4. Government Consumption

The data are taken from IMF, OECD, and Bundesbank statistics. Please see Appendix 4.6 for the documentation of the data. The numbers for the years 2016–2018 represent estimates. The statistics are loaded and graphed with the help of the Gauss program Ch4_data.g.

The spike in government spending in Germany during the period 1990–1996 was caused by German reunification and the higher public spending in East Germany.

In April 2015, the OECD invited Costa Rica and Lithuania to open formal OECD accession talks.

OECD average public and private pension spending amounted to 9.5%.

Please take care not to equate (private and public) health expenditures with health. For example, Italy spends only half as much on health as the United States; however, in 2014, the average life expectancy in Italy was approximately 4 years longer than in the US.

Again, take care to not equate higher education spending with better education. In their article on “The Economics of International Differences in Educational Achievement” in the Handbook of Economics of Education, Hanushek and Woessmann (2011) review the literature on the determinants of educational attainment. In particular, they find that input measures such as class size or educational expenditures show little impact, while several measures of institutional structures such as school autonomy, later tracking, and the quality of the teaching force explain a significant portion of the international differences in student achievements.

See also Footnote 6 in this section for an explanation of why years of schooling might represent a better measure of educational attainment.

NATO members such as Germany and Belgium agreed to spend 2% of GDP on defense. Evidently, many NATO countries interpret this official target as a guideline.

Please see Appendix 4.6 for a description of the data on government consumption. The source of the data on real GDP, private consumption, and labor supply which is used in the computation of the results displayed in Table 4.1 is presented in Appendix 2.​4.

The GAUSS computer program Ch4_data.g together with the data file Fred_data1a.txt that computes Figs. 4.7 and 4.8 is available as a download from my web page.

The HP Filter is described in Chap. 2 above. We use the parameter λ = 1600 for quarterly data.

See Brandner and Neusser (1992).

The observation that private consumption is more volatile than output does not hold for all subperiods. For example, Cooley and Prescott (1995) find that the relative volatility of personal consumption with respect to output is only 74% in the US during the period 1954–1991. In addition, these authors document that durable consumption expenditures are much more volatile than the consumption of non-durables and services. Similarly, Heer and Maußner (2009) present empirical evidence for West Germany prior to German reunification over the period 1975–1989, when consumption is only approximately half as volatile as output.

Compare this with Table 3 in Ambler and Paquet (1996). The time series are measured in logs and passed through the HP filter.

In most vector autoregression studies, the assumption that no innovation other than government spending shocks can affect government spending within a given quarter is used for identification.

On p. 2 and in Table 1 on p. 8, Murphy and Walsh (2016) summarizes the studies on the relationship between interest rates and government spending shocks.

This need not hold in all specifications of New Keynesian models. For example, Heer and Scharrer (2018) introduce a variable price of capital into these types of models, and consequently, real interest rates decline in response to higher unanticipated government consumption.

For this observation to hold, we need to assume that the change in government consumption is fully anticipated.

The special case of μ = 0 is considered by Baxter and King (1993) and Aiyagari, Christiano, and Eichenbaum (1994) and is often adapted in business cycle research.

Proportional income taxes will be introduced into the model in Chap. 5.

To derive the aggregate resource constraint (4.11), substitute (4.4), (4.8), (4.9), and (4.10) into (4.5).

Our notational convention in this book is that we use the variable x (X) as a subscript (superscript) of the parameter ρ, i.e. ρ _x (ρ ^X), in case of a utility parameter (autoregressive parameter or parameter of a policy rule). Accordingly, ρ _c denotes the substitution elasticity of private and public consumption, while ρ ^C denoted the autoregressive parameter of the technology shock in the consumption sector in Chap. 2.

Among others, the empirical estimates of the elasticities depend on the classification of the government expenditures, e.g., whether military spending is included.

In the Gauss computer program Ch4_subs_private_pub.g, the procedure steadystate1(.) is used in the non-linear equation problem solver to compute the solution to this problem.

The business cycle properties of the stochastic neoclassical model with government consumption will be studied subsequently. At this point, however, it may be instructive for the reader to see that one can show this result in the deterministic neoclassical growth model with the help of a simple solution technique. We will just use the non-linear equation solver that is applied abundantly in this book.

In addition to ϕ = 1, Aiyagari, Christiano, and Eichenbaum (1994) also assume that utility is additively logarithmic in total consumption and leisure.

You can also verify in the program Ch4_subs_private_pub_dyn.g that this results holds for other values of ρ _c ∈ [0,  1].

For example, Schmitt-Grohé and Uribe (2007) use ρ ^G = 0.87 and σ ^G = 0.016, while Christiano and Eichenbaum (1992) apply the estimates ρ ^G = 0.96 and σ ^G = 0.020.

Some studies prefer to display impulses responses for a shock of 1% rather than one standard deviation.

In each case where we changed the value of ϕ or/and ρ _c, we re-calibrated the parameter ι so that steady-state labor supply is equal to L = 0.30.

For our model and the calibration presented in Table 4.1, private consumption declines on impact for all ρ _c ≥ 0.67.

In Sect. 4.5, we also consider a standard New Keynesian model with frictions in the form of sticky prices and wages. Galí and Lopez-Salido (2007) show that this model is also able to replicate the empirical fact that private consumption rises in response to an unexpected increase in government consumption if one allows for the presence of rule-of-thumb consumers who do not save.

The Frisch labor supply elasticity is derived in Appendix 4.2.

Domeij and Floden (2006) argue that these estimates are biased downward due to the omission of borrowing constraints.

The only equilibrium conditions that change in (4.38) are (4.38a) and (4.38b), which are replaced by

You are asked to perform the numerical computation in Problem 4.3. The GAUSS program Ch4_RBC2.g that computes this problem can be downloaded from my homepage.

The magnitude and the sign of the impulse responses also depend on the functional form of utility. If we employ utility function (4.40) with η _L,w = 1.64 rather than Cobb-Douglas utility (4.28), private consumption also decreases in response to higher government consumption (not illustrated). As expected, the response of labor supply is much stronger than for the case with η _L,w = 0.30 and amounts to + 0.11%.

Even this statement is subject to restrictions. Preferences are not completely exogenous. For example, firms’ advertising is used to influence consumer preferences or political institutions may have an effect on cultural development and, therefore, our deep utility parameters. One of the first modern economist to point out the endogeneity of preferences was Carl Christian von Weizsäcker (see, e.g., von Weizsäcker (1971)).

The expression ‘limited participation,’ as introduced by Christiano, Eichenbaum, and Evans (1997), results from the constraints that agents face in the financial market. Households can only lend funds to the firms with the help of a financial intermediary at the beginning of the period. The central bank injects money into the banking sector after the households have deposited their money at the bank. Hence, households can no longer participate in the financial market, i.e., they have limited participation. At the end of the period, the financial intermediary retrieves the loans from the firms that need to pre-finance labor costs. The different ways to introduce a motive for money demand in general equilibrium models are reviewed in Walsh (2010), among others.

Both features help to increase the cost of intertemporal substitution of consumption for the household. As a consequence, the premium on risky assets increases, and the model is also in better accordance with asset price implications. See, for example, Jermann (1998) and Uhlig (2007).

To derive that 𝜖 _y is equal to the price elasticity, differentiate the demand equation (4.43) with respect to P _t(j).

We used the chain rule of differentiation and the Leibniz integral rule as presented in Footnote 42 of Chap. 2.

In Problem 4.6, you are asked to study the case in which the price P _Nt increases by the average inflation π rather than by the inflation in the last period. Also note that the inflation rate amounts to π − 1, while π denotes the inflation factor.

Heer and Maußner (2009) show that the (stock market) value of the firm at the beginning of period t + 1 is equal to the value of the capital at the end of period t (=beginning of period t + 1), \(V^{cd}_t= q_t K_{t+1}\). Accordingly, q _t describes the (market) value of the firm relative to the replacement cost of capital and, therefore, amounts to the definition of Tobin’s q.

The structure of the model seems to be very complicated. We distinguish three production sectors (final goods, wholesale, intermediate goods) and one employment agency. If you consider the alternative case where we only postulate one production sector without an employment agency, the benefits of this fragmentation of services in the production sector are evident. If we had only one production sector that is characterized by monopolistic competition and heterogeneous firms, each firm’s labor demand and price-setting behavior would depend on its marginal costs and, hence, its capital stock. As a consequence, we would not be able to derive simple index functions in the form of (4.45) and (4.59) for the aggregate price and aggregate wage. Instead, these aggregate prices would depend on the distribution of capital in the production sector.

This specification was introduced by Constandinides (1990). As an alternative, Abel (1990) uses the ratio of consumption and habits, \(C_t/\bar C_t\), in the utility function.

The results are not sensitive to this assumption.

An inflation reaction coefficient in excess of unity prevents self-fulfilling expectations with respect to the path of inflation. See, for example, Bullard and Mitra (2002). The intuition for this behavior is quite simple. Assume that aggregate demand and prices increase and that the other reaction coefficients are equal to zero, θ ^R = θ ^Y = 0. If the reaction coefficient θ ^π were less than one, nominal interest rates would rise less than prices so that the real interest rate would decline. As a consequence, aggregate demand would increase further and inflation went up even more. The monetary policy clearly would become unstable. While we exclude this kind of behavior in our model, we, however, refrain from imposing a lower zero bound on the net nominal interest rate Q _t − 1, as it rarely becomes binding in our simulations.

See Fig. 2.​15 and Eq. (2.​59) in Appendix 2.​1.

The reader is invited to experiment with the values of the parameters {φ _y, φ _w, 𝜖 _y, 𝜖 _w, ζ, χ} in the GAUSS program Ch4_newkeynesian.g in order to study the sensitivity of the labor impulse responses.

Farhi and Werning (2016) demonstrate in a standard New Keynesian model that the multiplier increases and exceeds unity in case of a liquidity trap (in which interest rates hit zero). Extending their model to the open economy, these authors find that the fiscal multiplier is smaller and below one for a country in a currency union. Erceg and Linde (2012) find that the fiscal multiplier is below one in an economy with fixed-exchange rates and, in accordance with the Mundell-Flemming model, above the one with flexible exchange rates. They show that their latter result is sensitive with respect to the slope of the Phillips curve and the presence of a persistent liquidity trap.

Of course, the response of hours depend on our assumption that taxes are lump-sum rather than proportional to wage income.

Linnemann and Schabert (2003) show analytically how the central bank’s rule affects the consequences of higher government consumption for labor, output, and prices. In response to higher (government) demand, labor demand increases, while the wealth effect drives up labor supply. The strength of the demand effect depends on the response of the real interest rate, which is governed by the monetary policy rule. When the rise in the real interest rate is dampened by an interest rate rule (as in our case), output and inflation can increase. They also show that, if the central bank follows a simple money-growth rule, fiscal expansions could be both deflationary and contractionary.

Ni (1995) provides empirical evidence that the estimates of the coefficient of public consumption in utility, (1 − ϕ)∕ϕ, are of small magnitude, with their signs depending on the measure of interest rates. If he uses net-of tax real taxes in his GMM estimation, he finds a negative coefficient, which corresponds to ϕ > 1 above.

Heer and Scharrer (2018) present a model that is in accordance with all the empirical impulse responses of output, labor, demand components, and factor prices. For this reason, they introduce both rule-of-thumb consumers and a variable price of capital in terms of the consumption goods into an otherwise standard New Keynesian model.

Nekarda and Ramey (2013) present evidence that the price-cost markup is procyclical or at best acyclical, which causes problems for standard New Keynesian models.

Since we simulate time series of output with the help of a random number generator for the three shocks 𝜖 ^Z, 𝜖 ^G, and 𝜖 ^Q, the results do not lie exactly on the curves displayed in Fig. 4.22. To smooth the curve, we fitted a polynomial of order two to the data points using a simply OLS regression. The estimation is contained in the GAUSS program Ch4_new_keynes_stabil.g.

At this point, we refrain from deriving the optimal fiscal policy because it would take us too far into the field of numerical methods. Using perturbation methods of higher order, Schmitt-Grohé and Uribe (2007) derive optimal monetary and fiscal policy rules. For the fiscal policy rule, they consider a tax rule that sets total taxes as a function of government liabilities and the fiscal deficit. They find that whether the fiscal policy rule is active or passive does not significantly affect welfare.

As another sensitivity analysis, we considered the case with ϕ = 1.0, such that public consumption does not affect household utility. In this case, the output-volatility-minimizing fiscal policy is specified with ρ ^Y = −1.3.

Our microfounded model has the benefit that we can quantitatively compare the welfare of different stabilization policies. In the present model, the equilibrium is not Pareto-efficient because various welfare distortions are present. First, firms in the wholesale sector operate as monopolistic competitors. Second, there is both price and wage dispersion.

We will introduce income taxes and debt in the upcoming Chaps. 5 and 7, respectively.

See, for example, Chapter 2 in Barro and Sala-i-Martin (2003) for a derivation of the transition dynamics in the continuous-time neoclassical growth model and, in particular, Section 2.6.6 for the speed of convergence.

You will be asked to compute the solution in Problem 4.1.

Appendices 4.​3 and 4.​4 were afforded in large parts by Alfred Maußner and are based upon the exposition in Heer, Maußner, and Ruf (2017). A more detailed description of the derivation of the microfoundations of Calvo price staggering can be found in Maußner (2000). I would like to thank Alfred for his thoughtful comments and support that have greatly helped to improve the presentation of the material in this chapter. All remaining errors are mine.