1. Modelling Core Inflation

As detailed in the introduction, the core inflation term will be based upon the backward-looking theory. The weighted average will be over the previous two years, with up to eight quarters, as determined econometrically, and of the general form:

p* = a + S_t=1L p_t-L

where p is inflation, p* represents core inflation, a is a constant and L is the lag length, such that 1<L<8.

The model chosen has six lags, therefore one and a half years, representing, in one way, the longevity of inflation in people's expectations.

p* = 0.426 + 1.234p_t-1 - 0.082p_t-2 - 0.206p_t-3 - 0.330p_t-4 + 0.498pt-5 - 0.166p_t-6 (2)

Clearly the inconsistency of the signs of each regressor is puzzling. One would expect that recent inflation would cause current inflation and hence a positive sign. The first lag has a strong effect, whereby last quarter's inflation has an effect on current inflation greater than its actual value, such that inflation of 5% in period 1 would have a value of just over 6%¹² in period 2. One interpretation of this is that, as well as the monetary effect, people fear inflation as they see it eroding their wealth and so there is a psychological effect. Therefore, when making their expectations for the next quarter, consumers will anticipate even higher inflation.

As well as the signs, the varying coefficients are unexpected, as there is no trend for past values to have significantly less effect. In fact, the coefficients of the lagged periods two, three and six could justifiably be set to zero ^{These lag lengths constrain all variables except incomes policy which can range from four to twelve lags. If more than one model satisfies both economic reasoning and econometric tests, I will select the most appropriate using the "general to simple" approach, discussed earlier.}

Having decided this, the functional form for inflation can be expressed as: p_t = a + p_t* + S_i=0¹ b_ix_1t-i + S_i=0⁴ b_ix_2t-i + S_i=0^L b_ix3_t-i, where L=4,8,12.

Having worked through the regression, the most suitable model was found to have four lags on the incomes policy. This comes as somewhat of a relief, as it is the most parsimonious model and hence easier to manipulate and discuss. Consequently, we have:

p_t = -0.096080 + 0.99517pt* + 0.039207x_1t + 0.94839x_1t-1 - 0.000156x_2t + 0.000273x_2t-1 - 0.000022x_2t-2 + 0.00003254x2t-3 - 0.000027x_2t-4 + 0.38992_x3t - 0.41723x_3t-1 -0.9017x_3t-2 - 0.18939x_3t-3 + 1.4065x_3t-4 (3)

Before commenting on this model, it is worth considering how one would expect the variables to behave. Starting with core inflation, I would anticipate a positive sign, given that consumers use past information. The higher the value of p*, the more emphasis is placed on past inflation when calculating expectations for future levels.

The relative price of imports variable should also have a positive sign for two reasons. Firstly, an increase in the relative import price will affect firms who import factors of production and increase costs. The second way is more direct. If consumer goods are amongst those imports which increase in price, the selling price in Britain will be higher. However, it is worth noting that, if the relative price does increase, consumers may switch to domestically produced goods, which would reduce the price effect somewhat, although not entirely as the domestic goods must have been more expensive, else they would already have been consumed. The higher the value of the coefficients, the greater the effect of the price rise on inflation.

I would also expect a positive sign on the demand shocks variable, as an increase in aggregate demand (AD) leads to a rise in prices, ceteris parabus. The actual value of the coefficients, also from Keynesian theory, depends on where the aggregate supply (AS) curve lies. Figure 2 shows the standard Keynes AS curve and three possible AD curves:

If the coefficients are close to zero it implies AD1 on the diagram, with the economy having spare resources. In this case, rising AD would have a very small effect on prices. As the coefficients increase in value, we move along the AS curve to AD2 and as resources start running short we approach AD3, which is full employment and any demand increase is purely inflationary.

Finally, the troublesome variable of incomes policy. Since this is a policy designed to prevent inflation, it should have a negative sign. The closer the coefficients are to -1, the more successful the policy has been.

Now, compare the actual results to the theory. The core inflation term is positive, as anticipated, and is close to one, reinforcing the theory that consumers are backward- looking and that they consider past inflation when making their predictions about future conditions. This is a key consideration for government planners, as it means that, when high inflation occurs, people become pessimistic and expect it to continue. In fact, the theory implies that inflation will continue increasing.

The relative price of imports have a positive sign on both terms, which is correct, and the lagged term is significant, although the present term's effect is small. This is consistent with my belief that the effect on inflation takes time to filter through and, consequently, we should consider the previous quarter's situation more than the current quarter.

Surprisingly, demand shocks are insignificant and also have mixed signs, in contrast to the theory. A minus sign, as appears on the current period and second and fourth lag, implies that increasing aggregate demand leads to lower inflation, which is against all theory. However, the small coefficients suggest that changes in AD have little effect on inflation. With the coefficient of core inflation being approximately one, the small demand shock coefficients suggests the economy is at the natural rate of unemployment.

The incomes policy term also has mixed signs. Considering first the size of the coefficient, the policy certainly has a significant effect on inflation. However, there is no pattern to the absolute value of the coefficients to suggest that the effect diminishes or increases over time. Returning to the sign of the coefficients, whilst being against what I expected, it is not altogether inconceivable that this could be the case. Considering the implication, incomes policy has caused higher inflation. This could happen if the policy was incorrectly used and the wrong outcome was achieved or could mean that, when the policy is not in effect, wages, for example, are increasing to compensate for the anticipated incomes policy.

3. Alternative Measure of Demand Shock

Given the insignificant values for GDP deviation as the demand shock, it is prudent to consider another measure, namely my alternative of capacity utilisation. Maintaining the same notation as previously, the model generated is with only the current level of capacity utilisation. p_t = -2.2326 + 1.0072p_t* -0.11058x_1t + 0.60565x_1t-1 + 0.066728x_2t - 0.22091x_3t + 0.23489x_3t-1 - 1.5216x_3t-2 - 0.87280x_3t-3 + 2.6447x_3t-4 (4)

Again the core inflation term has a coefficient of approximately one and there is a mixture of signs on the incomes policy lags. However, the effect of import prices in the current period appears incorrect, as the sign is now negative. Considering the significance of the demand shock proxy, we see a larger coefficient than with GDP deviations but still small compared to other variables, in some ways agreeing with the previous model that demand shocks are the minor player. The gain, therefore, from using capacity utilisation is trivial, so I will continue with equation (3).

Notes

12. Obviously this would not be the inflation rate for period 2, as there are other factors to consider.
13. That is, the coefficient lies within two standard deviations of zero and a null of equalling zero would not be rejected.

Estimation and Results part 2

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