CC BY
63
ББК У010.022
PUBLIC CAPITAL AND PRIVATE SECTOR PERFORMANCE: VAR/ECM MODELING Sh. Erenburg, O. Ponomareva
Department of Economics, Eastern Michigan University, Ypsilanti, MI, USA Represented by a Member of Editorial Board Professor V.I. Konovalov
Key words and phrases: 2-step Engle-Granger procedure; Impulse Response Functions; Granger Causality test; Public Capital; Private Sector Performance; Vector Autoregressive Model (VAR); Vector Error Correction Model (VECM).
Annotation: Empirical evidence on the dynamic effects of public capital on real economic growth in the United States is presented in this paper. The sample period covers the years 1971-2001. A five-variable VAR model and a Vector Error Correction (VEC) model are estimated using the following variables: public net capital stock, private net capital stock, the number of employed persons, an energy to all commodities price index ratio, real gross domestic product.
Notation
Akaike AIC - Akaike Information Criteria;
Adj R2 - a goodness-of-fit measure in multiple regression analysis that penalizes additional explanatory variables by using a degrees of freedom adjustment in estimating the error
variance;
d. w. d - Durbin Watson’s d statistic, provides testing for serial correlation in the observations;
d. w. h - Durbin Watson’s h statistic, provides testing for serial correlation in the observations if there is a lagged dependent variable present in the regression;
7(1) - denotes data being stationary in first difference form;
7(0) - denotes data being stationary in level form;
R2 - the square of the correlation coefficient is the proportion of the variability in one series that can be explained by the variability of one or more other series;
VAR - Vector Autoregressive model;
VECM - Vector Error Correction model;
VDC - Variance Decomposition;
IRF - Impulse Response Function.
Introduction
There have been many articles written on the statistical impact of government spending on real economic activity. Prior to the 1980’s, the main focus was the impact of government consumption on real output, interest rates, and private investment spending. During the 1980’s, increased attention was paid to the effect of public infrastructure spending on real economic activity. Different data were used estimating public and private sector performance: capital stock as well as investment data. This paper is focusing primarily on investigating public and private capital stock.
Various recent studies use vector autoregressive (VAR) models that - unlike the production function and cost function approaches - do not impose causal links among the variables under investigation. The use of VAR models tests whether the causal relationship assumed in other approaches is valid or whether there are feedback effects from output to public capital. Furthermore, the VAR approach tests for the indirect effects between the variables included in the model.
Model Specification
The estimating model used in this paper is based on Pereira’s model (2000). The estimation techniques include an Error Correction Model (ECM), a Vector Autoregressive (VAR) model and a Vector Error Correction (VEC) model that allows for an expanded analysis. The current model includes the effect of the energy price shocks on output over time using the ratio of the producer price index for energy products to the producer price index for all commodities.
The study focuses on the effect of public capital stock on private output measured as real GDP in 2000 prices. The model used in this study and the expected signs are specified as follows:
lnQt = a0 +ai lnKGt +a2 lnKt + a3 lnNt + a4 lnPPIt + et, (1)
(+) (+) (+) (-)
where Qt = real gross domestic product; KGt = public capital over the private capital stock ratio; Kt = ratio of past period private capital to current period private capital stock ratio; Nt = private employment level for nonagricultural industries 16 years and over, (in thousands); PPIt = ratio of producer price index for energy to producer price index for all commodities; et = normally and independently distributed random disturbance term.
Data
The construction of all variables is presented in Table 1 to this paper. Sources of data incude: Haver Analytics, Copyright 2001 Haver Analytics, Inc, Bureau of Economic Analysis web site data base (www.bea.gov) and Bureau of Labor Statistics (www.bls.gov). All data are annual. A correlation matrix using data in levels indicates a statistically significant correlation between all variables except public capital stock and the energy price index ratio.
Error Correction Model
Estimation of the current model is based on an ECM model using the two-step procedure developed by Engle and Granger (1987) which tests for cointegration at the levels stage before considering the short-run, dynamic properties. All variables used in the error correction model must be stationary.
Stationarity testing
Empirical work based on time series data assumes that the underlying time series are stationary. If the data are not stationary, one often obtains a very high R-squared although there is no meaningful relationship between the two. This situation exemplifies the problem of spurious regression. This problem arises if the time series involved exhibit strong trends (sustained downward or upward movements). The high R-squared observed is due to the presence of the trend, not to a true statistical relationship between the two.
A stochastic process is said to be stationary if the mean and variance are constant over time and the value of covariance between two time periods depends only on the distance or lag between the two time periods and not on the actual time at which the covariance is computed. Most aggregate time series data are rendered stationary when differenced once.
Augmented Dickey-Fuller tests were used to test for stationarity. The results indicate that all of the data used in the model are stationary in first difference form I(1).
The first stage of the Engle and Granger procedure involves exploring the levels of the equilibrium part of the error correction model to establish whether the variables cointegrate. Evidence of cointegration includes an R2 that is close to unity at the level stage, significant coefficients and the error term must be I(0). All cointegration tests were compared with the critical values presented in Dickey and Fuller (1979). The empirical results from estimating equation (1) are shown in column 1 and 2 of table 2. The public capital stock coefficient has the expected sign, but none of the variables appear to be significant. Readjusted is 0.775. The error term (et) is not stationary in levels form. It is I(1), not I(0), and, therefore, rejects evidence of cointegration of the variables in the model.
The second stage involves running regressions using data in stationary form (in this case, first differences). The lagged residual term, et-1, is included in the regression. It is intended to capture the error correction process as agents adjust for expectational errors around the long-run, equilibrium relationship.
The short run, dynamic model, was constructed with all the variables in first difference form. The lagged error term from the long run was not included in the short run model since it was not stationary in I(0) form. The short run model is written as follows:
d ln Qt = aj + a2d ln KGt + a3d ln KGt +a4d ln Kt + a5d ln Kt-1 +
(2)
+a6d ln Nt + a7d ln Nt _! + a8d ln PPIt +a9d ln PPIt _! + a^d ln Qt _! + ut.
The correlation matrix for the short run model indicates statistically significant multicollinearity between a number of variables. The highest correlation is indicated between private and public capital stocks, and public capital stock and employment. The energy price index ratio exhibits little if any multicollinearity with the other variables.
Table 2, column 4 shows the results of estimating equation 2. The reparameterized results are shown in column 5.
Table 2
Estimation results
Long run Short run
Variable Parameter Estimates (eq. 1) Variable Parameter Estimates (eq. 2) Reparameterized Estimates (eq. 2)
1 2 3 4 5
Intercept 17.086*** (2.362) Intercept 0.013 (0.012) 0.011* (0.005)
ln(KG)t 0.321 (0.223) dln(Q) t-1 0.826*** (0.122) 0.699*** (0.083)
ln(K) t -0.696* (0.374) dln(KG)t -0.239 (0.163)
ln(N)t -0.627*** (0.160) dln(KG) t-1 0.110 (0.156)
ln(PPI)t -0.256** (0.103) dln(K) t 0.226 (0.146)
dln(K) t-1 0.084 (0.077)
1 2 3 4 5
dln(N)t 1.032* (0.507) 0 991*** (0.188)
dln(N) t-1 -1.674*** (0.541) -1.561*** (0.214)
dln(PPI)t -0.112*** (0.028) -0.121*** (0.027)
dln(PPI) t-1 0.008 (0.038)
d.w.D 0.299 d.w.h -0.326439 -0.233297
R2 0.8047 R2 0.9111 0.8946
Adj R2 0.7746 Adj R2 0.8690 0.8771
(s.e.)
*** - statistically significant at 1%;
** - statistically significant at 5%;
^_________________________________________________________________________
All of the variables are significant in the reparameterized short run model (column 5) at 1 % level of significance. Changes in employment level and energy price level exert a significant effect on the change in private sector output in the short run.
Evidence of cointegration between the variables was not found in the long-run model. In addition, in the long run model, statistical results from the 2-step Engle-Granger procedure indicate that employment level and energy price index ratio have an effect on business output while in the short - run changes in business output are explained by current period employment and energy price index ratio, and past period output and employment.
VAR modeling
The VAR model is referred to as a forecasting model because all of the variables on the right-hand side of the estimating equation are lagged, while the dependent variable is the current observation. Therefore, changes in the lagged variables forecast the change in the dependent variable around its mean. The source of contemporaneous effects is the disturbance term, et. The effects on the dependent variable from the disturbance terms may be referred to as innovations.
According to Sims (1980), if there is a true simultaneity among a set of variables, they should all be treated on an equal footing; there should not be any priori distinction between endogenous and exogenous variables.
Given the expressions (3) and (4), Y is explained in terms of it’s own lagged values as well as the lagged values of X, and X is explained in terms of it’s own lagged values and the lagged values of Y.
n n
Yt=X aiXt-i+X biYt - j+uit; (3)
i=1 j=1
m m
Xt = X lYt-i + X diXt - j + u2t . (4)
i=1 j=1
This is an example of vector autoregressive models. The term autoregressive is due to the appearance of the lagged value of the dependent variable on the right-hand side and the term vector is due to the fact that we are dealing with a vector of two (or more) variables.
Variance Decomposition and Ordering of Variables
The ordering of the variables in a VAR model depends upon the set of questions to be addressed. The ordering in this model follows the procedure where variables that are the most exogenous are listed first. See Manchester (1989), for example.
The Engle-Granger (EG) test was performed to determine the existence of a lead lag relationship between the variables in the model (i.e. “Does Y Granger Cause X?”). The test is performed under assumption that u1t and u2t are not correlated in expressions
(3) and (4). The F statistic is used to reject the null of “Y does not Granger Cause X”. Granger Causality test indicated the reverse causality for public and private capital stocks, employment level and private capital stock variables. Such feedback corresponds with the correlation matrices where significant correlation was found between public and private capital stock and employment level variables.
The rational for the orderings used is based on the assumption that changes in public capital stock and private capital affect the energy price index ratio, employment and real output, as follows: [KG K PPI N GDP]. The most endogenous variables are placed last. When the public capital stock was placed before private capital stock, public capital stock dominated, but private capital stock dominated forecast variance in real output when it was placed first, reflecting the correlation between these 2 variables.
The VAR methodology is based on the implicit assumption of a known lag order p. In empirical applications, however, the lag order is typically unknown. The optimal number of lags, 2, was chosen based on Akaike Information Criteria (AIC) test. The five-variable VAR model was estimated using annual data in first difference form from 1974-2001. Vector Autoregression procedure results are presented in table 3.
The individual statistical effect of each coefficient cannot be determined due to multicollinearity. However, the energy price ratio does exert a statistically significant, negative effect on the real output. The adjusted R2 = 0.66 in the output equation (column
6 in table 3.)
The effects of output are evaluated by examining variance decompositions (VDCs) and impulse response functions (IRFs). VDCs show the proportion of k-step ahead forecast error variance for each variable that is attributable to its own innovations and to shocks to the other system variables. IRFs show the predictable response of each variable in the system to a one-standard deviation shock to one of the system’s variables and can be viewed as a type of dynamic multiplier that conveys information about the size and direction of effect of a shock to one variable on the other variables.
The VDCs, presented in table 4, reflect the percentage of the 10-step-ahead squared prediction error in each of the included variables attributed to innovations in each of the endogenous variables.
Since the focus is on the effects of output, only the point estimates of the proportions of the variation in dlnKG, dlnK, dlnPPI and dlnN explained by dGDP are presented. After own lags almost 40 percent of the 10-step-ahead squared prediction error in changes in GDP is explained by changes in public capital stock (lnKG) as indicated in the third column in table 4. Alternatively, 21 percent can be attributed to changes in private capital stock and 16 percent is explained by changes in the energy price ratio.
Table 3
Vector Autoregression Estimates (28 observations included, 1974 - 2001; standard errors & t-statistics in parentheses)
DLNKG DLNK DLNPPI DLNN DLNGDP
1 2 3 4 5 6
DLNKG(-1) 1.333746 (0.57026) (2.33883) 0.842996 (0.56228) (1.49924) -0.153134 (1.40995) (-0.10861) -0.110858 (0.15519) (-0.71436) -0.261589 (0.30628) (-0.85408)
DLNKG(-2) -0.195212 (0.48176) (-0.40521) -0.312675 (0.47501) (-0.65824) -1.769167 (1.19112) (-1.48529) -0.023047 (0.13110) (-0.17579) 0.181272 (0.25875) (0.70057)
DLNK(-1) -0.880802 (0.50958) (-1.72849) -1.016222 (0.50245) (-2.02255) -0.564726 (1.25991) (-0.44823) 0.111322 (0.13867) (0.80277) 0.469806 (0.27369) (1.71656)
DLNK(-2) -0.113021 (0.25018) (-0.45175) 0.011122 (0.24668) (0.04509) 0.699557 (0.61857) (1.13093) -0.032556 (0.06808) (-0.47819) -0.034687 (0.13437) (-0.25814)
DLNPPI(-1) 0.148862 (0.11922) (1.24863) 0.147704 (0.11755) (1.25650) 0.173297 (0.29477) (0.58791) -0.015299 (0.03244) (-0.47154) -0.062206 (0.06403) (-0.97148)
DLNPPI(-2) 0.118015 (0.13666) (0.86356) 0.174707 (0.13475) (1.29654) -0.094561 (0.33789) (-0.27986) -0.050779 (0.03719) (-1.36540) -0.054033 (0.07340) (-0.73615)
DLNN(-1) 1.708495 (1.71809) (0.99442) 2.934362 (1.69404) (1.73217) -2.438588 (4.24788) (-0.57407) -0.164888 (0.46754) (-0.35267) -0.636698 (0.92277) (-0.68999)
DLNN(-2) 0.228061 (2.11673) (0.10774) -1.021330 (2.08710) (-0.48935) -0.132808 (5.23350) (-0.02538) 0.273232 (0.57602) (0.47434) -1.243698 (1.13687) (-1.09396)
DLNGDP(-1) -0.386132 (0.73544) (-0.52503) -1.116410 (0.72515) (-1.53956) 0.098186 (1.81835) (0.05400) 0.382704 (0.20014) (1.91222) 0.627401 (0.39500) (1.58836)
DLNGDP(-2) 0.783482 (0.69603) (1.12565) 1.320115 (0.68628) (1.92357) -0.264551 (1.72089) (-0.15373) -0.460862 (0.18941) (-2.43316) 0.046878 (0.37383) (0.12540)
C -0.029835 (0.03835) (-0.77794) -0.034972 (0.03781) (-0.92481) 0.079427 (0.09482) (0.83764) 0.016644 (0.01044) (1.59480) 0.033778 (0.02060) (1.63985)
1 2 3 4 5 6
R-squared 0.607034 0.748658 0.342218 0.591960 0.785891
Adj. R-squared 0.375877 0.600810 -0.044713 0.351936 0.659944
Sum sq. resids 0.030205 0.029365 0.184644 0.002237 0.008713
S.E. equation 0.042152 0.041562 0.104218 0.011471 0.022639
Log likelihood 55.91705 56.31173 30.57118 92.35843 73.32153
Akaike AIC -3.208361 -3.236552 -1.397941 -5.811316 -4.451538
Schwarz SC -2.684995 -2.713186 -0.874575 -5.287950 -3.928172
Mean dependent 0.015706 0.007456 0.021388 0.017886 -0.012299
S.D. dependent 0.053356 0.065781 0.101963 0.014249 0.038823
Determinant Residual Covariance 2.74E-18
Log Likelihood 367.4992
Akaike Information Criteria -22.32137
Schwarz Criteria -19.70454
Table 4
Variance Decomposition of order [KG K PPI N GDP] 1974 to 2001
Variance Decomposition of DLNGDP:
Period S.E. DLNKG DLNK DLNPPI DLNN DLNGDP
1 0.017640 29.32308 8.072252 20.08330 13.94167 28.57970
2 0.025359 16.04724 33.82302 23.74969 7.106475 19.27358
3 0.027755 26.64077 28.33442 20.87913 7.431198 16.71448
4 0.030555 35.16037 24.79828 18.46151 6.281045 15.29880
5 0.032077 36.93036 23.81497 18.56803 6.034166 14.65248
6 0.032963 36.56819 22.56321 17.58572 6.110641 17.17224
7 0.033536 36.14708 22.78996 17.43660 5.927162 17.69920
8 0.034160 36.73498 22.59302 17.20618 5.779459 17.68636
9 0.034799 38.50750 21.87168 16.57979 5.634672 17.40636
10 0.035426 39.97061 21.13537 16.13598 5.437933 17.32010
In the diagram the point estimate of the Impulse Response Function (IRF) is plotted as the solid line while the dotted lines represent a two standard deviation band around the point estimate. The effects are judged to be insignificant if the two standard deviation band includes zero.
The IRFs for shocks to GDP for [KG K PPI N GDP] are presented in Fig. 1.
Response to One S.D. Innovations ± 2 S.E.
Response of DLNGDP to DLNKG
Response of DLNGDP to DLN PPI
Response of DLNGDP to DLNK
R e s po n s e o f D L N G D P to D L N N
0.03
12345678910 12345678910
Fig. 1 Impulse Response Functions for a Shock to GDP for [KG K PPI N GDP]
in first difference form
The particular ordering of variables has the following implication: GDP reacts
positively to shocks to private capital stock in the 2nd period and marginally reacts to the
shocks to public capital stock in the 3rd period, and negatively to shocks to the energy price ratio in the 1st and 2nd periods.
Vector Error Correction Model
A vector error correction model (VECM) is a restricted VAR that has cointegration restrictions built into the specification, so that it is designed for use with nonstationary series that are known to be cointegrated. The VECM specification restricts the long-run behavior of the endogenous variables to converge to their cointegrating relationships while allowing a wide range of short-run dynamics. The cointegration term is known as the error correction term since the deviation from long-run equilibrium is corrected gradually through a series of partial short-run adjustments.
The VECM that is estimated can be represented in general terms by
Xt - dt + AlXt— + A2Xt-2 + ••• + AhXt-h + B ECMf— + et
(5)
The equation has two components: a vector auto regressive part and an error correction term. In this equation, Xt-i are n x 1 vectors of stationary endogenous variables (first difference of log-levels, or growth rates) at time t - i, with I = 0,..., h, where h is the order of the VAR/ECM model. In turn, Ai are n x n matrices of estimated parameters, and dt is a n x 1 vector of estimated deterministic components. These represent the vector auto regressive component of the model. The error correction component is represented by the m x 1 vector ECMt-i, which denotes the deviations of the variables in their original form (log-levels) from their m < n long-term cointegration relationships. The n x m matrix B of estimated parameters filters the effect of such deviations into the auto-regressive component of the model. Finally, the VAR/ECM model includes et, a n x 1 vector of residuals.
0.0
0.0
-0.0
-0.0
-0.0
Testing for Cointegration
Given a group of non-stationary series, one may be interested in determining whether the series are cointegrated, and if they are, in identifying the cointegrating (long-run equilibrium) relationships. VAR-based cointegration tests are implemented using the methodology developed by Johansen (1991, 1995). Johansen’s method is to test the restrictions imposed by cointegration on the unrestricted VAR involving the series.
Johansen’s test results for five variables are shown in Table 5. We conclude that there is 1 cointegrating vector for data in first difference form. 1 % level of significance was used to reject the null hypothesis for the data in levels.
Estimation results of VECM with CE = 1 and Optimal number of lags (ONL = 2) are presented in T able 6.
T able 5
Johansen’s Cointegration Test results for VAR in levels and first difference form
Null hypothesis: number of cointegrating equations (CE) Eigenvalue: data in levels Eigenvalue: data in first differences 5 % critical value 1 % critical value
None 0.747508** 0.797837** 68.52 76.07
At most 1 0.634183* 0.676835 47.21 54.46
* (**) indicates rejection of null at 5 % (1 %) significance level.
Table 6
VECM results (28 observations, 1974 - 2001; standard errors & ¿-statistics in parentheses)
Cointegrating Eq: CointEq1
LNKG(-1) LNK(-1) LNPPI(-1) LNN(-1) 1 -35.4162 -27.8904 -1.26983 0.964227 -0.61319 -1.57248 0.843061 -0.91564 -0.92074
LNGDP(-1) C 0.279413 -0.61614 -0.45349 -12.1574
Error Correction: D(LNKG) D(LNK) D(LNPPI) D(LNN) D(LNGDP)
1 2 3 4 5 6
CointEq1 -0.0353 -0.0391 (-0.90296) 0.025591 -0.039 (-0.65622) 0.080842 -0.09701 (-0.83333) 0.004902 -0.01084 (-0.45229) -0.00647 -0.02147 (-0.30161)
1 2 3 4 5 6
D(LNKG(-1)) 1.209952 -0.58955 (-2.05234) 0.932736 -0.58806 (-1.58612) 0.130358 -1.4629 (-0.08911) -0.09367 -0.16343 (-0.57315) -0.28429 -0.32369 (-0.87829)
D(LNKG(-2)) -0.56694 -0.6357 (-0.89183) -0.04321 -0.6341 (-0.06814) -0.91791 -1.57742 (-0.58190) 0.028569 -0.17622 (-0.16212) 0.113099 -0.34903 (-0.32404)
D(LNK(-1)) -1.62734 -0.97266 (-1.67308) -0.47505 -0.97021 (-0.48964) 1.144866 -2.41354 (-0.47435) 0.214982 -0.26963 (-0.79732) 0.332894 -0.53403 (-0.62336)
D(LNK(-2)) -0.16063 -0.25702 (-0.62497) 0.045635 -0.25637 (-0.178) 0.808586 -0.63777 (-1.26783) -0.02595 -0.07125 (-0.36415) -0.04342 -0.14112 (-0.30768)
D(LNPPI(-1)) 0.209272 -0.13728 (-1.52442) 0.103912 -0.13693 (-0.75885) 0.034957 -0.34064 (-0.10262) -0.02369 -0.03806 (-0.62243) -0.05113 -0.07537 (-0.67833)
D(LNPPI(-2)) 0.144703 -0.14055 (-1.02953) 0.155361 -0.1402 (-1.10815) -0.15568 -0.34877 (-0.44636) -0.05449 -0.03896 (-1.39838) -0.04914 -0.07717 (-0.63676)
D(LNN(-1)) 3.079394 -2.29984 (-1.33896) 1.94058 -2.29404 (-0.84592) -5.578 -5.7068 (-0.97743) -0.35525 -0.63754 (-0.55721) -0.38528 -1.26272 (-0.30512)
D(LNN(-2)) 1.294751 -2.43419 (-0.5319) -1.79459 -2.42805 (-0.73911) -2.57557 -6.04016 (-0.42641) 0.125116 -0.67478 (-0.18542) -1.04807 -1.33648 (-0.78420)
D(LNGDP(-1)) -0.7801 -0.85859 (-0.90858) -0.83082 -0.85643 (-0.97010) 1.000379 -2.1305 (-0.46955) 0.437408 -0.23801 (-1.83777) 0.55515 -0.47141 (-1.17765)
D(LNGDP(-2)) 0.553614 -0.7447 (-0.7434) 1.486749 -0.74282 (-2.00148) 0.261858 -1.84789 (-0.14171) -0.42894 -0.20644 (-2.07782) 0.00472 -0.40888 (-0.01154)
C -0.08027 -0.06787 (-1.18265) 0.001586 -0.0677 (-0.02343) 0.194916 -0.16841 (-1.15738) 0.023647 -0.01881 (-1.25687) 0.024529 -0.03726 (-0.65827)
R-squared Adj. R-squared Sum sq. resids S.E. equation 0.626088 0.369023 0.02874 0.042383 0.755245 0.586976 0.028596 0.042276 0.369579 -0.06384 0.176963 0.105167 0.597111 0.320125 0.002209 0.011749 0.787101 0.640733 0.008664 0.02327
Log likelihood Akaike AIC 56.61288 -3.18663 56.68355 -3.19168 31.16599 -1.369 92.53629 -5.75259 73.40091 -4.38578
1 2 3 4 5 6
Schwarz SC Mean dependent S.D. dependent -2.61569 0.015706 0.053356 -2.62074 0.007456 0.065781 -0.79805 0.021388 0.101963 -5.18165 0.017886 0.014249 -3.81483 -0.0123 0.038823
Determinant Residual Cov Log Likelihood Akaike Information Criteria Schwarz Criteria 5.28E-19 390.5437 -23.2531 -20.1605
The results of table 6 report that there is indeed no evidence of cointegration in the model since the error correction term from the cointegration equation is statistically insignificant. The t-statistic is very close to zero, at just-0.03. This result confirms the findings of the 2 steps Engle-Granger model. The adjusted R is 0.63 in the output equation (column 6, table 6). These results suggest that the VAR model findings should be considered as main results of this study.
Conclusions
This paper has examined the effects of public capital on private sector performance using an error correction model (ECM), a vector autoregressive model (VAR), and a vector error correction (VEC) model.
Statistical results from the 2-step Engle-Granger procedure reveal no evidence of cointegration between the variables in the long-run model. In addition, in the long run model the employment level and energy price level have an effect on business output while in the short - run changes in business output are explained by current period employment level and energy price level and past period output and employment.
The VAR approach was used to test whether the causal relationship assumed in other approaches is valid or whether there are feedback effects from output to public capital. Reverse causality was determined for public and private capital stocks, employment level and private capital stock variables using the Granger Causality test. Such feedback corresponds with the significant correlation between public and private capital stock and employment level variables indicated by the correlation matrix. Moreover, when experimenting with the ordering for the vector autoregressive model, changes in the public capital stock dominated the k-step ahead forecast variance in changes in real output, when placed first in the ordering. However, changes in the private capital stock dominated when it was placed first.
The results of the VECM indicated that there was indeed no evidence of cointegration in the model. This supports the results of the 2 step Engle - Granger procedure.
Variance decomposition results from the VAR model indicate that almost 40 percent of the 10-step-ahead squared prediction error in changes in GDP to be explained by changes in public capital stock (lnKG). Alternatively, 21 percent is attributed to changes in private capital stock and 16 percent is explained by changes in the energy price ratio.
Impulse response functions based on the ordering [KG K PPI N GDP] indicated that GDP reacts positively to shocks to private capital stock in the short run (2nd period), marginally reacts to the shocks to public capital stock in the 3rd period, and negatively to shocks to the energy price ratio.
ISSN 0136-5835. Вестник ТГТУ. 2005. Том 11. № 4. Transactions TSTU. 1089
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Г осударственный основной капитал и производительность частного сектора: векторная авторегрессионная модель и векторная модель корректировки отклонений
Ш. Эренбург, О. Пономарева
Экономический факультет, Восточный Мичиганский Университет, Ипсиланти, Мичиган, США
Ключевые слова и фразы: векторная авторегрессионная модель; векторная модель корректировки отклонений; государственный основной капитал; двушаговый метод Энгла-Грейнджера; производительность частного сектора; тест причинности Грейнджера; функции импульсной характеристики.
Аннотация: Представлено эмпирическое подтверждение динамичных эффектов государственного капитала на реальный экономический рост в Соединенных Штатах Америки. Используемый период выборки включает в себя 1971-2001 годы. Векторная авторегрессионная модель и векторная модель корректировки отклонений были оценены с использованием следующих переменных: государственный чистый основной капитал, частный чистый основной капитал, количество работающих лиц, соотношение индексов цен электроэнергии и всех предметов потребления, чистый валовый внутренний продукт.
Staatliches Hauptkapital und Produktivität des Privatsektors: vektorielles Autoregressionsmodell und vektorielles Modell der Abweichungsrektifikation
Zusammenfassung: In diesem Artikel wird die empirische Bestätigung der dynamischen Effekte des staatlichen Kapitals auf die realen ökonomischen Steigerung in USA angeführt. Die anwendende Auswahlperiode besteht aus den Jahren 1971-2001. Vektorielles Autoregressionsmodell und vektorielles Modell der Abweichungsrektifikation wurden mit der Benutzung von folgenden Variablen eingeschätzt: staatliches reines Hauptkapital, reines Privatkapital, die Zahl der Beschäftigten, das Verhältnis der Preisindexe von Elektroenergie und aller Gebrauchsgüter, reines inneres Bruttoprodukt.
Capital public de base et productivité du secteur privé: modèle autorégressif vectoriel et modèle vectoriel de la correction des décalages
Résumé: Dans l’article est présentée l’affirmaton empirique des effets dynamiques du capital public sur l’essor économique aux USA. Les années 19712001 sont choisies pour une analyse. Le modèle autorégressif vectoriel et le modèle vectoriel de la correction des décalages ont été évalués avec l’utilisations des variables suivantes: capital public net, capital essentiel privé net, effectif, rapport des indices des prix de l’énergie élactrique et de tous les objets de consommation, produit intérieur net.
