Journal number 4 ∘ Giorgi Miqeladze ∘
Investments accelerator and Tobins Model (Case of Georgia)

Summary

The article discusses the importance of the total capital in the process of total investment studies, calculation method of Georgia’s total capital and the opportunity of practical realization of above mentioned method. Research uses quarterly empirical data from 2003-2016 years.

The article empirically examines Modified case of L.M. Koyck’s investments accelerator model and Tobin’s investments model on example of Georgia. Practical models consider country’s economic specification and important events (results of the war in august, 2008 year).

Empirical studies validate interrelation of GDP’s and total investments’ current and lagged values with total capital. Also, research estimates quarterly values of Georgia’s total capital from 2003 year to 2016 year and depreciation rate, which is equal to 5.7%.

Key words: total investments; Georgia’s total capital; L. M.Koyck’s investments accelerator model; Tobin’s investments model; GDP.

Introduction

After the collapse of Soviet Union in the end of XX century 15 independent countries emerged. After gaining political independence, post-soviet countries faced various challenges. One of them was determination of economic policy. They had to choose strategy of transformation to market economy based on the countries’ non-existing statistical data. With the efforts of International Monetary Fund above mentioned process progressed according to the preliminary determined strategy in short period of time.

Nowadays, various statistical indicators exist for describing Georgia’s economy, however, still, there is no information about such important indicator as volume of total capital. As investments are determined by the total capital, lack of stated information hinders building total investments model on Georgia’s economy. Most of the investments models in economic theory use volume of total capital as a factor variable.

Investments Accelerator Model

There is no statistical information about volume of total capital in Georgia. Accordingly, investments accelerator model, which does not include volume of capital as a variable is L.M. Koyck’s model (Bernd Ernst R., 2005):

                        (1)

where I_t  represents current value of investments, I_t-1 – lagged value of investments, Y_t - current value of GDP, Y_t-1 - lagged value of GDP, δ - depreciation rate of total capital, g - adjustment rate to desirable capital and, lastly, μ – ratio of desirable capital and GDP.

This model is based on several assumptions: 1) ratio of desirable capital and output is constant over time; 2) depreciation rate is not different time periods; 3) currents capital’s adjustment rate to desirable capital is constant.  For the estimation of investments accelerator model on case of Georgia it is optimal using modified variant of (1) model, where variables will be represented in logarithms. Particularly, we step from the additive connection among model variables to multiplicative connection. Stated assumption is based on connection between investments and growth rate of output in Georgian economy. Finally, model will take the following form:

           (2)

for the realization of expression (2) quarterly data of total investments and output is used from 2003 – 2016 years.

Nominal volume of investments is divided by GDP deflator for deriving investments real volume (GDP deflator is the ratio of nominal GDP and real GDP).

Time series include seasonal components. Based on the variables’ characteristics, for elimination of seasonal components the article uses multiplicative method of seasonal adjustment (Census X12) implemented by the bureau of population census of USA.

Time series should be tested whether they are TSP or DSP type by the procedure suggested by J. J. Dolado, T. Jenkinson and S. Sosvilla-Rivero. Particularly, TSP type implies that series are nonstationary because of variable trend, whereas DSP type implies nonstationarity because of variable variance (Dolado, Juan J., Tim Jenkinson, and Simon Sosvilla‐Rivero, 1990). Using Dickey-Fuller test for all four series null hypothesis is derived about having unit root, which implies their nonstationarity (Dickey, David A., and Wayne A. Fuller.,1979). Using differences for making series stationary identify that all four series are integrated of first order I(1).

Risk of false regression may arise while building model (2), because model’s series belong to nonstationary integrated of first order series.

Engle-Granger test checks the risk of false regression by testing the co integration between the values of total investments and output. Null hypothesis of Engle-Granger test implies absence of co integration between series, whereas according to alternative hypothesis co integration exists between series (Ananiashvili, I.2014).  Alternative hypothesis is approved with the 1% significance level about the existence of co integration between investments and output. While using above mentioned tests, lag length is 4, because quarterly data is used for the realization of the model.

Distribution of (2) model’s residual members estimated by using least square method will have the following form:

Table 1: Distribution of (2) model’s residual members

As the histogram shows, residual members do not have normal distribution. However, by further observation it is possible to make the following conclusion: distribution of residual members is very much alike normal distribution by excluding one outlier value. For determining this fact in (2) model it is desirable to estimate model coefficients and determine, which gives the opportunity to calculate residual members for each quarter.

(2) model by estimating with least square method will have the following form:

Table 2: Regression Results of model (2)

 

                               (3)

  g= 0.233604, μ =19.27548,  δ = 0.042707   

Residual members’     empirical values have the following form:

Table 3: Residual members values of model (3)

Year	Quarter		Year	Quarter		Year	Quarter
2003	2	-0.08466	2007	4	-0.17926	2012	2	0.019044
2003	3	-0.08202	2008	1	-0.016	2012	3	-0.0414
2003	4	-0.04632	2008	2	0.079245	2012	4	0.054094
2004	1	0.222127	2008	3	0.023866	2013	1	-0.03716
2004	2	-0.04499	2008	4	0.104529	2013	2	-0.01781
2004	3	0.005715	2009	1	-0.91364	2013	3	-0.02089
2004	4	-0.02772	2009	2	-0.06345	2013	4	-0.08965
2005	1	-0.05906	2009	3	0.119321	2014	1	0.185331
2005	2	0.106004	2009	4	-0.05967	2014	2	0.10849
2005	3	-0.00439	2010	1	-0.14261	2014	3	-0.01204
2005	4	0.08056	2010	2	0.113044	2014	4	0.143231
2006	1	-0.03323	2010	3	0.058623	2015	1	0.140492
2006	2	-0.05169	2010	4	-0.01266	2015	2	-0.01819
2006	3	-0.16025	2011	1	-0.05357	2015	3	0.067159
2006	4	0.078995	2011	2	-0.04132	2015	4	0.155113
2007	1	0.089376	2011	3	0.126777	2016	1	0.105341
2007	2	-0.21704	2011	4	-0.04932	2016	2	0.053521
2007	3	0.145506	2012	1	0.119419	2016	3	0.041622

Outlier value of residual members occurs in the first quarter of 2009 year. Economic interpretation of this fact can be easily found in the nearest history of Georgia. Particularly, Georgia had a war in third quarter of 2008 year, which had short-term economic effects in the first quarter of 2009 year.

Remark: August war had a short term economic effect on Georgia, because grants from world organizations and partner countries nullified long term economic effect.

It is desirable to include factor variable in (2) model which will characterize effects of the war. This will be binary variable with the values of 0 in all the time periods except the first quarter of 2009 year, where the value is 1. After taking into consideration stated modifications and empirical estimation, the model will take the following form:

Table 4: Regression results of model (4)

 

          (4)

 g= 0.236232, μ =11.64838,  δ = 0.057283

The distribution of the residual members in model (4) is normal.

Table 5: Distribution of (4) model’s  Residual members

 

Durbin-Watson test is not recommended for checking autocorrelation in residual member, because model assumptions are violated: model does not contain a constant member and, also, model includes lagged values of dependent variable as a factor variable. Breusch-Godfrey’s Lagrange multiplier (LM) test is recommended for checking serial correlation in residual member. According to the null hypothesis of LM test there is no autocorrelation in residual member, whereas alternative hypothesis states that there is serial correlation in residual member (Breusch, T. S.,1978; Godfrey, L. G.,1978) . Breusch-Godfrey test results show that null hypothesis is statistically significant, which states that there is no serial correlation in residual member.

While checking heteroscedasticity in residual member with Glejser null hypothesis is accepted with 99% confidence interval, which means existence of homoscedatsticity (Glejser, Herbert.,1969). Accordingly, variance of residual member is constant.

It is shown that all the coefficients of model (4) are statistically significant, as for all of them H₁ hypothesis of T-test is accepted for statistical significance (Ananiashvili, I.,2010). Also, coefficients of determination and corrected determination have quite high values - 0.93 and 0.92 accordingly, which shows that model variation is well explained by model variables. Also, F=153.53, F_cr=3.73, F> F_cr shows that model is valid.

If we take into account  and capital consumption values, which is , calculation of capital volume in different time periods is possible. 

Table 6: Total real capital values

Year	Quarter	Total capital consumption	GDP deflator	Total real capital consumption	Total real capital
2003	I	192.77	0.65	295.08	5151.35
2003	II	226.98	0.63	360.03	6285.15
2003	III	247.42	0.61	404.98	7069.86
2003	IV	265.76	0.59	449.73	7851.01
2004	I	221.35	0.67	330.27	5765.51
2004	II	238.75	0.68	349.88	6107.87
2004	III	248.94	0.67	370.04	6459.82
2004	IV	267.78	0.66	406.85	7102.46
2005	I	235.28	0.77	307.02	5359.65
2005	II	270.29	0.72	375.38	6553.03
2005	III	296.18	0.70	420.81	7346.11
2005	IV	311.71	0.71	436.26	7615.95
2006	I	271.36	0.79	342.17	5973.36
2006	II	309.73	0.80	387.35	6762.05
2006	III	348.10	0.77	454.89	7941.05
2006	IV	377.18	0.78	480.74	8392.38
2007	I	334.31	0.86	390.32	6813.89
2007	II	392.90	0.86	457.95	7994.52
2007	III	426.20	0.84	507.55	8860.40
2007	IV	463.61	0.88	526.91	9198.38
2008	I	381.77	0.95	402.46	7025.85
2008	II	440.39	0.96	459.60	8023.37
2008	III	475.87	0.93	509.94	8902.03
2008	IV	460.02	0.93	495.94	8657.80
2009	I	379.57	0.94	402.10	7019.55
2009	II	422.11	0.91	465.20	8121.15
2009	III	452.30	0.92	494.29	8628.90
2009	IV	497.39	0.92	539.79	9423.21
2010	I	460.93	1.00	460.93	8046.59
2010	II	512.60	1.00	512.60	8948.51
2010	III	549.25	1.00	549.25	9588.36
2010	IV	604.01	1.00	604.01	10544.25
2011	I	619.37	1.13	548.39	9573.33
2011	II	712.17	1.09	650.41	11354.37
2011	III	636.89	1.08	589.56	10292.09
2011	IV	692.33	1.08	639.68	11167.00
2012	I	687.83	1.16	593.02	10352.40
2012	II	774.41	1.11	694.81	12129.39
2012	III	653.87	1.09	601.88	10507.10
2012	IV	680.87	1.08	631.35	11021.54
2013	I	703.83	1.15	609.75	10644.48
2013	II	767.92	1.11	693.30	12103.14
2013	III	656.30	1.07	610.84	10663.51
2013	IV	681.46	1.07	636.20	11106.32
2014	I	717.29	1.17	611.30	10671.65
2014	II	843.22	1.16	728.78	12722.45
2014	III	712.08	1.13	632.61	11043.59
2014	IV	739.38	1.11	664.96	11608.29
2015	I	748.32	1.24	602.78	10522.85
2015	II	920.41	1.23	748.13	13060.26
2015	III	789.01	1.20	658.26	11491.29
2015	IV	815.78	1.17	698.70	12197.25
2016	I	802.47	1.29	620.59	10833.82
2016	II	987.32	1.24	799.01	13948.38
2016	III	864.01	1.24	698.16	12187.87

source: National statistic office of Georgia, total capital consumption.

At first, Total real capital consumption is calculated considering GDP deflator. Next step evaluates total capital real values, which is the ratio of total capital real consumption and depreciation rate.

Estimate results of model (4) are statistically valid, because there is no autocorrelation in residual member, which shows that model does not omit statistically significant independent variables and model has right functional specification. Residual member has constant variance, coefficients and the model are statistically significant. Moreover, there is low correlation level among the variables.

According to model (4) investments’ current value is positively related to the lagged value of investments. Growth in lagged value of investments stimulates investments in next period, particularly 1% growth in lagged value of investment increases investments of current period by 0.76%. Also, logically, output growth in current period increases current investment values. Output growth by 1% in current period increases investments by 3.46%. Current period’s investment volume is negatively related with output value of previous period.1% increase of the lagged value of output decreases investments values of current period by 3.26%. This negative relationship takes into consideration delayed process of investments’ realization. Investments that are planned in previous time period and are realized in current time period decrease investments in current period, because companies try to prevent increase of investments cost in short term. The war factor has a negative value, which means that the war is negatively related to total investments’ volume. Logically, period during the war the volume of total investments decreases in short term.

Tobin’s investments model Based on the USA’s economy R. Kopke empirically tested Tobin’s investments model, which had the following form (Bernd Ernst R.,2005):

                                (5)

where I_t is the volume of total investments, K_t – total capital values, q_t - Tobin’s coefficient in respective time period and b_j – coefficient.

It should be mentioned that empirical realization of Tobin’s investments model on Georgian economy case faces following problems:  1) there is no information about Tobin’s coefficient – q; 2) there is no empirical data on total capital. The later can be fixed by using the result from investments accelerator model, which estimates total capital values. However, because of the absence of Tobin’s coefficient values statistically valid model cannot be built on Georgian case.

Remark: Calculation of Tobin’s coefficient or replacing it with economically similar factor is not possible, because there are no economic indicators that could be used for fixing stated problem. Also, considering that technical estimation problem in model (5) should be fixed by assuming that Tobin’s coefficient is constant through time and creating new coefficients  has no valid economic logic, because above mentioned fact confronts Tobin’s theory.

Conclusion

Investments accelerator model well reflects Georgian economy’s reality. According to this model, investments are positively related to the lagged values of investments and current value of GDP. This result is in accordance with the economic theory. Also, increase in lagged value of GDP decreases investments values in current period. This relationship reflects delayed process of investments’ realization. Investments that are planned in previous time period and are realized in current time period decrease investments in current period, because companies try to prevent increase of investments cost in short term.

Depreciation rate of Georgia’s total capital is 5.7% and volume of total capital in last period is more than 12 billion Georgian Lari, which is approximately 5 billion US dollars.

The war in August, 2008 year had a short term negative effects on Georgia’s total investments, which is proved by the investments accelerator model.

During the realization of Tobin’s investments model on example of Georgian economy it is possible to use estimated values of total capital from investments accelerator model and to assume that using twice regressive model will not increase statistical errors. However, it is not recommended to use Tobin’s investments model on example of Georgian economy, because there is no empirical data about Tobin’s coefficient. Moreover, there is no economic variable that could be used as a replacement in the model. It is not economically reasonable to use the assumption that Tobin’s coefficient is constant through time for fixing above mentioned problem, because it confronts Tobin’s theory.

References

1. Ananiashvili, I. (2014).Timeline series analysis. TSU, Tbilisi.
2. Ananiashvili, I. (2010). Econometrics.Meridiani,Tbilisi.
3. Bernd Ernst R. (2005). “Classical and modern”. Applied  econometric. Moscow, Iuniti-dana,847.
4. Breusch, Trevor S. (1978). "Testing for autocorrelation in dynamic linear models." Australian Economic Papers 17.31, 334-355.
5. Dickey, David A., and Wayne A. Fuller. (1979). "Distribution of the estimators for autoregressive time series with a unit root." Journal of the American statistical association 74.366a, 427-431.
6. Dolado, Juan J., Tim Jenkinson, and Simon Sosvilla‐Rivero. (1990). "Cointegration and unit roots." Journal of economic surveys 4.3, 249-273.
7. Glejser, Herbert. (1969). "A new test for heteroskedasticity." Journal of the American Statistical Association 64.325, 316-323.
8. Godfrey, Leslie G. (1978). "Testing against general autoregressive and moving average error models when the regressors include lagged dependent variables." Econometrica: Journal of the Econometric Society,  1293-1301.
9. National statistic office of Georgia, Total capital consumption, available from: http://geostat.ge/index.php?action=page&p_id=119&lang=eng (Accessed 29 July 2017).

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