0.20 was fixed and 0.98 was estimated. The R~of Equation (9) is 0.973. Employment in investment industry, 6, appears nowhere as a lefthand side variable. it appears in Equation ( 9), just reviewed, and in (10): seems to define total output, u, as the sum of exports, u,,, and of consumption, u'. The u series has been constructed from production indexes and from information about agricultural production independently of u,, and u'.
As a definition Equation (5) thus holds only approximately and an intercept is added to absorb the average discrepancy. It is to be noted that production of investment goods is not taken into account.
Equation (11) can be seen as a way to describe value-added in production: where u~is imports of finished consumer goods and x~imports of raw materials for the production of consumer goods. The ccefficients of u~and x~have been estimated. The ccefficient of u~implies that value-added is about 0.72~1.72 -0.41 of the value of those consumer goods which are already technically finished when entering the country. It is the margin for storage, distribution and profits. For consumer goods which are domestically produced the fraction of value-added is 3.35~4.35 -0.77 (clearly much larger). The R2 of this relation is 0.855. We may note that it is implicitly assumed that ezported goods are consumer goods only, which might not be unrealistic for the Dutch economy in the period considered. The model does not contain a price of total output or a value of total output.

Labour market
The labour component of value-added in production is described by Equation (9), which can also be written as Equation (9a)

Other income
The last equation not yet reviewed is the one for other or non-labour income, Z, also called profits. In current modelling practice non-labour income is tuually determined as the difierence between national income at factor costs and the wage bill. This is also its national accounting definition. The concept of non-labour income used by Tinbergen is wider because it also includes capital gains. This makes sense in his model where Z, with appropriate lags, drives investment and consumer spending. In accordance with this wider interpretation of profits Tinbergen calculates his Z scries in an independent way. Its explanation~[Iso reflects the two aspects of his profits variable. One corresponds with the accounting identity aspect, the other with the capital gains component.
To start with the first, national income in current prices is implicitly defined by

U~tU~}Ur-(U~fV~tX~-~YÁ)tI (D)
where Ur is the value of the output of production goods and 1 is factor income received from abroad. The last term is supposed to reflect capital gains from domestic share investments. The first three terms represent those gains from the change in the prices of raw materials (or the production of investment goods, s~, those of raw materials used in the production of consumer goods, r~, and those of finished consumer goods, p'~respectively. The coefficients in (I) have not been estimated, probably because of multicollinearity. The sum of (I) and of (D), with Ur -V'~replaced by (H), constitutes Tinbergen's Equation (15), given in Table 2. In spite of it not having been estimated its R~equals 0.941. Equation (15) is of considerable importance for the dynamics of the model. In this connection the negative relation between Z and Z-t is of interest. Equation (15) plays the role of the balance equation in current models, except that Z has no immediate feedback on most of the other variables in the model.

A first evaluation
The structural equations are based on economic reasoning. The consumption explanation distinguishes between the eflects of labour and of non-labour income, a feature adopted by many later models. The same is true for allowing investment to depend on profits. One of the most striking features is the care with which the open nature of the Dutch economy has been modelled. Exports compete with the exports of other countries, imports compete with domestic production. This is also reflected in the formulation of the equations for the prices of consumer, producer and export goods: it is the unifying idea of the model. In terms of theoretical coherence the model is well ahead o( the models of the late 1950s.
The absence of a data base with the type of coherence

21p ECONOMIC MODELLING April 1989
When it all began: the 1936 Tinbergen model reuisited: G. Dhaene and A.P. Barten offered by the system of national accounts appears to be a serious handicap. We have to admire the inventiveness of Tinbergen in circumventing the absence of data for concepts like investment, gross national product and so on, which are essential variables of current models. The absence of taxes in the definition of (disposable) other income is striking and somewhat puzzling. No trace is (ound of government in general. The capital gains part of Z would have been an appropriate place to allow for the impact of monetary (actors. The 1936 model is solidly non-money-non-financial. This was not a matter of principle because subsequent Tinbergen models for the USA and the UK contain monetary and financial blocks.
The model is linear in the variables and the coefficients, a virtual necessity for the time at which it originated. It required a number of linearizations which are neither conceptually nor empirically distorting.
The determination of the coefficients took place in three ways. Coefficients in linearized identities were calculated from sample means. A number o( ccefficients, usually characterizing production processes, have been fixed on the basis of information other than that coming from time series, more or less in the same way that current models make use of input-output information. Ixast squares has been employed in the other cases. Ciiven the smaii sampic sii~eo~~~pictc reliance on least squares would have been asking for trouble.
Today a sample period of only 11 years would raise many an eyebrow. As we found out, the point estimates are in a few cases rather sensitive to slight changes in the size of the sample. The original paper gives no clue about the nature o( the trial and error process of which the published equations are the final result. The model was, however, not meant to discriminate between alternative approaches: it was meant as a descriptive tool. How it was in fact used is the subject of the following sections.

Solution
Given the linear nature of the model, it is a straightforward matter to obtain the reduced form o( the model; but this was not the way Tinbergen solved it. As a first step, the exogenous variables were replaced by their assumed values. These, multiplied by the appropriate ccefficients, were added to the intercepts. These intercepts were further modified according to the policy alternative considered. For instance, when increasing investment autonomously the intercept of Equation (8) is increased by I4 for three years. In the case of a devaluation all exogenous prices as well as 1, income from investment abroad, are increased. To take into account eventual reprisals the intercept of export equation ( 6), was reduced by 18. The next step was to treat l, the wage rate, as an exogenous variable and to delete one equation, Equation ( 17), from the model. The model is then in almost (ully recursive form with only two blocks, Equations (8) and ( 13) and Equations (2), (9), (11) and (12). This must have greatly facilitated calculations.
The model was then solved ie expressed in the wage rate, !, the lagged wage rate, 1-t, the lagged price difference, p-t -p-2, and Z-t next to the intercepts. In this process an error was made. In Equation (IS) U~was incorrectly replaced by U'~. Given the somewhat awkward notation such an ercor might be expected. In fact we found this error by making the same mistake when recalculating the Tinbergen results! In what follows we will use the correct solution.

Using three equations of this solution and Equations (16) and ( 17) of the original model Tinbergen formulated a five-equation recursive system for the endogenous variables that also appear with a lag in the model. This enabled him to quickly calculate a time path for each of these variables for each policy alternative; this was then used in the larger solved form to obtain a time path for the variables of interest such as employment and the balance of payments.
We wia ., ..-p:~du,.,. !his merhnd nf generatine results. Instead we will exploit the linear structure of the model. By basing our calculations on the reported values of the structural coefficients rather than on already further processed values we avoid some of the rounding errors which were understandably present in the Tinbergen results.

Dynamic properties
The dynamic properties of a linear dynamic model can be derived from the part of the reduced form that links the endogenous variables, which also appear with a lag, to their lagged values. For the 1936 Tinbergen model this part is given in Table 3. Thcre also the identity p-t -p-t is added to obtain a square matrix.
The eigenvalues and eigenvectors of this matrix are given in Table 4. No complex parts of eigenvalues were found. Two eigenvalues were virtually zero. None of the eigenvalues is in absolu[e value larger than or equal to unity. The model is obviously damped. There is one large positive eigenvalue. As can be seen from the eigenvectors this is primarily associated with 1, the wage rate. One glance at Equation (1) reveals the reason. It is fotmulated in the first difference in the wage rate. Although the high eigenvalue reflects slow convergence for 1 it may be presumed that it will not affect the convergence !or most of the other endogenous variables too much. The negatíve eigenvalue is substantial too. It causes a two-period cycle with slow convergence. As can be read oR (rom the eigenvector this is primarily true for Z, other income, and tor E', consumption out of other income. Going back to the structural Equation (1S) the negative relation between Z and Z-[ is obvious. In the same way Equation (17) specifies a negative dependence of E' on E' 1. In this case the two-period cycle may show up clearly only for Z and E' and far lessfor the other variables.
The two remaining non-zero eigenvalues are rather small. Apart from some variables the model is rather heavily damped. It is somewhat unfortunate that no pair of complex eigenvalues could be found corresponding to a business cycle of 8-11 years. For an economy like the Dutch the business cycle is mostly imported ie present in the exogenous variables of the system rather than endogenously generated by intertemporal interactions among the endogenous variables.

Multipliers
The dynamics of the model also express themselves in the values of the multipliers, in particular in those of the interim multipliers. Impact and interim multipliers are, of course, also of interest in their own right. In his policy application Tinbergen did not make use of them as such, although they are implicit in his dynamic simulations.
Among the many series of multipliers we will select those of autonomous investment and those of a devaluation. Among the endogenous variables the level of employment, a, the cost of living, p, and other  income, Z, were chosen. To these were added two composite variables

GDPQ-uf2Y~-u~-xw
hich is meant to represent gross domestic product in constant prices, and

TBV-U~-(U~fV~~-X~tY~)
which expresses the trade balance as the difierence between exports and imports of goods.
Autonomous investment is considered to be a unit shock in the disturbance of Equation (8), the investment equation. We consider two alternatives: a single unit shock in year zero and a permanent increase by one unit from year zero on. The results for the multipliers are given in  Table Sa comes close to the Keynesian investment multiplier. We may note that its impact value is less than one. We should realiu that GDPQ is value-added and that for an open economy thís is not equal to production. The impact multiplier effect on imports ( cf the impact multiplier on TBV ) is 0.65. The impact multiplier on production is then 1.36.
Another way of approaching the same issue is to rclate the value-added component ot autonomous investment to the total value-added generated by that investment. With u~i-3y~being investment, its valueadded is Per unit of investment it is 2yA~(vÁ t 3y' ,t). With vã nd y'~being roughly equal this ratio amounts to 0.5. Total value-added generated is 0.71. The multiplier is then 0.71~0.5 -1.42, a value in line with that of the multiplier for total production. The sequence of interim multipliers reflects the strong damping of the model, together with a two-year cycle. Activity levels quickly return to normal.
The impact on employment is rather modest and very transitory. We may note that the total multiplier is zero. This is the consequence of the specification of the equation (or wage formation, Equation (1) -see the discussion of that equation above. Wages and prices are initially increased, wages more than the cost of living, p. They return very slowly to their original level, as was predictable (rom the high eigenvalue associated with wages. Exports are almost entirely unaftected, so the TBV column reflects the effect on imports. Consistent with the rise in production, imports increase initially to return quickly to their old levels. The impact on Z is rather high. In part this is due to the increase in value-added, in part to capital gains on shares in domestic industries. The two-year cycle arising from the large negative eigenvalue is obvious here. The main picture is that after two years there is little effect to be expected from an incidental increase in autonomous investment.
A sustained increase of the same size gives rise to the multipliers of Table Sb. The bottom line gives the change in the stationary state as the consequence of such an increase. The (act that, due to the specification of the wage equation, employment is not sensitive in the long run is confirmed here. It also means that in the long run activity levels will not be changed very much. The rise in the domestic wage and price levels will increase imports of finished goods, causing the trade balance to be less favourable.
The other example o[ multipliers will be those (or a devaluation. The impulse here is a unit increase in all import prices, namely p~, q'~, r~, s~, and the world price level, pw. Table 6 gives the multipliers of a permanent shiR in the value of the guilder. The last line presents the change ín the stationary state values. The impact of the devaluation in year 0 is rather small except for Z, other income. The devaluation hardly aflects the volume of exports. Equation (tí) specifies exports to depend on the difference between pw, the world price level, and p,t, the export price icvei. Equation (4), however, links the latter closely to the former -Dutch exporters being price takers -so the difference is not allowed to become important. The increase in foreign prices relative to domestic prices causes a shi(t (rom imports of finished goods to imports of raw materials. This reduces imports somewhat and explains the positive effect on the trade balance (TBV ) in year 0. The ensuing increase in value-added and domestic activity levels leads to higher imports which more than compensate the reduction. This explains the perverse J effect and illustrates the possibilíty that a devaluation does not necessarily lead to an improvement in the trade balance.
The effects of the devaluation on GDP and employment, a, are strong but taper ofT. This is again due to the insensitivity of employment in the long run, which foras activity Icvels to return to their original values. Prices adjust slowly to international ones. In the long run there is even an overadjustment. We should remember that price homogeneity is not built into the structural form. The initial increase in Z reflects capital gains and later on also the increase in value-added.

Policy implications
Tinbergen built his mode) to give advice on policy. He

ECONOMIC MODELLING April 1989 213
When it dl óepan: the 1936 Tinberpen rnodef reoisited: G. Ohaene and A.P. Barten used what we would today call a scenario approach. Under certain assumptions about exogenous variables and alternative values fot policy instrumenu he generated a set o[ time paths for the endogenous variables, one for eacó policy alternative. These were compared with the no change case and the best one was selected. A first alternative, P, was an increase in investment. its model implementation amounted to adding a shift to Equation ( 8) of t 14 during three consecutive years. The trade balance deteriorates moderately and the initial increase in employment vanishes quickly. These outcomes are consistent with our multipliers in Table Sa.
Alternative Q concerns trade protection by the restriction of imports of finished consumer goods. This ís simulated by adding (not subtracting, as is incorrectly stated in the original memorandum) IS to the righthand side of Equation (t2), which explains the ratio of imporu of raw materials for consumption to those of finished consumer goods. The increase o[ this ratio means an increase of domestic production of consumer goods at the cost of a reduction in the imports tor those goods. The effects on employment are minor because of the resulting increase in prices, which reduces demand. The trade balana reacts very favourably.
A third alternative, R, is rationalization taking the (orm o( an increase in labour productivity and a decrease in prices. To simulate the consequences, the righthand side of Equation (9 ), the equation explaining employment in the consumer goods industry, is reduced by 10, while on the righthand side of Equation (2), the cost of living equation, 5 is subtracted. The effect on the trade balance is very small, that on employment unfavourable. The price decrease is unable to generate enough demand to compensate for the loss of jobs due to the productivity increase. A variant of this scenario, R', only reduces prices. Because the reduction in prices also reduces non-labour income and hence investment, employment is still negatively affected but much less than for case R.
Alternative S is a wage reduction scenario, subtracting 5 on the righthand side of Equation (1), the wage formation equation, for one ycar only. It results in an initial increase in employment levels followed by a return to normal levels. The trade balance develops unfavourably. Tinbergen's results do not agree with ours, which show a minor improvement of the trade balance because of increased exports and reduced imports.
The devaluation scenario T includes not only an increase in cxogenous import prices and the world market price by about 30"~o but also an increase by the same percentage in income from investment abroad. To take into account possible reprisals the export equation, ( 6), was reduced by 18 on the righthand side, equivalent to a reduction of about 20"~e. More or Iess in accordana with our Table 6 Tinbergen fmds that employment reacu favourably in the medium run and that the trade balance is affected unfavourably after year 0.
Among the various scenarios Tinbergen prefers the last one, that of devaluation. The initial position of the balance of payments is strong enough to absorb its adverse eflects. The employment effecu of a devaluation are clearly attractive. He suggests a devaluation of 20"Io. At the same timc he pointed to the possibility of combining the various scenarios.
The meeting of the Economics and Statistics Association for which the paper was prepared was held on 24 October 1936. The paper itself was already available in September. On 27 September the Netherlands abandoned the gold parity of the guilder, the last country of the gold block to do so. The guilder was eflectively devalued by t7-20"~0. Although Tinbergen's work was not the basis for the policy adopted, it was consistent with it.

Concluding remarks
The memorandum [or the Dutch Association for Economics and Statistics was understandably in Dutch. To present it to a wider public a modióed version of the 1936 model was published in Englisó shortly afterwards (Tinbergen [12]). The t937 model is very much like the 1936 model but incorporates some changes, mostly improvements.
Several other models were constructed before World War II. Radia [7] published a 6-equation quarterly model fitted to UK data for 1924-36. It represents a closed economy. Polak [6] built a multinational business cycle model using some of the Tinbergen estimation results. His model comprises the USA and seven European countries. Tinbergen himself constructed models for the USA and for the UK. The first was built when he and Polak were temporarily associated with the Economic Intelligence Service of the League of Nations. It consists of 48 equations and contains a monetary and financial submodel of 9 equations. It was fitted to annual data for 1919-32. Tinbergen's UK model counts 39 equations also including a 10-equation block for the money and capital market. It was fitted to data for 1870-1914 and was thus a historical exercise. It was published, after considerable delay, in 1951.
The period 1936-39 was extremely fruitful; but with the outbreak of war began a period of consolidation. The next ten years were barren as far as the construction of models is concerned. However, data bases were improved and methodological issues were tackled, so

ECONOMIC MODELLING April 1989
When it oll began: the 1936 TJnbergen model revisited: G. Dhaene and A.P. Barten that when model building was taken up again the initial conditions were much more favourable than when Tinbergen was working.
We look back at the Tinbergen 1936 model with mixed feelings. On the one hand we note certain shortcomings or unnecessarily complicated procedures. The short sample and the relatively low quality of the data rank high among the weaker points of the model. On the other hand, the realization that the 1936 model constitutes the first empirically verified dynamic macroeconomic model for an open economy fills one with respect for its buildec If we furthermore realize that it was indeed able to generate answers for the problems of the day this respect grows. Among the later models there are many with weaker theoretical foundations, smaller scope and less operationality. The mtxlelling profession has learned much since 1936, but perhaps less than it thinks. The least squarcs method may be inconsistent because of [he simultaneous determination of the endogenous variables, measurement ertors or because of the presena of lagged endogenous variables among the rcgresson when thc disturbances arc automrrelated. In principle, the method of instrumental variables (IV) with the exogenous variables as instruments is a consistent procedurc. Therc arc nine exogenous variables in the modcl of which four also occur with a lag. Given a mere elcven observations -for Equation In nearly all cases the Tinbergen values for the regression coefïicients are similar to the LS and the IV results. Differentm ay be due to the division by R or to a lower degree of computational prccision. These appear not to be substantial.

Appendix 2 Consistency tests
The 1936 model is not a fully recursive model and the data used arc surely not without error (two reasons for LS to be an inconsistent estimator). Moreover, there are lagged endogenous variables on the righthand side of several equations, while autocorrelated disturbances cannot be ruled out. This is another reason for inconsistency of LS.
Tinbergen used LS with the rcgression coefficients divided by [he square root of the coefficient of determination. We have not been able to generate exactly the same results.
However, as can be seen from Appendix 1, the difference between our LS results and the Tinbergen coefficients are in most cases not very important. Appendix 1 also reports the results of IV estimation, using a selection of the exogenous variables as instruments. Under sui[able conditions this prooedurc is consistent or, to oNer a morc pruden[ formulation, less inconsistent than LS. We may notc [hat [he IV and the Tinbergen coefficients and the IV and the LS resul[s are rather similar-('an wr 3ce~e rl.eir diR .enx s,,...,,.,c~u.,,.~. Since inconsistency would show up in such a difference, its significance can be seen as an indication of (serious) inconsistency. The absence of significance is not, of course, a rejection of inconsistency. ít simply means that serious inconsistency could not be found. One reason for Ihat could be that the smallness of the sample causes confidentx rcgions to be so wide that hardly any null hypothesis can be rcjected.
We will report here on [wo tests, applied to each estimated equation separately. The first one is a procedure proposed by Sargan [8], which tests whether the LS estimates lie outside the confidence region with the IV estimator as its centre. Here we will apply the test to the Tinbergen values. Note that we have estimated the intercept, which thorefore should not be used in the comparison. The test basically uses as the null hypothesis that the Tinbergen values arc the correct ones. Let b, be the vector of Tinbergen values and b[ those estimated by the IV procedurc. Let 67 and 6t be those vectors without intercepts. Morevoer, let V(6t) be the estimated covariance matrix of the IV estimator. Our Sargan test statistic is then The other test is a Hausman [5] test. It tests the significance of the difference betwecn b~and b~, being the least squares estimator. Let V(bt) be the estimatcd covariance The LS and [he IV results are rather close. Can we consider this as an indication of the absence of least squares inconsistencies ? The answer to this question is morc formally approached in Appendix 2. Here it suffices to point out that (in)consistency is a large sample property and that our sample is eztremely small.  (2) O.I03(1) 0.123 (3) 0.523 (2) 6.209 ( 2 ) 0.104 (1) 272t (2) 3.366(1) 0.117 (2) 0.318(1) 0.290 (2) 0.766 (2) 0.170 (3) 0.775(1) 0.000 (1) 2.039 ( I ) 1.730 (2) 0.011 (2) 0.373 (2) 0.401(]) 0.368 (2) 0.499(!) -,x o, t he f : e;in~~aioi and 'r(bt) ihat íor the LS estimatoc To obtain those covariance matrices the same estimate for the disturbance variance has becn used, namely that of the IV application. The Hausman test statistic is then

(b~-bt)"[V(bt)-V(bc))`(bc-bt)
The di(ference between the two covariance matrices does not have full rank when the exogenous variables in the equation arc part of the set of instruments, as is always the case in our application. This explains why the generalized invene has been taken. Under the null hypothesis of consistency of LS, this test statistic is distributed as txntral X~, with the number of endogenous variables on the righthand side of the equation as the number of degrees of freedom.
In Table 21 Table 8 and l2 in [hose cases also our LS results diBer strongly from the Tinbergen values. This suggests that the differcna is due to computational aspeas rather than to statistical properties.
In conclusion we may say that our experiments do not indicate that least squares inconsistency has caused serious problems.