This links in with Granger’s attempt to explain the great depression. As the figures show – investment falls then consumption and private wages fall with a slightly longer lag.
TWO STAGE LEAST SQUARES REGRESSION (TSLS)
Consumption
Using ordinary least squares (OLS) regression and TSLS the following results are obtained:
From these results one can say that significantly different estimations are obtained using TSLS rather than OLS for consumption. We can conclude also that the model is a good fit with R2 values of 0.97214 and 0.982007 for the OLS and TSLS regressions respectively. The signs of the coefficients for П and W1 are as expected; when profits and private wages rise one would expect consumption to rise too. One would expect П-1 to have a positive coefficient as in the TSLS regression rather than the negative one found in OLS, and therefore one can say that the TSLS estimates are consistent with expectations.
Investment
Using OLS and TSLS the following estimated were obtained:
Again, significantly different estimates are obtained using OLS and TSLS. There is no difference in the sign of coefficients across estimations. The coefficients are all as we expect from the predictions of the Klein model and one can conclude therefore that the TSLS estimates are better than OLS and are consistent. R2 values of 0.929682 and 0.902244 for OLS and TSLS respectively suggest the model is a good fit.
Private Wages
The following results were obtained using OLS and TSLS estimation:
The estimates using OLS and TSLS are almost identical and the signs of the coefficient are consistent with expectations. Near identical R2 values of 0.980973 and 0.980972 for OLS and TSLS respectively imply an excellent fit it both cases, and it is not of huge importance which method is used for estimation.
Correlogram
When we have time series data, where the observations follow a natural ordering through time, there is always a problem that successive errors we be correlated with each other.
Serial correlation is present when residuals correlate with their own lagged variables. This violates the standard assumption of regression theory that disturbances are not correlated with other disturbances. This is a problem as OLS is no longer efficient among linear estimators. Standard errors are not correct and are often understated and if there are lagged dependent variables on the right-hand side, OLS estimates are then biased and inconsistent.1
We can use the Correlogram to find out whether the series is stationary or non-stationary.
With a stationary series the autocorrelations gradually die out, indicating that the values further in the past are less correlated with the current value. For non-stationary the autocorrelations do not die out rapidly at all.
We have decided to plot correlograms for consumption (figure 4), investment (figure 5) and private wages (figure 6). All three of these graphs show the same thing, the autocorrelation drops fairly soon. It certainly does not stay. From this, one can assume that all three series are stationary. The regression is therefore not necessarily spurious. When non-stationary time series occur, the problem can be that the regression may indicate a significant relationship when actually there isn’t one. The correlogram has allowed us to see that the regression is not spurious and so the relationships are reliable. We can tell that there is serial correlation in the model as we have tested that at least some of the AC and PC are greater than zero. The Q-stats are significant the P values are low.
Time Series Methods
Vector Auto Regressive (VAR) modelling was developed by Christopher Sims in the 1970s. It does not put restrictions on variables like simultaneous equation models do.
Table 1 shows the VAR with a 1 1 lag.
Table 2 shows the VAR with a 2 2 lag.
Table 3 shows the VAR with a 5 5 lag.
Although the patterns of the coefficients are similar in all of these outputs, it should be noticed that with a 2 year lag they are the strongest. For example it can be seen that consumption is strongly (-2.26) negatively related to consumption with a two year lag. It can also been seen that wages (both private and total) are fairly strongly related to both inflation and consumption. There is a very strong negative coefficient between output and private wages.
Akaike AIC Criterion
The Akaike AIC criterion is a measure of the goodness of fit of lag length. One should seek to maximise the AIC value for better lag lengths:
Using EViews some differing lag lengths’ AIC criterion is reported above. For the series CO, P, I and X the lag length of two seems to be optimal in our sample. For W and W1 a lag of five seems more appropriate.
Granger Causality
Granger causality is a technique for determining whether one time series is useful in forecasting another. When two variables affect each other with lags we probably wish to determine which variables causes the movement of another So X is a cause of Y if X is useful for forecasting Y, so this notion of causality fits the notions that causes precede effects but does not apply naturally to contemporaneous X and Y. A time series X is said to Granger-cause Y if it can be shown, usually through a series of F-tests.
Eviews has a tool to work out if there is Granger causality. We used the program to test every variable. Granger causality was not detected for any variables (see figure X).
Though no causality is shown using the Granger test it is not possible to fully conclude that there is not causality due to weaknesses in Granger’s method.
Impulse Analysis
We produced impulse analysis graphs for the following lags:
After looking at these graphs and comparing them with the statistics in the VAR it became obvious that the two year lag was the most appropriate one to look at.
From the impulse analysis graphs alone it is shown that:
- Consumption (CO) is responsive positively to wages (W) and to output (X).
- Inflation is responsive to consumption (CO) and to output (X).
- Wages (W) are responsive to output (X).
- Private wages (W1) is responsive to output (X).
- Output (X) slightly responsive to consumption (CO).
A common feature with all these impulse responses is that it tends to take several periods for the full effect of the shock to be felt the analysed variable.
When the order of the variables is changed we obtained very slightly different graphs, however the difference is negligible. On another occasion a ‘near singular matrix’ is obtained, this would be due to the formation of the matrices.
Scalar AR
Table 5 - Consumption
Table 6 – Investment
Table 7 – Private Wages
A common feature of these scalar ARs that they all have a relatively high Akaike AIC value – meaning they are a relatively good fit.
Although modelling using a scalar AR does produce a reasonable result it is not as good as modelling with the VAR.
Conclusion
In conclusion when estimated using simultaneous equations methods the Klein model provides relatively good fit to the data and in doing so is able to explain possible causes for a great depression.
We have also concluded that the series Klein uses are stationary and when modelled using a VAR similar variables are found to be significant to the simultaneous model.
References
R. C. Hill et al (2001) Undergraduate Econometrics
D. N. Gujarati Basic Econometrics
Quantitative Micro Software Eviews 5.1 User’s Guide
J. Aldrich (2007) ECON2032 Lecture Notes