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Relative sensitivities of the Hungarian economy to internal and external shocks.

I. Introduction

Short term economic stability in any relatively small, trade dependent country is sensitive both to domestic policy and the vagaries of world economic activity. This is particularly true when such a country is undergoing transformation from a system of central planning with a limited number of trading partners to a market oriented economy with increasing participation in world markets. Shortly after the second world war the countries of Eastern Europe adopted the Soviet planning system and all are now attempting some degree of economic reform. Hungary took its first steps away from the Soviet model in 1957 with proposals designed to free some agricultural markets, and with more comprehensive programs since then it has been at the forefront of the reform process within Eastern Europe. One such program, and perhaps the most important in terms of setting guidelines for future reform, was the New Economic Mechanism (NEM), first introduced in 1968.(1) However, movement toward a market economy has been gradual and often slowed by limited political commitment, reversions to centralization and adverse conditions in world markets for goods and funds.

The purpose of this paper is to measure the relative importance of domestic versus external shocks on the Hungarian economy since the beginning of its reform process. We model domestic and external economic activity as a system of autoregressions and then introduce a sequence of standardized shocks to this model. Statistics summarizing the domestic responses to these shocks, such as sums of squared responses and mean-squared forecast errors (in-sample), give us the desired relative effects. Throughout the analysis we maintain the assumption that Hungary is too small to have any impact on external economic activity. In this way we can isolate effects on domestic indicators of both external and internal shocks without being concerned with spurious feedback. An internal innovation to the model is defined as an unanticipated change in any of five domestic macroeconomic indicators: three components of GNP, inflation and real wages. External shocks to the system are innovations to such exogenous factors as world oil prices and an indicator of conditions in world financial markets. The analysis covers the period 1957 through 1989 and uses annual data. The complete specification of the model is given in the next section of the paper.

Despite its progress toward reform, Hungary's economy was largely centrally planned throughout the 1957-89 period. It is reasonable to believe, therefore, that many static and dynamic structural relationships given by neo-classical economic theory may not be entirely relevant to the Hungarian situation during this time. An autoregressive modelling approach is thus a defensible one: it allows us to examine complicated processes without having to completely specify a multivariate system of structural relationships with possibly ad hoc restrictions. This is not to say, however, that knowledge of institutions or economic structure cannot be used in formulating the model. Knowledge of contemporaneous relationships is incorporated by imposing restrictions on correlations among system innovations |9~.

Most previous analyses of the Hungarian economy have concentrated on a single sector or on a particular set of innovations (mostly external; e.g., terms of trade and oil price shocks) during the 1970s.(2) A notable piece by Szakolczai, Bagdy and Vindics |29~ examines Hungary's dependence on the world economy for the years 1961-1981 but makes no comparisons between the effects of external and internal influences. Here we examine economy-wide effects of external and internal shocks throughout the entire 1957-89 period.

The paper is organized as follows. Section II discusses the model, details the data set used in the analysis and describes the estimation procedures. Some preliminary results are also given in section II. Section III discusses historical decompositions, variance decompositions and impulse response functions of the domestic time series. This is the heart of the paper: each of these empirical tools is based on predictions of the systematic components in the autoregressions and provides a measure of relative effects. Section IV concludes the study and offers some summary remarks.

II. The Model, Data and Some Preliminary Results

Let X(t) denote a vector of exogenous influences, Y(t) a vector of domestic macroeconomic indicators and describe the link between them with:

X(t) = A(L)X(t - 1) + ||epsilon~.sub.x~(t), (1a)

Y(t) = B(L)Y(t - 1) + C(L)X(t - 1) + ||epsilon~.sub.y~(t); t = 1,..., T. (1b)

A(L), B(L) and C(L) are matrix polynomials in the lag operator, L. The (random) innovation vectors, ||epsilon~.sub.x~(t) and ||epsilon~.sub.y~(t), are assumed to be jointly distributed with zero means and finite variances. Errors of individual equations within and across the X and Y groups of equations may be contemporaneously correlated. T denotes the number of observations on each element of X and Y. This system is a special case of the transfer-function-noise model often used in time series analysis |17~ and of a vector-autoregression |37; 30~.

The Y vector we consider has the following five elements: inflation of consumer prices (INFL), the real trade balance (TBH; total exports less total imports, both measured in millions of real foreign exchange units per year), the (natural) log of a real consumer plus real government material expenditures index (CG), the log of an index of real net capital formation (KFORM) and the log of a real wage index (RWAGE). These data are available in various issues of the Hunganan Statistical Yearbook |22~.(3) The reported wage index series is an index of average nominal wage per wage earner among workers and employees. The domestic consumer price index was used to deflate this and the trade balance series. Figure 1, part A, graphs the standardized values (mean zero, unit variance) of these five series, showing their relative movements for the 1957-89 period. The variable ordering in the estimated model coincides with the above listing, although other orderings were tried as a check on the robustness of the results presented below.(4)

The elements of the X(t) vector are, in the order in which they enter the estimated system: the prime rate of interest in the U.S., the log of the world price of oil (WOILPR; real dollars per barrel); the world-wide inflation rate (WINFL; annual percentage change in the world-wide index of consumer prices as reported by the IMF) and the real trade balance of the Soviet Union (TBSU; millions of real rubies per year).(5) Hungary has traded actively with the Soviet Union since the 1940s, relying particularly on the Soviets for raw materials for manufacturing and for oil. Typically, contracts with the Soviets have been long term and with prices tied to (but lagging) world prices. After the mid-1970s Hungary began purchasing increasing amounts of oil on world markets. The world inflation variable captures, among other things, effects of Hungary's increased trade with non-CMEA countries since the early 1960s. The U.S. prime rate (USPRM) is used to proxy conditions in world credit markets.(6) Figure 1, Part B graphs standardized observations of the X variables. WOILPR and TBSU were deflated by the IMF's world consumer price index.

Ignoring the error terms, system (1) models dynamic relationships, relating current Hungman economic activity to its past behavior and to past conditions in the world-wide economy. More specifically, equations (1a) describe the dynamics of the adjustments in the X's to an innovation in one of its own elements. An innovation to world oil prices causes continuing adjustment in various input markets throughout the world, for example. Such adjustments will be reflected not only in future oil prices but in such quantities as world inflation and interest rates. If the system is stable, all responses eventually damp out.

Equations (1b) trace domestic responses to external and internal shocks. An OPEC oil price shock, for example, will effect the Hungarian trade balance by (eventually) changing the terms of trade for oil. Continuing effects of this shock will be felt as both internal and external markets for energy and related goods adjust to the shock over time. Similarly, an internal shock, such TABULAR DATA OMITTED as an unanticipated change in CG, causes adjustments in domestic markets and are measured by the B(L)Y(t - 1) terms in equations (1b). However, domestic adjustments--regardless of the source of the shock--are not permitted to systematically effect external variables. It is doubtful, for example, that the domestic inflation rate has any effect on world inflation or that changes in Hungary's expenditures on imported oil have any effect on the world price. We maintain throughout the analysis, therefore, that past external adjustments influence future Y(t) values, but not vice versa, and for this reason no Hungarian indicators appear in the X(t) equations.

The only contemporaneous relationships permitted in the model are among innovations. Viewing system (1) as one of reduced forms, errors of individual equations are (potentially) related to all structural errors. The reduced form innovations should, therefore, reflect prior knowledge of structural relationships |9~. Table I shows the estimated relationships amongst innovations given the structure we imposed.(7) This particular specification permits oil price changes and world inflation rate changes to contemporaneously influence USPRM (by 0.428 and 0.299, respectively), WOILPR to affect world inflation changes and TBSU to be related to all external variations. The units of measure are percentages of conditional standard deviations; all error relationships have been standardized so as to make own effects unity. The real oil price is regarded as the only exogenous quantity in the system in the sense that its innovations are assumed to be unaffected by all others.

Only two sets of restrictions are imposed on domestic innovations: RWAGE innovations effect only themselves and external innovations are not contemporaneously influenced by domestic innovations. Not permitting domestic innovations to affect external innovations is consistent with our assumption that Hungary is too small to effect the world economy. If we err by not restricting other domestic relationships, we chose to do so on the side of over- rather than under-specification. Also notice in Table I that domestic relationships are not constrained to be pair-wise symmetric.

The regression estimates and associated summary statistics are given in Table II. Data prior to 195'7 were used to account for observations lost to lags and differencing operations. Seemingly unrelated regression techniques were used to estimate the system. The reported regressions each contain a constant term and two lags of each of the included indicators. We tested a three lag specification and found that third lags contribute very little to the model. Phillips-Perron |25~ tests at the 5 percent significance level on the data reveal a stochastic trend in every series except the Hungarian trade balance.(8) Therefore, with the exception of TBH, all estimation is carried out using first-differences of the data. The differenced series are stationary according to Phillips-Perron tests. Also included in each regression, again excepting the TBH regression, is an error correction variable, labelled ERCRCT in Table 11. This variable must be included in order to correct for the significant co-integration problems that exist in these data. ERCRCT was estimated from the principal components of the moment matrix of the original nine series in levels.(9) Also, note that in earlier analyses we included a dummy variable for the NEM in the domestic indicator equations. To save degrees of freedom, use of this variable was abandoned after finding it to be marginally significant in only one equation.

The summary statistics for the regressions indicate that the model specification is reasonable in the sense that the regression residuals are free (statistically) of serial correlation. This conclusion is based on portmanteau tests using the reported Q-statistics |23; 17~ and on the first-order serial correlation coefficient ("rho") estimates obtained from the residuals of each regression. The Q-statistics are chi-squared variates with fifteen degrees of freedom. Durbin h-statistics computed for these regressions suggest that serial correlation might be a problem in the TBSU, CG and RWAGE equations. However, this test, like most of those we tried, have low power in small samples. Durbin h-statistics are undefined for the WOILPR, WINFL and INFL equations. Based on the Q-tests and the rho estimates, no corrections for serial correlation were made.

The sign of the error correction coefficient is correct in all but the RWAGE equation. A negative ERCRCT effect indicates that a deviation from the steady state value of the dependent variable is reduced in subsequent periods. The ERCRCT effect in the INFL, RWAGE and USPRM equations is significant at the 10 percent level, giving additional verification that there is a problem with co-integration in this data set.

The positive and significant ERCRCT effect in the RWAGE equation is cause for concern. We will see later that RWAGE is probably the least stable of the domestic variables--its shock responses have the widest fluctuations and generally take the longest to damp out. The purpose of TABULAR DATA OMITTED including RWAGE in this analysis is to measure the effects of shocks on the purchasing power of consumers. However, given the factor payments structure in Hungary and various policies related to it, it is not very surprising that RWAGE is problematic. Until the 1980s, the Hungarian government had committed itself to raising living standards, and in fact, between 1957 and 1979, the Kadar regime was not willing to allow prices to increase faster than nominal wages. In the 1980s the real wage became much less of a policy concern because of foreign borrowing constraints and deteriorating terms of trade. Consequently, with increased inflation and decreased subsidies to enterprises, far more variation in real wages was observed. In fact, through most of this period, real wages declined.

Many of the lagged effects estimates in part A of Table II are significant (at the 10 percent level) despite our small sample size. Many have a predictable sign as well. Examples of the latter are the first lag TBH effect on INFL, the CG effects on RWAGE (wage bonuses are a part of CG) and the WINFL effects on the domestic inflation rate. There are also some apparent anomalies due to the peculiarities of a planned economy in transition. For example, there is an indication that past increases in the inflation rate tend to raise current real wages, prior RWAGE and other factors constant. These positive estimates are, however, consistent with the Kadar government's policy toward living standards. Another apparent problem is with the negative signs on the WOILPR coefficients in the INFL equation. The figures in Table I indicate that a contemporaneous change in the world oil price has only a minimal effect on INFL innovations. This can be explained by the pricing mechanism used for Soviet oil imports. The negative WOILPR effects on future inflation changes may reflect the imposition of price controls in response to actual or anticipated inflationary pressures through the 1970s.(10)

The errors of the world indicator regressions in Table II (part B) are also fairly free of serial correlation, and the error correction coefficients are all of the correct sign. Here again there are many significant coefficients in spite of the small sample, but the |R.sup.2~s of these regressions are generally lower than those of the domestic indicator regressions. Adding a third lag to these equations did little to improve their |R.sup.2~s, and the small number of degrees of freedom available prevented our trying to improve explanatory power by expanding the list of world indicators.

III. The Relative Effects of Internal versus External Shocks

Our measures of the relative effects on the Hungarian economy of internal and external innovations are obtained from historical decompositions, variance decompositions and impulse response functions of the five Hungarian indicators. Methodological summaries and the results of performing each of these procedures are given in turn in the following sub-sections.

Historical Decompositions

In a nutshell, this procedure decomposes a time series into expected and unexpected components and then identifies the sources within the model of the unexpected variation |32; 101. A brief outline of the computational procedure is the following. The estimated system (1) is used to compute forecast errors in all variables for periods |T.sub.0~ + 1 through |T.sub.0~ + s (1 |is less than or equal to~ s |is less than or equal to~ T - |T.sub.0~), where |T.sub.0~ is a pre-selected point within the observed sample. It is easily shown that the period |T.sub.0~ + j forecast error in, for example, TBH, is the sum of current and past orthogonalized innovations in USPRM, plus current and past orthogonalized innovations in WOILPR, and so on. The historical decomposition of TBH for period |T.sub.0~ + j thus relates unanticipated changes in TBH to unanticipated changes in USPRM, unanticipated variation in WOILPR and so on. This procedure can be repeated for all s steps in the forecast horizon and for all system variables.

Table III summarizes the historical decompositions of the domestic indicators for the periods 1968-78 and 1979-89. Entries in the "History of" column of the table are the subject domestic variables. Innovation sources are given across the top row. The following example illustrates the interpretation of the reported statistics. For 1968-78, unanticipated oil price variation contributes positively to the explanation of variation in TBH. In other words, a series made up of TBH forecasts plus effects due to WOILPR innovations is, for this forecast period, closer on the average to the actual TBH series than is the forecasted TBH series alone. Defining "closeness" in the mean square sense, the percentage reduction in the mean square forecast error (MSE) of TBH due to WOILPR innovations is 42.43 percent--roughly 42 percent of the unanticipated component of TBH is unanticipated variation in WOILPR. This effect is shown in the "total" row for TBH and the WOILPR column of the table. Also, on the average only own TBH effects (with a MSE reduction of 66.13 percent) do a better job than WOILPR effects of explaining unexpected fluctuations in TBH during this period. Adding all external innovations to the base forecast before computing the updated MSE, and likewise recomputing the MSE adding all internal innovations, aggregated external versus domestic effects on TBH are found to be roughly equal. A negative (total) percentage MSE reduction indicates that, on average, a forecast plus innovations is less accurate than the forecast alone.(11)

It is obvious from Table III that the sum of the "total" effects for mutually exhaustive sets of sources need not be 100 percent. The reason for this is non-zero correlations among innovations during the in-sample forecast period. Because such interaction effects are important in our data it is informative to separate them from total effects. The statistics reported in the "net" rows of Table III are MSE reductions net of the interactions. Simple algebra shows that a particular "net" statistic is just the sum of squared innovation effects in the associated source variable expressed as a percentage of the original MSE.(12)


Measuring either total or net effects, external shocks dominate CG, KFORM and RWAGE during the 1968-78 period. The unanticipated components of USPRM, TBSU and TBH are particularly important in explaining most of the domestic innovations. Interestingly, oil price shocks are important only in explaining the domestic trade balance. Interactions of WOILPR and WINFL innovations with shocks to remaining variables are large and consistent with policies (price equalization schemes, for example) aimed at insulating Hungary's economy from the world recession of the mid-1970s and the OPEC price shock in 1973.(13)

The dominance of TBH shocks clearly illustrate the trade dependence of the Hungarian economy. Aside from own effects (which are expected to play a large explanatory role) the only other relatively important domestic factor is that of CG innovations on RWAGE. This reflects the impact of the government's use of direct wage subsidies and general subsidies to enterprises in this period. These subsidies were often made regardless of the profitability of enterprises.

The 1979-89 results are dominated by interaction effects and, as with those for 1968-78, large interactions are consistent with policy mechanisms in force throughout the period. With the re-establishment of NEM-like reforms in 1979, domestic prices were again being gradually allowed to align with world prices. However, despite the official reform policy, through the early 1980s import controls were widely imposed as the government attempted to reduce trade deficits and their inflationary effects. There was also added (non-market) pressure on enterprises to revive the export sector.

Looking only at net effects for 1979-89, we see that USPRM, TBSU and TBH innovations remain important, but that WINFL and oil price shocks now have increased influence. The oil price effects are predictable given the change in Soviet oil pricing policy and Hungary's increased purchasing of oil on world markets during this period. The increased importance of WINFL reflects Hungary's increased openness to world import and export markets and decreased insulation of domestic prices from fluctuations in world prices after the reforms of 1979 and 1984.

Variance Decompositions

An analysis of variance decompositions |30; 31~ is, essentially, an analysis of out-of-sample forecasting errors. The s-step ahead forecast error in TBH (for example) depends on the errors in forecasting itself in the earlier s - 1 steps, on errors in forecasting USPRM over the prior steps, and so on through the variable list. The step s TBH error variance is thus the sum of a USPRM component, an INFL component, and so on. There are no interactions among these components because estimated errors are orthogonalized over the entire sample prior to computing the forecasts.

The variance decompositions of the domestic indicators are summarized in Table IV. For brevity, only the results for selected forecast periods are shown. The "External Source" column gives the proportion of the subject variables' forecast error variance due to external shocks. TABULAR DATA OMITTED These effects are obtained by adding variance shares attributable only to external indicators. The remaining columns of this table show effects of innovations assigned to the system variables individually.(14)

Table IV reveals that over a one or two period horizon, internal factors matter most to domestic inflation, the trade balance and capital formation. External shock effects on these three variables rapidly catch up, however. The only case where external factors strongly dominate in the longer run is with the KFORM variable. When variance shares are apportioned to individual domestic variables, trade balance effects constitute the bulk of total internal influences both in the short and long terms. CG shocks are relatively important mainly to itself (not surprisingly), to KFORM and to RWAGE. However, RWAGE is the only variable to which CG effects matter over the longer term. More generally though, remaining internal influences die out fairly quickly even when they start out relatively large. On the other hand, most influential effects of external shocks appear to be medium to long term. For example, effects of oil price shocks on inflation and the real trade balance do not become strong compared to other exogenous effects until late in the forecast horizon.

The more surprising effects among the exogenous shocks are the strength and longevity of USPRM shocks. One reason for including the financial conditions indicator is to measure the effects of the changing costs of Hungary's increased international borrowing since the early 1970s. That USPRM innovations are particularly influential on forecast variations in CG, KFORM and RWAGE indicates that there may be a substantial trade-off between capital spending and government expenditures on goods and wage bonuses when foreign borrowing costs are high. USPRM could also be proxying domestic interest rate effects. However, as indicated in footnote 13, credit was generally allocated by the government without much regard to (implicit) market conditions. Further, at the firm level, managers were rarely exposed to financial markets per se.

Impulse Responses

Impulse response functions trace the paths of shock responses, giving magnitudes and directions of adjustments as each shock works itself through the system |30; 31~. Table V, part A, reports selected steps in the adjustment of each Hungarian indicator to an (orthogonal) innovation in each system variable. Complete adjustment paths through twenty post-shock steps are shown graphically in Figure 2.(15) The magnitude of each shock to the system is one standardized unit, so the "step O" rows in Table V, part A, are the contemporaneous (standardized) correlations of the innovations discussed earlier. The reported responses can be interpreted as percentages of conditional standard deviations. The initial response in INFL to a 1 percent shock in USPRM is -0.451 percent, for example. The step-one value of the INFL response is -0.721 and is the result of one period of system-wide adjustment to the USPRM shock. Because calculation of impulse responses is essentially an out-of-sample forecasting exercise, orthogonal innovations imply no interactions among the responses.

A convenient way to measure relative effects within a set of innovations is to compare the total variation in the responses. For stationary and erogodic time series, total variation through step-s in a sequence of impulse responses is simply the sum of squared responses accumulated through step-s. The larger this variation the more destabilizing the associated shock. Total variation statistics are reported in Table V, part B.

The squared responses in Table V show that most of domestic adjustments to most shocks are accounted for within five periods of the innovation. This is a particularly comforting result in that it allays a priori concerns that unrealistically long-lived responses would be found simply because the data are observed annually.(16) Discounting own effects of internal innovations, these total variation statistics suggest that external shocks matter most to this economy. TBH shocks are also important, however, as responses to its shocks are found to be as volatile as those to many external shocks and in some cases more so. Among external shocks, the Soviet trade balance appears to be the least influential. Shocks to inflation and to real wages matter least among internal innovations. Regardless of the source of a shock, KFORM and RWAGE prove to be the most sensitive of the domestic variables.

Adjustments to shocks in the fiscal variables, CG and KFORM, are interesting. From part A of Table V, TBH responses to CG and KFORM shocks are relatively large but very short lived (responses to these shocks are within one-tenth of a standardized unit after only one step), and are fairly robust to whether the shock comes from CG or KFORM, at least through step-2 of adjustment. This supports the hypothesis that whenever Hungary has experienced an investment boom or large increases in consumption, the trade balance would usually deteriorate. On the other hand, CG and KFORM responses to a TBH shock are markedly different, the CG responses being far greater, prolonged and indicating that a TBH shock is typically followed by increases in domestic consumption.

CG and KFORM adjustments are very different depending on which of these two variables is perturbed. CG adjustments to a KFORM shock are zero (approximately) or negative, suggesting that KFORM shocks have a crowding out effect on CG. In contrast, KFORM adjustments to a CG shock show no such pattern. In fact, the step-l KFORM adjustment tends to reinforce the contemporaneous effect and then oscillates slowly back to zero.

Lastly, own shocks aside, the innovations most influential to inflation are those to the trade balance and capital formation. Given the literature on investment cycles, pronounced KFORM effects on inflation are not unexpected. In Hungary, KFORM effects may also act indirectly through the trade balance because increases in domestic investment have usually been accompanied by increases in imports. This result is in line with Tesche's |34~ structural model that showed investment shocks in the 1970s had larger effects on inflation and the dollar trade balance than changes in external prices. It is also consistent with the fact that many capital goods (equipment) must be imported.


IV. Concluding Remarks

Over the last thirty years Hungary has established its place as a leader in Eastern Europe in pursuing economic reform. However, the Hungarian economy has experienced almost continual external and domestic perturbations that have led (or have been used as an excuse by) policy makers to either postpone reform and/or tighten central control. Understanding the magnitudes and relative effects of external and internal shocks to this economy is, therefore, important to understanding its reform history.

The analysis we have presented represents one of the first attempts at measuring the effects of innovations on a planned economy in a comprehensive way using data. As such, many questions are left unaddressed or warrant additional research. Obvious issues are those of structural responses and structural change during the reforms. We work with a reduced form estimation model, and thus, have no intent on giving insight into structural effects or of making inferences about structural relationships. However, the results we obtain can be used as measures against which future findings of those working with structural models can be compared. Issues of structural change are difficult to address with existing data. Likely times for structural change to have occurred were with the NEM in 1968 and with additional reform attempts in 1979. We maintain the hypothesis of no structural change because too few degrees of freedom are available to construct meaningful F-tests for coefficient constancy across these periods in our model. Some of our historical decomposition results may be indicative of changing contemporaneous relationships but no test for this is possible with these data. On the other hand, there may be merit to arguments that structural change did not occur at these times, particularly with respect to the NEM. Post~ NEM programs, including those begun in 1979 and others implemented in the 1980s, provide evidence of earlier reform failures.

Another issue pertains to foreign trade. Our data set merges two distinct trade balances (ruble versus non-ruble) that behave differently, particularly with respect to the timing of their responses to shocks. Our results concur with those of other researchers about the importance of trade balance shocks to this economy. However, we may be understating trade effects simply because of the inability to separate the trade data into these components.

Finally, our finding that the Hungarian economy is very sensitive to variation in international financial conditions is an interesting one given that Hungary has only recently been active in foreign credit markets. This result certainly warrants further investigation once sufficient data become available because Hungary is likely to remain active in international funds markets as it continues to reform its economy.

1. Three specific goals of the NEM were balanced growth rather than industrialization, balance of payments equilibrium and gradual alignment of domestic prices with world prices. The NEM as originally proposed was never fully implemented. Attempts to reinstitute some of the fundamental NEM policies were made in 1979 and again in 1984. There are a number of interesting studies of the NEM |14; 27; 2; 18; 4; 38; 8; 21~.

2. Balassa and Tyson |5~ examine balance of payments and policy responses to the terms of trade deterioration during the period 1973-75, and effects of decreased export demand during the world recession of 1974-78. Balassa and Tyson |6~ extend this analysis through 1981. Both these studies compared extrapolated trends to observed data. Bekker |7~ did a follow-up to these studies using the same methods for the 1973-83 period, although she also examines the adjustment paths of some macroeconomic aggregates. Tesche |34~ distinguished between external shocks, system changes and policy interventions in an applied general equilibrium context. The two key contributions of this work were the analysis of the high growth in capital expenditures during the 1974-78 world recession, and of the effects of the partial return to price equalization schemes after the first OPEC oil price shock in 1973. There is a large body of literature on the general topic of the effects of external factors on developing economies |3; 24; 20~.

3. There are two separate trading systems in force: ruble trade with CMEA countries and non-ruble trade with the rest of the world. Ruble trade is mostly done under long term contracts with prices lagging world prices. In addition, goods traded under each system generally differ. Our analysis uses total trade statistics because component data are unavailable for the entire sample period.

4. Among other aggregates available to us were employment (total and in manufacturing only) and the exchange rate. Changes in employment levels mostly reflect increases in labor participation and population growth rather than responses to market conditions, and would thus add little insight to the study. The exchange rate (or, more accurately, rates) had no meaning as a price of foreign exchange until 1968. After the NEM there was an attempt to link domestic and world prices via the exchange rate but it was often adjusted (devalued) to limit the domestic effects of world inflation |38~. An obvious omission from the analysis is a domestic interest rate. Unfortunately, no such interest rate time series is available. Throughout the observation period credit was most often centrally allocated according to government priorities.

5. Sources for the X(t) data are: USPRM--Economic Report of the President |36~; WOILPR--annual averages of the Libyan, Venezuelan and the Saudi Arabian export prices, deflated as discussed above--International Financial Statistics |19~; the world-wide index of consumer prices--International Financial Statistics |19~; and TBSU--Handbook of Economic Statistics |11~ and Statistical Yearbook |35~.

6. Hungary's foreign debt has increased markedly since the early 1970s, financed almost entirely by foreign commercial banks rather than foreign governments or the IMF. The LIBOR was, thus, our preferred choice as a credit market indicator but this series is available only from 1971. An alternative credit price measure we tried was the real price of gold on the world market. The problem with this series was that the freeing of gold prices was coincident with the NEM, so we could not be sure whether the gold price variable would pick up financial market effects or NEM effects. However, results obtained using the real gold price were similar to those discussed below.

7. Let P denote the non-normalized form of the matrix in Table I. Then |Mathematical Expression Omitted~ the estimated covariance of the system-wide residuals. The factoring of S reported in Table I is just-identified, meaning that all original (estimated) error relationships are uniquely accounted for by this factoring. P essentially sets initial conditions for the analysis of a particular shock to the system. Many other factorizations are possible. The Cholesky decomposition and some over-identified specifications were examined. The overall conclusions of the analysis do not change when these factorings are used. in addition, it was suggested by the referee that because we are using annual data, RWAGE should contemporaneously affect CG (rather than as in Table 1). Changing the factoring to reflect this yields results that are virtually identical to those reported. We report the results obtained using the Table I factoring only because reversing the CG and RWAGE relationship caused a slight loss of generality among the relationships of the other domestic innovations.

8. The Phillips-Perron statistics for the Hungarian indicators were: INFL: 2.15; TBH: -13.81; CG: -1.17; KFORM: -3.36; and RWAGE: -2.16, and for the world indicators: USPRM: -5.79; WINFL: 2.15; WOILPR: -4.22 and TBSU: - 10.97. Two lags for the Bartlett window were used to compute these statistics. The critical value for the test is - 12.5 |15, Table 8.5.1~. Schwert |28~ provides a comparison of the properties of various unit root tests.

9. If X(t) is a vector of levels of difference stationary processes and if the quantity |Mathematical Expression Omitted~ is stationary, X(t) is co-integrated with q x n (q |is less than~ n) co-integration vector, |alpha~. Using the principal component method, the first row of |Mathematical Expression Omitted~ is the eigenvector associated with the least variance principal component of X(t), the second row is the eigenvector corresponding to the next smallest variance principal component of X(t), and so on |33; 26; 1~. The error correction terms are, therefore, |Mathematical Expression Omitted~. Omission of such terms from the appropriate regressions would underspecify these equations and cause bias |12~. Phillips-Perron tests on the |Mathematical Expression Omitted~ suggested that three co-integrating vectors might be present. However, the results presented below were estimated using only one. We re-estimated the system with three error correction terms in the appropriate equations but in terms of our general conclusions, there appeared to be no costs associated with trading the number of error correction terms for degrees of freedom. The power of any currently known test for the number of co-integrating vectors in as small a sample as ours is highly suspect.

10. The coefficient estimates reported in Table II may yield some insight into short term mechanisms ceteris peribus. However, drawing conclusions based solely on these estimates is a risky business. One aspect of a vector-autoregression that makes interpreting individual coefficients difficult is that contemporaneous effects are omitted from the regressions. The reported estimates are of one and two period ahead anticipated effects. In fact, it is only when the effects of an orthogonal shock are traced through the system that the effect of, say, an oil price shock becomes clear. Orthogonalizing the shocks implicitly accounts for contemporaneous effects. A change in WOILPR will, according to our estimates tend to increase Hungarian inflation in early rounds. Whether or not these effects hold over the longer term after other adjustments have taken place is one of the questions important to our analysis, and thus, one reason for computing impulse response functions.

11. As a check on how robust our results were to equation ordering we reversed the equations' order within the X and Y groups of variables, re-estimated the model and then recomputed the historical decompositions. Generally speaking, the results did not change, although there were some differences in specific outcomes. For example, for the aggregate measures during 1968-78, external innovations were found to overwhelm internal innovations in explaining CG and KFORM. However, there were few differences found in assigning innovation effects to the individual variables.

12. Let A denote the actual subject series, B denote the forecast of the subject series conditioned on information in the system through time |T.sub.0~ (|is less than~ T) and let |I.sub.1~, |I.sub.2~,..., and so on, be innovation effects attributable to variables 1, 2,..., etc. Note that A - B = |I.sub.1~ + |I.sub.2~ + .... Now, the percentage MSE reduction (PMR) due to the |I.sub.1~ effects (for example) is |Mathematical Expression Omitted~ where |Mathematical Expression Omitted~ and all summations run from |T.sub.0~ + 1 to T. It is easily shown that |Mathematical Expression Omitted~. The first part of this sum is reported in the "net" rows of Table III. The second part is the interaction effect. Although innovations are orthogonal they are so only for the entire sample period, not necessarily for the forecast period. Estimates of |I.sub.1~, |I.sub.2~,..., may, therefore, be correlated. When the interactions are sufficiently large, a PMR may be negative or net effects may exceed one-hundred percent.

13. During the 1970s it was typical that in the absence of controls on capital expenditures the trade balance tended to deteriorate. In addition, in spite of the NEM, domestic prices were being controlled in response to the OPEC oil price shocks. While also under government control, consumption and capital formation expenditures were permitted to grow as if there had been no change in world prices. Also during this period, particularly little attention was being paid to the cost of obtaining foreign credit to finance continued growth. Hence the beginning of large increases in foreign debt and the shortage of foreign currency. Also, although trade with the Soviet Union diminished during 1968-78, most of Hungary's oil and other raw materials continued to come from the Soviet Union. After 1976 the Soviets began annually adjusting prices in oil contracts according to changes in a five-year moving average of the world price.

14. Variance decompositions are also sometimes used as informal tests for Granger causality among variables |13~. Loosely, the term causality as it is often used in the applied macroeconomics literature is synonymous with predictive insight. In other words, the larger the proportion of the forecast error variance of TBH (for example) explained by WOILPR innovations, the stronger the "causality" running from WOILPR to TBH. Causality in this data set appears to run from TBH to remaining domestic indicators and from the external indicators to the domestic indicators.

15. The RWAGE responses given in Table V, part A, have been rescaled for the purposes of graphing. The scale factors were 1.5 for the responses to internal shocks and 3.2 for the responses to the external shocks.

16. Problems related to temporal aggregation are discussed extensively in the time series literature |16~. Also, the impulse responses are stable in the sense that they eventually damp to zero. Those for the (unreported) external indicators also possessed this stability. Because all the data used to estimate the system were verified to be stationary using the Phillips-Perron test, we would expect this. However, the power of this test in small samples is highly questionable, so the stability of the impulse responses supports the hypothesis of no unit roots in the final data set.


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Author:Tesche, Jean
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Date:Oct 1, 1992
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