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\title[Development Accounting]{Development Accounting}
\author[Steinsson]{Jón Steinsson}
\institute[]{University of California, Berkeley}
\date[]{Fall 2025}

\begin{document}

\begin{frame}
  \titlepage
\end{frame}


\begin{frame}{Development Accounting: Basics}
	\begin{itemize}
		\itemsep1em 
		\item How much of cross-country income differences are ``due to'':
		\begin{itemize}
			\item Factor inputs (capital, education)
			\item Efficiency
		\end{itemize}
		\item First step in understanding cross-country income differences \\ Doesn't attempt to explain why inputs differ
		\item Levels analog to growth accounting \\ {\small (sometimes called levels accounting)}
		\item {\small Goes back to Denison (1967), Christensen, Cummings, and Jorgenson (1981). \\ Modern literature starts with King and Levine (1994) and particularly \\ Klenow and Rodrigez-Claire (1997) and Hall and Jones (1999)}
	\end{itemize}
\end{frame}


\begin{frame}{Causes of Income Differences}
	\begin{figure}
		\centering
		\includegraphics[height = 0.38 \textheight]{FiguresTables/HsiehKlenow2010Page1.pdf}
	\end{figure}
	\begin{itemize}
		\item Development accounting is about right-most arrows
	\end{itemize}
	\vspace{4mm}
	{\scriptsize Source: Hsieh and Klenow (2010)}
\end{frame}


\begin{frame}{Development Accounting: Basics}
	\begin{itemize}
		\item Following Hall and Jones (1999): 
		\[ Y_i = K_i^{\alpha}(A_iH_i)^{1-\alpha} \]
		where 
		\[H_i = e^{\phi(E_i)}L_i \] \vspace{-15pt}
		\begin{itemize}
			\item $H_i$ denotes human capital (quality-adjusted labor)
			\item $L_i$ denotes ``raw'' labor
			\item $E_i$ denotes education (years of schooling)
		\end{itemize}
	\end{itemize}
\end{frame}


\begin{frame}{Measurement: Output}
	\begin{itemize}
		\itemsep1em 
		\item Main data source: Penn World Tables \\ {\small (Modern incarnation of Summers and Heston (1991) dataset)}
		\item Output: GDP per worker at PPP
		\item Penn World Tables:
		\begin{itemize}
			\item Basic idea: Correct GDP for difference in prices across space \\ (analogous to adjusting for inflation over time)
			\item Done using International Comparisons Program (ICP) price data 
			\item Has undergone substantial methodological changes over time \\ (Major change between V7 and V8)
			\item Many older results in literature not robust to these changes
			\item See Feenstra, Inklaar, Timmer (2015) for description of ``modern'' version
		\end{itemize}
	\end{itemize}
\end{frame}


\begin{frame}{Measurement: Capital}
	\begin{itemize}
		\itemsep1em 
		\item Early versions: Capital constructed from investment:
		\[K_{it} = I_{it} + (1-\delta) K_{i,t-1} \]
		With an initial capital stock of:
		\[K_{i,0} = \frac{I_{i,0}}{g+\delta} \]
		where
		\begin{itemize}
			\item $g$ is the average growth rate of investment before 1970
			\item $\delta = 0.06$
		\end{itemize} 
		\item More recent versions of PWT include capital series \\ {\small (which is constructed ``more carefully'' using perpetual inventory method)} 
	\end{itemize}
\end{frame}



\begin{frame}{Measurement: Human Capital}
	\[ H_{i} = e^{\phi(E_i)} \] \vspace{-15pt} 
	\begin{itemize} 
		\item Use average years of schooling as a proxy for $E_i$
		\item Data on average years of schooling from Barro and Lee (2013)
		\item With competitive factor markets, workers are paid their marginal product
		\item Use wages to inform $\phi(E_i)$ {\small(Mincerian wage regressions)}
		\item Assume $\phi(E_i)$ is piecewise linear with slopes:
		\begin{itemize}
			\item 0.134 for $s \leq 4$
			\item 0.101 for $4 < s \leq 8$
			\item 0.068 for $8 < s$ 
		\end{itemize}
		where $s$ is average years of schooling
		\item {\small Based on Psacharopoulos's (1994) survey of returns-to-schooling estimates} 
	\end{itemize}
\end{frame}


\begin{frame}{Measurement: $\alpha$ and Robustness}
	\begin{itemize}
		\item Typical to assume $\alpha = 1/3$ for all countries
		\item Gollin (2002) suggests this is reasonable \\ {\small (but Feenstra, Inklaar, Timmer (2015) disagree) }
		\item Caselli (2005) shows results are quite sensitive to this choice
		\item[]
		\item In contrast, Caselli argues that results are not very sensitive to:
		\begin{itemize}
			\item Depreciation rate
			\item Initial capital stock
			\item Reasonable variation in returns to schooling
			\item Mismeasurement of years of schooling
			\item Variation in hours worked per person
		\end{itemize}
	\end{itemize}
\end{frame}


\begin{frame}{Flavors of Development Accounting}
	\begin{itemize}
		\itemsep2em 
		\item Hall and Jones (1999) / Jones (2016):
		\[\log \left( \frac{Y_i}{L_i} \right) = \frac{\alpha}{1-\alpha}\log \left( \frac{K_i}{Y_i} \right) + \log \left( \frac{H_i}{L_i} \right) + \log A_i \]
		\item Caselli (2005):
		\[\log \left( \frac{Y_i}{L_i} \right) = \alpha \log \left( \frac{K_i}{L_i} \right) + (1-\alpha) \log \left( \frac{H_i}{L_i} \right) + \log A_i \]
		\[\log \left( \frac{Y_i}{L_i} \right) =   \log \left( \frac{Y_i}{L_i} \right)_{KH} + \log A_i \]
		\[ \log y_i = \log y_{i,KH} + \log A_i \] 
	\end{itemize}

	\vspace{5pt}
	{\scriptsize (Notice in Hall-Jones flavor it is $K/Y$ that shows up rather than $K/L$. See Growth Accounting lecture for \\ \vspace{-5pt} details. Caselli starts with $Y_i = A_i K_i^{\alpha}H_i^{1-\alpha}$.) $L$ is workers.}
\end{frame}


\begin{frame}
	\begin{figure}
		\centering
		\includegraphics[height = 0.95  \textheight]{FiguresTables/HallJones1999Table1.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Hall and Jones (1999). Comparison year: 1988}
\end{frame}


\begin{frame}{Hall and Jones (1999)}
	\begin{itemize}
		\itemsep1em 
		\item Comparing richest 5 and poorest 5:
		\begin{itemize}
			\item Difference in output per worker: factor of 31.7
			\item Difference in capital intensity: factor of 1.8
			\item Difference in human capital per worker: factor of 2.2
			\item Difference in productivity: factor of 8.3 
		\end{itemize}
		\item Productivity explains the bulk of cross-country income differences
	\end{itemize}
\end{frame}



\begin{frame}
	\begin{figure}
		\centering
		\includegraphics[height = 0.95  \textheight]{FiguresTables/Jones2016Table6.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Jones (2016)}
\end{frame}


\begin{frame}{Development Accounting: Mexico vs. U.S.}
	\begin{itemize}
		\itemsep1em 
		\item Output per worker in Mexico is 33.8\% of U.S. 
		\item Capital-output ratio of Mexico is 87\% of U.S.
		\begin{itemize}
			\item $0.87^{\alpha/(1-\alpha)} = 0.87^{1/2} = 0.931$
		\end{itemize}
		\item Schooling: 8.8 year in Mexico vs. 13.2 years in U.S.
		\begin{itemize}
			\item Difference: 4.6 years
			\item $0.068 \times 4.6 = 0.32$
			\item $0.76 = 1/1.32$
		\end{itemize}
		\item TFP is $0.338/(0.931 \times 0.760) = 0.477$ of U.S. level
	\end{itemize}
\end{frame}

\begin{frame}{Development Accounting: Mexico vs. U.S.}
	\begin{itemize}
		\itemsep1em 
		\item Inputs explain a factor of
		\[\frac{1}{0.931} \times \frac{1}{0.760} = 1.4 \]
		\item TFP explains the rest
		\[ \frac{1}{0.338} \times \frac{1}{1.4} = 2.1\]
		\item Fraction explained by TFP:
		\[ \frac{2.1}{1.4+2.1} = 0.597 \]
		{\small (Not sure this makes sense. Think of factors explaining 1.0.)}
	\end{itemize}
\end{frame}


\begin{frame}{Development Accounting: Mexico vs. U.S.}
	Alternative Decomposition:
	\begin{itemize}
		\itemsep0.5em
		\item Total difference $1/0.338 = 2.96$. In logs: 1.08
		\item Log difference explained by capital: $\log (1/0.931) = 0.07$
		\item Log difference explained by schooling: $\log (1/0.760) = 0.27$
		\item Log difference explained by TFP: $\log (1/0.477) = 0.74$
		\item Fraction explained by TFP: $0.74/1.08 = 0.68$
	\end{itemize}
\end{frame}


\begin{frame}{Hall and Jones (1999) vs. Jones (2016)}
	\begin{itemize}
		\itemsep1em 
		\item In Hall and Jones (1999) $K/Y$ explains factor of 2
		\item In Jones (2016) $K/Y$ explains essentially nothing
		\item Not totally clear why the difference
		\item One possibility: Jones (2016) uses PWT capital series which is constructed ``more carefully'' than Hall-Jones capital series
		\begin{itemize}
			\item Capital price series lower in poor countries than investment price series (used by Hall and Jones) because structures are more important in capital than in investment (because they depreciate slower) and structures are cheap in poor countries (see Feenstra, Inklaar, Timmer (2015, p. 3178)
			\item Lower capital prices in poor countries implies more capital [I think]
		\end{itemize}
	\end{itemize}
\end{frame}



\begin{frame}{Caselli's Decomposition}
	\begin{itemize}
		\item Question: What would cross-country income distribution look like if \\ all countries had the same TFP?
		\item Consider:
		\[ \text{var}[\log y_i] = \text{var}[\log y_{i,KH}] + \text{var}[\log A_i] + 2\text{cov}[\log y_{i,KH},\log A_i] \]
		\item If $A_i$ the same in all countries:
		\[ \text{var}[\log A_i] + 2\text{cov}[\log y_{i,KH},\log A_i] = 0 \] 
		\item Motivates using 
		\[ \text{success}_{1} = \frac{\text{var}[\log y_{i,KH}]}{\text{var}[\log y_{i}]} \]
		to measure role of factors
	\end{itemize}
\end{frame}


\begin{frame}
	\begin{figure}
		\centering
		\includegraphics[height = 0.4  \textheight]{FiguresTables/Caselli2005Table1.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Caselli (2005)}
\end{frame}


\begin{frame}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/Caselli2005Table2.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Caselli (2005)}
\end{frame}


\begin{frame}{Development Accounting: Basic Findings}
	\begin{itemize}
		\itemsep1em 
		\item Capital-Output ratio explains very little
		\begin{itemize}
			\item Depends on version of analysis (up to factor 2 (i.e., 20\%) in older versions)
		\end{itemize}
		\item Years of schooling explains a substantial amount
		\begin{itemize}
			\item Perhaps about 1/3 across rich vs. poor countries
		\end{itemize}
		\item TFP explains at least half
	\end{itemize}
\end{frame}


\begin{frame}{Interpretation of Basic Findings}
	\begin{itemize}
		\itemsep1em 
		\item Helps point to type of ``friction'' that plagues poor countries
		\item If $K/Y$ is low: problems associated with capital accumulation?
		\begin{itemize}
			\item Taxes on capital (implicit or explicit)
			\item Financial repression
			\item Restrictions of international capital flows
		\end{itemize}
		\item If education is low: problem in education sector?
		\begin{itemize}
			\item Insufficient supply of education (by government?)
			\item Low quality of education
			\item Low demand for education (culture/beliefs/high prices?)
		\end{itemize}
	\end{itemize}
\end{frame}


\begin{frame}{Four Strands of Subsequent Literature}
	\begin{enumerate}
		\itemsep1em 
		\item Is MPK larger for poor countries? \\ {\small (Lucas 90, Caselli-Feyrer 07, Hsieh-Klenow 07, Gerding-Henriksen-Simonovska 23)}
		\item Quality of schooling \\ {\small (Hendricks 02, Schoellman 12, Hendricks-Schoellman 18, 21, \\ Lagakos et al. 18)}
		\item Agricultural productivity gap \\ {\small (Caselli 05, Restuccia-Yang-Zhu 08, Gollin-Lagakos-Waugh 14, Boppart-Kiernan-Krusell-Malmberg 23) }
		\item Misallocation \\ {\small (Restuccia-Rogerson 08, Hsieh-Klenow 09, Moll 12, Midrigan-Xu 14) } 
	\end{enumerate}
\end{frame}



\begin{frame}{Why Doesn't Capital Flow to Poor Countries?}
	Lucas (1990):
	\begin{itemize}
		\item Two countries with same Cobb-Douglas production function:
		\[y = Ak^{\alpha} \]
		where $y$ is output per person and $k$ is capital per person
		\item Marginal product of capital is:
		\[r = \alpha A k^{\alpha-1} \]
		\item Using production function to plug in for $k$
		\[r = \alpha A^{1/\alpha} y^{(\alpha-1)/\alpha}  \] 
	\end{itemize}
\end{frame}

\begin{frame}{Why Doesn't Capital Flow to Poor Countries?}
	\begin{itemize}
		\itemsep1em 
		\item Taking a ratio of this equation for India vs. US:
		\[\frac{r^{\text{India}}}{r^{\text{US}}} = \left( \frac{y^{\text{India}}}{y^{\text{US}}} \right)^{(\alpha-1)/\alpha} \]
		\item Suppose 
		\[ \alpha = 0.4 \hspace{15pt} \text{and} \hspace{15pt}  \frac{y^{\text{India}}}{y^{\text{US}}} = \frac{1}{15} \]
		\item Then we have that
		\[ \frac{r^{\text{India}}}{r^{\text{US}}} = 15^{1.5} = 58 \]
		\item Marginal product of capital in India is 58 times higher than in the U.S. 
	\end{itemize}
\end{frame}


\begin{frame}{Why Doesn't Capital Flow to Poor Countries?}
	\begin{itemize}
		\itemsep1em 
		\item If the MPK is 58 times higher in India than U.S., why doesn't more capital flow to poor countries?
		\item Maybe because MPK is not 58 times higher in India \\ {\small (and since Lucas' paper was published, India has grown a lot)}
		\item Calculation assumes India and U.S. have same productivity
		\item Development accounting suggests this is not the case
	\end{itemize}
\end{frame}


\begin{frame}{Marginal Product of Capital}
	\begin{itemize}
		\itemsep1em 
		\item Let's combine 
		\[ r = \alpha A k^{\alpha-1} \hspace{15pt} \text{and} \hspace{15pt} y = Ak^{\alpha} \]
		to eliminate $A$:
		\[ r = \alpha \left( \frac{k}{y} \right)^{-1} \]
		\item Hall-Jones 99 results have India's $k/y$ at 50\% of U.S. level
		\item Implies MPK is twice as high in India \\ {\small (Jones 16 results don't imply this. But let's ignore that for now.)}
		\item Significant focus of literature in 1990s {\small (see, e.g., Mankiw 95)}
	\end{itemize}
\end{frame}


\begin{frame}{Naive Marginal Product of Capital}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/HsiehKlenow2010Figure3.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Hsieh and Klenow (2010) using data from Caselli and Feyrer (2007)}
\end{frame}


\begin{frame}{Caselli and Feyrer (2007)}
	Make two adjustments to naive MPK calculation: \vspace{10pt}
	\begin{enumerate}
		\itemsep2em 
		\item Adjust for non-reproducable capital {\small (land and natural resources)}
		\item Adjust for high price of capital relative to consumption in poor countries
	\end{enumerate}
\end{frame}


\begin{frame}{Caselli and Feyrer (2007)}
	\begin{itemize}
		\itemsep0.5em 
		\item Naive marginal product of capital:
		\[ \text{MPK} = \alpha \frac{Y}{K} \]
		where $\alpha$ is capital share of income
		\item Usual way to measure capital share of income:
		\begin{itemize}
			\item One minus labor share of income 
		\end{itemize}
		\item But that includes income to non-reproducable capital \\ {\small (land and natural resources)}
		\item While $K$ is only reproducable capital \\ {\small (constructed from perpetual inventory method)}
	\end{itemize}
\end{frame}

\begin{frame}{Caselli and Feyrer (2007)}
	\begin{itemize}
		\itemsep1em 
		\item So naive:
		\[ \text{MPK} = \alpha \frac{Y}{K} \]
		yields an estimate of MPK that is too high
		\item This bias is bigger for poor countries since  non-reproducable capital \\ is a larger share of capital in poor countries
		\item Makes MPK look higher for poor countries
		\item Counterpoint: Existence of land and natural resources my raise MPK \\ if these resources are under-exploited. 
	\end{itemize}
\end{frame}

\begin{frame}{Land and Natural Resources}
	\begin{figure}
		\centering
		\includegraphics[height = 0.7  \textheight]{FiguresTables/CaselliFeyrer2007Table1.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Caselli and Feyrer (2007)}
\end{frame}


\begin{frame}{Price of Capital Relative to Output}
	\begin{itemize}
		\itemsep1em 
		\item In ``one-good'' model, price of capital is the same as the price output
		\item In reality, this is not necessarily the case
		\item Recognizing this, return to capital is
		\[ \frac{P_y(t) MPK(t) + P_k(t+1)(1-\delta)}{P_k(t)} \]
		\item Ignoring capital gains, frictionless international capital markets imply
		\[ \frac{P_y MPK}{P_k} = R^{*} - (1-\delta) \] 
		\item This is what should be equal across countries
	\end{itemize}
\end{frame}


\begin{frame}{Price of Capital Relative to Output}
	\begin{itemize}
		\itemsep3em 
		\item Earlier estimate:
		\[ MPK = \alpha \frac{Y}{K} \]
		\item Adjusted estimate:
		\[ \frac{P_y MPK}{P_k} = \alpha \frac{P_y Y}{P_k K}\]   
	\end{itemize}
\end{frame}


\begin{frame}{Price of Output Relative to Capital}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/CaselliFeyrer2007Figure2.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Caselli and Feyrer (2007)}
\end{frame}


\begin{frame}{Equipment Prices Across Countries}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/HsiehKlenow2010Figure5.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Hsieh and Klenow (2010)}
\end{frame}


\begin{frame}{Consumption Prices Across Countries}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/HsiehKlenow2010Figure6.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Hsieh and Klenow (2010)}
\end{frame}


\begin{frame}{Adjusted Marginal Product of Capital}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/HsiehKlenow2010Figure4.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Hsieh and Klenow (2010) using data from Caselli and Feyrer (2007)}
\end{frame}

\begin{frame}{Caselli and Feyrer (2007)}
	Conclusion: \vspace{5pt}
	\begin{itemize}
		\itemsep1em 
		\item ``There is no \textit{prima facie} support for the view that international credit frictions play a major role in preventing capital flows from rich to poor countries''
		\item Low $K/L$ in poor countries due to:
		\begin{itemize}
			\item low endowments of complementary factors to capital
			\item low efficiency (TFP)
		\end{itemize}
	\end{itemize}
	\vspace{15pt}
	Capital may be misallocated \textbf{within} country. Misallocation literature following Hsieh and Klenow (2009)
\end{frame}


\begin{frame}{Gerding, Henriksen, Simonovska (2023)}
	\begin{itemize}
		\itemsep1em 
		\item Caselli-Feyrer results special to 1996
		\item Analyze average over 70 years (1950-2019)
		\item Find MPK is higher in poor countries
	\end{itemize}
\end{frame}


\begin{frame}{Marginal Product of Capital}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/GerdingHenriksenSimonovska2023Figure1.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Gerding, Henriksen, Simonovska (2023). Adjusts for relative price of output \\ \vspace{-7pt} but not for non-reproducable capital.}
\end{frame}


\begin{frame}{Marginal Product of Capital}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/GerdingHenriksenSimonovska2023Table13.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Gerding, Henriksen, Simonovska (2023).}
\end{frame}


\begin{frame}{Marginal Product of Capital in 1996}
	\begin{figure}
		\centering
		\includegraphics[height = 0.65  \textheight]{FiguresTables/GerdingHenriksenSimonovska2023Table14.pdf}
	\end{figure}
	\vspace{-2mm}
	{\scriptsize Source: Gerding, Henriksen, Simonovska (2023). $P_j$ denotes country-specific price of investment. \\ \vspace{-7pt} $\alpha_{jr}$ denotes adjustment for non-reproducable capital. }
\end{frame}


\begin{frame}{Human Capital: Evidence from Migration}
	\begin{itemize}
		\item Measure of human capital in standard development accounting \\ very crude (average years of schooling from Barro-Lee 13 times estimate of returns to schooling)
		\item How can we do better? \pause 
		\item How about looking at wage gains of migrants?
		\item Migrant wage gains a measure of country component of \\ income differences
		\item Residual due to human capital
	\end{itemize}
\end{frame}


\begin{frame}{Hendricks and Schoellman (2018)}
	\begin{itemize}
		\item Production function in per worker terms:
		\[y_c = \left( \frac{K_c}{Y_c} \right)^{\frac{\alpha}{1-\alpha}} A_c h_c \]
		\item Country component:
		\[z_c = \left( \frac{K_c}{Y_c} \right)^{\frac{\alpha}{1-\alpha}} A_c \]
		\item Take logs:
		\[ \log y_c = \log z_c + \log h_c \]
		\item Subtract one country from another and divide by income difference:
		\[ 1 = \frac{\log z_c - \log z_{c'}}{\log y_c - \log y_{c'}} + \frac{\log h_c - \log h_{c'}}{\log y_c - \log y_{c'}} = \text{share}_{\text{country}} + \text{share}_{\text{human capital}} \]     
	\end{itemize}
\end{frame}


\begin{frame}{Human Capital: Evidence from Migration}
	\begin{itemize}
		\itemsep1em 
		\item Two problems with evidence on migrants:
		\begin{itemize}
			\item Migrants are highly selected
			\item Human capital transfers imperfectly across countries
		\end{itemize}
		\item Data on pre- and post-migration wages of migrants addresses selection
		\item Trickier to address transferability of human capital \\ {\small (e.g., accreditation, licensure, discrimination)}
	\end{itemize}
\end{frame}

\begin{frame}{Human Capital's Role in Income Differences}
	\begin{itemize}
		\item Suppose labor is homogeneous and labor markets are competitive
		\item Then firms solve
		\[ \text{max}_{H_c} K^{\alpha}_c (A_c H_c)^{1-\alpha} - \omega_c H_c \]
		where $\omega_c$ is the wage per unit of human capital
		\item This yields $\omega_c = (1-\alpha) z_c$ and 
		\[\log w_{i,c} = \log [ (1-\alpha)z_c] + \log h_{i} \]
		where $w_{i,c}$ is the wage of a worker with human capital level $h_i$
		\item For migrants (assuming $h_i$ is transferable) we have
		\[ \frac{\log w_{i,US} - \log w_{i,c}}{\log y_{US} - \log y_{c}} = \frac{\log z_{US} - \log z_{c}}{\log y_{US} - \log y_{c}} = \text{share}_{\text{country}} \] 
	\end{itemize}
\end{frame}


\begin{frame}{Hendricks and Schoellman (2018): Data}
	\begin{figure}
		\centering
		\includegraphics[height = 0.65  \textheight]{FiguresTables/HendricksSchoellman2018Table1.pdf}
	\end{figure}
	\vspace{-2mm}
	{\scriptsize Source: Hendricks and Schoellman (2018). NIS is New Immigrant Survey (green card holders) \\ \vspace{-7pt} MP are Mexican and Latin American Migration Projects. NIS is early 2000s. }
\end{frame}


\begin{frame}{Wage Gains at Migration}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/HendricksSchoellman2018Figure1.pdf}
	\end{figure}
	\vspace{-5mm}
	{\scriptsize Source: Hendricks and Schoellman (2018). }
\end{frame}


\begin{frame}{Human Capital Share}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/HendricksSchoellman2018Table2.pdf}
	\end{figure}
	\vspace{-3mm}
	{\scriptsize Source: Hendricks and Schoellman (2018). }
\end{frame}


\begin{frame}{Human Capital Transferability}
	\begin{figure}
		\centering
		\includegraphics[height = 0.7  \textheight]{FiguresTables/HendricksSchoellman2018Table7.pdf}
	\end{figure}
	\vspace{-3mm}
	{\scriptsize Source: Hendricks and Schoellman (2018). }
\end{frame}


\begin{frame}{Human Capital Transferability}
	\begin{figure}
		\centering
		\includegraphics[height = 0.6  \textheight]{FiguresTables/HendricksSchoellman2018Table8.pdf}
	\end{figure}
	\vspace{-3mm}
	{\scriptsize Source: Hendricks and Schoellman (2018). NIS sample from countries with <1/4 US GDP per capita.}
\end{frame}


\begin{frame}{Agriculture and Development}
	\begin{itemize}
		\itemsep1em 
		\item A classic view is that development is about reallocation out of agriculture into ``modern'' sectors \\ {\small (Rosenstein-Rodin 43, Nurkse 53, Lewis 55, Rostow 60)  }
		\item Most people work in agriculture in poor countries
		\item Productivity is low in agriculture, especially in poor countries \\ {\small (Lewis 55, Kuznets 71)}
	\end{itemize}
\end{frame}


\begin{frame}{Importance of Agriculture}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/Caselli2005Figure15.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Caselli (2005)}
\end{frame}


\begin{frame}{Agriculture and Development: Two Views}
	\begin{enumerate}
		\itemsep1em 
		\item Unproductive urban sector is the problem
		\begin{itemize}
			\item Urban sector can't absorb labor 
			\item Unproductive or can't grow fast enough
			\item People in country-side are ``army of surplus labor''
			\item This is -- I think -- the more common view 
		\end{itemize}
		\item Unproductive agricultural sector is the problem
		\begin{itemize}
			\item Labor needed to produce food (``food problem'')
			\item Agricultural sector can't shed labor
			\item Timmer (1988), Gollin, Parente, Rogerson (2002, 2007)
		\end{itemize}
	\end{enumerate}
	\vspace{15pt}
	Not clear which of these stories is more important
\end{frame}


\begin{frame}{A Two Sector Model}
	\begin{itemize}
		\itemsep1em 
		\item Perfect labor mobility across sectors
		\item Competitive labor markets
		\item Production functions:
		\[ Y_a = A_a L_a^{\theta} K_a^{1-\theta} \hspace{40pt} Y_n = A_n L_n^{\theta} K_n^{1-\theta} \]
		\item Price of non-ag good is numeraire
		\item Price of ag good is $p_a$ 
	\end{itemize}

	\vspace{10pt}
	{\footnotesize (See Gollin, Lagakos, and Waugh (2014) for more details)} 
\end{frame}


\begin{frame}{A Two Sector Model}
	\begin{itemize}
		\itemsep0.5em
		\item Labor mobility implies common wage $w$
		\item Labor demand in each sector:
		\[ p_a \theta \frac{Y_a}{L_a} = w  \hspace{40pt} \theta \frac{Y_n}{L_n} = w \]
		\item Combining these implies
		\[ \frac{p_a Y_a/L_a}{Y_n/L_n} = \frac{VA_a/L_a}{VA_n/L_n} = 1 \] 
		\item Value added per worker should be the same in both sectors
		\[ \frac{VA_a}{L_a} = \frac{VA_n}{L_n} \] 
		\item True whether growth bottleneck is low $A_a$ or low $A_n$ 
	\end{itemize}
\end{frame}


\begin{frame}{Agricultural Productivity Gap}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/LagakosFigure1.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: David Lagakos}
\end{frame}


\begin{frame}{Agricultural Productivity Gap}
	\begin{itemize}
		\itemsep1em 
		\item Employment share in agriculture is larger than value added share
		\item Particularly so in poor countries
		\item Agricultural productivity gap:
		\[ APG = \frac{VA_n/L_n}{VA_a/L_a} \]
		\item Frictionless model implies $APG = 1$
	\end{itemize}
\end{frame}


\begin{frame}{Raw Agricultural Productivity Gap}
	\begin{figure}
		\centering
		\includegraphics[height = 0.65  \textheight]{FiguresTables/GollinLagakosWaugh2014Table1.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Gollin, Lagakos, Waugh (2014)}
\end{frame}


\begin{frame}{Agricultural Productivity Gap}
	\begin{itemize}
		\itemsep1em 
		\item Frictionless model implies $APG = 1$
		\item In practice, $APG = 3.5$ and even larger in poor countries
		\item Suggests large misallocation of labor across sectors  
	\end{itemize}
\end{frame}


\begin{frame}{Is it Real or Mismeasurement?}
	\begin{itemize}
		\itemsep1em 
		\item Agricultural workers may work fewer hours (lean season)
		\item Rural people may be misclassified as agricultural workers
		\item Agricultural output may be undermeasured due to home production
		\item Agricultural workers may have less human capital
	\end{itemize}
\end{frame}


\begin{frame}{Gollin, Lagakos, Waugh (2014)}
	\begin{itemize}
		\itemsep1em 
		\item Gather database of population censuses and household surveys \\ to better measure agricultural productivity gap
		\item Sector level data on:
		\begin{itemize}
			\item Average hours worked
			\item Average years of schooling
		\end{itemize}
		\item Findings:
		\begin{itemize}
			\item Non-ag workers work modestly more hours than ag workers
			\item Average schooling higher in non-ag
		\end{itemize}
		\item Can explain about 1/3 of agricultural productivity gap
	\end{itemize}
\end{frame}


\begin{frame}{Sectoral Human Capital Difference}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/GollinLagakosWaugh2014Figure3a.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Gollin, Lagakos, Waugh (2014)}
\end{frame}


\begin{frame}{Adjusted Agricultural Productivity Gap}
	\begin{figure}
		\centering
		\includegraphics[height = 0.65  \textheight]{FiguresTables/GollinLagakosWaugh2014Table3.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Gollin, Lagakos, Waugh (2014)}
\end{frame}


\begin{frame}{Gollin, Lagakos, Waugh (2014)}
	\begin{itemize}
		\itemsep1em 
		\item Construct alternative measures of value added by sector \\ using household surveys for 10 developing countries
		\item Measures output whether sold or consumed at home
		\item Result: Sectoral differences similar to NIPA data
		\item Mismeasurement of value added not likely to explain APG
	\end{itemize}
\end{frame}


\begin{frame}{Adjusted Agricultural Productivity Gap}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/GollinLagakosWaugh2014Table4.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Gollin, Lagakos, Waugh (2014)}
\end{frame}



\begin{frame}{Agriculture and Development}
	\begin{itemize}
		\itemsep1em 
		\item Poor countries employ most of their workers in a sector in which \\ they are particularly unproductive (it seems)
		\item Why this apparent deviation from comparative advantage? \pause
		\item Young (2013) and Hamory-Kleemans-Li-Miguel (2021) argue \\ difference is due to selective migration of high skill workers
		\item Munshi and Rosenzweig (2016) argue for trade-off between higher earnings in the city and access to caste-based insurance in the village in India
	\end{itemize}
\end{frame}


\begin{frame}{Is APG Driven by Selection?}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/HamoryKleemansLiMiguel2021Figure1.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Hamory, Kleemans, Li, and Miguel (2021). FE denotes worker fixed effects.}
\end{frame}


\begin{frame}{Agriculture and Trade}
	\begin{itemize}
		\itemsep1em 
		\item If agriculture is the bottleneck, why not import food?
		\item Poor countries import very little food
		\item Modest tariffs, but huge tariff equivalent costs in time delay to import
		\item Cost of import delays (Hummels and Schaur, 2013): 
		\begin{itemize}
			\item 3.1\% per day for agricultural goods
			\item 2\% for other consumer and capital goods  
		\end{itemize}
		\item To import food, need to export something else!
	\end{itemize}
\end{frame}


\begin{frame}{Little Agricultural Trade}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/Tombe2015Figure2A.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Tombe (2015).}
\end{frame}


\begin{frame}{More Manufacturing Trade}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/Tombe2015Figure2B.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Tombe (2015).}
\end{frame}


\begin{frame}{Agricultural Tariffs}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/Tombe2015Figure3A.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Tombe (2015).}
\end{frame}


\begin{frame}{Manufacturing Tariffs}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/Tombe2015Figure3B.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Tombe (2015).}
\end{frame}


\begin{frame}{Delay Costs: Agriculture}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/Tombe2015Figure3C.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Tombe (2015).}
\end{frame}


\begin{frame}{Delay Costs: Manufacturing}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/Tombe2015Figure3D.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Tombe (2015).}
\end{frame}


\begin{frame}{Restuccia, Yang, Zhu (2008)}
	\begin{itemize}
		\itemsep1em 
		\item Agriculture becomes productive by using modern inputs \\ (tractors, fertilizer, better seeds, etc.)
		\item Barriers to input use can result in low productivity agriculture
		\begin{itemize}
			\item Direct barriers: High cost inputs
			\item indirect barriers: Low wage workers
		\end{itemize}
		\item Build two sector model with barriers to explain low agricultural productivity
	\end{itemize}
\end{frame}


\begin{frame}{Restuccia, Yang, Zhu (2008)}
	\begin{itemize}
		\item Production function in agriculture:
		\[Y_a = X^\alpha (Z^{1-\sigma}(\kappa A L_a)^\sigma )^{1-\alpha} \]
		{\small $Z$ is land (fixed), $X$ is intermediate inputs, $\kappa$ relative prod. of agriculture}
		\item Production function in non-agriculture:
		\[Y_n = A L_n \] 
	\end{itemize}
\end{frame}


\begin{frame}{Restuccia, Yang, Zhu (2008)}
	\begin{itemize}
		\item Price of non-agricultural goods is numeraire
		\item Price of intermediate inputs: $\pi>1$ (direct barriers)
		\item Wages in non-agriculture: $w_n = A$
		\item Wages in agriculture: $w_a = (1-\theta) w_n$ (indirect barriers)
		\item Demand for intermediate goods:
		\[ \frac{X}{Y_a} = \alpha \frac{p_a}{\pi} \]
		\item Low $w_a$ will push down $p_a$ and therefore intermediate input use
	\end{itemize}
\end{frame}


\begin{frame}{Restuccia, Yang, Zhu (2008)}
	\begin{itemize}
		\itemsep1em
		\item Stone-Geary preferences for food:
		\[ U = a \log(c_a - \bar a) + (1-a) \log(c_n) \]
		\item Goods demand:
		\[ c_a = \bar a + a p^{-1}_a (y-p_a \bar a) \]
		\[ c_n = (1-a) (y - p_a \bar a)\]    
	\end{itemize}
\end{frame}


\begin{frame}{Restuccia, Yang, Zhu (2008)}
	Features:
	\begin{itemize}
		\item Two sectors
		\item Diminishing returns in agriculture due to land
		\item Intermediate input use in agriculture
		\item Subsistence demand for agricultural goods
		\item Direct ($\pi > 1$) and indirect ($w_a = (1-\theta) w_n$) barriers to \\ input use in agriculture 
	\end{itemize}
	\vspace{10pt}
	Can these features explain cross-country differences in: 
	\[ L_a/N \hspace{15pt} Y_a/L_a \hspace{15pt} Y/N \]
\end{frame}


\begin{frame}{Restuccia, Yang, Zhu (2008)}
	\begin{itemize}
		\item Messy to solve analytically
		\item With $a=0$ (only subsistence demand for agriculture) less messy
		\item Intermediate input use:
		\[\frac{X}{Y_a} = \left[ \left(\frac{1-\theta}{\pi \kappa} \frac{\alpha}{(1-\alpha)\sigma} \right)^{\sigma} \left( \frac{\bar a}{(Z/N)} \right)^{1-\sigma} \right]^{(1-\alpha)/(\alpha+\sigma(1-\alpha))} \]
		\item Fraction of labor in agriculture:
		\[\frac{L_a}{N} = \frac{1}{\kappa A} \left(\frac{\bar a}{(Z/n)^{1-\sigma}(X/Y_a)^{\alpha/(1-\alpha)}} \right)^{1/\sigma} \]
		\item Labor productivity in agriculture:
		\[ \frac{Y_a}{L_a} = \kappa A \left( \frac{(Z/N)^{1-\sigma}(X/Y_a)^{\alpha/(1-\alpha)}}{\bar a^{1-\sigma}} \right)^{1/\sigma} \] 
	\end{itemize}
\end{frame}


\begin{frame}{Restuccia, Yang, Zhu (2008)}
	Calibration: 
	\begin{itemize}
		\item Hold many parameters fixed across countries: $a$, $\bar a$, $\alpha$, $\sigma$, $\kappa$
		\item Allow to vary across countries: $A$, $\pi$, $1-\theta$, $Z/N$
		\begin{itemize}
			\item $A$: labor productivity in non-agriculture
			\item $\pi$: Price of ag. inputs relative to non-ag goods
			\item $1-\theta$: price of ag. goods times average product of labor in agriculture over average product of labor in non-agriculture (don't have sectoral wages)
			\item $Z/N$: arable land per person
		\end{itemize}
		\item This is all taken as exogenous. Not explained!
	\end{itemize}
\end{frame}


\begin{frame}{Direct and Indirect Barriers}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/RestucciaYangZhu2008Figure4.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Restuccia, Yang, Zhu (2008).}
\end{frame}


\begin{frame}{How Much Do Barriers Explain?}
	\begin{figure}
		\centering
		\includegraphics[height = 0.53  \textheight]{FiguresTables/RestucciaYangZhu2008Table2.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Restuccia, Yang, Zhu (2008).}
\end{frame}


\begin{frame}{Boppart, Kiernan, Krusell, Malmberg (2023)}
	\begin{itemize}
		\itemsep1em 
		\item Production function in agriculture differs from non-agriculture
		\item Perhaps this can help explain low labor productivity in agriculture \\ in poor countries
		\item Labor is particularly cheap in poor countries
		\item Perhaps this leads to very labor intensive agriculture \\ (more so than in non-agriculture)
	\end{itemize}
\end{frame}


\begin{frame}{Agriculture: Price and Quantity Ratios}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/BoppartKiernanKrusellMalmberg2023Figure2.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Boppart, Kiernan, Krusell, Malmberg (2023).}
\end{frame}


\begin{frame}{Boppart, Kiernan, Krusell, Malmberg (2023)}
	\begin{itemize}
		\itemsep1em 
		\item Slopes of relative quantities and prices do not sum to zero
		\item This implies that input share are not constant along \\ the development spectrum
		\[ \Delta \log S(y) = \Delta \log Q(y) + \Delta \log P(y) \] 
		\item Labor share in agriculture falls sharply as countries develop
		\begin{itemize}
			\item Relative price of labor rises
			\item Relative quantity of labor fall much more rapidly
		\end{itemize}
		\item Notation: Instead of everything being a function of time $t$, \\ they assume everything is a function of ``level of development'' $y$
	\end{itemize}
\end{frame}


\begin{frame}{Factor Shares in Agriculture}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/BoppartKiernanKrusellMalmberg2023Figure4.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Boppart, Kiernan, Krusell, Malmberg (2023).}
\end{frame}


\begin{frame}{Labor Productivity versus TFP}
	\begin{itemize}
		\itemsep1em 
		\item Since labor share in agriculture falls with development, labor productivity rises more than TFP
		\[ w_y = (1-\alpha_y)\frac{Y_y}{L_y} \hspace{15pt} \rightarrow \hspace{15pt} \frac{Y_y}{L_y} = \frac{w_y}{1-\alpha_y} \] 
		\item Use development accounting approach to back out TFP differences \\ in agriculture (and non-agriculture)
	\end{itemize}
\end{frame}


\begin{frame}{Development Accounting in Agriculture}
	\begin{itemize}
		\itemsep1em  
		\item Production function for agriculture:
		\[ \frac{y_a}{h_a}(y) = F\left(\frac{k_a}{h_a}(y),1,\frac{x_a}{h_a}(y),\frac{l}{h_a}(y),y \right) \]
		\item Differentiate with respect to $y$ (level of development):
		\includegraphics[width = 1.2  \textheight]{FiguresTables/BoppartKiernanKrusellMalmberg2023Equation4.pdf} \vspace{-15pt} 
		where $\epsilon_{F,k}(y)$ is the elasticity of output with respect to $k$ \vspace{10pt}
		\item Use factor shares estimated above as measures of output elasticities 
	\end{itemize}
\end{frame}


\begin{frame}{Non-Agricultural Production}
	\begin{itemize}
		\item They assume three types of non-agricultural production:
		\begin{itemize}
			\item Consumption goods
			\item Investment goods (capital goods)
			\item Intermediate inputs
		\end{itemize}
		\item They assume production has the same shape for these three \\ (same isoquants) but allow for differing Hicks neutral productivity:
		\[y_n(y) = A_n(y) g(k_n(y),h_n(y)) \]
		\[y_k(y) = A_k(y) A_n(y) g(k_k(y),h_k(y)) \]
		\[y_x(y) = A_x(y) A_n(y) g(k_x(y),h_x(y)) \] 
		\item Differentiate these with respect to $y$ to construct TFP as a function of $y$ just as in agriculture
	\end{itemize}
\end{frame}


\begin{frame}{TFP by Sector}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/BoppartKiernanKrusellMalmberg2023Figure8.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Boppart, Kiernan, Krusell, Malmberg (2023).}
\end{frame}


\begin{frame}{Agriculture: Labor Productivity vs. TFP}
	\begin{figure}
		\centering
		\includegraphics[height = 0.75  \textheight]{FiguresTables/BoppartKiernanKrusellMalmberg2023Figure9.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Boppart, Kiernan, Krusell, Malmberg (2023).}
\end{frame}


\begin{frame}{Boppart, Kiernan, Krusell, Malmberg (2023)}
	\begin{itemize}
		\itemsep1em 
		\item Go on to estimate production functions
		\item Estimate high elasticities of substitution in agriculture \\ more so that in non-agriculture
		\item Low price of labor in poor countries leads to very labor intensive agriculture and thus low labor productivity in agriculture
		\item Development leads to ``intensification'' of agriculture \\ (more capital and intermediates)
		\item Need to assume low human capital in agriculture \\ and some frictions to fit the data. 
	\end{itemize}
\end{frame}


\begin{frame}{Rural-Urban Income Gap}
	\begin{itemize}
		\itemsep1em 
		\item Rural incomes are lower than urban incomes in poor countries
		\item Why don't people move to cities?
		\item Two classes of explanations:
		\begin{itemize}
			\item Selection: People in rural areas are less productive
			\item Frictions: Something prevents them from moving
		\end{itemize}
		\item Quite a few quasi-experimental studies support substantial frictions
	\end{itemize}
\end{frame}


\begin{frame}{Quasi-Experimental Evidence on Mobility}
	\begin{itemize}
		\itemsep1em 
		\item Bryan, Chowdhury, Mobarak (2014): Randomly giving workers in rural Bangladesh a bus ticket (\$8.50) led to large increase in consumption 
		\item Sarvimäki, Uusitalo, Jäntti (2022): Forced migration in Finland after WWII led to large increases in income for people that started off in agriculture
		\item Chetty, Hendren, Katz (2016): Giving families in high poverty areas vouchers to move to lower-poverty areas raises long-term outcomes \\ of young children
		\item Nakamura, Sigurdsson, Steinsson (2021): People induced to move from high income village due to volcanic eruption saw large increase \\ in income (how could this work?)
	\end{itemize}
\end{frame}


\begin{frame}{Comparative Advantage}
	\begin{figure}
		\centering
		\includegraphics[height = 0.8  \textheight]{FiguresTables/NakamuraSigurdssonSteinsson2021Figure8.pdf}
	\end{figure}
	\vspace{-4mm}
	{\scriptsize Source: Nakamura, Sigurdsson, Steinsson (2021)}
\end{frame}

\begin{frame}{Absolute vs. Comparative Advantage}
	\begin{itemize}
		\itemsep1em 
		\item Absolute advantage: Someone is better at everything
		\item Fixed effects regressions control for absolute advantage
		\begin{itemize}
			\item Abowd, Kramarz, Margolis (1999) 
		\end{itemize}
		\item Comparative advantage:
		\begin{itemize}
			\item Some people are good at fishing
			\item Others are good at rabbit hunting
		\end{itemize}
		\item ``Roy model'' means model with comparative advantage {\small (Roy, 1951)} \\ {\small (as does Ricardian model)} 
	\end{itemize}
\end{frame}


\end{document}

