KIS-CES: Keynesian Synthesis with CES

• KIS-CES is a macroeconomic framework that integrates New Keynesian intertemporal optimization with Post-Keynesian behavioral and distributional mechanisms.
• It replaces the Cobb–Douglas function with a CES production function, making factor shares endogenous and highlighting public investment's role in crowding in private capital.
• The model features heterogeneous households with state-dependent MPCs, linking fiscal transmission and monetary constraints, particularly at the zero lower bound.

Searching arXiv for the cited KIS-CES macroeconomics paper and a closely related application paper. Searching arXiv for ([2508.00224](/papers/2508.00224)). The Keynesian Intertemporal Synthesis with CES production, usually abbreviated KIS-CES, is a macroeconomic framework designed to reconcile the empirical strengths of the Post-Keynesian and New Keynesian traditions. It retains the intertemporal, microfounded structure of New Keynesian models—optimizing agents, Euler equations, and a Taylor rule—while embedding the behavioral, distributional, and demand-driven mechanisms emphasized by Post-Keynesian macroeconomics, including heterogeneous marginal propensities to consume, financial stress, endogenous income distribution, and crowding-in from public investment. Its central innovation is the replacement of the Cobb–Douglas production function with a Constant Elasticity of Substitution specification calibrated to meta-analytic evidence rejecting unit elasticity of substitution, so that household heterogeneity, wealth/debt behavior, explicit public capital, and a monetary policy constrained by the zero lower bound are integrated into a single empirically disciplined synthesis (Salguero, 1 Aug 2025).

1. Conceptual synthesis and empirical discipline

KIS-CES is explicitly positioned as a framework meant to do two things at once. First, it preserves the intertemporal architecture associated with New Keynesian macroeconomics. Second, it incorporates the behavioral and distributional mechanisms emphasized by Post-Keynesian analysis. In the model’s own positioning, this means combining optimizing agents, Euler equations, and a Taylor rule with heterogeneous MPC, financial stress, income distribution, and crowding-in from public investment (Salguero, 1 Aug 2025).

Its empirical discipline is organized around a set of meta-analytic findings treated as calibration targets. These include the rejection of Cobb–Douglas production through evidence that the elasticity of substitution between capital and labor satisfies $\sigma_{\text{prod}}<1$; higher fiscal multipliers in recessions and at the zero lower bound; an output elasticity of public capital of approximately $0.1$; a hierarchy in which spending multipliers, and especially public-investment multipliers, exceed those of taxes and transfers; and aggregate evidence inconsistent with full Ricardian neutrality. The model therefore defines itself not as a purely normative microfounded construction, but as an NK-style intertemporal model with PK-style heterogeneity, wealth/debt behavior, non-unit production elasticities, and explicit public capital calibrated to match meta-analytical stylized facts about fiscal policy (Salguero, 1 Aug 2025).

This positioning matters analytically because the model treats fiscal transmission, income distribution, and productive public expenditure as jointly determined. A plausible implication is that the KIS-CES framework is best understood not as a marginal modification of a standard DSGE model, but as a re-specification of the macroeconomic core around empirically constrained structural parameters.

2. CES production, public capital, and endogenous factor shares

On the production side, aggregate output is generated by private capital $K_t$, labor $L_t$, and public capital $K_t^P$ through a three-factor CES technology,

$$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$

with $\alpha_K,\alpha_L,\alpha_P>0$, $\alpha_K+\alpha_L+\alpha_P=1$, and

$$\rho = \frac{\sigma_{\text{prod}}-1}{\sigma_{\text{prod}}}, \qquad \sigma_{\text{prod}} = \frac{1}{1-\rho}.$$

Because the calibration targets imply $0<\sigma_{\text{prod}}<1$, the model operates with $0.1$0, so private capital, labor, and public capital are treated as gross complements rather than as Cobb–Douglas inputs (Salguero, 1 Aug 2025).

The representative firm solves a standard profit-maximization problem over private capital and labor. Factor prices equal marginal products, but the crucial departure from Cobb–Douglas lies in factor shares. Labor’s share is

$0.1$1

Under Cobb–Douglas, $0.1$2 is constant. Under KIS-CES, with $0.1$3, factor shares depend on relative factor quantities and productivity, so the functional distribution of income becomes endogenous (Salguero, 1 Aug 2025).

The same CES structure makes public capital central to macro transmission. Since

$0.1$4

public capital raises the marginal product of private capital, and by the same logic also raises the marginal product of labor. The model therefore treats public investment not only as a demand impulse but also as a factor that disproportionately enhances the productivity of private inputs when $0.1$5. This complementarity is the formal basis for crowding-in of private investment and for larger public-investment multipliers than public-consumption multipliers (Salguero, 1 Aug 2025).

A central consequence is distributional. Because factor shares are endogenous, shocks to public capital and productivity can alter labor and capital shares, and these changes feed back into aggregate demand once heterogeneous MPC are introduced. This is one of the model’s defining bridges between production structure and demand determination.

3. Households, non-standard preferences, and endogenous MPC

The household sector is a continuum split into Liquidity-Constrained (LC) households with population share $0.1$6 and Wealth-Accumulating (WA) households with share $0.1$7. LC households consume current disposable income period by period,

$0.1$8

so their MPC is fixed at one. This is presented as a structural way of breaking Ricardian equivalence and matching micro evidence of high MPC among constrained or hand-to-mouth households (Salguero, 1 Aug 2025).

WA households solve an intertemporal optimization problem with non-standard preferences:

$0.1$9

where

$K_t$0

subject to

$K_t$1

The distinctive element is that wealth enters utility directly. In the model’s interpretation, this means the household values wealth and penalizes debt, thereby generating precautionary and balance-sheet motives consistent with PK and behavioral insights (Salguero, 1 Aug 2025).

The first-order conditions imply a modified Euler equation,

$K_t$2

Relative to a standard Euler equation, the additional wealth term dampens the pure intertemporal substitution response to interest rates, steepens the IS curve, and makes monetary policy less dominant (Salguero, 1 Aug 2025).

For a temporary unexpected income shock, the model derives an endogenous MPC for WA households,

$K_t$3

which satisfies $K_t$4 and rises in stressed states with low wealth and low income. Aggregate consumption is

$K_t$5

so the aggregate MPC is

$K_t$6

Because $K_t$7 depends on wealth, income, and the interest rate, aggregate MPC becomes state-dependent. In recessions, WA wealth falls and LC households become a larger share of effective demand, so aggregate MPC rises and fiscal multipliers increase (Salguero, 1 Aug 2025).

4. Fiscal instruments, public capital accumulation, and multiplier structure

Fiscal policy is decomposed into public consumption $K_t$8, public investment $K_t$9, transfers $L_t$0, taxes $L_t$1, and debt $L_t$2. Total government spending satisfies

$L_t$3

public capital accumulates according to

$L_t$4

and the government budget constraint is

$L_t$5

Within this structure, public consumption is a pure demand instrument, while public investment is both a demand instrument and a supply instrument because it augments productive public capital (Salguero, 1 Aug 2025).

The output elasticity of public capital is

$L_t$6

Calibration targets $L_t$7, following Bom and Ligthart’s meta-analysis. The stated purpose of this calibration is to make public investment mildly but clearly productive: not a source of implausibly large infrastructure effects, but definitely non-zero (Salguero, 1 Aug 2025).

The multiplier algebra follows from the national-income identity

$L_t$8

with private investment approximated as

$L_t$9

Under accommodative monetary policy, the model gives the approximate short-run multipliers

$K_t^P$0

Since $K_t^P$1 and complementarity strengthens crowding-in, the model implies

$K_t^P$2

This is the theoretical counterpart of the empirical hierarchy in which public investment dominates public consumption, and both dominate transfers or tax cuts (Salguero, 1 Aug 2025).

The fiscal transmission mechanism is therefore dual. Public consumption works through demand, heterogeneous MPC, investment feedback, and monetary offset. Public investment works through the same channels and also through public-capital accumulation, higher marginal products of private inputs, and a structurally stronger private-investment response. A common misconception is to treat all spending components as equivalent once their budgetary cost is fixed. The KIS-CES formulation rejects that equivalence at the structural level.

5. Monetary policy, the zero lower bound, and crisis nonlinearity

Monetary policy follows a Taylor rule with an explicit zero lower bound,

$K_t^P$3

and the real rate satisfies the Fisher relation

$K_t^P$4

In normal times, the central bank offsets fiscal expansions by raising nominal rates when output or inflation exceed target. At the zero lower bound, $K_t^P$5, so the central bank cannot offset fiscal shocks in the usual way and the real rate is pinned mainly by inflation expectations (Salguero, 1 Aug 2025).

In KIS-CES, the ZLB does not merely amplify a standard New Keynesian mechanism. It interacts with the model’s state-dependent MPC, low-wealth balance-sheet effects, and CES complementarity. As fiscal expansion raises output and inflation, expected inflation can reduce the real rate, which relaxes intertemporal constraints and encourages consumption and investment. Because recessions are also states in which WA wealth is lower and aggregate MPC is higher, the ZLB enters a broader nonlinear propagation system rather than a single-channel IS effect (Salguero, 1 Aug 2025).

The paper therefore characterizes multipliers as nonlinear and state-dependent for three reasons: aggregate MPC rises in recessions; monetary-policy reaction weakens at the ZLB; and the private-investment response can increase when the economy is far below capacity and public capital raises profitability. In normal times, multipliers are described as near, but often below or around, $K_t^P$6. In deep recessions and at the ZLB, they can increase dramatically. Lower values of $K_t^P$7 intensify this outcome by strengthening complementarity, making the public-investment channel especially powerful (Salguero, 1 Aug 2025).

These crisis properties also have a distributional dimension. Because CES production makes factor shares endogenous, public investment can alter wage and profit shares; because households have heterogeneous MPC, those distributional changes feed back into aggregate demand. The model thus links crisis nonlinearity, productive public expenditure, and functional income distribution within a single transmission mechanism.

6. Calibration, quantitative exercises, and applied extensions

The paper reports a representative crisis calibration consistent with its meta-analytic targets. Illustrative values include $K_t^P$8, $K_t^P$9, $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$0, and $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$1. Additional crisis-exercise parameters include a devaluation elasticity of net exports of $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$2 and a debt effect on demand of $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$3, described as mild but non-neutral and consistent with partial but not full Ricardian behavior. Under this calibration, a budget-neutral switch from $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$4 of GDP in $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$5 to $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$6 of GDP in $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$7 yields an output increase of roughly $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$8 of GDP in the short run, driven by composition effects rather than by a larger aggregate fiscal stance (Salguero, 1 Aug 2025).

These numerical exercises are used to support three claims internal to the framework: multipliers around $$Y_t^{\text{agg}} = Z_t \Big[ \alpha_K K_t^{\rho} + \alpha_L L_t^{\rho} + \alpha_P (K_t^P)^{\rho} \Big]^{1/\rho},$$9 in normal times; very high multipliers in crises, especially with ZLB and slack; and a structural gap between public-investment and public-consumption multipliers. The model interprets these outcomes as the joint result of high MPC among LC and lower-wealth WA households, complementarity between public and private capital, non-Ricardian debt effects, and moderated monetary offset in crisis conditions (Salguero, 1 Aug 2025).

A later application appears in the “Crisis Simulator for Bolivia (KISr-p),” a quarterly stochastic model that adopts the theoretical architecture of a Keynesian Intertemporal Synthesis with a Constant Elasticity of Substitution production function. In that report, actual output is demand-determined in the short run, while potential output evolves according to an underlying CES technology in which public capital is a complementary factor and the elasticity of substitution is empirically set below one. The production block is written in reduced form rather than as the full multi-factor system, but the report identifies the KIS-CES structure as the backbone of the real block and uses regime-specific fiscal multipliers, public-capital accumulation, inequality effects, and nonlinear debt and risk dynamics to study policy trade-offs in Bolivia (Salguero, 18 Oct 2025).

This extension suggests that KIS-CES can function both as a full structural model and as a background architecture for applied country simulators. The Bolivia application does not print the full CES aggregator but treats the reduced-form potential-output block as operationalizing the same complementarity-based logic.

7. Comparative interpretation and terminological scope

Relative to standard New Keynesian DSGE models, KIS-CES retains intertemporal optimization and a Taylor rule but differs by using explicit LC versus WA heterogeneity, wealth in utility, endogenous MPC, CES production with endogenous factor shares, and a stronger role for productive public investment. Relative to traditional Post-Keynesian models, it embeds effective-demand, distributional, and financial-stress mechanisms inside a fully dynamic intertemporal structure. The model’s stated ambition is therefore neither a return to representative-agent NK nor a rejection of formal intertemporal analysis, but a bridge between NK rigor and PK realism built around empirically constrained fiscal transmission (Salguero, 1 Aug 2025).

Its policy implications follow directly from that structure. Composition matters more than size because a budget-neutral reallocation toward public investment can be expansionary. Public investment dominates public consumption because it raises demand, is productive, and crowds in private capital when $\alpha_K,\alpha_L,\alpha_P>0$0. Aggressive fiscal expansion is most warranted in deep recessions and at the ZLB, while monetary policy is important but not omnipotent because heterogeneity and wealth-in-utility flatten the response of households to interest rates. Debt is not Ricardian, but its demand effects are moderate rather than fully offsetting (Salguero, 1 Aug 2025).

The term KIS-CES is, however, not unique to macroeconomics. In a separate and unrelated literature on dye aggregates, applications of the coherent exciton scattering approximation are also referred to as a KIS-CES model in the sense of using the monomer spectrum as a kernel to generate aggregate spectra. That usage concerns excitonic spectroscopy and the aggregate Green’s function generated from a monomer spectrum, not fiscal macroeconomics, and should not be conflated with the Keynesian Intertemporal Synthesis with CES production (Roden et al., 2010).