2. Related literature

The relationship between population dynamics, land scarcity, and economic performance has a long intellectual lineage that traces back to the classical political economists. Malthus (Reference Malthus1798) famously argued that population growth tends to outpace food production because land is fixed, generating diminishing returns that depress per-capita income. In this classical Malthusian world, living standards stagnate because demographic pressures repeatedly collide with resource constraints. Although technological change and demographic transitions eventually relaxed these constraints in many countries, recent work suggests that land scarcity continues to shape development outcomes, particularly in economies where agriculture remains dominant or structural transformation is slow.

Modern growth theory has revisited these classical ideas through several channels. A first strand highlights the macroeconomic consequences of land as a fixed factor of production. Hansen and Prescott (Reference Hansen and Prescott2002) incorporate land into a two-sector model to explain the transition from Malthusian stagnation to modern growth, showing that technological progress and structural transformation jointly determine when economies escape resource-driven stagnation. Restuccia et al. (Reference Restuccia, Yang and Zhu2008) emphasize the role of agricultural productivity and land constraints in explaining cross-country income differences. Similarly, Vollrath (Reference Vollrath2011) shows that land scarcity affects the size of the agricultural sector and thereby shapes economy-wide productivity. These models underline that land plays a quantitatively important role as long as a significant share of labor remains in agriculture; only once labor reallocates toward land-free industries does land scarcity cease to bind.

A second strand of literature focuses more directly on the interaction between population growth and land intensity. Karras (Reference Karras2010) provides a particularly relevant benchmark for the present paper. Using a Solow model with land, he shows that the effect of population growth on output depends critically on the economy’s effective land intensity—defined by the land share in production and the share of agriculture in aggregate output. Empirically, he finds stronger negative effects of population growth on growth in countries with larger agricultural sectors. This paper builds on his insight but departs from it in two key dimensions: (i) effective land intensity is endogenized through a two-sector structure rather than treated as fixed, and (ii) migration is introduced as an explicit demographic adjustment margin.

A related set of studies examines the role of technological progress in relaxing Malthusian constraints. Kremer (Reference Kremer1993) links population size to technological change, arguing that larger populations generate more ideas and thus faster innovation. Ashraf and Galor (Reference Ashraf and Galor2011) similarly emphasize feedback between population density, technological progress, and long-run development. Yet while larger populations may foster innovation, they also increase pressure on fixed land resources. Land-saving technological change—through improved crop varieties, fertilizers, irrigation, and mechanization—plays a crucial role in determining whether population growth is ultimately beneficial or harmful. Empirical studies show that Green Revolution technologies significantly raised agricultural yields, effectively reducing land scarcity in many developing economies. The present paper incorporates this channel by examining how cereal yield growth and related proxies for land-augmenting innovation modify the population–growth relationship.

A third literature examines the macroeconomic impact of migration. Migration has long been viewed as a mechanism that reallocates labor from low-productivity to high-productivity regions, mitigates local resource constraints, and smooths demographic shocks. Clemens (Reference Clemens2011) outlines the potential gains from labor mobility, emphasizing that migration can sharply increase productivity by moving workers away from constrained environments. Ortega and Peri (Reference Ortega and Peri2013) show that migration responds strongly to economic differentials across countries, including differences driven by demographic pressure and resource scarcity. In the context of global demographic imbalances, migration acts as a vent that reduces congestion in densely populated or land-scarce economies. Despite this, relatively few studies integrate migration into growth models that incorporate land as a fixed factor. The present paper contributes to this gap by modeling migration as an endogenous response to local land scarcity and showing how this channel mediates the impact of population growth on income dynamics. In doing so, it links demographic adjustment directly to the effective land intensity mechanism emphasized in the theoretical framework.

A fourth and increasingly influential strand concerns structural transformation—the reallocation of labor and output from agriculture to manufacturing and services. Herrendorf et al. (Reference Herrendorf, Rogerson, Valentinyi, Herrendorf, Rogerson and Valentinyi2014) document the universal nature of this process and emphasize its implications for aggregate productivity. Duarte and Restuccia (Reference Duarte and Restuccia2010) show that structural transformation explains a substantial portion of cross-country income differences. McMillan and Rodrik (Reference McMillan, Rodrik, McMillan and Rodrik2011) highlight how sectoral labor shifts contribute to growth in developing countries. Since agriculture is the only sector that uses land as a factor of production, the pace of structural transformation directly affects an economy’s effective land intensity. As countries industrialize, the land constraint weakens endogenously. This paper formalizes this link by allowing effective land intensity to evolve with structural transformation rather than treating it as a fixed parameter. The paper explicitly incorporates this mechanism: the agricultural share determines how strongly population growth affects output, and empirical results show that the demographic penalty is far larger in agriculture-intensive economies.

Finally, empirical work on population and growth has produced mixed results, reflecting underlying heterogeneity across countries. Some studies find that population growth hampers growth by diluting capital or straining resources, particularly in low-income or land-scarce settings. Others find neutral or positive effects when economies are structurally diversified or when labor markets are flexible. Kelley and Schmidt (Reference Kelley and Schmidt2005), Bloom and Canning (Reference Bloom and Canning2003), and others highlight that demographic effects depend on age structure, human capital, and economic context. The ambiguous findings point to the need for frameworks that incorporate structural and resource-based heterogeneity—precisely the gap addressed by this paper.

In sum, this paper contributes to four strands of research: (i) growth models with land and resource constraints; (ii) empirical studies on population growth and economic performance; (iii) migration as a demographic adjustment mechanism; and (iv) structural transformation and the decline of land dependence. By jointly endogenizing effective land intensity and incorporating migration as a response to land scarcity, the paper provides new evidence that population growth is growth-reducing mainly in economies where land constraints bind and structural transformation is incomplete, while migration and land-saving innovation help mitigate these pressures. This approach generates a richer and more nuanced understanding of demographic dynamics in the global economy.

3. Theoretical framework

This section develops a two-sector growth model in which land is a fixed factor used exclusively in agriculture, while the non-agricultural sector relies solely on reproducible inputs. This structure embeds a modern Malthusian mechanism directly into the Solow framework: population growth increases pressure on land only insofar as labor remains allocated to agriculture. As economies undergo structural transformation and the agricultural share declines, the relevance of the land constraint diminishes, and the adverse demographic effect weakens.

Building on Karras (Reference Karras2010), who shows that population growth lowers per-capita income growth in proportion to an economy’s effective land intensity—defined as the product of the land share in production and the agricultural share of GDP—this paper extends that insight by demonstrating that demographic expansion is not universally harmful; instead, its effect varies systematically with the importance of land in aggregate production. The present framework builds directly on this insight but introduces two refinements that sharpen its theoretical and empirical implications. First, rather than treating effective land intensity as a fixed structural parameter, we explicitly derive it from a two-sector economy in which only agriculture uses land. This makes land intensity endogenous to the pace of structural transformation, so that the strength of demographic effects evolves with development. Second, the model introduces migration as an endogenous response to demographic pressure, allowing population growth to trigger labor reallocation both across sectors and across locations. This additional adjustment margin is absent in Karras (Reference Karras2010) and implies that demographic pressure can be partially offset through labor mobility. It is also empirically relevant in many developing economies where net migration responds strongly to land scarcity, wage gaps, and rural–urban congestion.

Agricultural and non-agricultural output are produced according to

(1) \begin{align} Y_{A} &=A_{A}{K}_{A}^{\alpha }{L}_{A}^{1-\alpha -\theta }T^{\theta } \\[-10pt] \nonumber \end{align}

(2) \begin{align} Y_{N} &=A_{N}{K}_{N}^{\beta }{L}_{N}^{1-\beta } \\[10pt] \nonumber \end{align}

where $Y_{A}$ and $Y_{N}$ denote agricultural and non-agricultural output, $A_{A}$ and $A_{N}$ are sector-specific productivity levels, $K_{i}$ and $L_{i}$ denote capital and labor in sector $i\in \{A,N\}$ , and $T$ is a fixed land endowment. Parameters satisfy $\alpha ,\beta \in (0,1)$ , $\theta \in (0,1)$ , and $\alpha +\theta \lt 1$ , ensuring diminishing returns to reproducible factors. Land enters only agricultural production, capturing the idea that congestion arises through the land–labor ratio in that sector.

Labor satisfies $L=L_{A}+L_{N}$ , and the stock of land $T$ is fixed. Aggregate output is a CES composite of the two sectors:

(3) \begin{equation} \begin{array}{l} \begin{array}{llll} & Y=\left[\mu {Y}_{A}^{\rho }+(1-\mu ){Y}_{N}^{\rho }\right]^{1/\rho } \end{array} \end{array} \end{equation}

where $\mu \in (0,1)$ denotes the agricultural share in output and $\rho \leq 1$ governs the elasticity of substitution across sectors. The parameter $\mu$ captures the economy’s structural composition and declines with development as labor and production shift toward non-agriculture. This formulation implies that the macroeconomic relevance of land depends not only on its technological role in agriculture but also on the size of the agricultural sector itself.

The degree to which land matters for aggregate production is therefore summarized by

(4) \begin{equation} \begin{array}{l} \begin{array}{llll} & \phi \equiv \mu \theta\end{array} \end{array} \end{equation}

where $\phi$ denotes effective land intensity. Unlike in George Karras (Reference Karras2010), where this parameter is treated as fixed, here it varies endogenously with structural transformation through $\mu$ . As economies develop and agriculture shrinks, $\phi$ declines, weakening the land constraint over time.

Capital accumulates according to

(5) \begin{equation} \begin{array}{l} \begin{array}{llll} & \dot{K}=sY-\delta K \end{array} \end{array} \end{equation}

and population evolves according to

(6) \begin{equation} \begin{array}{l} \begin{array}{llll} & \frac{\dot{L}}{L}=n+m \end{array} \end{array} \end{equation}

where $s$ is the savings rate, $\delta$ the depreciation rate, $n$ the natural population growth rate, and $m$ the net migration rate. The inclusion of $m$ allows population dynamics to respond endogenously to economic conditions, in contrast to standard Solow frameworks.

To characterize the effect of demographic expansion, consider a first-order log-linear approximation of aggregate output around a balanced growth path. Using the fact that only agriculture depends on land, and aggregating across sectors, per-capita output growth can be expressed as

(7) \begin{equation} \begin{array}{l} \begin{array}{llll} & g_{y}=g_{A}+(1-\phi )g_{k}-\phi (n+m) \end{array} \end{array} \end{equation}

where $g_{y}\equiv \dot{y}/y$ is per-capita output growth, $g_{A}$ is aggregate productivity growth, and $g_{k}$ captures capital deepening. The term $-\phi (n+m)$ represents the land congestion effect: an increase in labor reduces output per worker in proportion to the economy’s effective land intensity. This provides a direct macroeconomic channel through which population growth affects income dynamics.

This expression implies the reduced-form relationship

(8) \begin{equation} \begin{array}{l} \begin{array}{llll} & g_{y}=\gamma -\beta \phi (n+m) \end{array} \end{array} \end{equation}

where $\gamma \equiv g_{A}+(1-\phi )g_{k}$ collects growth components unrelated to demographics, and $\beta \gt 0$ is a constant parameter scaling the effect of effective land intensity. The demographic drag is therefore proportional to $\phi$ , so that its magnitude increases with effective land intensity, reflecting the role of land in amplifying congestion effects. This reproduces the central insight of Karras (Reference Karras2010), but here $\phi$ evolves endogenously rather than being fixed.

An important departure from Karras (Reference Karras2010) is the explicit modeling of migration as a demographic adjustment mechanism. Population growth reduces the land–labor ratio in agriculture, lowering marginal productivity and wages in that sector relative to non-agriculture or foreign labor markets. These differentials generate incentives for labor reallocation across sectors and locations.

The resulting migration response is captured in reduced form as

(9) \begin{equation} \begin{array}{l} \begin{array}{llll} & m=-\eta \phi n \end{array} \end{array} \end{equation}

where $\eta \gt 0$ measures the responsiveness of migration to land-induced demographic pressure. The negative sign reflects that higher population growth in land-constrained economies leads to net outflows. This specification should be interpreted as a reduced-form representation of standard arbitrage mechanisms rather than a fully microfounded migration model.

Substituting (9) into (8) yields

(10) \begin{equation} \begin{array}{l} \begin{array}{llll} & g_{y}=\gamma -\beta \phi \,n(1-\eta \phi )\end{array} \end{array} \end{equation}

This expression makes clear that the effective demographic burden depends not only on population growth $n$ , but also on the interaction between land intensity $\phi$ and migration responsiveness $\eta$ . When $\eta$ is large, migration absorbs part of the population increase, reducing the impact of land congestion on per-capita output. Migration therefore acts as a “safety valve,” reallocating labor away from land-intensive production and dampening the adverse growth effects of demographic expansion.

The framework also allows for land-saving technological change. Let effective land evolve as

(11) \begin{equation}T_{e}=Te^{\psi t}\end{equation}

where $\psi \gt 0$ is the rate of land-augmenting technological progress. This raises the productivity of the fixed land stock and reduces effective scarcity over time.

This implies a time-varying effective land intensity

(12) \begin{equation} \begin{array}{l} \begin{array}{llll} & \phi _{t}=\mu \theta e^{-\psi t}\end{array} \end{array} \end{equation}

and the growth equation becomes

(13) \begin{equation} \begin{array}{l} \begin{array}{llll} & g_{y}=\gamma -\beta \phi _{t}(n+m) \end{array} \end{array} \end{equation}

Thus, technological progress provides an additional mechanism mitigating the impact of population growth by lowering the effective importance of land in production.

Where Karras (Reference Karras2010) emphasizes cross-country differences in $\phi$ , this formulation highlights that $\phi$ evolves endogenously over time and across countries through structural transformation and technological progress, while migration provides an additional mechanism dampening demographic pressure. Equations (10)–(13) jointly imply that the growth effect of population dynamics depends jointly on effective land intensity, migration responsiveness, and land-augmenting technological change. Overall, the model delivers four testable predictions that generalize and extend the insight of Karras (Reference Karras2010):

1. (H1) Land intensity. Population growth is more harmful for per-capita income growth where effective land intensity $\phi$ is high. Empirically, this implies a negative interaction between population growth and agricultural dependence.

2. (H2) Land abundance. Greater land availability per worker mitigates the adverse impact of population growth by reducing effective congestion. This implies a positive interaction between population growth and arable land per capita.

3. (H3) Land-saving technology. Land-augmenting technological progress (higher $\psi$ ) weakens the congestion effect generated by demographic expansion. This implies a positive interaction between population growth and the land-technology index.

4. (H4) Migration adjustment. Migration operates as an adjustment margin to land scarcity. A higher responsiveness of migration ( $\eta$ ) reduces the effective demographic burden, although net emigration may lower short-run output by shrinking the labor force, particularly in agriculture-dependent economies. This implies that the interaction between migration and agricultural dependence is negative.

These predictions follow directly from the reduced-form growth equation (13) and map into the interaction terms of the empirical specification, providing clear sign restrictions that guide the interpretation of the regression results in Section 5.

4. Data and empirical specification

To examine the mechanisms outlined in the theoretical framework, we combine a broad set of macroeconomic and structural indicators in an unbalanced panel of 152 countries covering 1960–2023. The long time span and large cross-sectional variation allow the analysis to capture differential demographic and structural conditions across countries and stages of development. The dependent variable is real GDP per capita growth, computed as the annual log-difference of real GDP per capita from the Penn World Table (PWT 11). The PWT provides purchasing-power–adjusted income measures that ensure comparability across space and time, and its long horizon is well suited to studying slow-moving demographic and structural processes.

Natural population growth is constructed from World Development Indicators (WDI) data as the difference between the total population growth rate and the net migration rate. This measure captures the demographic component that increases the labor force independently of cross-border population movements. Net migration is taken from the WDI and reflects cross-border population movements driven by economic incentives, wages, labor demand, and demographic pressure. Although migration data are often measured with error, the WDI series is widely used in cross-country macroeconomic studies and provides consistent annual estimates for a large set of economies. In the context of this paper, natural population growth and net migration play distinct conceptual roles consistent with the theoretical model: the former increases the domestic labor force mechanically, while the latter represents a behavioral adjustment that can alleviate or amplify demographic pressures.

To operationalize the “effective land intensity” mechanism, we employ several WDI variables. Agriculture’s share in GDP proxies the structural composition parameter $\mu$ in the model and measures the extent to which aggregate production depends on land-intensive activities. Arable land per capita captures the physical scarcity of land relative to population size, which influences the degree to which demographic expansion increases congestion. Cereal yields, measured as kilograms per hectare, serve as a proxy for land-saving technological progress—the $\psi$ term in the theoretical framework—and help assess whether improvements in productivity mitigate the negative effects of population growth. Together, these variables permit a rich empirical characterization of how land availability, land use, and technological progress shape the demographic–growth relationship.

A set of standard macroeconomic controls is included to isolate the channels of interest. The investment share of GDP accounts for capital accumulation, secondary-school attainment captures human capital, and terms-of-trade growth controls for external shocks that affect income independently of demographics. The urbanization rate is also included because it reflects structural transformation and internal migration patterns; although it is not a perfect substitute for net migration, it helps capture broader spatial reallocation of labor. All of these controls are obtained from the WDI, ensuring consistency of definitions and coverage.

The empirical specification follows directly from the reduced-form growth equation derived in Section 3. Equation (13) implies that the effect of demographic expansion on per-capita income growth depends on (i) natural population growth and migration, which determine labor force dynamics; (ii) effective land intensity, captured by the interaction between agricultural dependence and the role of land in production; and (iii) land-saving technological progress, which attenuates the congestion effect of population pressure. To take this implication to the data, we model per-capita GDP growth as a function of lagged population growth and net migration, interacted with observable proxies for effective land intensity and land-augmenting innovation. Agriculture’s share in GDP serves as an empirical counterpart to the structural parameter $\mu$ , arable land per capita captures physical land scarcity, and cereal yields proxy land-saving technological progress. The resulting regression provides a direct empirical analog of equation (13), allowing the marginal effect of population growth to vary systematically with structural composition, land endowments, and technological conditions, as implied by the theoretical framework. To assess the predictions of the model, we estimate the following specification:

(14) \begin{align} \begin{array}{l} \begin{array}{llll} & \begin{array}{ll} {\unicode[Arial]{x0394}} \ln y_{it}= & \rho \ln y_{i,t-1}+\beta _{1}n_{i,t-1}+\beta _{2}m_{i,t-1}\\[3pt] & +\beta _{3}(n_{i,t-1}\times \text{AgrShare}_{i,t-1})+\beta _{4}(m_{i,t-1}\times \text{AgrShare}_{i,t-1})\\[3pt] & +\beta _{5}(n_{i,t-1}\times \text{LandPC}_{i,t-1})+\beta _{6}(n_{i,t-1}\times \text{LandTech}_{i,t-1})\\[3pt] & +{X}_{i,t-1}^{\mathrm{'}}\Gamma +\mu _{i}+\tau _{t}+\varepsilon _{it} \end{array} \end{array} \end{array} \\[-20pt] \nonumber \end{align}

where $y_{it}$ denotes real GDP per capita, $b_{it}\equiv n_{it}$ is natural population growth from the theoretical model, $m_{it}$ is the net migration rate, $\text{AgrShare}_{it}$ the share of agriculture in GDP, $\text{LandPC}_{it}$ arable land per capita, $\text{LandTech}_{it}$ land-saving technological progress, $X_{it}$ a vector of controls, $\mu _{i}$ country fixed effects, and $\tau _{t}$ year fixed effects. Standard errors are clustered at the country level to account for serial correlation and heteroskedasticity.

Equation (14) is specified in conditional convergence form through the inclusion of lagged income. A negative coefficient on lagged log GDP per capita indicates convergence toward a country-specific steady state. The estimated coefficients therefore capture transitional growth dynamics rather than steady-state growth effects, and measure how population dynamics interact with land scarcity and structural characteristics along the convergence path.

Each set of coefficients corresponds to a component of the theoretical framework. The coefficient $\beta _{1}$ measures the average effect of natural population growth on transitional per-capita income growth. The coefficient $\beta _{2}$ captures the independent role of migration, reflecting how net inflows or outflows affect growth conditional on natural population dynamics. The interaction terms reflect the central prediction of the model that demographic effects depend on the economy’s structural and resource environment. The term $\beta _{3}$ tests whether the effect of population growth is more adverse in economies with larger agricultural sectors, consistent with higher effective land intensity $(\phi )$ . The coefficient $\beta _{4}$ captures whether the growth effect of migration itself varies with agricultural dependence, in line with the view that migration constitutes a more important adjustment margin in land-intensive economies. The interaction with arable land per capita, $\beta _{5}$ , allows the effect of population growth to depend on land availability per worker, while $\beta _{6}$ examines whether land-saving technological progress mitigates demographic pressure by raising the effective productivity of the fixed land stock.

The vector $X_{i,t-1}$ contains the baseline controls discussed above. Country fixed effects ensure that identification comes from within-country variation over time, thereby controlling for time-invariant characteristics such as geography and long-run institutional differences. Year fixed effects capture global shocks common to all countries, including commodity price movements and worldwide business-cycle fluctuations. Descriptive statistics and nomenclature for all variables appear in Tables A1 and A2 in the Appendix.

The panel is unbalanced due to historical data limitations, especially for migration and agricultural variables in the earlier decades, but the coverage is sufficiently broad to allow precise estimation of interaction terms. Together, this empirical design enables a direct test of the model’s predictions: whether natural population growth slows income growth more sharply in land-scarce and agriculture-dependent economies, and whether migration and land-saving innovations alleviate these effects.

The theoretical model yields clear priors for the interaction coefficients. In particular, the interaction between natural population growth and agricultural dependence is predicted to be negative, reflecting the stronger land constraint in more agrarian economies. By contrast, the interaction between population growth and land-saving technological progress is expected to be positive, since higher land productivity mitigates the adverse effect of demographic expansion. The interaction between population growth and arable land per capita captures the role of land abundance and is therefore also expected to attenuate the negative demographic effect. Finally, the interaction between migration and agricultural dependence reflects the adjustment mechanism embedded in the model and is predicted to attenuate the growth penalty associated with demographic pressure in land-intensive economies.