2.1 IS relation

The IS equation relates output in the economy to deviations of the real interest rate from the level consistent with stable output and inflation in the medium term. Equations of this form are a staple of macroeconomic modelling and appear, in some form, in all New-Keynesian models.

The standard forward-looking consumption IS relation is given by,

      (2.1)

Where       (2.2)

Equation 2.1 represents the baseline consumption Euler equation that arises from the representative household's optimisation problem. It has been log-linearised around its steady state so c_t represents the deviation of consumption from its steady-state growth path, is the expected deviation of consumption from its steady state, conditioned on information available at time t, r_t is the real interest rate gap and is an independent, identically-distributed consumption shock. The nominal interest rate and expected rate of inflation are given by i_t and respectively.

The consumption Euler equation simply states that, in equilibrium, the representative household is unable to increase its utility by shifting consumption between periods - that is, the marginal utility of consumption today is balanced with the discounted marginal utility of consumption tomorrow.

Such an equation implies the immediate adjustment of output as households update their expectations. In practice, consumption appears to react quite slowly to changes in interest rates, for example, and a number of studies attempt to explain this behaviour. One such endeavour is the habit formation model of Fuhrer (2000). Fuhrer postulates that the utility derived from consumption depends both on the absolute level of consumption and the level of current consumption relative to past consumption - that households do not like consuming less than they have been and initially resist changes, before eventually adjusting. This modification was shown to substantially improve the fit of the model.[4]

Other work, predominantly concerned with why the behaviour of consumption appears to invalidate the permanent income hypothesis, such as Muellbauer (1988), suggests that households may be myopic in their consumption choices. Campbell & Mankiw (1989) offer the hypothesis that households do not have the resources to engage in producing full forecasts and so it is optimal for them to use a rule of thumb when updating their consumption plans in response to income shocks.

That lagged output improves the fit with the data is important, but whether one accepts the habit formation story, the rule of thumb hypothesis or simply assumes that households are less forward-looking than is often suggested, is less important for the specification of the IS relation. In empirical work, an assumption of habit formation or myopia in household consumption choices is not uncommon and both Batini & Haldane (1999) and Smets & Wouters (2003) allow for it in their respective models of the UK and the euro area economies. Indeed, neither Carlin & Soskice (2010) nor Ryan & Szeto (2009) include expected output in their baseline IS relations for the UK and New Zealand respectively.

With this in mind, I introduce persistence to the output gap process by assuming a degree of external habit formation in consumption (given by α_c) - while acknowledging that the true source could be myopia, rule of thumb behaviour or a failure of rational expectations, resulting in an equation of the form,

     (2.3)

To capture the effect of discretionary fiscal policy on the economy I allow for the possibility of non-Ricardian behaviour, in a similar way to Ratto et al (2006). Ricardian behaviour states that, faced with a reduction in taxes, for example, households will tend to save the associated additional income since they know it heralds higher taxation or lower spending in the future. The effect on permanent incomes is zero and, therefore, so is the output response. In this model I allow for non-Ricardian behaviour by specifying the proportion of households who are affected by discretionary fiscal policy.

The consumption of Ricardian households does not respond to changes in public spending and taxation so changes in the fiscal balance do not feature in the consumption equation and this is given by the standard IS relation presented in 2.4, but Ricardian consumption is denoted by a superscript R.

      (2.4)

Non-Ricardian households spend all the additional income/reduce consumption by the full extent of the fiscal tightening and so the change in the fiscal stance is introduced to the consumption equation, where ƒ_t represents the fiscal impulse - a similar measure to the change in the cyclically-adjusted budget balance,[5]

     (2.5)

The proportion of non-Ricardian households is indexed by the parameter, α_NR, giving rise to the aggregate consumption equation

            (2.6)

Separating out the term capturing the change in the fiscal stance,

            (2.7)

and then aggregating the remaining Ricardian and Non-Ricardian terms gives:

      (2.8)

Based on its structural interpretation, the indexing coefficient, α_NR, should be bounded by 0 and unity. But there how much output changes in the short run for a given discretionary policy measure may depend on the precise policy package. There are several ways to bring about a structural adjustment in the public finances. These include revenue measures, such as consumption or income tax changes, and spending measures, such as changes in departmental expenditure or welfare policies. In practice, each of these measures is likely to be associated with a different multiplier, since they tend to affect different groups in society, for example. In this sense, households, in aggregate, might be less 'Ricardian’ in their response to some measures than to others.

A comprehensive analysis would estimate different α_NR parameters for different types of policy measure. This would not be practical here, since I focus only on New Zealand and the time series with which I am working are relatively short. There simply is not enough variation in the series to provide reliable estimates at a granular level. Instead, I focus on the overall (average) fiscal impact multiplier and use changes in the government's cyclically-adjusted budget balance to estimate its size. This is consistent with the estimated parameter relating to the direct effects of a fiscal policy package of average composition.

Furthermore, because the effects of fiscal policy on the net trade position are not explicitly articulated in the model, the effects of such 'leakages' are reflected in the estimate of the parameter α_NR. In what follows, I describe this coefficient as the degree of non-Ricardian behaviour but readers should be aware that, due to the reduced-form nature of the model, this parameter captures more than this structural parameter alone - another way to think of it may be as the direct fiscal impact multiplier, before any offset from monetary policy, for example.

In this model, the fiscal policy stance is determined exogenously and follows an autoregressive process,

[6]       (2.9)

To get from the consumption Euler equation to the IS equation I assume that the behaviour of the consumer can explain whole-economy behaviour. This is a common assumption in small models of the economy but is not completely satisfactory given, in particular, the contribution of business and inventory investment to the cyclical volatility of output.

Without deriving the behaviour of firms explicitly from microeconomic foundations here, it suffices to say that the change in output associated with firms' responses to changes in real interest rates is in the same direction as that implied by the response of households. Intuitively, if the real rate of interest falls, this lowers the cost of borrowing and increases the overall rate of return of an investment project. Therefore, any profit-maximising firm has a greater incentive to invest.[7]

There are a number of extensions to these simple theories, which highlight the role of uncertainty and irreversible costs in the investment decision - see Leahy & Whited (1995) and Pyndick & Solimano (1993), for example. Like habit formation in consumption, these extensions serve to increase the persistence of the model. While the these theories are not articulated within the modelling framework here, the cyclicality of business investment and its contribution to output volatility should already be captured by the reduced-form parameters of the IS relation.

Aggregating the consumption Euler equation to the whole economy level gives equation 2.10. In the spirit of Gali & Monacelli (2005), I also include a term for changes in the trade-weighted real effective exchange rate, which is intended to capture the effect on output of changes in relative prices which serve to shift the allocation of resources to and from the export-facing sector,

[8]       (2.10)

y_t is the output gap, is the expected output gap at time t and r _t-1 is the real interest rate gap, is the change in the lagged real expected exchange rate gap and is an independent and identically-distributed aggregate demand shock. I include four lags of the change in the real exchange rate to allow output to respond slowly to changes in relative prices.